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_build/
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_opam/
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*.install
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.merlin
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out/
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book/
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*.cmi
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*.cmo
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*.cmx
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*.o
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An implementation of stochastic context free grammar induction, following Stolcke and Omohundro's
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[Inducing Probabilistic Grammars by Bayesian Model Merging](https://arxiv.org/abs/cmp-lg/9409010) (ICGI 1994).
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<p align="center">
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<img src="meta/paper-and-induced.svg" alt="the paper's Figure 2 and Table 1, and the eleven induced grammars" width="900">
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</p>
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We start from the most specific grammar the data permits: every sample contributes its own production, and every terminal that occurs gets a corresponding nonterminal. At this stage there's effectively no sharing between samples, so the grammar is just memorising the corpus rather than generalising beyond it.
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From there, we generalise with two operators, merging and chunking. Merging takes a pair of nonterminals and folds them into a single nonterminal containing the union of their productions; chunking replaces a contiguous sequence of symbols with a fresh nonterminal. Chunking doesn't itself change the language the grammar generates, but it changes the internal structure in a way that can expose useful merges which weren't previously available.
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We rank candidate grammars by the posterior `P(M | X) ∝ P(M) P(X | M)`, where the prior is a description length and the likelihood integrates over the production probabilities under symmetric Dirichlet priors. The scoring therefore accounts for uncertainty in the production probabilities, rather than relying on a single fitted parameterisation.
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We explore the resulting grammar space using either beam or best first search, then fit the parameters by expectation maximisation once the grammar structure is fixed. Parsing is a generalised CYK or inside computation over spans, which lets the grammar be scored directly without an intermediate conversion into Chomsky normal form.
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(executable
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(name main)
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(flags (:standard -warn-error -a))
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(libraries scfg))
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+289
@@ -0,0 +1,289 @@
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open Scfg
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let read_file path =
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let ic = open_in path in
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let n = in_channel_length ic in
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let s = really_input_string ic n in
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close_in ic;
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s
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let mkdir_p dir = ignore (Sys.command ("mkdir -p " ^ Filename.quote dir))
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let parse_args rest =
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let rec go opts = function
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| [] -> opts
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| x :: v :: tl
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when String.length x > 2
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&& String.sub x 0 2 = "--"
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&& String.length v > 0
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&& v.[0] <> '-' ->
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go ((String.sub x 2 (String.length x - 2), v) :: opts) tl
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| x :: tl when String.length x > 2 && String.sub x 0 2 = "--" ->
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go ((String.sub x 2 (String.length x - 2), "true") :: opts) tl
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| _ :: tl -> go opts tl
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in
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go [] rest
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let opt opts k d = match List.assoc_opt k opts with Some v -> v | None -> d
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let float_opt opts k d =
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match List.assoc_opt k opts with
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| Some v -> (match float_of_string_opt v with Some f -> f | None -> d)
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| None -> d
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let int_opt opts k d =
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match List.assoc_opt k opts with
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| Some v -> (match int_of_string_opt v with Some i -> i | None -> d)
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| None -> d
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let flag opts k = List.mem_assoc k opts
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let config_of_opts opts =
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{
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Scoring.default_config with
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alpha = float_opt opts "alpha" Scoring.default_config.alpha;
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prior_weight = float_opt opts "prior" Scoring.default_config.prior_weight;
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em_iters = int_opt opts "em-iters" Scoring.default_config.em_iters;
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max_chunk = int_opt opts "max-chunk" Scoring.default_config.max_chunk;
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mode =
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(match opt opts "mode" "marginal" with
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| "ml" -> Scoring.Maximum_likelihood
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| "variational" -> Scoring.Variational
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| _ -> Scoring.Marginal);
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chunk_occurrence =
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(if opt opts "chunk-occurrence" "all" = "first" then
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Scoring.First_occurrence
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else Scoring.All_occurrences);
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}
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let usage () =
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print_endline
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"SCFG induction by Bayesian model merging (Stolcke & Omohundro 1994)\n\n\
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Usage: scfg-induction <command> [options]\n\n\
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Commands:\n\
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\ induce --corpus FILE [--out DIR] [--beam N] [--max-steps N]\n\
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\ [--patience N] [--alpha A] [--prior W] [--max-chunk N]\n\
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\ [--em-iters N] [--mode marginal|ml|variational]\n\
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\ [--chunk-occurrence all|first] [--render]\n\
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\ [--search beam|bestfirst] [--frontier N] [--max-expansions N]\n\
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\ score --grammar FILE --corpus FILE [--alpha A] [--prior W]\n\
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\ parse --grammar FILE --input \"a b c\" [--dot FILE]\n\
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\ dot --grammar FILE --out FILE [--svg FILE] [--title T]\n\
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\ experiments [--out DIR] [--seed N] [--beam N] [--max-steps N]\n\
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\ [--patience N] [--max-len N] [--only NAME] [--quick]\n\n\
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Corpus format: one sequence per line, whitespace-separated tokens.\n\
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An optional \"count:\" prefix sets the sample count, e.g. \"3: a b c\".\n\
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Grammar format: \"S -> A B [0.5]\"; uppercase-initial symbols are\n\
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nonterminals, other symbols are terminals."
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let cmd_induce opts =
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let corpus_path = opt opts "corpus" "" in
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if corpus_path = "" then (prerr_endline "induce: --corpus is required"; exit 2);
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let out_dir = opt opts "out" "out" in
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mkdir_p out_dir;
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let steps_dir = Filename.concat out_dir "steps" in
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mkdir_p steps_dir;
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let render = flag opts "render" in
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let config = config_of_opts opts in
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let beam = int_opt opts "beam" 4 in
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let max_steps = int_opt opts "max-steps" 25 in
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let patience = int_opt opts "patience" 5 in
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let corpus = Corpus.of_file corpus_path in
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let initial =
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Grammar.initial_grammar
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(List.map (fun s -> (s.Corpus.tokens, s.Corpus.count)) corpus)
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in
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Printf.printf "corpus: %d distinct samples, total count %g\n"
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(List.length corpus) (Corpus.total_count corpus);
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Printf.printf "initial grammar: %d nonterminals, %d productions\n"
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(List.length (Grammar.nonterminals initial))
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(List.length initial.Grammar.productions);
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let result =
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if opt opts "search" "beam" = "bestfirst" then
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Search.run_best_first ~config
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~frontier_cap:(int_opt opts "frontier" 200)
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~max_expansions:(int_opt opts "max-expansions" 300)
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~patience initial corpus
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else Search.run ~config ~beam_width:beam ~max_steps ~patience initial corpus
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in
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List.iteri
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(fun i (s : Search.step) ->
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let ch = Transform.change_of s.Search.parent s.Search.transform s.Search.result in
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let base =
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Filename.concat steps_dir (Printf.sprintf "step%03d" (i + 1))
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in
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let dot_before =
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Dot.dot_grammar ~highlight_nts:ch.Transform.before_nts
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~highlight_prods:ch.Transform.before_prods
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~title:
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(Printf.sprintf "step %d before: %s" (i + 1)
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(Transform.describe s.Search.transform))
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s.Search.parent
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in
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let dot_after =
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Dot.dot_grammar ~highlight_nts:ch.Transform.after_nts
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~highlight_prods:ch.Transform.after_prods
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~title:
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(Printf.sprintf "step %d after: %s" (i + 1)
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(Transform.describe s.Search.transform))
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s.Search.result
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in
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let svg_before = if render then Some (base ^ "-before.svg") else None in
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let svg_after = if render then Some (base ^ "-after.svg") else None in
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ignore
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(Dot.render ?out_svg:svg_before ~out_dot:(base ^ "-before.dot") dot_before);
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ignore
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(Dot.render ?out_svg:svg_after ~out_dot:(base ^ "-after.dot") dot_after);
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Printf.printf " accepted step %d: %s score %.4f -> %.4f\n" (i + 1)
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(Transform.describe s.Search.transform)
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s.Search.parent_score s.Search.score)
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result.Search.steps;
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let details = Scoring.details ~config result.Search.best corpus in
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Dot.write_file (Filename.concat out_dir "grammar-final.dot")
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(Dot.dot_grammar ~title:"induced grammar" result.Search.best);
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if render then
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ignore
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(Dot.render ~out_svg:(Filename.concat out_dir "grammar-final.svg")
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~out_dot:(Filename.concat out_dir "grammar-final.dot")
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(Dot.dot_grammar ~title:"induced grammar" result.Search.best));
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Dot.write_file (Filename.concat out_dir "grammar-initial.dot")
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(Dot.dot_grammar ~title:"initial grammar" initial);
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Dot.write_file (Filename.concat out_dir "grammar-final.txt")
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(Grammar.to_string result.Search.best);
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Dot.write_file (Filename.concat out_dir "search-steps.tsv")
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(Search.steps_to_tsv result);
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Dot.write_file (Filename.concat out_dir "search-proposals.tsv")
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(Search.proposals_to_tsv result);
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Printf.printf "\nsearch: %d iterations, %d accepted steps\n"
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result.Search.iterations (List.length result.Search.steps);
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Printf.printf "posterior: %.4f -> %.4f\n" result.Search.initial_score
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result.Search.best_score;
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Printf.printf "structure prior %.4f, marginal loglik %.4f, dl %.1f bits\n"
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details.Scoring.prior details.Scoring.marginal details.Scoring.dl_bits;
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Printf.printf "final grammar: %d nonterminals, %d productions\n"
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details.Scoring.num_nonterminals details.Scoring.num_productions;
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print_endline "\nfinal grammar:";
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print_endline (Grammar.to_string result.Search.best);
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Printf.printf "\nwrote %s\n" out_dir
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let cmd_score opts =
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let grammar_path = opt opts "grammar" "" in
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let corpus_path = opt opts "corpus" "" in
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if grammar_path = "" || corpus_path = "" then
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(prerr_endline "score: --grammar and --corpus are required"; exit 2);
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let config = config_of_opts opts in
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let g = Grammar.of_string (read_file grammar_path) in
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let corpus = Corpus.of_file corpus_path in
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let d = Scoring.details ~config g corpus in
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Printf.printf "posterior %.6f\n" d.Scoring.posterior;
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Printf.printf "structural prior %.6f\n" d.Scoring.prior;
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Printf.printf "marginal loglik %.6f\n" d.Scoring.marginal;
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Printf.printf "ML corpus loglik %.6f\n" d.Scoring.ml_loglik;
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Printf.printf "description length %.2f bits\n" d.Scoring.dl_bits;
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Printf.printf "nonterminals %d\n" d.Scoring.num_nonterminals;
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Printf.printf "productions %d\n" d.Scoring.num_productions
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let cmd_parse opts =
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let grammar_path = opt opts "grammar" "" in
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||||
let input = opt opts "input" "" in
|
||||
if grammar_path = "" || input = "" then
|
||||
(prerr_endline "parse: --grammar and --input are required"; exit 2);
|
||||
let g = Grammar.normalize (Grammar.of_string (read_file grammar_path)) in
|
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let tokens =
|
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String.split_on_char ' ' (String.trim input)
|
||||
|> List.filter (fun s -> String.length s > 0)
|
||||
in
|
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let prep = Parse.prepare g in
|
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let p = Parse.inside prep tokens in
|
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let vp, tree = Parse.viterbi prep tokens in
|
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Printf.printf "tokens: %s\n" (String.concat " " tokens);
|
||||
Printf.printf "P(string): %.10g\n" p;
|
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Printf.printf "best parse: %.10g\n" vp;
|
||||
(match tree with
|
||||
| Some t -> Printf.printf "%s\n" (Parse.tree_to_string t)
|
||||
| None -> print_endline "(no parse)");
|
||||
(match List.assoc_opt "dot" opts with
|
||||
| Some path -> (
|
||||
match tree with
|
||||
| Some t ->
|
||||
Dot.write_file path (Dot.dot_tree ~title:"Viterbi parse" t);
|
||||
Printf.printf "wrote %s\n" path
|
||||
| None -> ())
|
||||
| None -> ())
|
||||
|
||||
let cmd_dot opts =
|
||||
let grammar_path = opt opts "grammar" "" in
|
||||
let out = opt opts "out" "" in
|
||||
if grammar_path = "" || out = "" then
|
||||
(prerr_endline "dot: --grammar and --out are required"; exit 2);
|
||||
let g = Grammar.normalize (Grammar.of_string (read_file grammar_path)) in
|
||||
let title = opt opts "title" "grammar" in
|
||||
let svg = List.assoc_opt "svg" opts in
|
||||
let res =
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||||
Dot.render ?out_svg:svg ~out_dot:out (Dot.dot_grammar ~title g)
|
||||
in
|
||||
Printf.printf "wrote %s%s\n" out
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||||
(match res with Some s -> " and " ^ s | None -> "")
|
||||
|
||||
let cmd_experiments opts =
|
||||
let out_dir = opt opts "out" "experiments" in
|
||||
mkdir_p out_dir;
|
||||
mkdir_p (Filename.concat out_dir "steps");
|
||||
let render = flag opts "render" in
|
||||
let quick = flag opts "quick" in
|
||||
let config = config_of_opts opts in
|
||||
let seed = int_opt opts "seed" 1 in
|
||||
let beam = int_opt opts "beam" 3 in
|
||||
let max_steps = int_opt opts "max-steps" (if quick then 12 else 25) in
|
||||
let patience = int_opt opts "patience" (if quick then 3 else 5) in
|
||||
let max_len = int_opt opts "max-len" (if quick then 6 else 7) in
|
||||
let only = List.assoc_opt "only" opts in
|
||||
let results =
|
||||
Experiment.run_all
|
||||
~export_dir:(if render then Some (Filename.concat out_dir "steps") else None)
|
||||
~config ~beam_width:beam ~max_steps ~patience ~seed ~max_len ~only ()
|
||||
in
|
||||
if render then
|
||||
List.iter
|
||||
(fun (r : Experiment.result) ->
|
||||
let base = Filename.concat out_dir r.Experiment.target.Experiment.name in
|
||||
ignore
|
||||
(Dot.render ~out_svg:(base ^ "-final.svg") ~out_dot:(base ^ "-final.dot")
|
||||
(Dot.dot_grammar
|
||||
~title:(Printf.sprintf "%s (induced)" r.Experiment.target.Experiment.name)
|
||||
r.Experiment.final_grammar)))
|
||||
results;
|
||||
Dot.write_file (Filename.concat out_dir "results.tsv")
|
||||
(Experiment.to_tsv results);
|
||||
Dot.write_file (Filename.concat out_dir "report.md")
|
||||
(Experiment.report_markdown results);
|
||||
List.iter
|
||||
(fun (r : Experiment.result) ->
|
||||
let base = Filename.concat out_dir r.Experiment.target.Experiment.name in
|
||||
Dot.write_file (base ^ "-final.dot")
|
||||
(Dot.dot_grammar
|
||||
~title:(Printf.sprintf "%s (induced)" r.Experiment.target.Experiment.name)
|
||||
r.Experiment.final_grammar);
|
||||
Dot.write_file (base ^ "-final.txt")
|
||||
(Grammar.to_string r.Experiment.final_grammar))
|
||||
results;
|
||||
print_endline (Experiment.to_tsv results);
|
||||
Printf.printf "\nwrote %s\n" out_dir
|
||||
|
||||
let () =
|
||||
match Array.to_list Sys.argv with
|
||||
| _ :: cmd :: rest -> (
|
||||
let opts = parse_args rest in
|
||||
match cmd with
|
||||
| "induce" -> cmd_induce opts
|
||||
| "score" -> cmd_score opts
|
||||
| "parse" -> cmd_parse opts
|
||||
| "dot" -> cmd_dot opts
|
||||
| "experiments" -> cmd_experiments opts
|
||||
| "help" | "-h" | "--help" -> usage ()
|
||||
| other ->
|
||||
Printf.eprintf "unknown command: %s\n\n" other;
|
||||
usage ();
|
||||
exit 2)
|
||||
| _ -> usage ()
|
||||
@@ -0,0 +1,2 @@
|
||||
(lang dune 3.0)
|
||||
(name scfg_induction)
|
||||
@@ -0,0 +1,7 @@
|
||||
# The paper's running example {ab, aabb, aaabbb}, counts summing to 50.
|
||||
# Cook et al.'s exact relative frequencies are not reprinted in the paper, so a
|
||||
# decaying distribution is used; uniform counts (e.g. 17/17/16) correctly block
|
||||
# the inductive leap under the Bayesian criterion (see the report).
|
||||
30: a b
|
||||
15: a a b b
|
||||
5: a a a b b b
|
||||
@@ -0,0 +1,4 @@
|
||||
# Paper, Table 1, row "wcwR, w in {a,b}*": S -> c | aSa | bSb
|
||||
S -> c [0.333]
|
||||
S -> a S a [0.333]
|
||||
S -> b S b [0.333]
|
||||
@@ -0,0 +1,106 @@
|
||||
<?xml version="1.0" encoding="UTF-8" standalone="no"?>
|
||||
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
|
||||
"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
|
||||
<!-- Generated by graphviz version 16.0.0 (0)
|
||||
-->
|
||||
<!-- Title: grammar Pages: 1 -->
|
||||
<svg width="429pt" height="136pt"
|
||||
viewBox="0.00 0.00 429.00 136.00" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
|
||||
<g id="graph0" class="graph" transform="scale(1 1) rotate(0) translate(4 131.5)">
|
||||
<title>grammar</title>
|
||||
<polygon fill="white" stroke="none" points="-4,4 -4,-131.5 424.75,-131.5 424.75,4 -4,4"/>
|
||||
<text xml:space="preserve" text-anchor="middle" x="210.38" y="-110.2" font-family="Times,serif" font-size="14.00">a2n (induced)</text>
|
||||
<!-- nt_S -->
|
||||
<g id="node1" class="node">
|
||||
<title>nt_S</title>
|
||||
<ellipse fill="none" stroke="black" stroke-width="2" cx="22" cy="-68" rx="18" ry="18"/>
|
||||
<ellipse fill="none" stroke="black" stroke-width="2" cx="22" cy="-68" rx="22" ry="22"/>
|
||||
<text xml:space="preserve" text-anchor="middle" x="22" y="-64.5" font-family="Helvetica,sans-Serif" font-size="10.00">S</text>
|
||||
</g>
|
||||
<!-- pr_0 -->
|
||||
<g id="node4" class="node">
|
||||
<title>pr_0</title>
|
||||
<polygon fill="none" stroke="black" points="139.25,-103 85.25,-103 85.25,-67 139.25,-67 139.25,-103"/>
|
||||
<text xml:space="preserve" text-anchor="middle" x="112.25" y="-87.5" font-family="Helvetica,sans-Serif" font-size="10.00">S S</text>
|
||||
<text xml:space="preserve" text-anchor="middle" x="112.25" y="-75.5" font-family="Helvetica,sans-Serif" font-size="10.00">p=0.600</text>
|
||||
</g>
|
||||
<!-- nt_S->pr_0 -->
|
||||
<g id="edge1" class="edge">
|
||||
<title>nt_S->pr_0</title>
|
||||
<path fill="none" stroke="black" d="M38.36,-83C45.06,-88.53 53.35,-94.14 62,-97 65.79,-98.25 69.79,-98.69 73.79,-98.55"/>
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<polygon fill="black" stroke="black" points="74.09,-102.05 83.46,-97.09 73.05,-95.12 74.09,-102.05"/>
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</g>
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<!-- pr_1 -->
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<g id="node5" class="node">
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<title>pr_1</title>
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<polygon fill="none" stroke="black" points="139.25,-36 85.25,-36 85.25,0 139.25,0 139.25,-36"/>
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<text xml:space="preserve" text-anchor="middle" x="112.25" y="-20.5" font-family="Helvetica,sans-Serif" font-size="10.00">T_a T_a</text>
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<text xml:space="preserve" text-anchor="middle" x="112.25" y="-8.5" font-family="Helvetica,sans-Serif" font-size="10.00">p=0.400</text>
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</g>
|
||||
<!-- nt_S->pr_1 -->
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<g id="edge4" class="edge">
|
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<title>nt_S->pr_1</title>
|
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<path fill="none" stroke="black" d="M41.72,-57.4C51.42,-51.9 63.61,-44.99 75.07,-38.5"/>
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<polygon fill="black" stroke="black" points="76.57,-41.67 83.54,-33.7 73.12,-35.58 76.57,-41.67"/>
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||||
</g>
|
||||
<!-- nt_T_a -->
|
||||
<g id="node2" class="node">
|
||||
<title>nt_T_a</title>
|
||||
<ellipse fill="none" stroke="black" cx="207.5" cy="-18" rx="27" ry="18"/>
|
||||
<text xml:space="preserve" text-anchor="middle" x="207.5" y="-14.5" font-family="Helvetica,sans-Serif" font-size="10.00">T_a</text>
|
||||
</g>
|
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<!-- pr_2 -->
|
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<g id="node6" class="node">
|
||||
<title>pr_2</title>
|
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<polygon fill="none" stroke="black" points="325.5,-36 271.5,-36 271.5,0 325.5,0 325.5,-36"/>
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<text xml:space="preserve" text-anchor="middle" x="298.5" y="-20.5" font-family="Helvetica,sans-Serif" font-size="10.00">a</text>
|
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<text xml:space="preserve" text-anchor="middle" x="298.5" y="-8.5" font-family="Helvetica,sans-Serif" font-size="10.00">p=1.000</text>
|
||||
</g>
|
||||
<!-- nt_T_a->pr_2 -->
|
||||
<g id="edge7" class="edge">
|
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<title>nt_T_a->pr_2</title>
|
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<path fill="none" stroke="black" d="M234.72,-18C242.62,-18 251.44,-18 259.93,-18"/>
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<polygon fill="black" stroke="black" points="259.64,-21.5 269.64,-18 259.64,-14.5 259.64,-21.5"/>
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</g>
|
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<!-- tm_a -->
|
||||
<g id="node3" class="node">
|
||||
<title>tm_a</title>
|
||||
<text xml:space="preserve" text-anchor="middle" x="393.75" y="-14.5" font-family="Helvetica,sans-Serif" font-size="10.00" fill="#666666">a</text>
|
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</g>
|
||||
<!-- pr_0->nt_S -->
|
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<g id="edge2" class="edge">
|
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<title>pr_0->nt_S</title>
|
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<path fill="none" stroke="black" d="M84.79,-79.9C75.49,-78.11 64.94,-76.08 55.22,-74.21"/>
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<polygon fill="black" stroke="black" points="55.88,-70.77 45.4,-72.32 54.56,-77.64 55.88,-70.77"/>
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<text xml:space="preserve" text-anchor="middle" x="64.62" y="-78.45" font-family="Helvetica,sans-Serif" font-size="9.00">1</text>
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</g>
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<!-- pr_0->nt_S -->
|
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<g id="edge3" class="edge">
|
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<title>pr_0->nt_S</title>
|
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<path fill="none" stroke="black" d="M85.11,-68.38C79.43,-65.54 73.3,-63.01 67.25,-61.5 63.17,-60.48 58.83,-60.18 54.53,-60.35"/>
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<polygon fill="black" stroke="black" points="54.44,-56.83 44.94,-61.5 55.28,-63.78 54.44,-56.83"/>
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<text xml:space="preserve" text-anchor="middle" x="64.62" y="-63.45" font-family="Helvetica,sans-Serif" font-size="9.00">2</text>
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</g>
|
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<!-- pr_1->nt_T_a -->
|
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<g id="edge5" class="edge">
|
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<title>pr_1->nt_T_a</title>
|
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<path fill="none" stroke="black" d="M139.72,-18C148.76,-18 159.04,-18 168.79,-18"/>
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<polygon fill="black" stroke="black" points="168.77,-21.5 178.77,-18 168.77,-14.5 168.77,-21.5"/>
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<text xml:space="preserve" text-anchor="middle" x="159.88" y="-19.95" font-family="Helvetica,sans-Serif" font-size="9.00">1</text>
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</g>
|
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<!-- pr_1->nt_T_a -->
|
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<g id="edge6" class="edge">
|
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<title>pr_1->nt_T_a</title>
|
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<path fill="none" stroke="black" d="M139.55,-5.7C146.89,-3.52 154.93,-2.29 162.5,-3.5 165.88,-4.04 169.36,-4.81 172.81,-5.7"/>
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<polygon fill="black" stroke="black" points="171.52,-8.97 182.1,-8.48 173.52,-2.26 171.52,-8.97"/>
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<text xml:space="preserve" text-anchor="middle" x="159.88" y="-5.45" font-family="Helvetica,sans-Serif" font-size="9.00">2</text>
|
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</g>
|
||||
<!-- pr_2->tm_a -->
|
||||
<g id="edge8" class="edge">
|
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<title>pr_2->tm_a</title>
|
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<path fill="none" stroke="black" d="M325.97,-18C335.18,-18 345.69,-18 355.61,-18"/>
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<polygon fill="black" stroke="black" points="355.34,-21.5 365.34,-18 355.34,-14.5 355.34,-21.5"/>
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<text xml:space="preserve" text-anchor="middle" x="346.12" y="-19.95" font-family="Helvetica,sans-Serif" font-size="9.00">1</text>
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</g>
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</g>
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</svg>
|
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|
After Width: | Height: | Size: 5.8 KiB |
@@ -0,0 +1,4 @@
|
||||
# start = S, 2 nonterminals, 1 terminals, 3 productions
|
||||
S -> S S [0.600]
|
||||
S -> T_a T_a [0.400]
|
||||
T_a -> a [1.000]
|
||||
@@ -0,0 +1,137 @@
|
||||
<?xml version="1.0" encoding="UTF-8" standalone="no"?>
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<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
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"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
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<!-- Generated by graphviz version 16.0.0 (0)
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-->
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<!-- Title: grammar Pages: 1 -->
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<svg width="429pt" height="163pt"
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viewBox="0.00 0.00 429.00 163.00" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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<g id="graph0" class="graph" transform="scale(1 1) rotate(0) translate(4 158.5)">
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<title>grammar</title>
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<polygon fill="white" stroke="none" points="-4,4 -4,-158.5 424.75,-158.5 424.75,4 -4,4"/>
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<text xml:space="preserve" text-anchor="middle" x="210.38" y="-137.2" font-family="Times,serif" font-size="14.00">abn (induced)</text>
|
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<!-- nt_S -->
|
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<g id="node1" class="node">
|
||||
<title>nt_S</title>
|
||||
<ellipse fill="none" stroke="black" stroke-width="2" cx="22" cy="-95" rx="18" ry="18"/>
|
||||
<ellipse fill="none" stroke="black" stroke-width="2" cx="22" cy="-95" rx="22" ry="22"/>
|
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<text xml:space="preserve" text-anchor="middle" x="22" y="-91.5" font-family="Helvetica,sans-Serif" font-size="10.00">S</text>
|
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</g>
|
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<!-- pr_0 -->
|
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<g id="node6" class="node">
|
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<title>pr_0</title>
|
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<polygon fill="none" stroke="black" points="139.25,-130 85.25,-130 85.25,-94 139.25,-94 139.25,-130"/>
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<text xml:space="preserve" text-anchor="middle" x="112.25" y="-114.5" font-family="Helvetica,sans-Serif" font-size="10.00">S S</text>
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<text xml:space="preserve" text-anchor="middle" x="112.25" y="-102.5" font-family="Helvetica,sans-Serif" font-size="10.00">p=0.600</text>
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</g>
|
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<!-- nt_S->pr_0 -->
|
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<g id="edge1" class="edge">
|
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<title>nt_S->pr_0</title>
|
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<path fill="none" stroke="black" d="M38.36,-110C45.06,-115.53 53.35,-121.14 62,-124 65.79,-125.25 69.79,-125.69 73.79,-125.55"/>
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<polygon fill="black" stroke="black" points="74.09,-129.05 83.46,-124.09 73.05,-122.12 74.09,-129.05"/>
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</g>
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<!-- pr_2 -->
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<g id="node8" class="node">
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<title>pr_2</title>
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<polygon fill="none" stroke="black" points="139.25,-63 85.25,-63 85.25,-27 139.25,-27 139.25,-63"/>
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<text xml:space="preserve" text-anchor="middle" x="112.25" y="-47.5" font-family="Helvetica,sans-Serif" font-size="10.00">T_a T_b</text>
|
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<text xml:space="preserve" text-anchor="middle" x="112.25" y="-35.5" font-family="Helvetica,sans-Serif" font-size="10.00">p=0.400</text>
|
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</g>
|
||||
<!-- nt_S->pr_2 -->
|
||||
<g id="edge6" class="edge">
|
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<title>nt_S->pr_2</title>
|
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<path fill="none" stroke="black" d="M41.72,-84.4C51.42,-78.9 63.61,-71.99 75.07,-65.5"/>
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<polygon fill="black" stroke="black" points="76.57,-68.67 83.54,-60.7 73.12,-62.58 76.57,-68.67"/>
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</g>
|
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<!-- nt_T_a -->
|
||||
<g id="node2" class="node">
|
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<title>nt_T_a</title>
|
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<ellipse fill="none" stroke="black" cx="207.5" cy="-72" rx="27" ry="18"/>
|
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<text xml:space="preserve" text-anchor="middle" x="207.5" y="-68.5" font-family="Helvetica,sans-Serif" font-size="10.00">T_a</text>
|
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</g>
|
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<!-- pr_3 -->
|
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<g id="node9" class="node">
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<title>pr_3</title>
|
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<polygon fill="none" stroke="black" points="325.5,-90 271.5,-90 271.5,-54 325.5,-54 325.5,-90"/>
|
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<text xml:space="preserve" text-anchor="middle" x="298.5" y="-74.5" font-family="Helvetica,sans-Serif" font-size="10.00">a</text>
|
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<text xml:space="preserve" text-anchor="middle" x="298.5" y="-62.5" font-family="Helvetica,sans-Serif" font-size="10.00">p=1.000</text>
|
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</g>
|
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<!-- nt_T_a->pr_3 -->
|
||||
<g id="edge9" class="edge">
|
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<title>nt_T_a->pr_3</title>
|
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<path fill="none" stroke="black" d="M234.72,-72C242.62,-72 251.44,-72 259.93,-72"/>
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<polygon fill="black" stroke="black" points="259.64,-75.5 269.64,-72 259.64,-68.5 259.64,-75.5"/>
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</g>
|
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<!-- nt_T_b -->
|
||||
<g id="node3" class="node">
|
||||
<title>nt_T_b</title>
|
||||
<ellipse fill="none" stroke="black" cx="207.5" cy="-18" rx="27" ry="18"/>
|
||||
<text xml:space="preserve" text-anchor="middle" x="207.5" y="-14.5" font-family="Helvetica,sans-Serif" font-size="10.00">T_b</text>
|
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</g>
|
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<!-- pr_1 -->
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<g id="node7" class="node">
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<title>pr_1</title>
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<polygon fill="none" stroke="black" points="325.5,-36 271.5,-36 271.5,0 325.5,0 325.5,-36"/>
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<text xml:space="preserve" text-anchor="middle" x="298.5" y="-20.5" font-family="Helvetica,sans-Serif" font-size="10.00">b</text>
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<text xml:space="preserve" text-anchor="middle" x="298.5" y="-8.5" font-family="Helvetica,sans-Serif" font-size="10.00">p=1.000</text>
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</g>
|
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<!-- nt_T_b->pr_1 -->
|
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<g id="edge4" class="edge">
|
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<title>nt_T_b->pr_1</title>
|
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<path fill="none" stroke="black" d="M234.72,-18C242.62,-18 251.44,-18 259.93,-18"/>
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<polygon fill="black" stroke="black" points="259.64,-21.5 269.64,-18 259.64,-14.5 259.64,-21.5"/>
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</g>
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<!-- tm_a -->
|
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<g id="node4" class="node">
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<title>tm_a</title>
|
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<text xml:space="preserve" text-anchor="middle" x="393.75" y="-68.5" font-family="Helvetica,sans-Serif" font-size="10.00" fill="#666666">a</text>
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</g>
|
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<!-- tm_b -->
|
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<g id="node5" class="node">
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<title>tm_b</title>
|
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<text xml:space="preserve" text-anchor="middle" x="393.75" y="-14.5" font-family="Helvetica,sans-Serif" font-size="10.00" fill="#666666">b</text>
|
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</g>
|
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<!-- pr_0->nt_S -->
|
||||
<g id="edge2" class="edge">
|
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<title>pr_0->nt_S</title>
|
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<path fill="none" stroke="black" d="M84.79,-106.9C75.49,-105.11 64.94,-103.08 55.22,-101.21"/>
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<polygon fill="black" stroke="black" points="55.88,-97.77 45.4,-99.32 54.56,-104.64 55.88,-97.77"/>
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<text xml:space="preserve" text-anchor="middle" x="64.62" y="-105.45" font-family="Helvetica,sans-Serif" font-size="9.00">1</text>
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</g>
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<!-- pr_0->nt_S -->
|
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<g id="edge3" class="edge">
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<title>pr_0->nt_S</title>
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<path fill="none" stroke="black" d="M85.11,-95.38C79.43,-92.54 73.3,-90.01 67.25,-88.5 63.17,-87.48 58.83,-87.18 54.53,-87.35"/>
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<polygon fill="black" stroke="black" points="54.44,-83.83 44.94,-88.5 55.28,-90.78 54.44,-83.83"/>
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<text xml:space="preserve" text-anchor="middle" x="64.62" y="-90.45" font-family="Helvetica,sans-Serif" font-size="9.00">2</text>
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</g>
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<!-- pr_1->tm_b -->
|
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<g id="edge5" class="edge">
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<title>pr_1->tm_b</title>
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<path fill="none" stroke="black" d="M325.97,-18C335.18,-18 345.69,-18 355.61,-18"/>
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<polygon fill="black" stroke="black" points="355.34,-21.5 365.34,-18 355.34,-14.5 355.34,-21.5"/>
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<text xml:space="preserve" text-anchor="middle" x="346.12" y="-19.95" font-family="Helvetica,sans-Serif" font-size="9.00">1</text>
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</g>
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<!-- pr_2->nt_T_a -->
|
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<g id="edge7" class="edge">
|
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<title>pr_2->nt_T_a</title>
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<path fill="none" stroke="black" d="M139.72,-52.66C149.53,-55.5 160.81,-58.77 171.27,-61.8"/>
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<polygon fill="black" stroke="black" points="170.16,-65.12 180.74,-64.54 172.11,-58.4 170.16,-65.12"/>
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<text xml:space="preserve" text-anchor="middle" x="159.88" y="-60.45" font-family="Helvetica,sans-Serif" font-size="9.00">1</text>
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</g>
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<!-- pr_2->nt_T_b -->
|
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<g id="edge8" class="edge">
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<title>pr_2->nt_T_b</title>
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<path fill="none" stroke="black" d="M139.72,-37.34C149.53,-34.5 160.81,-31.23 171.27,-28.2"/>
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<polygon fill="black" stroke="black" points="172.11,-31.6 180.74,-25.46 170.16,-24.88 172.11,-31.6"/>
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<text xml:space="preserve" text-anchor="middle" x="159.88" y="-33.45" font-family="Helvetica,sans-Serif" font-size="9.00">2</text>
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</g>
|
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<!-- pr_3->tm_a -->
|
||||
<g id="edge10" class="edge">
|
||||
<title>pr_3->tm_a</title>
|
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<path fill="none" stroke="black" d="M325.97,-72C335.18,-72 345.69,-72 355.61,-72"/>
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<polygon fill="black" stroke="black" points="355.34,-75.5 365.34,-72 355.34,-68.5 355.34,-75.5"/>
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<text xml:space="preserve" text-anchor="middle" x="346.12" y="-73.95" font-family="Helvetica,sans-Serif" font-size="9.00">1</text>
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</g>
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</svg>
|
||||
|
After Width: | Height: | Size: 7.3 KiB |
@@ -0,0 +1,5 @@
|
||||
# start = S, 3 nonterminals, 2 terminals, 4 productions
|
||||
S -> S S [0.600]
|
||||
T_b -> b [1.000]
|
||||
S -> T_a T_b [0.400]
|
||||
T_a -> a [1.000]
|
||||
@@ -0,0 +1,210 @@
|
||||
<?xml version="1.0" encoding="UTF-8" standalone="no"?>
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<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
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"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
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<!-- Generated by graphviz version 16.0.0 (0)
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-->
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<!-- Title: grammar Pages: 1 -->
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<svg width="431pt" height="249pt"
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viewBox="0.00 0.00 431.00 249.00" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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<g id="graph0" class="graph" transform="scale(1 1) rotate(0) translate(4 244.5)">
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<title>grammar</title>
|
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<polygon fill="white" stroke="none" points="-4,4 -4,-244.5 427.25,-244.5 427.25,4 -4,4"/>
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<text xml:space="preserve" text-anchor="middle" x="211.62" y="-223.2" font-family="Times,serif" font-size="14.00">addition (induced)</text>
|
||||
<!-- nt_S -->
|
||||
<g id="node1" class="node">
|
||||
<title>nt_S</title>
|
||||
<ellipse fill="none" stroke="black" stroke-width="2" cx="22" cy="-111" rx="18" ry="18"/>
|
||||
<ellipse fill="none" stroke="black" stroke-width="2" cx="22" cy="-111" rx="22" ry="22"/>
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<text xml:space="preserve" text-anchor="middle" x="22" y="-107.5" font-family="Helvetica,sans-Serif" font-size="10.00">S</text>
|
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</g>
|
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<!-- pr_0 -->
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<g id="node6" class="node">
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<title>pr_0</title>
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<polygon fill="none" stroke="black" points="140.5,-216 86.5,-216 86.5,-180 140.5,-180 140.5,-216"/>
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<text xml:space="preserve" text-anchor="middle" x="113.5" y="-200.5" font-family="Helvetica,sans-Serif" font-size="10.00">b</text>
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<text xml:space="preserve" text-anchor="middle" x="113.5" y="-188.5" font-family="Helvetica,sans-Serif" font-size="10.00">p=0.143</text>
|
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</g>
|
||||
<!-- nt_S->pr_0 -->
|
||||
<g id="edge1" class="edge">
|
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<title>nt_S->pr_0</title>
|
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<path fill="none" stroke="black" d="M32.47,-130.66C39.32,-143.35 49.55,-159.57 62,-171 66.28,-174.93 71.25,-178.48 76.36,-181.61"/>
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<polygon fill="black" stroke="black" points="74.46,-184.56 84.9,-186.37 77.87,-178.44 74.46,-184.56"/>
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</g>
|
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<!-- pr_2 -->
|
||||
<g id="node8" class="node">
|
||||
<title>pr_2</title>
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<!-- nt_S->pr_2 -->
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<g id="edge5" class="edge">
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<title>nt_S->pr_2</title>
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<path fill="none" stroke="black" d="M33.79,-129.84C40.52,-139.6 50.15,-150.59 62,-156 65.68,-157.68 69.62,-158.4 73.61,-158.45"/>
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<polygon fill="black" stroke="black" points="73.87,-161.95 83.36,-157.23 73,-155 73.87,-161.95"/>
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<g id="node9" class="node">
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<title>pr_3</title>
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<text xml:space="preserve" text-anchor="middle" x="113.5" y="-87.5" font-family="Helvetica,sans-Serif" font-size="10.00">S T_+ S</text>
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<text xml:space="preserve" text-anchor="middle" x="113.5" y="-75.5" font-family="Helvetica,sans-Serif" font-size="10.00">p=0.143</text>
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</g>
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<!-- nt_S->pr_3 -->
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<g id="edge9" class="edge">
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<title>nt_S->pr_3</title>
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<path fill="none" stroke="black" d="M43.31,-105.1C52.73,-102.36 64.22,-99.02 75.12,-95.86"/>
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<g id="node11" class="node">
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<title>pr_5</title>
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<polygon fill="none" stroke="black" points="140.5,-36 86.5,-36 86.5,0 140.5,0 140.5,-36"/>
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<text xml:space="preserve" text-anchor="middle" x="113.5" y="-20.5" font-family="Helvetica,sans-Serif" font-size="10.00">a</text>
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<text xml:space="preserve" text-anchor="middle" x="113.5" y="-8.5" font-family="Helvetica,sans-Serif" font-size="10.00">p=0.143</text>
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<g id="edge15" class="edge">
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<title>nt_S->pr_5</title>
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<g id="node2" class="node">
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<title>nt_T__</title>
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<ellipse fill="none" stroke="black" cx="210" cy="-119" rx="27" ry="18"/>
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<text xml:space="preserve" text-anchor="middle" x="210" y="-115.5" font-family="Helvetica,sans-Serif" font-size="10.00">T_+</text>
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<g id="node7" class="node">
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<title>pr_1</title>
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<text xml:space="preserve" text-anchor="middle" x="301" y="-175.5" font-family="Helvetica,sans-Serif" font-size="10.00">)</text>
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<text xml:space="preserve" text-anchor="middle" x="301" y="-163.5" font-family="Helvetica,sans-Serif" font-size="10.00">p=1.000</text>
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<g id="edge3" class="edge">
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<title>nt_T__->pr_1</title>
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<path fill="none" stroke="black" d="M230.75,-130.98C240.5,-136.9 252.56,-144.22 263.88,-151.08"/>
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<polygon fill="black" stroke="black" points="261.89,-153.97 272.26,-156.17 265.52,-147.99 261.89,-153.97"/>
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</g>
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<g id="node10" class="node">
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<title>pr_4</title>
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<polygon fill="none" stroke="black" points="328,-137 274,-137 274,-101 328,-101 328,-137"/>
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<text xml:space="preserve" text-anchor="middle" x="301" y="-121.5" font-family="Helvetica,sans-Serif" font-size="10.00">(</text>
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<text xml:space="preserve" text-anchor="middle" x="301" y="-109.5" font-family="Helvetica,sans-Serif" font-size="10.00">p=1.000</text>
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</g>
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<!-- nt_T__->pr_4 -->
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<g id="edge13" class="edge">
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<title>nt_T__->pr_4</title>
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<path fill="none" stroke="black" d="M237.22,-119C245.12,-119 253.94,-119 262.43,-119"/>
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<polygon fill="black" stroke="black" points="262.14,-122.5 272.14,-119 262.14,-115.5 262.14,-122.5"/>
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</g>
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<g id="node12" class="node">
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<title>pr_6</title>
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<polygon fill="none" stroke="black" points="328,-83 274,-83 274,-47 328,-47 328,-83"/>
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<text xml:space="preserve" text-anchor="middle" x="301" y="-67.5" font-family="Helvetica,sans-Serif" font-size="10.00">+</text>
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<text xml:space="preserve" text-anchor="middle" x="301" y="-55.5" font-family="Helvetica,sans-Serif" font-size="10.00">p=1.000</text>
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</g>
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<!-- nt_T__->pr_6 -->
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<g id="edge17" class="edge">
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<title>nt_T__->pr_6</title>
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<path fill="none" stroke="black" d="M230.75,-107.02C240.5,-101.1 252.56,-93.78 263.88,-86.92"/>
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<polygon fill="black" stroke="black" points="265.52,-90.01 272.26,-81.83 261.89,-84.03 265.52,-90.01"/>
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</g>
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<!-- tm__ -->
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<g id="node3" class="node">
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<title>tm__</title>
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<text xml:space="preserve" text-anchor="middle" x="396.25" y="-115.5" font-family="Helvetica,sans-Serif" font-size="10.00" fill="#666666">+</text>
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</g>
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<!-- tm_a -->
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<g id="node4" class="node">
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<title>tm_a</title>
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<text xml:space="preserve" text-anchor="middle" x="210" y="-14.5" font-family="Helvetica,sans-Serif" font-size="10.00" fill="#666666">a</text>
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</g>
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<!-- tm_b -->
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<g id="node5" class="node">
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<title>tm_b</title>
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<text xml:space="preserve" text-anchor="middle" x="210" y="-194.5" font-family="Helvetica,sans-Serif" font-size="10.00" fill="#666666">b</text>
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</g>
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<!-- pr_0->tm_b -->
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<g id="edge2" class="edge">
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<title>pr_0->tm_b</title>
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<path fill="none" stroke="black" d="M140.82,-198C150.43,-198 161.47,-198 171.84,-198"/>
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<polygon fill="black" stroke="black" points="171.63,-201.5 181.63,-198 171.63,-194.5 171.63,-201.5"/>
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<text xml:space="preserve" text-anchor="middle" x="162.38" y="-199.95" font-family="Helvetica,sans-Serif" font-size="9.00">1</text>
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</g>
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<!-- pr_1->tm__ -->
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<g id="edge4" class="edge">
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<title>pr_1->tm__</title>
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<path fill="none" stroke="black" d="M328.47,-157.67C338.08,-152.1 349.11,-145.72 359.4,-139.76"/>
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<polygon fill="black" stroke="black" points="361.15,-142.79 368.05,-134.75 357.64,-136.74 361.15,-142.79"/>
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<text xml:space="preserve" text-anchor="middle" x="348.62" y="-147.95" font-family="Helvetica,sans-Serif" font-size="9.00">1</text>
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</g>
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<!-- pr_2->nt_S -->
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<g id="edge7" class="edge">
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<title>pr_2->nt_S</title>
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<path fill="none" stroke="black" d="M84.89,-133.82C74.91,-130.14 63.59,-125.96 53.38,-122.2"/>
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<polygon fill="black" stroke="black" points="54.88,-119.02 44.28,-118.85 52.45,-125.59 54.88,-119.02"/>
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<text xml:space="preserve" text-anchor="middle" x="64.62" y="-128.46" font-family="Helvetica,sans-Serif" font-size="9.00">2</text>
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</g>
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<!-- pr_2->nt_T__ -->
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<g id="edge6" class="edge">
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<title>pr_2->nt_T__</title>
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<path fill="none" stroke="black" d="M142.04,-136.99C149.5,-135.07 157.56,-132.97 165,-131 167.91,-130.23 170.93,-129.42 173.96,-128.6"/>
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<polygon fill="black" stroke="black" points="174.61,-132.05 183.35,-126.06 172.78,-125.3 174.61,-132.05"/>
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<text xml:space="preserve" text-anchor="middle" x="162.38" y="-134.03" font-family="Helvetica,sans-Serif" font-size="9.00">1</text>
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</g>
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<!-- pr_2->nt_T__ -->
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<g id="edge8" class="edge">
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<title>pr_2->nt_T__</title>
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<path fill="none" stroke="black" d="M141.78,-125.71C147.49,-122.73 153.64,-120.1 159.75,-118.5 163.55,-117.5 167.56,-116.88 171.6,-116.53"/>
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<polygon fill="black" stroke="black" points="171.47,-120.04 181.35,-116.22 171.25,-113.04 171.47,-120.04"/>
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<text xml:space="preserve" text-anchor="middle" x="162.38" y="-120.45" font-family="Helvetica,sans-Serif" font-size="9.00">3</text>
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</g>
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<!-- pr_3->nt_S -->
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<g id="edge10" class="edge">
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<title>pr_3->nt_S</title>
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<path fill="none" stroke="black" d="M86.11,-81.72C78.21,-81.54 69.63,-82.15 62,-84.5 57.42,-85.91 52.9,-88.06 48.65,-90.53"/>
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<polygon fill="black" stroke="black" points="46.98,-87.44 40.58,-95.88 50.85,-93.28 46.98,-87.44"/>
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<text xml:space="preserve" text-anchor="middle" x="64.62" y="-86.45" font-family="Helvetica,sans-Serif" font-size="9.00">1</text>
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</g>
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<!-- pr_3->nt_S -->
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<g id="edge12" class="edge">
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<title>pr_3->nt_S</title>
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<path fill="none" stroke="black" d="M86.18,-69.06C78.29,-66.23 69.68,-65.12 62,-68.5 54.18,-71.94 47.25,-77.8 41.48,-84.09"/>
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<polygon fill="black" stroke="black" points="38.96,-81.63 35.31,-91.57 44.37,-86.08 38.96,-81.63"/>
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<text xml:space="preserve" text-anchor="middle" x="64.62" y="-70.45" font-family="Helvetica,sans-Serif" font-size="9.00">3</text>
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</g>
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<!-- pr_3->nt_T__ -->
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<g id="edge11" class="edge">
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<title>pr_3->nt_T__</title>
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<path fill="none" stroke="black" d="M140.75,-93.96C148.57,-96.66 157.14,-99.67 165,-102.5 168.45,-103.75 172.05,-105.06 175.64,-106.39"/>
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<polygon fill="black" stroke="black" points="174.19,-109.59 184.79,-109.8 176.64,-103.03 174.19,-109.59"/>
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<text xml:space="preserve" text-anchor="middle" x="162.38" y="-104.45" font-family="Helvetica,sans-Serif" font-size="9.00">2</text>
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</g>
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<!-- pr_4->tm__ -->
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<g id="edge14" class="edge">
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<title>pr_4->tm__</title>
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<path fill="none" stroke="black" d="M328.47,-119C337.68,-119 348.19,-119 358.11,-119"/>
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<polygon fill="black" stroke="black" points="357.84,-122.5 367.84,-119 357.84,-115.5 357.84,-122.5"/>
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<text xml:space="preserve" text-anchor="middle" x="348.62" y="-120.95" font-family="Helvetica,sans-Serif" font-size="9.00">1</text>
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</g>
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<!-- pr_5->tm_a -->
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<g id="edge16" class="edge">
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<title>pr_5->tm_a</title>
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<path fill="none" stroke="black" d="M140.82,-18C150.43,-18 161.47,-18 171.84,-18"/>
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<polygon fill="black" stroke="black" points="171.63,-21.5 181.63,-18 171.63,-14.5 171.63,-21.5"/>
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<text xml:space="preserve" text-anchor="middle" x="162.38" y="-19.95" font-family="Helvetica,sans-Serif" font-size="9.00">1</text>
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<!-- pr_6->tm__ -->
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<g id="edge18" class="edge">
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<title>pr_6->tm__</title>
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<path fill="none" stroke="black" d="M328.47,-80.33C338.08,-85.9 349.11,-92.28 359.4,-98.24"/>
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<polygon fill="black" stroke="black" points="357.64,-101.26 368.05,-103.25 361.15,-95.21 357.64,-101.26"/>
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<text xml:space="preserve" text-anchor="middle" x="348.62" y="-93.95" font-family="Helvetica,sans-Serif" font-size="9.00">1</text>
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</svg>
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|
After Width: | Height: | Size: 12 KiB |
@@ -0,0 +1,8 @@
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# start = S, 4 nonterminals, 5 terminals, 7 productions
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S -> b [0.143]
|
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T_) -> ) [1.000]
|
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S -> T_( S T_) [0.571]
|
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S -> S T_+ S [0.143]
|
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T_( -> ( [1.000]
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S -> a [0.143]
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T_+ -> + [1.000]
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@@ -0,0 +1,144 @@
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<!-- Title: grammar Pages: 1 -->
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<g id="graph0" class="graph" transform="scale(1 1) rotate(0) translate(4 136.07)">
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<title>grammar</title>
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<g id="node1" class="node">
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<title>nt_S</title>
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<ellipse fill="none" stroke="black" stroke-width="2" cx="22" cy="-47.57" rx="18" ry="18"/>
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<ellipse fill="none" stroke="black" stroke-width="2" cx="22" cy="-47.57" rx="22" ry="22"/>
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<text xml:space="preserve" text-anchor="middle" x="22" y="-44.07" font-family="Helvetica,sans-Serif" font-size="10.00">S</text>
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<title>pr_1</title>
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<!-- nt_S->pr_1 -->
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<g id="edge3" class="edge">
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<title>nt_S->pr_1</title>
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<text xml:space="preserve" text-anchor="middle" x="115.75" y="-25.07" font-family="Helvetica,sans-Serif" font-size="10.00">T_a T_b</text>
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<!-- nt_S->pr_2 -->
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<g id="edge7" class="edge">
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<title>nt_S->pr_2</title>
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<text xml:space="preserve" text-anchor="middle" x="214.5" y="-86.07" font-family="Helvetica,sans-Serif" font-size="10.00">T_a</text>
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<g id="node9" class="node">
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<g id="edge10" class="edge">
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<title>nt_T_a->pr_3</title>
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<g id="node3" class="node">
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<text xml:space="preserve" text-anchor="middle" x="214.5" y="-20.07" font-family="Helvetica,sans-Serif" font-size="10.00">T_b</text>
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<g id="node6" class="node">
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<title>pr_0</title>
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<g id="edge8" class="edge">
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<g id="edge11" class="edge">
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<title>pr_3->tm_a</title>
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After Width: | Height: | Size: 8.0 KiB |
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# start = S, 3 nonterminals, 2 terminals, 4 productions
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T_b -> b [1.000]
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S -> T_a S T_b [0.786]
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S -> T_a T_b [0.214]
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T_a -> a [1.000]
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<g id="edge9" class="edge">
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<g id="node3" class="node">
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After Width: | Height: | Size: 39 KiB |
@@ -0,0 +1,23 @@
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# start = S, 11 nonterminals, 17 terminals, 22 productions
|
||||
T_here -> here [0.500]
|
||||
S -> T_he T_is T_here [0.420]
|
||||
T_they -> they [0.333]
|
||||
S -> T_I T_am T_here [0.080]
|
||||
T_he -> she [0.333]
|
||||
T_that -> that [0.500]
|
||||
T_he -> it [0.333]
|
||||
T_am -> am [1.000]
|
||||
T_is -> is [1.000]
|
||||
T_man -> woman [0.500]
|
||||
S -> T_that T_man T_is T_here [0.080]
|
||||
T_that -> this [0.500]
|
||||
T_they -> we [0.333]
|
||||
T_are -> are [1.000]
|
||||
S -> T_that T_is T_a T_man [0.160]
|
||||
T_here -> there [0.500]
|
||||
T_he -> he [0.333]
|
||||
S -> T_they T_are T_here [0.260]
|
||||
T_a -> a [1.000]
|
||||
T_man -> man [0.500]
|
||||
T_I -> I [1.000]
|
||||
T_they -> you [0.333]
|
||||
@@ -0,0 +1,230 @@
|
||||
<?xml version="1.0" encoding="UTF-8" standalone="no"?>
|
||||
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
|
||||
"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
|
||||
<!-- Generated by graphviz version 16.0.0 (0)
|
||||
-->
|
||||
<!-- Title: grammar Pages: 1 -->
|
||||
<svg width="431pt" height="246pt"
|
||||
viewBox="0.00 0.00 431.00 246.00" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
|
||||
<g id="graph0" class="graph" transform="scale(1 1) rotate(0) translate(4 241.5)">
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||||
<title>grammar</title>
|
||||
<polygon fill="white" stroke="none" points="-4,4 -4,-241.5 427.25,-241.5 427.25,4 -4,4"/>
|
||||
<text xml:space="preserve" text-anchor="middle" x="211.62" y="-220.2" font-family="Times,serif" font-size="14.00">expr (induced)</text>
|
||||
<!-- nt_S -->
|
||||
<g id="node1" class="node">
|
||||
<title>nt_S</title>
|
||||
<ellipse fill="none" stroke="black" stroke-width="2" cx="22" cy="-110" rx="18" ry="18"/>
|
||||
<ellipse fill="none" stroke="black" stroke-width="2" cx="22" cy="-110" rx="22" ry="22"/>
|
||||
<text xml:space="preserve" text-anchor="middle" x="22" y="-106.5" font-family="Helvetica,sans-Serif" font-size="10.00">S</text>
|
||||
</g>
|
||||
<!-- pr_1 -->
|
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<g id="node7" class="node">
|
||||
<title>pr_1</title>
|
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<polygon fill="none" stroke="black" points="140.5,-213 86.5,-213 86.5,-177 140.5,-177 140.5,-213"/>
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<text xml:space="preserve" text-anchor="middle" x="113.5" y="-197.5" font-family="Helvetica,sans-Serif" font-size="10.00">b</text>
|
||||
<text xml:space="preserve" text-anchor="middle" x="113.5" y="-185.5" font-family="Helvetica,sans-Serif" font-size="10.00">p=0.200</text>
|
||||
</g>
|
||||
<!-- nt_S->pr_1 -->
|
||||
<g id="edge3" class="edge">
|
||||
<title>nt_S->pr_1</title>
|
||||
<path fill="none" stroke="black" d="M36.93,-126.43C44.15,-134.66 53.27,-144.63 62,-153 67.83,-158.59 74.3,-164.3 80.61,-169.63"/>
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<polygon fill="black" stroke="black" points="77.94,-171.97 87.87,-175.67 82.42,-166.58 77.94,-171.97"/>
|
||||
</g>
|
||||
<!-- pr_3 -->
|
||||
<g id="node9" class="node">
|
||||
<title>pr_3</title>
|
||||
<polygon fill="none" stroke="black" points="141.75,-157 85.25,-157 85.25,-121 141.75,-121 141.75,-157"/>
|
||||
<text xml:space="preserve" text-anchor="middle" x="113.5" y="-141.5" font-family="Helvetica,sans-Serif" font-size="10.00">T_( S T_)</text>
|
||||
<text xml:space="preserve" text-anchor="middle" x="113.5" y="-129.5" font-family="Helvetica,sans-Serif" font-size="10.00">p=0.200</text>
|
||||
</g>
|
||||
<!-- nt_S->pr_3 -->
|
||||
<g id="edge7" class="edge">
|
||||
<title>nt_S->pr_3</title>
|
||||
<path fill="none" stroke="black" d="M43.31,-116.58C52.42,-119.53 63.48,-123.12 74.06,-126.54"/>
|
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<polygon fill="black" stroke="black" points="72.78,-129.81 83.37,-129.56 74.93,-123.15 72.78,-129.81"/>
|
||||
</g>
|
||||
<!-- pr_6 -->
|
||||
<g id="node12" class="node">
|
||||
<title>pr_6</title>
|
||||
<polygon fill="none" stroke="black" points="140.5,-36 86.5,-36 86.5,0 140.5,0 140.5,-36"/>
|
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<text xml:space="preserve" text-anchor="middle" x="113.5" y="-20.5" font-family="Helvetica,sans-Serif" font-size="10.00">a</text>
|
||||
<text xml:space="preserve" text-anchor="middle" x="113.5" y="-8.5" font-family="Helvetica,sans-Serif" font-size="10.00">p=0.200</text>
|
||||
</g>
|
||||
<!-- nt_S->pr_6 -->
|
||||
<g id="edge15" class="edge">
|
||||
<title>nt_S->pr_6</title>
|
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<path fill="none" stroke="black" d="M38.18,-94.39C51.52,-80.69 71.19,-60.46 86.95,-44.26"/>
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<polygon fill="black" stroke="black" points="89.26,-46.91 93.72,-37.3 84.24,-42.03 89.26,-46.91"/>
|
||||
</g>
|
||||
<!-- pr_7 -->
|
||||
<g id="node13" class="node">
|
||||
<title>pr_7</title>
|
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<polygon fill="none" stroke="black" points="140.5,-95 86.5,-95 86.5,-59 140.5,-59 140.5,-95"/>
|
||||
<text xml:space="preserve" text-anchor="middle" x="113.5" y="-79.5" font-family="Helvetica,sans-Serif" font-size="10.00">S T_* S</text>
|
||||
<text xml:space="preserve" text-anchor="middle" x="113.5" y="-67.5" font-family="Helvetica,sans-Serif" font-size="10.00">p=0.400</text>
|
||||
</g>
|
||||
<!-- nt_S->pr_7 -->
|
||||
<g id="edge17" class="edge">
|
||||
<title>nt_S->pr_7</title>
|
||||
<path fill="none" stroke="black" d="M41.74,-100.01C48.06,-96.87 55.24,-93.56 62,-91 66.23,-89.4 70.73,-87.89 75.23,-86.5"/>
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<polygon fill="black" stroke="black" points="76.17,-89.87 84.8,-83.72 74.22,-83.14 76.17,-89.87"/>
|
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</g>
|
||||
<!-- nt_T__ -->
|
||||
<g id="node2" class="node">
|
||||
<title>nt_T__</title>
|
||||
<ellipse fill="none" stroke="black" cx="210" cy="-111" rx="27" ry="18"/>
|
||||
<text xml:space="preserve" text-anchor="middle" x="210" y="-107.5" font-family="Helvetica,sans-Serif" font-size="10.00">T_*</text>
|
||||
</g>
|
||||
<!-- pr_0 -->
|
||||
<g id="node6" class="node">
|
||||
<title>pr_0</title>
|
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<polygon fill="none" stroke="black" points="328,-210 274,-210 274,-174 328,-174 328,-210"/>
|
||||
<text xml:space="preserve" text-anchor="middle" x="301" y="-194.5" font-family="Helvetica,sans-Serif" font-size="10.00">*</text>
|
||||
<text xml:space="preserve" text-anchor="middle" x="301" y="-182.5" font-family="Helvetica,sans-Serif" font-size="10.00">p=0.500</text>
|
||||
</g>
|
||||
<!-- nt_T__->pr_0 -->
|
||||
<g id="edge1" class="edge">
|
||||
<title>nt_T__->pr_0</title>
|
||||
<path fill="none" stroke="black" d="M226.91,-125.48C239.28,-136.74 256.77,-152.65 271.53,-166.09"/>
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<polygon fill="black" stroke="black" points="268.98,-168.5 278.73,-172.65 273.69,-163.33 268.98,-168.5"/>
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</g>
|
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<!-- pr_2 -->
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<g id="node8" class="node">
|
||||
<title>pr_2</title>
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<polygon fill="none" stroke="black" points="328,-156 274,-156 274,-120 328,-120 328,-156"/>
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<text xml:space="preserve" text-anchor="middle" x="301" y="-140.5" font-family="Helvetica,sans-Serif" font-size="10.00">)</text>
|
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<text xml:space="preserve" text-anchor="middle" x="301" y="-128.5" font-family="Helvetica,sans-Serif" font-size="10.00">p=1.000</text>
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||||
</g>
|
||||
<!-- nt_T__->pr_2 -->
|
||||
<g id="edge5" class="edge">
|
||||
<title>nt_T__->pr_2</title>
|
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<path fill="none" stroke="black" d="M234.85,-118.24C243.44,-120.84 253.34,-123.84 262.79,-126.71"/>
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<polygon fill="black" stroke="black" points="261.54,-129.99 272.13,-129.54 263.57,-123.29 261.54,-129.99"/>
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</g>
|
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<!-- pr_4 -->
|
||||
<g id="node10" class="node">
|
||||
<title>pr_4</title>
|
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<polygon fill="none" stroke="black" points="328,-102 274,-102 274,-66 328,-66 328,-102"/>
|
||||
<text xml:space="preserve" text-anchor="middle" x="301" y="-86.5" font-family="Helvetica,sans-Serif" font-size="10.00">+</text>
|
||||
<text xml:space="preserve" text-anchor="middle" x="301" y="-74.5" font-family="Helvetica,sans-Serif" font-size="10.00">p=0.500</text>
|
||||
</g>
|
||||
<!-- nt_T__->pr_4 -->
|
||||
<g id="edge11" class="edge">
|
||||
<title>nt_T__->pr_4</title>
|
||||
<path fill="none" stroke="black" d="M234.85,-103.76C243.44,-101.16 253.34,-98.16 262.79,-95.29"/>
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<polygon fill="black" stroke="black" points="263.57,-98.71 272.13,-92.46 261.54,-92.01 263.57,-98.71"/>
|
||||
</g>
|
||||
<!-- pr_5 -->
|
||||
<g id="node11" class="node">
|
||||
<title>pr_5</title>
|
||||
<polygon fill="none" stroke="black" points="328,-48 274,-48 274,-12 328,-12 328,-48"/>
|
||||
<text xml:space="preserve" text-anchor="middle" x="301" y="-32.5" font-family="Helvetica,sans-Serif" font-size="10.00">(</text>
|
||||
<text xml:space="preserve" text-anchor="middle" x="301" y="-20.5" font-family="Helvetica,sans-Serif" font-size="10.00">p=1.000</text>
|
||||
</g>
|
||||
<!-- nt_T__->pr_5 -->
|
||||
<g id="edge13" class="edge">
|
||||
<title>nt_T__->pr_5</title>
|
||||
<path fill="none" stroke="black" d="M226.91,-96.52C239.28,-85.26 256.77,-69.35 271.53,-55.91"/>
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<polygon fill="black" stroke="black" points="273.69,-58.67 278.73,-49.35 268.98,-53.5 273.69,-58.67"/>
|
||||
</g>
|
||||
<!-- tm__ -->
|
||||
<g id="node3" class="node">
|
||||
<title>tm__</title>
|
||||
<text xml:space="preserve" text-anchor="middle" x="396.25" y="-102.5" font-family="Helvetica,sans-Serif" font-size="10.00" fill="#666666">+</text>
|
||||
</g>
|
||||
<!-- tm_a -->
|
||||
<g id="node4" class="node">
|
||||
<title>tm_a</title>
|
||||
<text xml:space="preserve" text-anchor="middle" x="210" y="-14.5" font-family="Helvetica,sans-Serif" font-size="10.00" fill="#666666">a</text>
|
||||
</g>
|
||||
<!-- tm_b -->
|
||||
<g id="node5" class="node">
|
||||
<title>tm_b</title>
|
||||
<text xml:space="preserve" text-anchor="middle" x="210" y="-191.5" font-family="Helvetica,sans-Serif" font-size="10.00" fill="#666666">b</text>
|
||||
</g>
|
||||
<!-- pr_0->tm__ -->
|
||||
<g id="edge2" class="edge">
|
||||
<title>pr_0->tm__</title>
|
||||
<path fill="none" stroke="black" d="M321.78,-173.76C335.09,-161.48 352.85,-145.11 367.56,-131.53"/>
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<polygon fill="black" stroke="black" points="369.73,-134.3 374.71,-124.94 364.99,-129.15 369.73,-134.3"/>
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<text xml:space="preserve" text-anchor="middle" x="348.62" y="-150.95" font-family="Helvetica,sans-Serif" font-size="9.00">1</text>
|
||||
</g>
|
||||
<!-- pr_1->tm_b -->
|
||||
<g id="edge4" class="edge">
|
||||
<title>pr_1->tm_b</title>
|
||||
<path fill="none" stroke="black" d="M140.82,-195C150.43,-195 161.47,-195 171.84,-195"/>
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<polygon fill="black" stroke="black" points="171.63,-198.5 181.63,-195 171.63,-191.5 171.63,-198.5"/>
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<text xml:space="preserve" text-anchor="middle" x="162.38" y="-196.95" font-family="Helvetica,sans-Serif" font-size="9.00">1</text>
|
||||
</g>
|
||||
<!-- pr_2->tm__ -->
|
||||
<g id="edge6" class="edge">
|
||||
<title>pr_2->tm__</title>
|
||||
<path fill="none" stroke="black" d="M328.47,-128.92C337.88,-125.69 348.65,-121.99 358.75,-118.52"/>
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<polygon fill="black" stroke="black" points="359.6,-121.93 367.92,-115.38 357.33,-115.31 359.6,-121.93"/>
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<text xml:space="preserve" text-anchor="middle" x="348.62" y="-123.95" font-family="Helvetica,sans-Serif" font-size="9.00">1</text>
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||||
</g>
|
||||
<!-- pr_3->nt_S -->
|
||||
<g id="edge9" class="edge">
|
||||
<title>pr_3->nt_S</title>
|
||||
<path fill="none" stroke="black" d="M85,-140.7C77.39,-140.43 69.24,-139.42 62,-137 57.34,-135.44 52.74,-133.15 48.42,-130.54"/>
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<polygon fill="black" stroke="black" points="50.44,-127.68 40.2,-124.95 46.5,-133.47 50.44,-127.68"/>
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<text xml:space="preserve" text-anchor="middle" x="64.62" y="-140.43" font-family="Helvetica,sans-Serif" font-size="9.00">2</text>
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||||
</g>
|
||||
<!-- pr_3->nt_T__ -->
|
||||
<g id="edge8" class="edge">
|
||||
<title>pr_3->nt_T__</title>
|
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<path fill="none" stroke="black" d="M142.09,-130.83C152.01,-127.89 163.34,-124.53 173.82,-121.42"/>
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<polygon fill="black" stroke="black" points="174.71,-124.81 183.3,-118.61 172.72,-118.1 174.71,-124.81"/>
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<text xml:space="preserve" text-anchor="middle" x="162.38" y="-126.95" font-family="Helvetica,sans-Serif" font-size="9.00">1</text>
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</g>
|
||||
<!-- pr_3->nt_T__ -->
|
||||
<g id="edge10" class="edge">
|
||||
<title>pr_3->nt_T__</title>
|
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<path fill="none" stroke="black" d="M138.18,-120.62C144.81,-116.47 152.26,-112.66 159.75,-110.5 163.56,-109.4 167.61,-108.71 171.68,-108.33"/>
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<polygon fill="black" stroke="black" points="171.67,-111.83 181.55,-108 171.43,-104.84 171.67,-111.83"/>
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<text xml:space="preserve" text-anchor="middle" x="162.38" y="-112.45" font-family="Helvetica,sans-Serif" font-size="9.00">3</text>
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</g>
|
||||
<!-- pr_4->tm__ -->
|
||||
<g id="edge12" class="edge">
|
||||
<title>pr_4->tm__</title>
|
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<path fill="none" stroke="black" d="M328.47,-90.25C337.78,-92.44 348.42,-94.95 358.43,-97.31"/>
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<polygon fill="black" stroke="black" points="357.35,-100.65 367.88,-99.54 358.95,-93.84 357.35,-100.65"/>
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<text xml:space="preserve" text-anchor="middle" x="348.62" y="-96.95" font-family="Helvetica,sans-Serif" font-size="9.00">1</text>
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</g>
|
||||
<!-- pr_5->tm__ -->
|
||||
<g id="edge14" class="edge">
|
||||
<title>pr_5->tm__</title>
|
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<path fill="none" stroke="black" d="M324.57,-48.4C336.57,-58.18 351.5,-70.34 364.54,-80.97"/>
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<polygon fill="black" stroke="black" points="362.07,-83.47 372.03,-87.08 366.49,-78.05 362.07,-83.47"/>
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<text xml:space="preserve" text-anchor="middle" x="348.62" y="-69.95" font-family="Helvetica,sans-Serif" font-size="9.00">1</text>
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</g>
|
||||
<!-- pr_6->tm_a -->
|
||||
<g id="edge16" class="edge">
|
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<title>pr_6->tm_a</title>
|
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<path fill="none" stroke="black" d="M140.82,-18C150.43,-18 161.47,-18 171.84,-18"/>
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<polygon fill="black" stroke="black" points="171.63,-21.5 181.63,-18 171.63,-14.5 171.63,-21.5"/>
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<text xml:space="preserve" text-anchor="middle" x="162.38" y="-19.95" font-family="Helvetica,sans-Serif" font-size="9.00">1</text>
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</g>
|
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<!-- pr_7->nt_S -->
|
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<g id="edge18" class="edge">
|
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<title>pr_7->nt_S</title>
|
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<path fill="none" stroke="black" d="M86.17,-72.42C78.19,-72.03 69.55,-72.64 62,-75.5 55.98,-77.78 50.29,-81.47 45.21,-85.59"/>
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</g>
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<!-- pr_7->nt_S -->
|
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<g id="edge20" class="edge">
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<title>pr_7->nt_S</title>
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<path fill="none" stroke="black" d="M86.24,-86.68C75.95,-90.48 64.07,-94.86 53.41,-98.79"/>
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<text xml:space="preserve" text-anchor="middle" x="64.62" y="-97.43" font-family="Helvetica,sans-Serif" font-size="9.00">3</text>
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</g>
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<!-- pr_7->nt_T__ -->
|
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<g id="edge19" class="edge">
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<title>pr_7->nt_T__</title>
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<path fill="none" stroke="black" d="M140.75,-85.96C148.57,-88.66 157.14,-91.67 165,-94.5 168.45,-95.75 172.05,-97.06 175.64,-98.39"/>
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</g>
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</g>
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</svg>
|
||||
|
After Width: | Height: | Size: 13 KiB |
@@ -0,0 +1,9 @@
|
||||
# start = S, 4 nonterminals, 6 terminals, 8 productions
|
||||
T_* -> * [0.500]
|
||||
S -> b [0.200]
|
||||
T_) -> ) [1.000]
|
||||
S -> T_( S T_) [0.200]
|
||||
T_* -> + [0.500]
|
||||
T_( -> ( [1.000]
|
||||
S -> a [0.200]
|
||||
S -> S T_* S [0.400]
|
||||
@@ -0,0 +1,142 @@
|
||||
<?xml version="1.0" encoding="UTF-8" standalone="no"?>
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<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
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"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
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<!-- Generated by graphviz version 16.0.0 (0)
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# start = S, 3 nonterminals, 3 terminals, 4 productions
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T_b -> b [1.000]
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S -> c [0.059]
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S -> T_a S T_b [0.941]
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T_a -> a [1.000]
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<text xml:space="preserve" text-anchor="middle" x="348.62" y="-96.45" font-family="Helvetica,sans-Serif" font-size="9.00">1</text>
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</g>
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<!-- pr_2->nt_S -->
|
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<g id="edge8" class="edge">
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<title>pr_2->nt_S</title>
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<path fill="none" stroke="black" d="M84.94,-69.09C77.41,-68.41 69.31,-68.54 62,-70.5 58.11,-71.54 54.2,-73.08 50.44,-74.87"/>
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<polygon fill="black" stroke="black" points="48.8,-71.77 41.71,-79.64 52.16,-77.91 48.8,-71.77"/>
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<text xml:space="preserve" text-anchor="middle" x="64.62" y="-72.45" font-family="Helvetica,sans-Serif" font-size="9.00">2</text>
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</g>
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<!-- pr_2->nt_T__ -->
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<g id="edge7" class="edge">
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<title>pr_2->nt_T__</title>
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<path fill="none" stroke="black" d="M142.09,-77.63C151.33,-78.51 161.79,-79.5 171.65,-80.44"/>
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<polygon fill="black" stroke="black" points="171.05,-83.9 181.33,-81.36 171.71,-76.93 171.05,-83.9"/>
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<text xml:space="preserve" text-anchor="middle" x="162.38" y="-81.72" font-family="Helvetica,sans-Serif" font-size="9.00">1</text>
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</g>
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<!-- pr_2->nt_T__ -->
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<g id="edge9" class="edge">
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<title>pr_2->nt_T__</title>
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<path fill="none" stroke="black" d="M142.05,-65.94C149.5,-64.54 157.57,-64 165,-65.5 169.14,-66.34 173.38,-67.57 177.51,-69.02"/>
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<text xml:space="preserve" text-anchor="middle" x="162.38" y="-67.45" font-family="Helvetica,sans-Serif" font-size="9.00">3</text>
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</g>
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<!-- pr_3->tm__ -->
|
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<g id="edge11" class="edge">
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<title>pr_3->tm__</title>
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<path fill="none" stroke="black" d="M328.47,-61.66C337.78,-64.36 348.42,-67.44 358.43,-70.34"/>
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<polygon fill="black" stroke="black" points="357.32,-73.66 367.9,-73.08 359.27,-66.94 357.32,-73.66"/>
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<text xml:space="preserve" text-anchor="middle" x="348.62" y="-69.45" font-family="Helvetica,sans-Serif" font-size="9.00">1</text>
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</g>
|
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<!-- pr_4->tm_a -->
|
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<g id="edge13" class="edge">
|
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<title>pr_4->tm_a</title>
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<path fill="none" stroke="black" d="M140.82,-18C150.43,-18 161.47,-18 171.84,-18"/>
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<polygon fill="black" stroke="black" points="171.63,-21.5 181.63,-18 171.63,-14.5 171.63,-21.5"/>
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<text xml:space="preserve" text-anchor="middle" x="162.38" y="-19.95" font-family="Helvetica,sans-Serif" font-size="9.00">1</text>
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</g>
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</g>
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</svg>
|
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|
After Width: | Height: | Size: 8.7 KiB |
@@ -0,0 +1,6 @@
|
||||
# start = S, 3 nonterminals, 3 terminals, 5 productions
|
||||
S -> S S [0.300]
|
||||
T_) -> ) [1.000]
|
||||
S -> T_( S T_) [0.600]
|
||||
T_( -> ( [1.000]
|
||||
S -> a [0.100]
|
||||
@@ -0,0 +1,176 @@
|
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<?xml version="1.0" encoding="UTF-8" standalone="no"?>
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<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
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"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
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<!-- Generated by graphviz version 16.0.0 (0)
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-->
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<!-- Title: grammar Pages: 1 -->
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<svg width="436pt" height="192pt"
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viewBox="0.00 0.00 436.00 192.00" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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<g id="graph0" class="graph" transform="scale(1 1) rotate(0) translate(4 187.5)">
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<title>grammar</title>
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<polygon fill="white" stroke="none" points="-4,4 -4,-187.5 431.75,-187.5 431.75,4 -4,4"/>
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<text xml:space="preserve" text-anchor="middle" x="213.88" y="-166.2" font-family="Times,serif" font-size="14.00">palindrome (induced)</text>
|
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<!-- nt_S -->
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<g id="node1" class="node">
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<title>nt_S</title>
|
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<ellipse fill="none" stroke="black" stroke-width="2" cx="22" cy="-87" rx="18" ry="18"/>
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<ellipse fill="none" stroke="black" stroke-width="2" cx="22" cy="-87" rx="22" ry="22"/>
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<text xml:space="preserve" text-anchor="middle" x="22" y="-83.5" font-family="Helvetica,sans-Serif" font-size="10.00">S</text>
|
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</g>
|
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<!-- pr_1 -->
|
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<g id="node8" class="node">
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<title>pr_1</title>
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<polygon fill="none" stroke="black" points="142.75,-159 88.75,-159 88.75,-123 142.75,-123 142.75,-159"/>
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<text xml:space="preserve" text-anchor="middle" x="115.75" y="-143.5" font-family="Helvetica,sans-Serif" font-size="10.00">c</text>
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<text xml:space="preserve" text-anchor="middle" x="115.75" y="-131.5" font-family="Helvetica,sans-Serif" font-size="10.00">p=0.083</text>
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</g>
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<!-- nt_S->pr_1 -->
|
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<g id="edge3" class="edge">
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<title>nt_S->pr_1</title>
|
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<path fill="none" stroke="black" d="M40.62,-99.29C47.23,-103.76 54.87,-108.75 62,-113 67.29,-116.15 72.96,-119.35 78.55,-122.4"/>
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<polygon fill="black" stroke="black" points="76.64,-125.35 87.1,-126.98 79.94,-119.17 76.64,-125.35"/>
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</g>
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<!-- pr_2 -->
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<g id="node9" class="node">
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<title>pr_2</title>
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<polygon fill="none" stroke="black" points="146.25,-105 85.25,-105 85.25,-69 146.25,-69 146.25,-105"/>
|
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<text xml:space="preserve" text-anchor="middle" x="115.75" y="-89.5" font-family="Helvetica,sans-Serif" font-size="10.00">T_b S T_b</text>
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<text xml:space="preserve" text-anchor="middle" x="115.75" y="-77.5" font-family="Helvetica,sans-Serif" font-size="10.00">p=0.417</text>
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</g>
|
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<!-- nt_S->pr_2 -->
|
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<g id="edge5" class="edge">
|
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<title>nt_S->pr_2</title>
|
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<path fill="none" stroke="black" d="M42.98,-94.4C49,-96.29 55.7,-98.05 62,-99 65.72,-99.56 69.56,-99.65 73.4,-99.41"/>
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<polygon fill="black" stroke="black" points="73.86,-102.88 83.27,-98.01 72.88,-95.94 73.86,-102.88"/>
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</g>
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<!-- pr_4 -->
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<g id="node11" class="node">
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<title>pr_4</title>
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<polygon fill="none" stroke="black" points="146.25,-48 85.25,-48 85.25,-12 146.25,-12 146.25,-48"/>
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<text xml:space="preserve" text-anchor="middle" x="115.75" y="-32.5" font-family="Helvetica,sans-Serif" font-size="10.00">T_a S T_a</text>
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<text xml:space="preserve" text-anchor="middle" x="115.75" y="-20.5" font-family="Helvetica,sans-Serif" font-size="10.00">p=0.500</text>
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</g>
|
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<!-- nt_S->pr_4 -->
|
||||
<g id="edge11" class="edge">
|
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<title>nt_S->pr_4</title>
|
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<path fill="none" stroke="black" d="M41.13,-75.74C51.02,-69.59 63.66,-61.74 75.67,-54.28"/>
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<polygon fill="black" stroke="black" points="77.17,-57.47 83.82,-49.22 73.48,-51.52 77.17,-57.47"/>
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</g>
|
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<!-- nt_T_a -->
|
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<g id="node2" class="node">
|
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<title>nt_T_a</title>
|
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<ellipse fill="none" stroke="black" cx="214.5" cy="-18" rx="27" ry="18"/>
|
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<text xml:space="preserve" text-anchor="middle" x="214.5" y="-14.5" font-family="Helvetica,sans-Serif" font-size="10.00">T_a</text>
|
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</g>
|
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<!-- pr_3 -->
|
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<g id="node10" class="node">
|
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<title>pr_3</title>
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<polygon fill="none" stroke="black" points="332.5,-36 278.5,-36 278.5,0 332.5,0 332.5,-36"/>
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<text xml:space="preserve" text-anchor="middle" x="305.5" y="-20.5" font-family="Helvetica,sans-Serif" font-size="10.00">a</text>
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<text xml:space="preserve" text-anchor="middle" x="305.5" y="-8.5" font-family="Helvetica,sans-Serif" font-size="10.00">p=1.000</text>
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</g>
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<!-- nt_T_a->pr_3 -->
|
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<g id="edge9" class="edge">
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<title>nt_T_a->pr_3</title>
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<path fill="none" stroke="black" d="M241.72,-18C249.62,-18 258.44,-18 266.93,-18"/>
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<polygon fill="black" stroke="black" points="266.64,-21.5 276.64,-18 266.64,-14.5 266.64,-21.5"/>
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</g>
|
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<!-- nt_T_b -->
|
||||
<g id="node3" class="node">
|
||||
<title>nt_T_b</title>
|
||||
<ellipse fill="none" stroke="black" cx="214.5" cy="-79" rx="27" ry="18"/>
|
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<text xml:space="preserve" text-anchor="middle" x="214.5" y="-75.5" font-family="Helvetica,sans-Serif" font-size="10.00">T_b</text>
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</g>
|
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<!-- pr_0 -->
|
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<g id="node7" class="node">
|
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<title>pr_0</title>
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<polygon fill="none" stroke="black" points="332.5,-97 278.5,-97 278.5,-61 332.5,-61 332.5,-97"/>
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<text xml:space="preserve" text-anchor="middle" x="305.5" y="-81.5" font-family="Helvetica,sans-Serif" font-size="10.00">b</text>
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<text xml:space="preserve" text-anchor="middle" x="305.5" y="-69.5" font-family="Helvetica,sans-Serif" font-size="10.00">p=1.000</text>
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</g>
|
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<!-- nt_T_b->pr_0 -->
|
||||
<g id="edge1" class="edge">
|
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<title>nt_T_b->pr_0</title>
|
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<path fill="none" stroke="black" d="M241.72,-79C249.62,-79 258.44,-79 266.93,-79"/>
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<polygon fill="black" stroke="black" points="266.64,-82.5 276.64,-79 266.64,-75.5 266.64,-82.5"/>
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</g>
|
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<!-- tm_a -->
|
||||
<g id="node4" class="node">
|
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<title>tm_a</title>
|
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<text xml:space="preserve" text-anchor="middle" x="400.75" y="-14.5" font-family="Helvetica,sans-Serif" font-size="10.00" fill="#666666">a</text>
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</g>
|
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<!-- tm_b -->
|
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<g id="node5" class="node">
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<title>tm_b</title>
|
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<text xml:space="preserve" text-anchor="middle" x="400.75" y="-75.5" font-family="Helvetica,sans-Serif" font-size="10.00" fill="#666666">b</text>
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</g>
|
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<!-- tm_c -->
|
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<g id="node6" class="node">
|
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<title>tm_c</title>
|
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<text xml:space="preserve" text-anchor="middle" x="214.5" y="-137.5" font-family="Helvetica,sans-Serif" font-size="10.00" fill="#666666">c</text>
|
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</g>
|
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<!-- pr_0->tm_b -->
|
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<g id="edge2" class="edge">
|
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<title>pr_0->tm_b</title>
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<path fill="none" stroke="black" d="M332.97,-79C342.18,-79 352.69,-79 362.61,-79"/>
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<polygon fill="black" stroke="black" points="362.34,-82.5 372.34,-79 362.34,-75.5 362.34,-82.5"/>
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<text xml:space="preserve" text-anchor="middle" x="353.12" y="-80.95" font-family="Helvetica,sans-Serif" font-size="9.00">1</text>
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</g>
|
||||
<!-- pr_1->tm_c -->
|
||||
<g id="edge4" class="edge">
|
||||
<title>pr_1->tm_c</title>
|
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<path fill="none" stroke="black" d="M143.19,-141C153.49,-141 165.47,-141 176.59,-141"/>
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<polygon fill="black" stroke="black" points="176.25,-144.5 186.25,-141 176.25,-137.5 176.25,-144.5"/>
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<text xml:space="preserve" text-anchor="middle" x="166.88" y="-142.95" font-family="Helvetica,sans-Serif" font-size="9.00">1</text>
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</g>
|
||||
<!-- pr_2->nt_S -->
|
||||
<g id="edge7" class="edge">
|
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<title>pr_2->nt_S</title>
|
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<path fill="none" stroke="black" d="M84.9,-86.55C77.42,-86.49 69.42,-86.45 62,-86.5 59.96,-86.51 57.85,-86.53 55.73,-86.55"/>
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<polygon fill="black" stroke="black" points="55.93,-83.05 45.97,-86.66 56.01,-90.05 55.93,-83.05"/>
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<text xml:space="preserve" text-anchor="middle" x="64.62" y="-88.45" font-family="Helvetica,sans-Serif" font-size="9.00">2</text>
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</g>
|
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<!-- pr_2->nt_T_b -->
|
||||
<g id="edge6" class="edge">
|
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<title>pr_2->nt_T_b</title>
|
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<path fill="none" stroke="black" d="M146.61,-84.81C154.08,-84.25 162.09,-83.62 169.5,-83 171.68,-82.82 173.92,-82.63 176.18,-82.43"/>
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<polygon fill="black" stroke="black" points="176.29,-85.94 185.94,-81.57 175.67,-78.96 176.29,-85.94"/>
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<text xml:space="preserve" text-anchor="middle" x="166.88" y="-85.3" font-family="Helvetica,sans-Serif" font-size="9.00">1</text>
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</g>
|
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<!-- pr_2->nt_T_b -->
|
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<g id="edge8" class="edge">
|
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<title>pr_2->nt_T_b</title>
|
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<path fill="none" stroke="black" d="M146.51,-74.97C152.3,-73.11 158.4,-71.49 164.25,-70.5 168.74,-69.74 173.46,-69.65 178.13,-69.99"/>
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<polygon fill="black" stroke="black" points="177.57,-73.45 187.96,-71.36 178.54,-66.51 177.57,-73.45"/>
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<text xml:space="preserve" text-anchor="middle" x="166.88" y="-72.45" font-family="Helvetica,sans-Serif" font-size="9.00">3</text>
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</g>
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<!-- pr_3->tm_a -->
|
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<g id="edge10" class="edge">
|
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<title>pr_3->tm_a</title>
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<path fill="none" stroke="black" d="M332.97,-18C342.18,-18 352.69,-18 362.61,-18"/>
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<polygon fill="black" stroke="black" points="362.34,-21.5 372.34,-18 362.34,-14.5 362.34,-21.5"/>
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<text xml:space="preserve" text-anchor="middle" x="353.12" y="-19.95" font-family="Helvetica,sans-Serif" font-size="9.00">1</text>
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</g>
|
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<!-- pr_4->nt_S -->
|
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<g id="edge13" class="edge">
|
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<title>pr_4->nt_S</title>
|
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<path fill="none" stroke="black" d="M84.84,-35.82C77.05,-38.12 68.91,-41.25 62,-45.5 55.21,-49.67 48.83,-55.34 43.27,-61.13"/>
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<polygon fill="black" stroke="black" points="40.8,-58.64 36.77,-68.44 46.04,-63.29 40.8,-58.64"/>
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<text xml:space="preserve" text-anchor="middle" x="64.62" y="-47.45" font-family="Helvetica,sans-Serif" font-size="9.00">2</text>
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</g>
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<!-- pr_4->nt_T_a -->
|
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<g id="edge12" class="edge">
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<title>pr_4->nt_T_a</title>
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<path fill="none" stroke="black" d="M146.57,-26.3C155.99,-25.13 166.51,-23.83 176.37,-22.6"/>
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<polygon fill="black" stroke="black" points="176.55,-26.11 186.04,-21.41 175.69,-19.16 176.55,-26.11"/>
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<text xml:space="preserve" text-anchor="middle" x="166.88" y="-25.95" font-family="Helvetica,sans-Serif" font-size="9.00">1</text>
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</g>
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<!-- pr_4->nt_T_a -->
|
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<g id="edge14" class="edge">
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<title>pr_4->nt_T_a</title>
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<path fill="none" stroke="black" d="M146.56,-14.97C152.29,-12.7 158.36,-10.72 164.25,-9.5 168.93,-8.53 173.88,-8.38 178.77,-8.73"/>
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<polygon fill="black" stroke="black" points="178,-12.15 188.39,-10.1 178.99,-5.22 178,-12.15"/>
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<text xml:space="preserve" text-anchor="middle" x="166.88" y="-11.45" font-family="Helvetica,sans-Serif" font-size="9.00">3</text>
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</g>
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</g>
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</svg>
|
||||
|
After Width: | Height: | Size: 9.7 KiB |
@@ -0,0 +1,6 @@
|
||||
# start = S, 3 nonterminals, 3 terminals, 5 productions
|
||||
T_b -> b [1.000]
|
||||
S -> c [0.083]
|
||||
S -> T_b S T_b [0.417]
|
||||
T_a -> a [1.000]
|
||||
S -> T_a S T_a [0.500]
|
||||
@@ -0,0 +1,160 @@
|
||||
<?xml version="1.0" encoding="UTF-8" standalone="no"?>
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<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
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<!-- Generated by graphviz version 16.0.0 (0)
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-->
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<!-- Title: grammar Pages: 1 -->
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<svg width="431pt" height="187pt"
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viewBox="0.00 0.00 431.00 187.00" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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<g id="graph0" class="graph" transform="scale(1 1) rotate(0) translate(4 182.5)">
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<title>grammar</title>
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<polygon fill="white" stroke="none" points="-4,4 -4,-182.5 427.25,-182.5 427.25,4 -4,4"/>
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<text xml:space="preserve" text-anchor="middle" x="211.62" y="-161.2" font-family="Times,serif" font-size="14.00">parens (induced)</text>
|
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<!-- nt_S -->
|
||||
<g id="node1" class="node">
|
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<title>nt_S</title>
|
||||
<ellipse fill="none" stroke="black" stroke-width="2" cx="22" cy="-85" rx="18" ry="18"/>
|
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<ellipse fill="none" stroke="black" stroke-width="2" cx="22" cy="-85" rx="22" ry="22"/>
|
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<text xml:space="preserve" text-anchor="middle" x="22" y="-81.5" font-family="Helvetica,sans-Serif" font-size="10.00">S</text>
|
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</g>
|
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<!-- pr_0 -->
|
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<g id="node4" class="node">
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<title>pr_0</title>
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<polygon fill="none" stroke="black" points="140.5,-154 86.5,-154 86.5,-118 140.5,-118 140.5,-154"/>
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<text xml:space="preserve" text-anchor="middle" x="113.5" y="-138.5" font-family="Helvetica,sans-Serif" font-size="10.00">S S</text>
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<text xml:space="preserve" text-anchor="middle" x="113.5" y="-126.5" font-family="Helvetica,sans-Serif" font-size="10.00">p=0.190</text>
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</g>
|
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<!-- nt_S->pr_0 -->
|
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<g id="edge1" class="edge">
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<title>nt_S->pr_0</title>
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<title>nt_S->pr_3</title>
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<title>nt_T__->pr_1</title>
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<g id="node3" class="node">
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<title>tm__</title>
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<g id="edge2" class="edge">
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<title>pr_0->nt_S</title>
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<g id="edge3" class="edge">
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<title>pr_0->nt_S</title>
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<title>pr_1->tm__</title>
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<g id="edge8" class="edge">
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<title>pr_2->nt_T__</title>
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<path fill="none" stroke="black" d="M140.82,-64.48C151.04,-61.56 162.89,-58.18 173.81,-55.05"/>
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<g id="edge11" class="edge">
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<title>pr_3->nt_S</title>
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<text xml:space="preserve" text-anchor="middle" x="64.62" y="-41.45" font-family="Helvetica,sans-Serif" font-size="9.00">2</text>
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<g id="edge10" class="edge">
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<title>pr_3->nt_T__</title>
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<g id="edge12" class="edge">
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<title>pr_3->nt_T__</title>
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<g id="edge14" class="edge">
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<title>pr_4->tm__</title>
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After Width: | Height: | Size: 9.0 KiB |
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# start = S, 3 nonterminals, 2 terminals, 5 productions
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S -> S S [0.190]
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T_) -> ) [1.000]
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S -> T_( T_) [0.429]
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S -> T_( S T_) [0.381]
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T_( -> ( [1.000]
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group name nts prods initial_score final_score heldout_avg unparseable covers precision exact recursive steps iterations
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paper parens 3 5 -124.812 -100.91 -0.437804 0 true 1.0000 true true 2 7
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paper a2n 2 3 -60.667 -54.4321 -0.290242 0 true 1.0000 true true 2 7
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paper abn 3 4 -68.0175 -58.5388 -0.290242 0 true 1.0000 true true 2 7
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paper anbn 3 4 -76.1383 -68.7322 -0.336244 0 true 1.0000 true true 2 7
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paper palindrome 3 5 -198.878 -120.804 -0.716536 0 true 1.0000 true true 1 6
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paper addition 4 7 -203.571 -134.296 -1.11968 0 true 1.0000 true true 2 7
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paper shape 5 7 -251.225 -140.646 -0.646156 0 true 1.0000 true true 4 9
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paper basic_english 11 22 -470.394 -286.801 -0.986128 0 true 1.0000 true false 7 12
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synthetic nested_parens 3 5 -267.458 -149.867 -0.793712 0 true 1.0000 true true 1 6
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synthetic nested_anbn 3 4 -93.6716 -68.1568 -0.481173 0 true 1.0000 true true 1 6
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synthetic expr 4 8 -424.161 -223.342 -1.29086 0 true 1.0000 true true 3 8
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<title>nt_S</title>
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<ellipse fill="none" stroke="black" stroke-width="2" cx="22" cy="-100" rx="18" ry="18"/>
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<title>nt_S->pr_0</title>
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<g id="node13" class="node">
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<title>pr_3</title>
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<text xml:space="preserve" text-anchor="middle" x="496" y="-62.5" font-family="Helvetica,sans-Serif" font-size="10.00">p=1.000</text>
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<g id="edge9" class="edge">
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<title>nt_T_c->pr_3</title>
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<path fill="none" stroke="black" d="M432.22,-72C440.12,-72 448.94,-72 457.43,-72"/>
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<polygon fill="black" stroke="black" points="457.14,-75.5 467.14,-72 457.14,-68.5 457.14,-75.5"/>
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<g id="node5" class="node">
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<title>nt_T_d</title>
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<ellipse fill="none" stroke="black" cx="214.5" cy="-159" rx="27" ry="18"/>
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<text xml:space="preserve" text-anchor="middle" x="214.5" y="-155.5" font-family="Helvetica,sans-Serif" font-size="10.00">T_d</text>
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<g id="node14" class="node">
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<title>pr_4</title>
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<text xml:space="preserve" text-anchor="middle" x="309.75" y="-182.5" font-family="Helvetica,sans-Serif" font-size="10.00">d</text>
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<g id="edge11" class="edge">
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<title>nt_T_d->pr_4</title>
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<g id="node6" class="node">
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<title>tm_a</title>
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<text xml:space="preserve" text-anchor="middle" x="405" y="-122.5" font-family="Helvetica,sans-Serif" font-size="10.00" fill="#666666">a</text>
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<g id="node7" class="node">
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<title>tm_b</title>
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<g id="node8" class="node">
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<title>tm_c</title>
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<text xml:space="preserve" text-anchor="middle" x="591.25" y="-68.5" font-family="Helvetica,sans-Serif" font-size="10.00" fill="#666666">c</text>
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<g id="node9" class="node">
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<title>tm_d</title>
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<g id="edge3" class="edge">
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<title>pr_0->nt_T_a</title>
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<g id="edge2" class="edge">
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<title>pr_0->nt_T_d</title>
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<path fill="none" stroke="black" d="M143.19,-136.47C154.21,-140 167.16,-144.15 178.93,-147.92"/>
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<g id="edge5" class="edge">
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<title>pr_1->tm_b</title>
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</g>
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<g id="edge8" class="edge">
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<title>pr_2->nt_T_a</title>
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<path fill="none" stroke="black" d="M282.32,-69.03C274.84,-68.91 266.75,-69.49 259.5,-71.5 253.74,-73.1 247.98,-75.68 242.62,-78.62"/>
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<g id="edge7" class="edge">
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<title>pr_2->nt_T_c</title>
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<polygon fill="black" stroke="black" points="366.27,-75.5 376.27,-72 366.27,-68.5 366.27,-75.5"/>
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<g id="edge10" class="edge">
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<title>pr_3->tm_c</title>
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<polygon fill="black" stroke="black" points="552.84,-75.5 562.84,-72 552.84,-68.5 552.84,-75.5"/>
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<text xml:space="preserve" text-anchor="middle" x="543.62" y="-73.95" font-family="Helvetica,sans-Serif" font-size="9.00">1</text>
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</g>
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<!-- pr_4->tm_d -->
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<g id="edge12" class="edge">
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<title>pr_4->tm_d</title>
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<path fill="none" stroke="black" d="M337.22,-180C346.43,-180 356.94,-180 366.86,-180"/>
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<polygon fill="black" stroke="black" points="366.59,-183.5 376.59,-180 366.59,-176.5 366.59,-183.5"/>
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<text xml:space="preserve" text-anchor="middle" x="357.38" y="-181.95" font-family="Helvetica,sans-Serif" font-size="9.00">1</text>
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<g id="edge14" class="edge">
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<title>pr_5->tm_a</title>
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<path fill="none" stroke="black" d="M337.22,-126C346.43,-126 356.94,-126 366.86,-126"/>
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<polygon fill="black" stroke="black" points="366.59,-129.5 376.59,-126 366.59,-122.5 366.59,-129.5"/>
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<text xml:space="preserve" text-anchor="middle" x="357.38" y="-127.95" font-family="Helvetica,sans-Serif" font-size="9.00">1</text>
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</g>
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<!-- pr_6->nt_S -->
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<g id="edge18" class="edge">
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<title>pr_6->nt_S</title>
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<path fill="none" stroke="black" d="M84.99,-70.56C77.36,-70.53 69.27,-71.27 62,-73.5 57.42,-74.91 52.9,-77.06 48.65,-79.53"/>
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<polygon fill="black" stroke="black" points="46.98,-76.44 40.58,-84.88 50.85,-82.28 46.98,-76.44"/>
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<g id="edge17" class="edge">
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<title>pr_6->nt_T_a</title>
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<g id="edge16" class="edge">
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<title>pr_6->nt_T_b</title>
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<polygon fill="black" stroke="black" points="180.88,-53.22 188.97,-46.38 178.38,-46.68 180.88,-53.22"/>
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<text xml:space="preserve" text-anchor="middle" x="166.88" y="-57.45" font-family="Helvetica,sans-Serif" font-size="9.00">1</text>
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After Width: | Height: | Size: 13 KiB |
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# start = S, 5 nonterminals, 4 terminals, 7 productions
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S -> T_d T_a [0.273]
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T_b -> b [1.000]
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T_a -> T_c T_a [0.917]
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T_c -> c [1.000]
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T_d -> d [1.000]
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T_a -> a [0.083]
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S -> T_b T_a S [0.727]
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@@ -0,0 +1,166 @@
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<g id="graph0" class="graph" transform="scale(1 1) rotate(0) translate(4 199.9)">
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<title>grammar</title>
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<title>nt_S</title>
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<ellipse fill="none" stroke="black" stroke-width="2" cx="22" cy="-79" rx="18" ry="18"/>
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<ellipse fill="none" stroke="black" stroke-width="2" cx="22" cy="-79" rx="22" ry="22"/>
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<g id="node3" class="node">
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<title>nt_X</title>
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<g id="edge10" class="edge">
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<g id="node4" class="node">
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<title>pr_0->tm__</title>
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<title>pr_1->tm__</title>
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<g id="edge22" class="edge">
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<title>pr_8->tm__</title>
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<title>nt_T_b->pr_2</title>
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<title>pr_3->nt_T_a</title>
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<title>nt_S->pr_8</title>
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<title>nt_S->pr_11</title>
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<title>pr_12</title>
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<g id="edge54" class="edge">
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<title>nt_S->pr_12</title>
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<text xml:space="preserve" text-anchor="middle" x="153.5" y="-1965.56" font-family="Helvetica,sans-Serif" font-size="10.00">T_b T_a T_b T_c T_a T_d T_a</text>
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<g id="edge62" class="edge">
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<title>nt_S->pr_13</title>
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<text xml:space="preserve" text-anchor="middle" x="153.5" y="-401.56" font-family="Helvetica,sans-Serif" font-size="10.00">T_b T_c T_c T_c T_a T_d T_a</text>
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<g id="edge70" class="edge">
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<title>nt_S->pr_14</title>
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<g id="edge78" class="edge">
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<title>nt_S->pr_15</title>
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<g id="node2" class="node">
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<title>nt_T_a</title>
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<text xml:space="preserve" text-anchor="middle" x="294.25" y="-1228.56" font-family="Helvetica,sans-Serif" font-size="10.00">T_a</text>
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<g id="edge3" class="edge">
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<title>nt_T_a->pr_1</title>
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<g id="node3" class="node">
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<title>nt_T_b</title>
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<ellipse fill="none" stroke="black" cx="294.25" cy="-1470.06" rx="27" ry="18"/>
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<text xml:space="preserve" text-anchor="middle" x="294.25" y="-1466.56" font-family="Helvetica,sans-Serif" font-size="10.00">T_b</text>
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<g id="edge8" class="edge">
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<title>nt_T_b->pr_3</title>
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<title>nt_T_c</title>
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<g id="edge10" class="edge">
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<title>nt_T_c->pr_4</title>
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<title>nt_T_d</title>
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<text xml:space="preserve" text-anchor="middle" x="294.25" y="-973.56" font-family="Helvetica,sans-Serif" font-size="10.00">T_d</text>
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<g id="node10" class="node">
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<g id="edge1" class="edge">
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<title>nt_T_d->pr_0</title>
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<g id="node6" class="node">
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<g id="edge2" class="edge">
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<title>pr_0->tm_d</title>
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<g id="edge4" class="edge">
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<title>pr_1->tm_a</title>
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<g id="edge7" class="edge">
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<title>pr_2->nt_T_a</title>
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<g id="edge6" class="edge">
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<title>pr_2->nt_T_d</title>
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<title>nt_T_d</title>
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<title>nt_T_d->pr_5</title>
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<g id="node6" class="node">
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<title>tm_a</title>
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<g id="node7" class="node">
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<title>tm_b</title>
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<g id="node8" class="node">
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<title>tm_c</title>
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<g id="node9" class="node">
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<title>tm_d</title>
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<g id="edge3" class="edge">
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<g id="edge2" class="edge">
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<title>pr_0->nt_T_b</title>
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<g id="edge4" class="edge">
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<title>pr_0->nt_T_d</title>
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<g id="edge8" class="edge">
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<title>pr_1->nt_T_a</title>
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<g id="edge7" class="edge">
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<title>pr_1->nt_T_d</title>
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<g id="edge10" class="edge">
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<title>pr_2->tm_b</title>
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<title>pr_3->nt_T_a</title>
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<g id="edge4" class="edge">
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<g id="node4" class="node">
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<g id="node13" class="node">
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<g id="edge9" class="edge">
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<title>nt_T_c->pr_3</title>
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<g id="node5" class="node">
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<title>nt_T_d</title>
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<g id="node14" class="node">
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<g id="edge11" class="edge">
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<title>nt_T_d->pr_4</title>
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<path fill="none" stroke="black" d="M240.49,-164.63C250,-166.77 261.05,-169.26 271.45,-171.6"/>
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<polygon fill="black" stroke="black" points="270.39,-174.95 280.91,-173.73 271.92,-168.12 270.39,-174.95"/>
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<g id="node6" class="node">
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<title>tm_a</title>
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<text xml:space="preserve" text-anchor="middle" x="405" y="-122.5" font-family="Helvetica,sans-Serif" font-size="10.00" fill="#666666">a</text>
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<g id="node7" class="node">
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<title>tm_b</title>
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<text xml:space="preserve" text-anchor="middle" x="405" y="-14.5" font-family="Helvetica,sans-Serif" font-size="10.00" fill="#666666">b</text>
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<g id="node8" class="node">
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<g id="node9" class="node">
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<title>tm_d</title>
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<text xml:space="preserve" text-anchor="middle" x="405" y="-176.5" font-family="Helvetica,sans-Serif" font-size="10.00" fill="#666666">d</text>
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<g id="edge3" class="edge">
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<g id="edge2" class="edge">
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<path fill="none" stroke="black" d="M143.96,-136.72C154.89,-140.22 167.61,-144.3 179.16,-148"/>
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<g id="edge5" class="edge">
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<g id="edge8" class="edge">
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<g id="edge7" class="edge">
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<polygon fill="black" stroke="black" points="366.27,-75.5 376.27,-72 366.27,-68.5 366.27,-75.5"/>
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<polygon fill="black" stroke="black" points="552.84,-75.5 562.84,-72 552.84,-68.5 552.84,-75.5"/>
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<g id="edge12" class="edge">
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<polygon fill="black" stroke="black" points="366.59,-183.5 376.59,-180 366.59,-176.5 366.59,-183.5"/>
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<g id="edge14" class="edge">
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<title>pr_5->tm_a</title>
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<polygon fill="black" stroke="black" points="366.59,-129.5 376.59,-126 366.59,-122.5 366.59,-129.5"/>
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<g id="edge18" class="edge">
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<title>pr_6->nt_S</title>
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<text xml:space="preserve" text-anchor="middle" x="130.25" y="-79.5" font-family="Helvetica,sans-Serif" font-size="10.00" fill="red">T_b T_a T_b T_a X</text>
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|
||||
type sample = { tokens : string list; count : float }
|
||||
|
||||
type t = sample list
|
||||
|
||||
let total_count corpus =
|
||||
List.fold_left (fun s x -> s +. x.count) 0.0 corpus
|
||||
|
||||
let distinct corpus = List.length corpus
|
||||
|
||||
let tokens_to_string toks = String.concat " " toks
|
||||
|
||||
let of_string text =
|
||||
let lines = String.split_on_char '\n' text in
|
||||
let acc = Hashtbl.create 64 in
|
||||
let order = ref [] in
|
||||
List.iter
|
||||
(fun line ->
|
||||
let line = String.trim line in
|
||||
if String.length line > 0 && line.[0] <> '#' then begin
|
||||
|
||||
let count, rest =
|
||||
match String.index_opt line ':' with
|
||||
| Some i -> (
|
||||
match
|
||||
float_of_string_opt (String.trim (String.sub line 0 i))
|
||||
with
|
||||
| Some c ->
|
||||
( c,
|
||||
String.sub line (i + 1) (String.length line - i - 1) )
|
||||
| None -> (1.0, line))
|
||||
| None -> (1.0, line)
|
||||
in
|
||||
let toks =
|
||||
String.split_on_char ' ' (String.trim rest)
|
||||
|> List.filter (fun s -> String.length s > 0)
|
||||
in
|
||||
if toks <> [] then begin
|
||||
let key = tokens_to_string toks in
|
||||
(match Hashtbl.find_opt acc key with
|
||||
| Some c -> Hashtbl.replace acc key (c +. count)
|
||||
| None ->
|
||||
Hashtbl.replace acc key count;
|
||||
order := key :: !order);
|
||||
()
|
||||
end
|
||||
end)
|
||||
lines;
|
||||
List.rev !order
|
||||
|> List.map (fun key ->
|
||||
let toks =
|
||||
String.split_on_char ' ' key
|
||||
|> List.filter (fun s -> String.length s > 0)
|
||||
in
|
||||
{ tokens = toks; count = Hashtbl.find acc key })
|
||||
|
||||
let to_string corpus =
|
||||
List.map
|
||||
(fun s -> Printf.sprintf "%g: %s" s.count (tokens_to_string s.tokens))
|
||||
corpus
|
||||
|> String.concat "\n"
|
||||
|
||||
let of_file path =
|
||||
let ic = open_in path in
|
||||
let n = in_channel_length ic in
|
||||
let s = really_input_string ic n in
|
||||
close_in ic;
|
||||
of_string s
|
||||
+143
@@ -0,0 +1,143 @@
|
||||
let escape s =
|
||||
let b = Buffer.create (String.length s) in
|
||||
String.iter
|
||||
(fun c ->
|
||||
match c with
|
||||
| '"' -> Buffer.add_string b "\\\""
|
||||
| '\\' -> Buffer.add_string b "\\\\"
|
||||
| '\n' -> Buffer.add_string b "\\n"
|
||||
| c -> Buffer.add_char b c)
|
||||
s;
|
||||
Buffer.contents b
|
||||
|
||||
let sanitize s =
|
||||
String.map
|
||||
(fun c ->
|
||||
if
|
||||
(c >= 'a' && c <= 'z')
|
||||
|| (c >= 'A' && c <= 'Z')
|
||||
|| (c >= '0' && c <= '9')
|
||||
|| c = '_'
|
||||
then c
|
||||
else '_')
|
||||
s
|
||||
|
||||
let nt_id name = "nt_" ^ sanitize name
|
||||
|
||||
let prob_of probs lhs rhs =
|
||||
match Hashtbl.find_opt probs lhs with
|
||||
| None -> 0.0
|
||||
| Some l -> (
|
||||
match List.find_opt (fun (q, _) -> Grammar.equal_rhs q.Grammar.rhs rhs) l with
|
||||
| Some (_, x) -> x
|
||||
| None -> 0.0)
|
||||
|
||||
let prod_key p =
|
||||
(p.Grammar.lhs, String.concat " " (List.map Grammar.symbol_to_string p.Grammar.rhs))
|
||||
|
||||
let dot_grammar ?(highlight_nts = []) ?(highlight_prods = [])
|
||||
?(title = "grammar") g =
|
||||
let probs = Grammar.probabilities g in
|
||||
let hl_nt name = List.mem name highlight_nts in
|
||||
let hl_prods = List.map prod_key highlight_prods in
|
||||
let buf = Buffer.create 2048 in
|
||||
Buffer.add_string buf "digraph grammar {\n";
|
||||
Buffer.add_string buf " rankdir=LR;\n";
|
||||
Buffer.add_string buf " labelloc=\"t\";\n";
|
||||
Buffer.add_string buf (Printf.sprintf " label=\"%s\";\n" (escape title));
|
||||
Buffer.add_string buf
|
||||
" node [fontname=\"Helvetica\", fontsize=10];\n edge [fontname=\"Helvetica\", fontsize=9];\n";
|
||||
List.iter
|
||||
(fun nt ->
|
||||
let is_start = String.equal nt g.Grammar.start in
|
||||
let hl = hl_nt nt in
|
||||
Buffer.add_string buf
|
||||
(Printf.sprintf
|
||||
" %s [label=\"%s\", shape=%s%s%s];\n"
|
||||
(nt_id nt) (escape nt)
|
||||
(if is_start then "doublecircle" else "ellipse")
|
||||
(if hl then ", color=red, penwidth=2.5, fontcolor=red" else "")
|
||||
(if is_start then ", style=bold" else "")))
|
||||
(Grammar.nonterminals g);
|
||||
List.iter
|
||||
(fun t ->
|
||||
Buffer.add_string buf
|
||||
(Printf.sprintf
|
||||
" tm_%s [label=\"%s\", shape=plaintext, fontcolor=\"#666666\"];\n"
|
||||
(sanitize t) (escape t)))
|
||||
(Grammar.terminals g);
|
||||
List.iteri
|
||||
(fun i p ->
|
||||
let pr = prob_of probs p.Grammar.lhs p.Grammar.rhs in
|
||||
let hl = List.mem (prod_key p) hl_prods in
|
||||
let rhs_text =
|
||||
String.concat " " (List.map Grammar.symbol_to_string p.Grammar.rhs)
|
||||
in
|
||||
Buffer.add_string buf
|
||||
(Printf.sprintf
|
||||
" pr_%d [label=\"%s\\np=%.3f\", shape=box%s];\n"
|
||||
i (escape rhs_text) pr
|
||||
(if hl then ", color=red, penwidth=2.5, fontcolor=red" else ""));
|
||||
Buffer.add_string buf
|
||||
(Printf.sprintf " %s -> pr_%d;\n" (nt_id p.Grammar.lhs) i);
|
||||
List.iteri
|
||||
(fun k s ->
|
||||
let target =
|
||||
match s with
|
||||
| Grammar.Nonterm x -> nt_id x
|
||||
| Grammar.Term t -> "tm_" ^ sanitize t
|
||||
in
|
||||
Buffer.add_string buf
|
||||
(Printf.sprintf " pr_%d -> %s [label=\"%d\"];\n" i target (k + 1)))
|
||||
p.Grammar.rhs)
|
||||
g.Grammar.productions;
|
||||
Buffer.add_string buf "}\n";
|
||||
Buffer.contents buf
|
||||
|
||||
let dot_tree ?(title = "parse") tree =
|
||||
let buf = Buffer.create 1024 in
|
||||
Buffer.add_string buf "digraph parse {\n";
|
||||
Buffer.add_string buf " rankdir=TB;\n";
|
||||
Buffer.add_string buf (Printf.sprintf " label=\"%s\";\n" (escape title));
|
||||
Buffer.add_string buf
|
||||
" node [fontname=\"Helvetica\", fontsize=10, shape=ellipse];\n";
|
||||
let counter = ref 0 in
|
||||
let rec go tree =
|
||||
let id = !counter in
|
||||
incr counter;
|
||||
match tree with
|
||||
| Parse.Leaf s ->
|
||||
Buffer.add_string buf
|
||||
(Printf.sprintf " n%d [label=\"%s\", shape=plaintext, fontcolor=\"#666666\"];\n"
|
||||
id (escape s));
|
||||
id
|
||||
| Parse.Node (nt, children) ->
|
||||
Buffer.add_string buf
|
||||
(Printf.sprintf " n%d [label=\"%s\"];\n" id (escape nt));
|
||||
List.iteri
|
||||
(fun k child ->
|
||||
let cid = go child in
|
||||
Buffer.add_string buf
|
||||
(Printf.sprintf " n%d -> n%d [label=\"%d\"];\n" id cid (k + 1)))
|
||||
children;
|
||||
id
|
||||
in
|
||||
ignore (go tree);
|
||||
Buffer.add_string buf "}\n";
|
||||
Buffer.contents buf
|
||||
|
||||
let write_file path contents =
|
||||
let oc = open_out path in
|
||||
output_string oc contents;
|
||||
close_out oc
|
||||
|
||||
let render ?out_svg ~out_dot dot_string =
|
||||
write_file out_dot dot_string;
|
||||
match out_svg with
|
||||
| None -> None
|
||||
| Some svg ->
|
||||
let cmd =
|
||||
Printf.sprintf "dot -Tsvg %s -o %s 2>/dev/null"
|
||||
(Filename.quote out_dot) (Filename.quote svg)
|
||||
in
|
||||
if Sys.command cmd = 0 then Some svg else None
|
||||
@@ -0,0 +1,4 @@
|
||||
(library
|
||||
(name scfg)
|
||||
(flags (:standard -warn-error -a))
|
||||
(modules grammar corpus parse scoring transform search dot experiment))
|
||||
@@ -0,0 +1,282 @@
|
||||
type target = {
|
||||
name : string;
|
||||
group : string;
|
||||
desc : string;
|
||||
grammar : Grammar.t;
|
||||
}
|
||||
|
||||
let tm x = Grammar.Term x
|
||||
let nt x = Grammar.Nonterm x
|
||||
|
||||
let tg group name desc start prods =
|
||||
let productions =
|
||||
List.map
|
||||
(fun (lhs, rhs, count) -> { Grammar.lhs; rhs; count })
|
||||
prods
|
||||
in
|
||||
{ group; name; desc; grammar = Grammar.make ~start productions }
|
||||
|
||||
let targets =
|
||||
[
|
||||
tg "paper" "parens" "balanced parentheses S -> () | (S) | SS" "S"
|
||||
[ ("S", [ tm "("; tm ")" ], 1.0); ("S", [ tm "("; nt "S"; tm ")" ], 1.0);
|
||||
("S", [ nt "S"; nt "S" ], 1.0) ];
|
||||
tg "paper" "a2n" "even-length strings of a S -> aa | SS" "S"
|
||||
[ ("S", [ tm "a"; tm "a" ], 1.0); ("S", [ nt "S"; nt "S" ], 1.0) ];
|
||||
tg "paper" "abn" "(ab)^n S -> ab | SS" "S"
|
||||
[ ("S", [ tm "a"; tm "b" ], 1.0); ("S", [ nt "S"; nt "S" ], 1.0) ];
|
||||
tg "paper" "anbn" "a^n b^n S -> ab | aSb" "S"
|
||||
[ ("S", [ tm "a"; tm "b" ], 1.0); ("S", [ tm "a"; nt "S"; tm "b" ], 1.0) ];
|
||||
tg "paper" "palindrome" "w c w^R S -> c | aSa | bSb" "S"
|
||||
[ ("S", [ tm "c" ], 1.0); ("S", [ tm "a"; nt "S"; tm "a" ], 1.0);
|
||||
("S", [ tm "b"; nt "S"; tm "b" ], 1.0) ];
|
||||
tg "paper" "addition" "addition strings S -> a | b | (S) | S+S" "S"
|
||||
[ ("S", [ tm "a" ], 1.0); ("S", [ tm "b" ], 1.0);
|
||||
("S", [ tm "("; nt "S"; tm ")" ], 1.0);
|
||||
("S", [ nt "S"; tm "+"; nt "S" ], 1.0) ];
|
||||
tg "paper" "shape" "shape grammar S -> dY | bYS ; Y -> a | cY" "S"
|
||||
[ ("S", [ tm "d"; nt "Y" ], 1.0);
|
||||
("S", [ tm "b"; nt "Y"; nt "S" ], 1.0); ("Y", [ tm "a" ], 1.0);
|
||||
("Y", [ tm "c"; nt "Y" ], 1.0) ];
|
||||
tg "paper" "basic_english"
|
||||
"basic English S -> I am A | he T | ..." "S"
|
||||
[ ("S", [ tm "I"; tm "am"; nt "A" ], 1.0);
|
||||
("S", [ tm "he"; nt "T" ], 1.0);
|
||||
("S", [ tm "she"; nt "T" ], 1.0);
|
||||
("S", [ tm "it"; nt "T" ], 1.0);
|
||||
("S", [ tm "they"; nt "V" ], 1.0);
|
||||
("S", [ tm "you"; nt "V" ], 1.0);
|
||||
("S", [ tm "we"; nt "V" ], 1.0);
|
||||
("S", [ tm "this"; nt "C" ], 1.0);
|
||||
("S", [ tm "that"; nt "C" ], 1.0);
|
||||
("T", [ tm "is"; nt "A" ], 1.0);
|
||||
("V", [ tm "are"; nt "A" ], 1.0);
|
||||
("A", [ tm "there" ], 1.0); ("A", [ tm "here" ], 1.0);
|
||||
("C", [ tm "is"; tm "a"; nt "Z" ], 1.0);
|
||||
("C", [ nt "Z"; nt "T" ], 1.0);
|
||||
("Z", [ tm "man" ], 1.0); ("Z", [ tm "woman" ], 1.0) ];
|
||||
tg "synthetic" "nested_parens" "nested + concatenation S -> a | (S) | SS" "S"
|
||||
[ ("S", [ tm "a" ], 1.0); ("S", [ tm "("; nt "S"; tm ")" ], 1.0);
|
||||
("S", [ nt "S"; nt "S" ], 1.0) ];
|
||||
tg "synthetic" "nested_anbn" "nested a^n b^n S -> aSb | c" "S"
|
||||
[ ("S", [ tm "a"; nt "S"; tm "b" ], 1.0); ("S", [ tm "c" ], 1.0) ];
|
||||
tg "synthetic" "expr" "arithmetic S -> S+T | T ; T -> T*F | F ; F -> (S) | a | b" "S"
|
||||
[ ("S", [ nt "S"; tm "+"; nt "T" ], 1.0); ("S", [ nt "T" ], 1.0);
|
||||
("T", [ nt "T"; tm "*"; nt "F" ], 1.0); ("T", [ nt "F" ], 1.0);
|
||||
("F", [ tm "("; nt "S"; tm ")" ], 1.0); ("F", [ tm "a" ], 1.0);
|
||||
("F", [ tm "b" ], 1.0) ];
|
||||
]
|
||||
|
||||
let sample_one probs start rng max_pending =
|
||||
let rec derive pending =
|
||||
if List.length pending > max_pending then None
|
||||
else
|
||||
match pending with
|
||||
| [] -> Some []
|
||||
| Grammar.Term a :: rest -> (
|
||||
match derive rest with Some l -> Some (a :: l) | None -> None)
|
||||
| Grammar.Nonterm x :: rest -> (
|
||||
match Hashtbl.find_opt probs x with
|
||||
| None | Some [] -> None
|
||||
| Some ps ->
|
||||
let tot = List.fold_left (fun s (_, p) -> s +. p) 0.0 ps in
|
||||
let r = Random.State.float rng tot in
|
||||
let rec pick acc = function
|
||||
| [] -> fst (List.hd ps)
|
||||
| (p, pr) :: tl -> if acc +. pr >= r then p else pick (acc +. pr) tl
|
||||
in
|
||||
let p = pick 0.0 ps in
|
||||
derive (p.Grammar.rhs @ rest))
|
||||
in
|
||||
derive [ Grammar.Nonterm start ]
|
||||
|
||||
let sample_counts target draws seed max_len =
|
||||
let probs = Grammar.probabilities target.grammar in
|
||||
let rng = Random.State.make [| seed |] in
|
||||
let tbl = Hashtbl.create 256 in
|
||||
let order = ref [] in
|
||||
let rec go i tries =
|
||||
if i >= draws || tries > draws * 100 then ()
|
||||
else
|
||||
match sample_one probs target.grammar.Grammar.start rng (2 * max_len) with
|
||||
| Some s when List.length s >= 1 && List.length s <= max_len ->
|
||||
(match Hashtbl.find_opt tbl s with
|
||||
| Some c -> Hashtbl.replace tbl s (c + 1)
|
||||
| None ->
|
||||
Hashtbl.replace tbl s 1;
|
||||
order := s :: !order);
|
||||
go (i + 1) (tries + 1)
|
||||
| _ -> go i (tries + 1)
|
||||
in
|
||||
go 0 0;
|
||||
List.rev !order
|
||||
|> List.map (fun s ->
|
||||
{ Corpus.tokens = s; count = float_of_int (Hashtbl.find tbl s) })
|
||||
|
||||
let initial_of_corpus corpus =
|
||||
Grammar.initial_grammar
|
||||
(List.map (fun s -> (s.Corpus.tokens, s.Corpus.count)) corpus)
|
||||
|
||||
type result = {
|
||||
target : target;
|
||||
train : Corpus.t;
|
||||
test : Corpus.t;
|
||||
initial : Grammar.t;
|
||||
final_grammar : Grammar.t;
|
||||
initial_score : float;
|
||||
final_score : float;
|
||||
nts : int;
|
||||
prods : int;
|
||||
heldout_avg : float;
|
||||
unparseable_test : int;
|
||||
covers_target : bool;
|
||||
precision : float;
|
||||
exact_language : bool;
|
||||
recursive : bool;
|
||||
steps : int;
|
||||
iterations : int;
|
||||
}
|
||||
|
||||
let language_sets target final_grammar max_len =
|
||||
let tlang = Grammar.language_up_to target.grammar max_len in
|
||||
let flang = Grammar.language_up_to final_grammar max_len in
|
||||
let covers = List.for_all (fun s -> List.mem s flang) tlang in
|
||||
let precision =
|
||||
if flang = [] then 0.0
|
||||
else
|
||||
float_of_int
|
||||
(List.length (List.filter (fun s -> List.mem s tlang) flang))
|
||||
/. float_of_int (List.length flang)
|
||||
in
|
||||
let exact =
|
||||
List.length tlang = List.length flang
|
||||
&& List.for_all (fun s -> List.mem s flang) tlang
|
||||
in
|
||||
(covers, precision, exact)
|
||||
|
||||
let run_one ?(export_dir = None) ~config ~beam_width ~max_steps ~patience ~seed
|
||||
~max_len target =
|
||||
let train = sample_counts target 50 seed max_len in
|
||||
let test = sample_counts target 200 (seed + 1000) max_len in
|
||||
let initial = initial_of_corpus train in
|
||||
let search =
|
||||
Search.run ~config ~beam_width ~max_steps ~patience initial train
|
||||
in
|
||||
(match export_dir with
|
||||
| None -> ()
|
||||
| Some dir ->
|
||||
List.iteri
|
||||
(fun i (s : Search.step) ->
|
||||
let ch =
|
||||
Transform.change_of s.Search.parent s.Search.transform s.Search.result
|
||||
in
|
||||
let base =
|
||||
Filename.concat dir
|
||||
(Printf.sprintf "%s-step%03d" target.name (i + 1))
|
||||
in
|
||||
ignore
|
||||
(Dot.render ~out_svg:(base ^ "-before.svg")
|
||||
~out_dot:(base ^ "-before.dot")
|
||||
(Dot.dot_grammar ~highlight_nts:ch.Transform.before_nts
|
||||
~highlight_prods:ch.Transform.before_prods
|
||||
~title:
|
||||
(Printf.sprintf "%s step %d before: %s" target.name (i + 1)
|
||||
(Transform.describe s.Search.transform))
|
||||
s.Search.parent));
|
||||
ignore
|
||||
(Dot.render ~out_svg:(base ^ "-after.svg")
|
||||
~out_dot:(base ^ "-after.dot")
|
||||
(Dot.dot_grammar ~highlight_nts:ch.Transform.after_nts
|
||||
~highlight_prods:ch.Transform.after_prods
|
||||
~title:
|
||||
(Printf.sprintf "%s step %d after: %s" target.name (i + 1)
|
||||
(Transform.describe s.Search.transform))
|
||||
s.Search.result)))
|
||||
search.Search.steps);
|
||||
|
||||
let final_grammar = search.Search.best in
|
||||
let heldout_avg, _, _, unparseable =
|
||||
Scoring.heldout ~config final_grammar ~train test
|
||||
in
|
||||
let covers, precision, exact = language_sets target final_grammar max_len in
|
||||
{
|
||||
target;
|
||||
train;
|
||||
test;
|
||||
initial;
|
||||
final_grammar;
|
||||
initial_score = search.Search.initial_score;
|
||||
final_score = search.Search.best_score;
|
||||
nts = List.length (Grammar.nonterminals final_grammar);
|
||||
prods = List.length final_grammar.Grammar.productions;
|
||||
heldout_avg;
|
||||
unparseable_test = unparseable;
|
||||
covers_target = covers;
|
||||
precision;
|
||||
exact_language = exact;
|
||||
recursive = Grammar.is_recursive final_grammar;
|
||||
steps = List.length search.Search.steps;
|
||||
iterations = search.Search.iterations;
|
||||
}
|
||||
|
||||
let header () =
|
||||
"group\tname\tnts\tprods\tinitial_score\tfinal_score\theldout_avg\tunparseable\t\
|
||||
covers\tprecision\texact\trecursive\tsteps\titerations"
|
||||
|
||||
let row r =
|
||||
Printf.sprintf
|
||||
"%s\t%s\t%d\t%d\t%.6g\t%.6g\t%.6g\t%d\t%b\t%.4f\t%b\t%b\t%d\t%d"
|
||||
r.target.group r.target.name r.nts r.prods r.initial_score r.final_score
|
||||
r.heldout_avg r.unparseable_test r.covers_target r.precision
|
||||
r.exact_language r.recursive r.steps r.iterations
|
||||
|
||||
let to_tsv results = String.concat "\n" (header () :: List.map row results)
|
||||
|
||||
let report_markdown results =
|
||||
let b = Buffer.create 4096 in
|
||||
Buffer.add_string b "# SCFG induction experiments\n\n";
|
||||
Buffer.add_string b
|
||||
"Scores are natural-log posterior values. `heldout_avg` is the average \
|
||||
log-likelihood per token on a held-out sample drawn from the same target \
|
||||
grammar (higher is better). `precision` is the fraction of strings the \
|
||||
induced grammar generates up to the comparison length that belong to the \
|
||||
target language.\n\n";
|
||||
Buffer.add_string b
|
||||
"| group | target | nonterms | prods | initial | final | heldout/token | \
|
||||
covers | precision | exact | recursive | steps |\n";
|
||||
Buffer.add_string b
|
||||
"|---|---|---|---|---|---|---|---|---|---|---|---|\n";
|
||||
List.iter
|
||||
(fun r ->
|
||||
Buffer.add_string b
|
||||
(Printf.sprintf
|
||||
"| %s | %s | %d | %d | %.2f | %.2f | %.3f | %b | %.3f | %b | %b | %d |\n"
|
||||
r.target.group r.target.name r.nts r.prods r.initial_score
|
||||
r.final_score r.heldout_avg r.covers_target r.precision
|
||||
r.exact_language r.recursive r.steps))
|
||||
results;
|
||||
Buffer.add_string b "\n## Final grammars\n\n";
|
||||
List.iter
|
||||
(fun r ->
|
||||
Buffer.add_string b
|
||||
(Printf.sprintf "### %s (%s)\n\n%s\n\n" r.target.name r.target.group
|
||||
r.target.desc);
|
||||
Buffer.add_string b "```\n";
|
||||
Buffer.add_string b (Grammar.to_string r.final_grammar);
|
||||
Buffer.add_string b "\n```\n\n")
|
||||
results;
|
||||
Buffer.contents b
|
||||
|
||||
let run_all ?(export_dir = None) ?(config = Scoring.default_config)
|
||||
?(beam_width = 3) ?(max_steps = 25) ?(patience = 5) ?(seed = 1)
|
||||
?(max_len = 8) ?(only = None) () =
|
||||
let ts =
|
||||
match only with
|
||||
| None -> targets
|
||||
| Some name -> List.filter (fun t -> String.equal t.name name) targets
|
||||
in
|
||||
List.map
|
||||
(fun target ->
|
||||
run_one ~export_dir ~config ~beam_width ~max_steps ~patience ~seed ~max_len
|
||||
target)
|
||||
ts
|
||||
+522
@@ -0,0 +1,522 @@
|
||||
type symbol = Term of string | Nonterm of string
|
||||
|
||||
type production = {
|
||||
lhs : string;
|
||||
rhs : symbol list;
|
||||
count : float;
|
||||
}
|
||||
|
||||
type t = {
|
||||
start : string;
|
||||
productions : production list;
|
||||
}
|
||||
|
||||
module SSet = Set.Make (String)
|
||||
|
||||
let symbol_to_string = function Term s -> s | Nonterm s -> s
|
||||
|
||||
let symbol_key = function Term s -> "t:" ^ s | Nonterm s -> "n:" ^ s
|
||||
|
||||
let symbol_is_nonterm = function Nonterm _ -> true | Term _ -> false
|
||||
|
||||
let equal_symbol a b =
|
||||
match (a, b) with
|
||||
| Term x, Term y | Nonterm x, Nonterm y -> String.equal x y
|
||||
| _ -> false
|
||||
|
||||
let equal_rhs a b =
|
||||
List.length a = List.length b && List.for_all2 equal_symbol a b
|
||||
|
||||
let rhs_to_string rhs = String.concat " " (List.map symbol_to_string rhs)
|
||||
|
||||
let production_to_string p =
|
||||
Printf.sprintf "%s -> %s" p.lhs (rhs_to_string p.rhs)
|
||||
|
||||
let make ~start productions = { start; productions }
|
||||
|
||||
let nonterminals g =
|
||||
let acc = ref (SSet.singleton g.start) in
|
||||
List.iter
|
||||
(fun p ->
|
||||
acc := SSet.add p.lhs !acc;
|
||||
List.iter
|
||||
(function Nonterm x -> acc := SSet.add x !acc | Term _ -> ())
|
||||
p.rhs)
|
||||
g.productions;
|
||||
SSet.elements !acc
|
||||
|
||||
let terminals g =
|
||||
let acc = ref SSet.empty in
|
||||
List.iter
|
||||
(fun p ->
|
||||
List.iter
|
||||
(function Term x -> acc := SSet.add x !acc | Nonterm _ -> ())
|
||||
p.rhs)
|
||||
g.productions;
|
||||
SSet.elements !acc
|
||||
|
||||
let productions_of g lhs =
|
||||
List.filter (fun p -> String.equal p.lhs lhs) g.productions
|
||||
|
||||
let total_count prods = List.fold_left (fun s p -> s +. p.count) 0.0 prods
|
||||
|
||||
let probabilities g =
|
||||
let by_lhs = Hashtbl.create 64 in
|
||||
List.iter
|
||||
(fun p ->
|
||||
let l =
|
||||
match Hashtbl.find_opt by_lhs p.lhs with Some l -> l | None -> []
|
||||
in
|
||||
Hashtbl.replace by_lhs p.lhs (p :: l))
|
||||
g.productions;
|
||||
let tbl = Hashtbl.create 64 in
|
||||
Hashtbl.iter
|
||||
(fun lhs ps ->
|
||||
let ps = List.rev ps in
|
||||
let tot = total_count ps in
|
||||
let k = List.length ps in
|
||||
let probs =
|
||||
if tot > 0.0 then List.map (fun p -> (p, p.count /. tot)) ps
|
||||
else List.map (fun p -> (p, 1.0 /. float_of_int k)) ps
|
||||
in
|
||||
Hashtbl.replace tbl lhs probs)
|
||||
by_lhs;
|
||||
tbl
|
||||
|
||||
let canonical_string g =
|
||||
let seen = Hashtbl.create 64 in
|
||||
let order = ref [] in
|
||||
let q = Queue.create () in
|
||||
Queue.add g.start q;
|
||||
Hashtbl.replace seen g.start ();
|
||||
while not (Queue.is_empty q) do
|
||||
let a = Queue.pop q in
|
||||
order := a :: !order;
|
||||
List.iter
|
||||
(fun p ->
|
||||
if String.equal p.lhs a then
|
||||
List.iter
|
||||
(function
|
||||
| Nonterm x ->
|
||||
if not (Hashtbl.mem seen x) then begin
|
||||
Hashtbl.replace seen x ();
|
||||
Queue.add x q
|
||||
end
|
||||
| Term _ -> ())
|
||||
p.rhs)
|
||||
g.productions
|
||||
done;
|
||||
let order = List.rev !order in
|
||||
let idx = Hashtbl.create 64 in
|
||||
List.iteri (fun i a -> Hashtbl.replace idx a i) order;
|
||||
let name a =
|
||||
match Hashtbl.find_opt idx a with
|
||||
| Some i -> Printf.sprintf "N%d" i
|
||||
| None -> a
|
||||
in
|
||||
let sym = function Term s -> "t:" ^ s | Nonterm s -> name s in
|
||||
let pstr p =
|
||||
Printf.sprintf "%s -> %s" (name p.lhs)
|
||||
(String.concat " " (List.map sym p.rhs))
|
||||
in
|
||||
g.productions |> List.map pstr |> List.sort String.compare
|
||||
|> String.concat "\n"
|
||||
|
||||
let equal_structure a b = String.equal (canonical_string a) (canonical_string b)
|
||||
|
||||
let copy_with g productions = { g with productions }
|
||||
|
||||
let prods_of_list prods lhs =
|
||||
List.filter (fun p -> String.equal p.lhs lhs) prods
|
||||
|
||||
let dedupe prods =
|
||||
let tbl = Hashtbl.create 64 in
|
||||
List.iter
|
||||
(fun p ->
|
||||
match Hashtbl.find_opt tbl (p.lhs, p.rhs) with
|
||||
| Some c -> Hashtbl.replace tbl (p.lhs, p.rhs) (c +. p.count)
|
||||
| None -> Hashtbl.replace tbl (p.lhs, p.rhs) p.count)
|
||||
prods;
|
||||
Hashtbl.fold (fun (lhs, rhs) count acc -> { lhs; rhs; count } :: acc) tbl []
|
||||
|
||||
let remove_unit_cycles prods =
|
||||
let unit_edges = Hashtbl.create 64 in
|
||||
List.iter
|
||||
(fun (p : production) ->
|
||||
match p.rhs with
|
||||
| [ Nonterm b ] ->
|
||||
let l =
|
||||
match Hashtbl.find_opt unit_edges p.lhs with
|
||||
| Some l -> l
|
||||
| None -> []
|
||||
in
|
||||
Hashtbl.replace unit_edges p.lhs (b :: l)
|
||||
| _ -> ())
|
||||
prods;
|
||||
let reaches a target =
|
||||
let seen = Hashtbl.create 16 in
|
||||
let rec go x =
|
||||
if String.equal x target then true
|
||||
else if Hashtbl.mem seen x then false
|
||||
else begin
|
||||
Hashtbl.replace seen x ();
|
||||
List.exists go
|
||||
(Option.value ~default:[] (Hashtbl.find_opt unit_edges x))
|
||||
end
|
||||
in
|
||||
go a
|
||||
in
|
||||
List.filter
|
||||
(fun (p : production) ->
|
||||
match p.rhs with
|
||||
| [ Nonterm b ] ->
|
||||
not (String.equal p.lhs b) && not (reaches b p.lhs)
|
||||
| _ -> true)
|
||||
prods
|
||||
|
||||
let productive_set prods =
|
||||
let tbl = Hashtbl.create 64 in
|
||||
let changed = ref true in
|
||||
while !changed do
|
||||
changed := false;
|
||||
List.iter
|
||||
(fun p ->
|
||||
if not (Hashtbl.mem tbl p.lhs) then begin
|
||||
let ok =
|
||||
List.for_all
|
||||
(function Term _ -> true | Nonterm x -> Hashtbl.mem tbl x)
|
||||
p.rhs
|
||||
in
|
||||
if ok then begin
|
||||
Hashtbl.replace tbl p.lhs ();
|
||||
changed := true
|
||||
end
|
||||
end)
|
||||
prods
|
||||
done;
|
||||
tbl
|
||||
|
||||
let remove_nonproductive prods =
|
||||
let prod = productive_set prods in
|
||||
List.filter
|
||||
(fun p ->
|
||||
Hashtbl.mem prod p.lhs
|
||||
&& List.for_all
|
||||
(function Term _ -> true | Nonterm x -> Hashtbl.mem prod x)
|
||||
p.rhs)
|
||||
prods
|
||||
|
||||
let remove_unreachable start prods =
|
||||
let tbl = Hashtbl.create 64 in
|
||||
Hashtbl.replace tbl start ();
|
||||
let changed = ref true in
|
||||
while !changed do
|
||||
changed := false;
|
||||
List.iter
|
||||
(fun p ->
|
||||
if Hashtbl.mem tbl p.lhs then
|
||||
List.iter
|
||||
(function
|
||||
| Nonterm x ->
|
||||
if not (Hashtbl.mem tbl x) then begin
|
||||
Hashtbl.replace tbl x ();
|
||||
changed := true
|
||||
end
|
||||
| Term _ -> ())
|
||||
p.rhs)
|
||||
prods
|
||||
done;
|
||||
List.filter (fun p -> Hashtbl.mem tbl p.lhs) prods
|
||||
|
||||
let derives_form g start target =
|
||||
let n = List.length target in
|
||||
let arr = Array.of_list target in
|
||||
let key = symbol_key in
|
||||
let d = Array.make_matrix (n + 1) (n + 1) SSet.empty in
|
||||
for i = 0 to n - 1 do
|
||||
d.(i).(i + 1) <- SSet.singleton (key arr.(i))
|
||||
done;
|
||||
let rhs_matches rhs i j =
|
||||
let rec go rhs p =
|
||||
match rhs with
|
||||
| [] -> p = j
|
||||
| [ last ] -> p < j && SSet.mem (key last) d.(p).(j)
|
||||
| s :: rest ->
|
||||
let rem = List.length rest in
|
||||
let rec try_q q =
|
||||
if q > j - rem then false
|
||||
else if SSet.mem (key s) d.(p).(q) && go rest q then true
|
||||
else try_q (q + 1)
|
||||
in
|
||||
try_q (p + 1)
|
||||
in
|
||||
List.length rhs > 0 && go rhs i
|
||||
in
|
||||
for len = 1 to n do
|
||||
for i = 0 to n - len do
|
||||
let j = i + len in
|
||||
let changed = ref true in
|
||||
while !changed do
|
||||
changed := false;
|
||||
List.iter
|
||||
(fun (p : production) ->
|
||||
let lhs_key = key (Nonterm p.lhs) in
|
||||
if not (SSet.mem lhs_key d.(i).(j)) then begin
|
||||
let ok =
|
||||
match p.rhs with
|
||||
| [ y ] -> SSet.mem (key y) d.(i).(j)
|
||||
| _ -> rhs_matches p.rhs i j
|
||||
in
|
||||
if ok then begin
|
||||
d.(i).(j) <- SSet.add lhs_key d.(i).(j);
|
||||
changed := true
|
||||
end
|
||||
end)
|
||||
g.productions
|
||||
done
|
||||
done
|
||||
done;
|
||||
SSet.mem (key (Nonterm start)) d.(0).(n)
|
||||
|
||||
let prune_redundant g =
|
||||
let prods = ref (dedupe g.productions) in
|
||||
let changed = ref true in
|
||||
while !changed do
|
||||
changed := false;
|
||||
let victim = ref None in
|
||||
(try
|
||||
List.iter
|
||||
(fun (p : production) ->
|
||||
let g' =
|
||||
{ g with productions = List.filter (fun q -> not (q == p)) !prods }
|
||||
in
|
||||
if derives_form g' p.lhs p.rhs then begin
|
||||
victim := Some p;
|
||||
raise Exit
|
||||
end)
|
||||
!prods
|
||||
with Exit -> ());
|
||||
match !victim with
|
||||
| Some p ->
|
||||
prods := List.filter (fun q -> not (q == p)) !prods;
|
||||
changed := true
|
||||
| None -> ()
|
||||
done;
|
||||
{ g with productions = !prods }
|
||||
|
||||
let normalize g =
|
||||
let step prods =
|
||||
prods |> dedupe |> remove_unit_cycles |> remove_nonproductive
|
||||
|> remove_unreachable g.start
|
||||
in
|
||||
let p1 = step g.productions in
|
||||
let p2 = step p1 in
|
||||
let g1 = { g with productions = p2 } in
|
||||
let g2 = prune_redundant g1 in
|
||||
let g3 = step g2.productions in
|
||||
{ g with productions = g3 }
|
||||
|
||||
let language_up_to g max_len =
|
||||
let tbl = Hashtbl.create 256 in
|
||||
let get x len =
|
||||
Option.value ~default:[] (Hashtbl.find_opt tbl (x, len))
|
||||
in
|
||||
for len = 1 to max_len do
|
||||
|
||||
let changed = ref true in
|
||||
while !changed do
|
||||
changed := false;
|
||||
List.iter
|
||||
(fun x ->
|
||||
let acc = ref (get x len) in
|
||||
List.iter
|
||||
(fun (p : production) ->
|
||||
let rhs = p.rhs in
|
||||
let m = List.length rhs in
|
||||
let rec gen rhs l =
|
||||
match rhs with
|
||||
| [] -> if l = 0 then [ [] ] else []
|
||||
| s :: rest ->
|
||||
let out = ref [] in
|
||||
for k = 1 to l - (List.length rest) do
|
||||
let ss =
|
||||
match s with
|
||||
| Term a -> if k = 1 then [ [ a ] ] else []
|
||||
| Nonterm y -> get y k
|
||||
in
|
||||
let rs = gen rest (l - k) in
|
||||
List.iter
|
||||
(fun a ->
|
||||
List.iter (fun b -> out := (a @ b) :: !out) rs)
|
||||
ss
|
||||
done;
|
||||
!out
|
||||
in
|
||||
if len >= m then acc := gen rhs len @ !acc)
|
||||
(productions_of g x);
|
||||
let acc = List.sort_uniq compare !acc in
|
||||
if List.length acc > List.length (get x len) then begin
|
||||
Hashtbl.replace tbl (x, len) acc;
|
||||
changed := true
|
||||
end)
|
||||
(nonterminals g)
|
||||
done
|
||||
done;
|
||||
let all = List.concat (List.init max_len (fun i -> get g.start (i + 1))) in
|
||||
List.sort_uniq compare all
|
||||
|
||||
let initial_grammar ?(start = "S") samples =
|
||||
let term_nts = Hashtbl.create 64 in
|
||||
let prods = ref [] in
|
||||
List.iter
|
||||
(fun (tokens, count) ->
|
||||
let rhs =
|
||||
List.map
|
||||
(fun tok ->
|
||||
match Hashtbl.find_opt term_nts tok with
|
||||
| Some nt -> Nonterm nt
|
||||
| None ->
|
||||
let nt = "T_" ^ tok in
|
||||
Hashtbl.replace term_nts tok nt;
|
||||
prods := { lhs = nt; rhs = [ Term tok ]; count = 1.0 } :: !prods;
|
||||
Nonterm nt)
|
||||
tokens
|
||||
in
|
||||
prods := { lhs = start; rhs; count } :: !prods)
|
||||
samples;
|
||||
make ~start (List.rev !prods)
|
||||
|
||||
let is_recursive g =
|
||||
let deps = Hashtbl.create 64 in
|
||||
List.iter
|
||||
(fun x ->
|
||||
let l =
|
||||
List.concat_map
|
||||
(fun p ->
|
||||
List.filter_map
|
||||
(function Nonterm y -> Some y | Term _ -> None)
|
||||
p.rhs)
|
||||
(productions_of g x)
|
||||
in
|
||||
Hashtbl.replace deps x l)
|
||||
(nonterminals g);
|
||||
List.exists
|
||||
(fun a ->
|
||||
let seen = Hashtbl.create 64 in
|
||||
let rec go x =
|
||||
List.exists
|
||||
(fun y ->
|
||||
if String.equal y a then true
|
||||
else if Hashtbl.mem seen y then false
|
||||
else begin
|
||||
Hashtbl.replace seen y ();
|
||||
go y
|
||||
end)
|
||||
(Option.value ~default:[] (Hashtbl.find_opt deps x))
|
||||
in
|
||||
go a)
|
||||
(nonterminals g)
|
||||
|
||||
let to_string ?(decimals = 3) g =
|
||||
let probs = probabilities g in
|
||||
let fmt p =
|
||||
let pr =
|
||||
match Hashtbl.find_opt probs p.lhs with
|
||||
| None -> 0.0
|
||||
| Some l -> (
|
||||
match List.find_opt (fun (q, _) -> q == p) l with
|
||||
| Some (_, x) -> x
|
||||
| None -> 0.0)
|
||||
in
|
||||
Printf.sprintf "%-8s -> %-24s [%.*f]" p.lhs (rhs_to_string p.rhs) decimals
|
||||
pr
|
||||
in
|
||||
let header =
|
||||
Printf.sprintf "# start = %s, %d nonterminals, %d terminals, %d productions"
|
||||
g.start
|
||||
(List.length (nonterminals g))
|
||||
(List.length (terminals g))
|
||||
(List.length g.productions)
|
||||
in
|
||||
String.concat "\n" (header :: List.map fmt g.productions)
|
||||
|
||||
let is_nonterminal_name s =
|
||||
String.length s > 0
|
||||
&&
|
||||
let c = s.[0] in
|
||||
(c >= 'A' && c <= 'Z') || c = '_' || c = '<'
|
||||
|
||||
let find_sub s sub =
|
||||
let n = String.length s and m = String.length sub in
|
||||
let rec go i =
|
||||
if i + m > n then None
|
||||
else if String.equal (String.sub s i m) sub then Some i
|
||||
else go (i + 1)
|
||||
in
|
||||
go 0
|
||||
|
||||
let parse_start line =
|
||||
match find_sub line "start =" with
|
||||
| None -> None
|
||||
| Some i ->
|
||||
let rest =
|
||||
String.sub line (i + 7) (String.length line - i - 7) |> String.trim
|
||||
in
|
||||
let stop =
|
||||
match (String.index_opt rest ' ', String.index_opt rest ',') with
|
||||
| Some a, Some b -> min a b
|
||||
| Some a, None | None, Some a -> a
|
||||
| None, None -> String.length rest
|
||||
in
|
||||
let name = String.sub rest 0 stop in
|
||||
if String.length name = 0 then None else Some name
|
||||
|
||||
let of_string text =
|
||||
let lines = String.split_on_char '\n' text in
|
||||
let prods = ref [] in
|
||||
let start = ref None in
|
||||
List.iter
|
||||
(fun raw ->
|
||||
let trimmed = String.trim raw in
|
||||
if String.length trimmed > 0 && trimmed.[0] = '#' then
|
||||
match parse_start trimmed with
|
||||
| Some s -> start := Some s
|
||||
| None -> ()
|
||||
else begin
|
||||
let line =
|
||||
match String.index_opt raw '#' with
|
||||
| Some i -> String.sub raw 0 i
|
||||
| None -> raw
|
||||
in
|
||||
let toks =
|
||||
String.split_on_char ' ' (String.trim line)
|
||||
|> List.filter (fun s -> String.length s > 0)
|
||||
in
|
||||
match toks with
|
||||
| [] -> ()
|
||||
| lhs :: arrow :: rhs_toks when String.equal arrow "->" ->
|
||||
let rhs_toks, prob =
|
||||
match List.rev rhs_toks with
|
||||
| last :: rest_rev
|
||||
when String.length last > 2 && last.[0] = '[' -> (
|
||||
match
|
||||
float_of_string_opt
|
||||
(String.sub last 1 (String.length last - 2))
|
||||
with
|
||||
| Some p -> (List.rev rest_rev, Some p)
|
||||
| None -> (rhs_toks, None))
|
||||
| _ -> (rhs_toks, None)
|
||||
in
|
||||
let rhs =
|
||||
List.map
|
||||
(fun s -> if is_nonterminal_name s then Nonterm s else Term s)
|
||||
rhs_toks
|
||||
in
|
||||
if !start = None then start := Some lhs;
|
||||
prods :=
|
||||
{ lhs; rhs; count = Option.value ~default:1.0 prob } :: !prods
|
||||
| _ -> ()
|
||||
end)
|
||||
lines;
|
||||
let start = Option.value ~default:"S" !start in
|
||||
make ~start (List.rev !prods)
|
||||
+355
@@ -0,0 +1,355 @@
|
||||
type tree = Node of string * tree list | Leaf of string
|
||||
|
||||
let rec tree_yield = function
|
||||
| Leaf s -> [ s ]
|
||||
| Node (_, children) -> List.concat_map tree_yield children
|
||||
|
||||
type prep = {
|
||||
prods : Grammar.production array;
|
||||
mutable probs : float array;
|
||||
by_lhs : (string, int list) Hashtbl.t;
|
||||
lhs_list : string list;
|
||||
start : string;
|
||||
}
|
||||
|
||||
let prepare (g : Grammar.t) =
|
||||
let prods : Grammar.production array = Array.of_list g.productions in
|
||||
let n = Array.length prods in
|
||||
let probs = Array.make n 0.0 in
|
||||
let by_lhs = Hashtbl.create 64 in
|
||||
Array.iteri
|
||||
(fun i (p : Grammar.production) ->
|
||||
let l =
|
||||
match Hashtbl.find_opt by_lhs p.lhs with Some l -> l | None -> []
|
||||
in
|
||||
Hashtbl.replace by_lhs p.lhs (i :: l))
|
||||
prods;
|
||||
Hashtbl.iter
|
||||
(fun _ idxs ->
|
||||
let tot =
|
||||
List.fold_left (fun s i -> s +. prods.(i).count) 0.0 idxs
|
||||
in
|
||||
let k = List.length idxs in
|
||||
List.iter
|
||||
(fun i ->
|
||||
probs.(i) <-
|
||||
(if tot > 0.0 then prods.(i).count /. tot
|
||||
else 1.0 /. float_of_int k))
|
||||
idxs)
|
||||
by_lhs;
|
||||
{
|
||||
prods;
|
||||
probs;
|
||||
by_lhs;
|
||||
lhs_list = Hashtbl.fold (fun k _ acc -> k :: acc) by_lhs [];
|
||||
start = g.start;
|
||||
}
|
||||
|
||||
let prepare_uniform (g : Grammar.t) =
|
||||
let prep = prepare g in
|
||||
Array.fill prep.probs 0 (Array.length prep.probs) 0.0;
|
||||
Hashtbl.iter
|
||||
(fun _ idxs ->
|
||||
let k = List.length idxs in
|
||||
if k > 0 then
|
||||
List.iter (fun i -> prep.probs.(i) <- 1.0 /. float_of_int k) idxs)
|
||||
prep.by_lhs;
|
||||
prep
|
||||
|
||||
let prob_of_prod prep (p : Grammar.production) =
|
||||
let idxs =
|
||||
Option.value ~default:[] (Hashtbl.find_opt prep.by_lhs p.lhs)
|
||||
in
|
||||
let rec find = function
|
||||
| [] -> 0.0
|
||||
| i :: rest ->
|
||||
if Grammar.equal_rhs prep.prods.(i).rhs p.rhs then prep.probs.(i)
|
||||
else find rest
|
||||
in
|
||||
find idxs
|
||||
|
||||
let inside prep tokens =
|
||||
let n = List.length tokens in
|
||||
let w = Array.of_list tokens in
|
||||
let imemo = Hashtbl.create 1024 in
|
||||
let smemo = Hashtbl.create 1024 in
|
||||
let rec inside_nt nt i j =
|
||||
if j <= i then 0.0
|
||||
else
|
||||
match Hashtbl.find_opt imemo (nt, i, j) with
|
||||
| Some v -> v
|
||||
| None ->
|
||||
let idxs =
|
||||
Option.value ~default:[] (Hashtbl.find_opt prep.by_lhs nt)
|
||||
in
|
||||
let v =
|
||||
List.fold_left
|
||||
(fun acc pi ->
|
||||
acc
|
||||
+. (prep.probs.(pi) *. seq_inside prep.prods.(pi).rhs i j))
|
||||
0.0 idxs
|
||||
in
|
||||
Hashtbl.replace imemo (nt, i, j) v;
|
||||
v
|
||||
and seq_inside rhs i j =
|
||||
match Hashtbl.find_opt smemo (rhs, i, j) with
|
||||
| Some v -> v
|
||||
| None ->
|
||||
let v =
|
||||
match rhs with
|
||||
| [] -> if i = j then 1.0 else 0.0
|
||||
| Grammar.Term a :: rest ->
|
||||
if i < n && String.equal w.(i) a then
|
||||
seq_inside rest (i + 1) j
|
||||
else 0.0
|
||||
| Grammar.Nonterm x :: rest ->
|
||||
|
||||
let acc = ref 0.0 in
|
||||
for k = i + 1 to j - List.length rest do
|
||||
let a = inside_nt x i k in
|
||||
if a > 0.0 then acc := !acc +. (a *. seq_inside rest k j)
|
||||
done;
|
||||
!acc
|
||||
in
|
||||
Hashtbl.replace smemo (rhs, i, j) v;
|
||||
v
|
||||
in
|
||||
inside_nt prep.start 0 n
|
||||
|
||||
let log_inside prep tokens =
|
||||
let p = inside prep tokens in
|
||||
if p > 0.0 then Some (log p) else None
|
||||
|
||||
let viterbi prep tokens =
|
||||
let n = List.length tokens in
|
||||
let w = Array.of_list tokens in
|
||||
let vmemo = Hashtbl.create 1024 in
|
||||
let smemo = Hashtbl.create 1024 in
|
||||
let rec vnt nt i j =
|
||||
if j <= i then (0.0, None)
|
||||
else
|
||||
match Hashtbl.find_opt vmemo (nt, i, j) with
|
||||
| Some v -> v
|
||||
| None ->
|
||||
let idxs =
|
||||
Option.value ~default:[] (Hashtbl.find_opt prep.by_lhs nt)
|
||||
in
|
||||
let bestp = ref 0.0 and bestt = ref None in
|
||||
List.iter
|
||||
(fun pi ->
|
||||
let p = prep.prods.(pi) in
|
||||
let sp, sch = seq_vit p.rhs i j in
|
||||
if sp > 0.0 then begin
|
||||
let v = prep.probs.(pi) *. sp in
|
||||
if v > !bestp then begin
|
||||
bestp := v;
|
||||
bestt :=
|
||||
(match sch with
|
||||
| Some ch -> Some (Node (nt, ch))
|
||||
| None -> None)
|
||||
end
|
||||
end)
|
||||
idxs;
|
||||
let res = (!bestp, !bestt) in
|
||||
Hashtbl.replace vmemo (nt, i, j) res;
|
||||
res
|
||||
and seq_vit rhs i j =
|
||||
match Hashtbl.find_opt smemo (rhs, i, j) with
|
||||
| Some v -> v
|
||||
| None ->
|
||||
let v =
|
||||
match rhs with
|
||||
| [] -> if i = j then (1.0, Some []) else (0.0, None)
|
||||
| Grammar.Term a :: rest ->
|
||||
if i < n && String.equal w.(i) a then (
|
||||
match seq_vit rest (i + 1) j with
|
||||
| p, Some ts -> (p, Some (Leaf a :: ts))
|
||||
| z -> z)
|
||||
else (0.0, None)
|
||||
| Grammar.Nonterm x :: rest ->
|
||||
let bestp = ref 0.0 and bestch = ref None in
|
||||
for k = i + 1 to j - List.length rest do
|
||||
let px, tx = vnt x i k in
|
||||
if px > 0.0 then begin
|
||||
let pr, tr = seq_vit rest k j in
|
||||
if pr > 0.0 then begin
|
||||
let v = px *. pr in
|
||||
if v > !bestp then begin
|
||||
bestp := v;
|
||||
bestch :=
|
||||
(match (tx, tr) with
|
||||
| Some tx, Some tr -> Some (tx :: tr)
|
||||
| _ -> None)
|
||||
end
|
||||
end
|
||||
end
|
||||
done;
|
||||
(!bestp, !bestch)
|
||||
in
|
||||
Hashtbl.replace smemo (rhs, i, j) v;
|
||||
v
|
||||
in
|
||||
vnt prep.start 0 n
|
||||
|
||||
let tree_to_string ?(indent = 0) tree =
|
||||
let rec go indent tree =
|
||||
let pad = String.make (2 * indent) ' ' in
|
||||
match tree with
|
||||
| Leaf s -> pad ^ s
|
||||
| Node (nt, children) ->
|
||||
pad ^ nt ^ "\n"
|
||||
^ String.concat "\n" (List.map (go (indent + 1)) children)
|
||||
in
|
||||
go indent tree
|
||||
|
||||
let expected_counts prep tokens =
|
||||
let n = List.length tokens in
|
||||
let w = Array.of_list tokens in
|
||||
let imemo = Hashtbl.create 1024 in
|
||||
let smemo = Hashtbl.create 1024 in
|
||||
let rec inside_nt nt i j =
|
||||
if j <= i then 0.0
|
||||
else
|
||||
match Hashtbl.find_opt imemo (nt, i, j) with
|
||||
| Some v -> v
|
||||
| None ->
|
||||
let idxs =
|
||||
Option.value ~default:[] (Hashtbl.find_opt prep.by_lhs nt)
|
||||
in
|
||||
let v =
|
||||
List.fold_left
|
||||
(fun acc pi ->
|
||||
acc
|
||||
+. (prep.probs.(pi) *. seq_inside prep.prods.(pi).rhs i j))
|
||||
0.0 idxs
|
||||
in
|
||||
Hashtbl.replace imemo (nt, i, j) v;
|
||||
v
|
||||
and seq_inside rhs i j =
|
||||
match Hashtbl.find_opt smemo (rhs, i, j) with
|
||||
| Some v -> v
|
||||
| None ->
|
||||
let v =
|
||||
match rhs with
|
||||
| [] -> if i = j then 1.0 else 0.0
|
||||
| Grammar.Term a :: rest ->
|
||||
if i < n && String.equal w.(i) a then seq_inside rest (i + 1) j
|
||||
else 0.0
|
||||
| Grammar.Nonterm x :: rest ->
|
||||
|
||||
let acc = ref 0.0 in
|
||||
for k = i + 1 to j - List.length rest do
|
||||
let a = inside_nt x i k in
|
||||
if a > 0.0 then acc := !acc +. (a *. seq_inside rest k j)
|
||||
done;
|
||||
!acc
|
||||
in
|
||||
Hashtbl.replace smemo (rhs, i, j) v;
|
||||
v
|
||||
in
|
||||
let ptotal = inside_nt prep.start 0 n in
|
||||
let np = Array.length prep.prods in
|
||||
if ptotal <= 0.0 then (Array.make np 0.0, 0.0)
|
||||
else begin
|
||||
let omemo = Hashtbl.create 1024 in
|
||||
let get_o nt i j =
|
||||
Option.value ~default:0.0 (Hashtbl.find_opt omemo (nt, i, j))
|
||||
in
|
||||
let add_o nt i j v =
|
||||
Hashtbl.replace omemo (nt, i, j) (get_o nt i j +. v)
|
||||
in
|
||||
add_o prep.start 0 n 1.0;
|
||||
for len = n downto 1 do
|
||||
for p = 0 to n - len do
|
||||
let q = p + len in
|
||||
List.iter
|
||||
(fun b ->
|
||||
let ob = get_o b p q in
|
||||
if ob > 0.0 then
|
||||
List.iter
|
||||
(fun pi ->
|
||||
let prod = prep.prods.(pi) in
|
||||
if String.equal prod.lhs b then begin
|
||||
let prob = prep.probs.(pi) in
|
||||
let arr = Array.of_list prod.rhs in
|
||||
let m = Array.length arr in
|
||||
Array.iteri
|
||||
(fun k s ->
|
||||
match s with
|
||||
| Grammar.Nonterm x ->
|
||||
let left =
|
||||
Array.to_list (Array.sub arr 0 k)
|
||||
in
|
||||
let right =
|
||||
Array.to_list
|
||||
(Array.sub arr (k + 1) (m - k - 1))
|
||||
in
|
||||
for i = p to q do
|
||||
let lw = seq_inside left p i in
|
||||
if lw > 0.0 then
|
||||
for j = i to q do
|
||||
let rw = seq_inside right j q in
|
||||
if rw > 0.0 then
|
||||
add_o x i j
|
||||
(ob *. prob *. lw *. rw)
|
||||
done
|
||||
done
|
||||
| Grammar.Term _ -> ())
|
||||
arr
|
||||
end)
|
||||
(Option.value ~default:[]
|
||||
(Hashtbl.find_opt prep.by_lhs b)))
|
||||
prep.lhs_list
|
||||
done
|
||||
done;
|
||||
let counts = Array.make np 0.0 in
|
||||
Array.iteri
|
||||
(fun pi (prod : Grammar.production) ->
|
||||
let prob = prep.probs.(pi) in
|
||||
let s = ref 0.0 in
|
||||
for i = 0 to n do
|
||||
for j = i to n do
|
||||
let o = get_o prod.lhs i j in
|
||||
if o > 0.0 then
|
||||
s := !s +. (o *. seq_inside prod.rhs i j)
|
||||
done
|
||||
done;
|
||||
counts.(pi) <- prob *. !s /. ptotal)
|
||||
prep.prods;
|
||||
(counts, ptotal)
|
||||
end
|
||||
|
||||
let fit_em prep (corpus : Corpus.t) ~iters ~tol =
|
||||
let np = Array.length prep.prods in
|
||||
let last_ll = ref neg_infinity in
|
||||
let ll = ref 0.0 in
|
||||
let counts = ref (Array.make np 0.0) in
|
||||
(try
|
||||
for _ = 1 to iters do
|
||||
let acc = Array.make np 0.0 in
|
||||
ll := 0.0;
|
||||
List.iter
|
||||
(fun s ->
|
||||
let cnt, p = expected_counts prep s.Corpus.tokens in
|
||||
if p > 0.0 then begin
|
||||
Array.iteri
|
||||
(fun i x -> acc.(i) <- acc.(i) +. (s.Corpus.count *. x))
|
||||
cnt;
|
||||
ll := !ll +. (s.Corpus.count *. log p)
|
||||
end)
|
||||
corpus;
|
||||
Hashtbl.iter
|
||||
(fun _ idxs ->
|
||||
let tot = List.fold_left (fun s i -> s +. acc.(i)) 0.0 idxs in
|
||||
if tot > 0.0 then
|
||||
List.iter (fun i -> prep.probs.(i) <- acc.(i) /. tot) idxs)
|
||||
prep.by_lhs;
|
||||
counts := acc;
|
||||
if
|
||||
!last_ll <> neg_infinity
|
||||
&& abs_float (!ll -. !last_ll) < tol
|
||||
then raise Exit;
|
||||
last_ll := !ll
|
||||
done
|
||||
with Exit -> ());
|
||||
(!counts, !ll)
|
||||
+278
@@ -0,0 +1,278 @@
|
||||
type score_mode = Marginal | Maximum_likelihood | Variational
|
||||
|
||||
type chunk_occurrence = All_occurrences | First_occurrence
|
||||
|
||||
type config = {
|
||||
alpha : float;
|
||||
prior_weight : float;
|
||||
em_iters : int;
|
||||
em_tol : float;
|
||||
max_chunk : int;
|
||||
mode : score_mode;
|
||||
chunk_occurrence : chunk_occurrence;
|
||||
}
|
||||
|
||||
let default_config =
|
||||
{
|
||||
alpha = 0.1;
|
||||
prior_weight = 1.0;
|
||||
em_iters = 8;
|
||||
em_tol = 1e-7;
|
||||
max_chunk = 2;
|
||||
mode = Marginal;
|
||||
chunk_occurrence = All_occurrences;
|
||||
}
|
||||
|
||||
let rec log_gamma x =
|
||||
let g = 7.0 in
|
||||
let c =
|
||||
[|
|
||||
0.99999999999980993;
|
||||
676.5203681218851;
|
||||
-1259.1392167224028;
|
||||
771.32342877765313;
|
||||
-176.61502916214059;
|
||||
12.507343278686905;
|
||||
-0.13857109526572012;
|
||||
9.9843695780195716e-6;
|
||||
1.5056327351493116e-7;
|
||||
|]
|
||||
in
|
||||
if x < 0.5 then
|
||||
log (Float.pi /. sin (Float.pi *. x)) -. log_gamma (1.0 -. x)
|
||||
else begin
|
||||
let x = x -. 1.0 in
|
||||
let a = ref c.(0) in
|
||||
for i = 1 to 8 do
|
||||
a := !a +. (c.(i) /. (x +. float_of_int i))
|
||||
done;
|
||||
let t = x +. g +. 0.5 in
|
||||
(0.5 *. log (2.0 *. Float.pi))
|
||||
+. ((x +. 0.5) *. log t)
|
||||
-. t +. log !a
|
||||
end
|
||||
|
||||
let rec digamma x =
|
||||
if x < 6.0 then digamma (x +. 1.0) -. (1.0 /. x)
|
||||
else
|
||||
let inv = 1.0 /. x in
|
||||
let inv2 = inv *. inv in
|
||||
log x -. (0.5 *. inv)
|
||||
-. (inv2
|
||||
*. (1.0 /. 12.0
|
||||
-. (inv2
|
||||
*. (1.0 /. 120.0
|
||||
-. (inv2
|
||||
*. (1.0 /. 252.0
|
||||
-. (inv2 *. (1.0 /. 240.0 -. (inv2 *. (1.0 /. 132.0))))))))))
|
||||
|
||||
let bits x = if x <= 0.0 then 0.0 else log x /. log 2.0
|
||||
|
||||
let description_length_bits (g : Grammar.t) =
|
||||
let nts = Grammar.nonterminals g in
|
||||
let ts = Grammar.terminals g in
|
||||
let nn = float_of_int (List.length nts) in
|
||||
let nt_terms = float_of_int (List.length ts) in
|
||||
let bnt = bits nn in
|
||||
let bt = bits nt_terms in
|
||||
let total = ref (bits nn +. bits nt_terms) in
|
||||
List.iter
|
||||
(fun a ->
|
||||
let ps = Grammar.productions_of g a in
|
||||
total := !total +. bits (float_of_int (List.length ps));
|
||||
List.iter
|
||||
(fun (p : Grammar.production) ->
|
||||
total := !total +. bits (float_of_int (List.length p.rhs));
|
||||
List.iter
|
||||
(function
|
||||
| Grammar.Nonterm _ -> total := !total +. bnt
|
||||
| Grammar.Term _ -> total := !total +. bt)
|
||||
p.rhs)
|
||||
ps)
|
||||
nts;
|
||||
!total
|
||||
|
||||
let structural_logprior ?(config = default_config) (g : Grammar.t) =
|
||||
-.config.prior_weight *. description_length_bits g *. log 2.0
|
||||
|
||||
let marginal_loglik ?(config = default_config) (g : Grammar.t) (corpus : Corpus.t) =
|
||||
|
||||
let uprep = Parse.prepare_uniform g in
|
||||
if not (List.for_all (fun s -> Parse.inside uprep s.Corpus.tokens > 0.0) corpus)
|
||||
then (neg_infinity, neg_infinity, [||], Parse.prepare g)
|
||||
else begin
|
||||
let prep = Parse.prepare g in
|
||||
ignore (Parse.fit_em prep corpus ~iters:config.em_iters ~tol:config.em_tol);
|
||||
|
||||
let ll =
|
||||
List.fold_left
|
||||
(fun acc s ->
|
||||
let p = Parse.inside prep s.Corpus.tokens in
|
||||
if p > 0.0 then acc +. (s.Corpus.count *. log p) else neg_infinity)
|
||||
0.0 corpus
|
||||
in
|
||||
if ll = neg_infinity then (neg_infinity, neg_infinity, [||], prep)
|
||||
else begin
|
||||
|
||||
let np = Array.length prep.prods in
|
||||
let counts = Array.make np 0.0 in
|
||||
List.iter
|
||||
(fun s ->
|
||||
let cnt, _ = Parse.expected_counts prep s.Corpus.tokens in
|
||||
Array.iteri
|
||||
(fun i x -> counts.(i) <- counts.(i) +. (s.Corpus.count *. x))
|
||||
cnt)
|
||||
corpus;
|
||||
let dirichlet = ref 0.0 and ml_count = ref 0.0 in
|
||||
Hashtbl.iter
|
||||
(fun _ idxs ->
|
||||
let k = List.length idxs in
|
||||
if k > 0 then begin
|
||||
let n = List.fold_left (fun s i -> s +. counts.(i)) 0.0 idxs in
|
||||
if n > 0.0 then begin
|
||||
dirichlet :=
|
||||
!dirichlet
|
||||
+. (log_gamma (float_of_int k *. config.alpha)
|
||||
-. log_gamma (n +. (float_of_int k *. config.alpha)));
|
||||
List.iter
|
||||
(fun i ->
|
||||
if counts.(i) > 0.0 then begin
|
||||
dirichlet :=
|
||||
!dirichlet
|
||||
+. (log_gamma (counts.(i) +. config.alpha)
|
||||
-. log_gamma config.alpha);
|
||||
ml_count :=
|
||||
!ml_count +. (counts.(i) *. log (counts.(i) /. n))
|
||||
end)
|
||||
idxs
|
||||
end
|
||||
end)
|
||||
prep.by_lhs;
|
||||
let occam = !dirichlet -. !ml_count in
|
||||
(ll +. occam, ll, counts, prep)
|
||||
end
|
||||
end
|
||||
|
||||
let variational_loglik ?(config = default_config) (g : Grammar.t) (corpus : Corpus.t) =
|
||||
let prep = Parse.prepare g in
|
||||
let np = Array.length prep.prods in
|
||||
let beta = Array.make np config.alpha in
|
||||
let kl = ref 0.0 in
|
||||
let set_theta_bar () =
|
||||
Hashtbl.iter
|
||||
(fun _ idxs ->
|
||||
let bsum = List.fold_left (fun s i -> s +. beta.(i)) 0.0 idxs in
|
||||
let bpsi = digamma bsum in
|
||||
List.iter (fun i -> prep.probs.(i) <- exp (digamma beta.(i) -. bpsi)) idxs)
|
||||
prep.by_lhs
|
||||
in
|
||||
let update_kl () =
|
||||
kl := 0.0;
|
||||
Hashtbl.iter
|
||||
(fun _ idxs ->
|
||||
let k = List.length idxs in
|
||||
if k > 0 then begin
|
||||
let bsum = List.fold_left (fun s i -> s +. beta.(i)) 0.0 idxs in
|
||||
let bpsi = digamma bsum in
|
||||
let log_b_alpha =
|
||||
(float_of_int k *. log_gamma config.alpha)
|
||||
-. log_gamma (float_of_int k *. config.alpha)
|
||||
in
|
||||
let log_b_beta =
|
||||
List.fold_left (fun s i -> s +. log_gamma beta.(i)) 0.0 idxs
|
||||
-. log_gamma bsum
|
||||
in
|
||||
let term =
|
||||
List.fold_left
|
||||
(fun s i ->
|
||||
s +. ((beta.(i) -. config.alpha) *. (digamma beta.(i) -. bpsi)))
|
||||
0.0 idxs
|
||||
in
|
||||
kl := !kl +. (log_b_alpha -. log_b_beta +. term)
|
||||
end)
|
||||
prep.by_lhs
|
||||
in
|
||||
for _ = 1 to max 1 config.em_iters do
|
||||
set_theta_bar ();
|
||||
let acc = Array.make np 0.0 in
|
||||
List.iter
|
||||
(fun s ->
|
||||
let cnt, _ = Parse.expected_counts prep s.Corpus.tokens in
|
||||
Array.iteri
|
||||
(fun i x -> acc.(i) <- acc.(i) +. (s.Corpus.count *. x))
|
||||
cnt)
|
||||
corpus;
|
||||
for i = 0 to np - 1 do
|
||||
beta.(i) <- config.alpha +. acc.(i)
|
||||
done;
|
||||
update_kl ()
|
||||
done;
|
||||
set_theta_bar ();
|
||||
let log_z = ref 0.0 in
|
||||
List.iter
|
||||
(fun s ->
|
||||
let z = Parse.inside prep s.Corpus.tokens in
|
||||
if z > 0.0 then log_z := !log_z +. (s.Corpus.count *. log z)
|
||||
else log_z := neg_infinity)
|
||||
corpus;
|
||||
!log_z -. !kl
|
||||
|
||||
let posterior ?(config = default_config) g corpus =
|
||||
let prior = structural_logprior ~config g in
|
||||
match config.mode with
|
||||
| Variational -> prior +. variational_loglik ~config g corpus
|
||||
| _ ->
|
||||
let marg, ll, _, _ = marginal_loglik ~config g corpus in
|
||||
(match config.mode with
|
||||
| Marginal -> prior +. marg
|
||||
| Maximum_likelihood -> prior +. ll
|
||||
| Variational -> assert false)
|
||||
|
||||
type details = {
|
||||
prior : float;
|
||||
marginal : float;
|
||||
ml_loglik : float;
|
||||
posterior : float;
|
||||
dl_bits : float;
|
||||
num_nonterminals : int;
|
||||
num_productions : int;
|
||||
}
|
||||
|
||||
let details ?(config = default_config) (g : Grammar.t) (corpus : Corpus.t) =
|
||||
let marg, ll, _, _ = marginal_loglik ~config g corpus in
|
||||
let prior = structural_logprior ~config g in
|
||||
let dl = description_length_bits g in
|
||||
let likelihood =
|
||||
match config.mode with
|
||||
| Marginal -> marg
|
||||
| Maximum_likelihood -> ll
|
||||
| Variational -> variational_loglik ~config g corpus
|
||||
in
|
||||
{
|
||||
prior;
|
||||
marginal = likelihood;
|
||||
ml_loglik = ll;
|
||||
posterior = prior +. likelihood;
|
||||
dl_bits = dl;
|
||||
num_nonterminals = List.length (Grammar.nonterminals g);
|
||||
num_productions = List.length g.Grammar.productions;
|
||||
}
|
||||
|
||||
let heldout ?(config = default_config) (g : Grammar.t) ~train (test : Corpus.t) =
|
||||
let prep = Parse.prepare g in
|
||||
ignore (Parse.fit_em prep train ~iters:config.em_iters ~tol:config.em_tol);
|
||||
let total = ref 0.0 in
|
||||
let ntok = ref 0.0 in
|
||||
let unparseable = ref 0 in
|
||||
List.iter
|
||||
(fun s ->
|
||||
let p = Parse.inside prep s.Corpus.tokens in
|
||||
if p > 0.0 then begin
|
||||
total := !total +. (s.Corpus.count *. log p);
|
||||
ntok := !ntok +. (s.Corpus.count *. float_of_int (List.length s.Corpus.tokens))
|
||||
end
|
||||
else incr unparseable)
|
||||
test;
|
||||
if !ntok > 0.0 then
|
||||
(!total /. !ntok, !total, !ntok, !unparseable)
|
||||
else (neg_infinity, !total, 0.0, !unparseable)
|
||||
+250
@@ -0,0 +1,250 @@
|
||||
type step = {
|
||||
transform : Transform.t;
|
||||
parent : Grammar.t;
|
||||
result : Grammar.t;
|
||||
parent_score : float;
|
||||
score : float;
|
||||
}
|
||||
|
||||
type proposal = {
|
||||
iteration : int;
|
||||
transform : Transform.t;
|
||||
parent_key : string;
|
||||
score : float;
|
||||
accepted : bool;
|
||||
}
|
||||
|
||||
type entry = { g : Grammar.t; score : float; hist : step list }
|
||||
|
||||
type result = {
|
||||
best : Grammar.t;
|
||||
best_score : float;
|
||||
initial_score : float;
|
||||
steps : step list;
|
||||
proposals : proposal list;
|
||||
iterations : int;
|
||||
}
|
||||
|
||||
let key_of = Grammar.canonical_string
|
||||
|
||||
let transform_key (s : step) =
|
||||
(key_of s.parent, Transform.describe s.transform)
|
||||
|
||||
let run ~config ~beam_width ~max_steps ~patience ?(on_step = fun _ _ -> ()) g0
|
||||
corpus =
|
||||
let score g = Scoring.posterior ~config g corpus in
|
||||
let s0 = score g0 in
|
||||
let beam = ref [ { g = g0; score = s0; hist = [] } ] in
|
||||
let best = ref { g = g0; score = s0; hist = [] } in
|
||||
let proposals = ref [] in
|
||||
let accepted = Hashtbl.create 64 in
|
||||
let no_improve = ref 0 in
|
||||
let iter = ref 0 in
|
||||
let stop = ref false in
|
||||
while (not !stop) && !iter < max_steps do
|
||||
incr iter;
|
||||
let cands =
|
||||
List.concat_map
|
||||
(fun e ->
|
||||
List.filter_map
|
||||
(fun t ->
|
||||
let g' = Grammar.normalize (Transform.apply ~occurrence:config.chunk_occurrence e.g t) in
|
||||
let s' = score g' in
|
||||
if s' = neg_infinity then None
|
||||
else
|
||||
let step =
|
||||
{
|
||||
transform = t;
|
||||
parent = e.g;
|
||||
result = g';
|
||||
parent_score = e.score;
|
||||
score = s';
|
||||
}
|
||||
in
|
||||
Some { g = g'; score = s'; hist = step :: e.hist })
|
||||
(Transform.candidates e.g config))
|
||||
!beam
|
||||
in
|
||||
let tbl = Hashtbl.create 128 in
|
||||
List.iter
|
||||
(fun e ->
|
||||
let k = key_of e.g in
|
||||
match Hashtbl.find_opt tbl k with
|
||||
| Some e0 when e0.score >= e.score -> ()
|
||||
| _ -> Hashtbl.replace tbl k e)
|
||||
cands;
|
||||
let cands = Hashtbl.fold (fun _ e acc -> e :: acc) tbl [] in
|
||||
List.iter
|
||||
(fun e ->
|
||||
match e.hist with
|
||||
| step :: _ ->
|
||||
proposals :=
|
||||
{
|
||||
iteration = !iter;
|
||||
transform = step.transform;
|
||||
parent_key = key_of step.parent;
|
||||
score = e.score;
|
||||
accepted = false;
|
||||
}
|
||||
:: !proposals
|
||||
| [] -> ())
|
||||
cands;
|
||||
let sorted = List.sort (fun a b -> compare b.score a.score) cands in
|
||||
let newbeam = List.filteri (fun i _ -> i < beam_width) sorted in
|
||||
(match newbeam with
|
||||
| e :: _ when e.score > !best.score +. 1e-9 ->
|
||||
best := e;
|
||||
(match e.hist with
|
||||
| step :: _ ->
|
||||
Hashtbl.replace accepted (transform_key step) ();
|
||||
on_step !iter step
|
||||
| [] -> ());
|
||||
no_improve := 0
|
||||
| _ -> incr no_improve);
|
||||
beam := newbeam;
|
||||
if newbeam = [] then stop := true;
|
||||
if !no_improve >= patience then stop := true
|
||||
done;
|
||||
let steps = List.rev !best.hist in
|
||||
let proposals =
|
||||
List.rev !proposals
|
||||
|> List.map (fun p ->
|
||||
{
|
||||
p with
|
||||
accepted =
|
||||
Hashtbl.mem accepted
|
||||
(p.parent_key, Transform.describe p.transform);
|
||||
})
|
||||
in
|
||||
{
|
||||
best = !best.g;
|
||||
best_score = !best.score;
|
||||
initial_score = s0;
|
||||
steps;
|
||||
proposals;
|
||||
iterations = !iter;
|
||||
}
|
||||
|
||||
let run_best_first ~config ~frontier_cap ~max_expansions ~patience g0 corpus =
|
||||
let score g = Scoring.posterior ~config g corpus in
|
||||
let s0 = score g0 in
|
||||
let frontier = ref [ { g = g0; score = s0; hist = [] } ] in
|
||||
let best = ref { g = g0; score = s0; hist = [] } in
|
||||
let proposals = ref [] in
|
||||
let accepted = Hashtbl.create 64 in
|
||||
let no_improve = ref 0 in
|
||||
let expansions = ref 0 in
|
||||
let iter = ref 0 in
|
||||
let dedupe entries =
|
||||
let tbl = Hashtbl.create 256 in
|
||||
List.iter
|
||||
(fun e ->
|
||||
let k = key_of e.g in
|
||||
match Hashtbl.find_opt tbl k with
|
||||
| Some e0 when e0.score >= e.score -> ()
|
||||
| _ -> Hashtbl.replace tbl k e)
|
||||
entries;
|
||||
Hashtbl.fold (fun _ e acc -> e :: acc) tbl []
|
||||
in
|
||||
while
|
||||
!frontier <> [] && !expansions < max_expansions && !no_improve < patience
|
||||
do
|
||||
incr iter;
|
||||
let sorted = List.sort (fun a b -> compare b.score a.score) !frontier in
|
||||
let e = List.hd sorted in
|
||||
frontier := List.tl sorted;
|
||||
incr expansions;
|
||||
let cands =
|
||||
List.filter_map
|
||||
(fun t ->
|
||||
let g' = Grammar.normalize (Transform.apply ~occurrence:config.chunk_occurrence e.g t) in
|
||||
let s' = score g' in
|
||||
if s' = neg_infinity then None
|
||||
else
|
||||
Some
|
||||
{
|
||||
g = g';
|
||||
score = s';
|
||||
hist =
|
||||
{
|
||||
transform = t;
|
||||
parent = e.g;
|
||||
result = g';
|
||||
parent_score = e.score;
|
||||
score = s';
|
||||
}
|
||||
:: e.hist;
|
||||
})
|
||||
(Transform.candidates e.g config)
|
||||
in
|
||||
List.iter
|
||||
(fun c ->
|
||||
match c.hist with
|
||||
| step :: _ ->
|
||||
proposals :=
|
||||
{
|
||||
iteration = !iter;
|
||||
transform = step.transform;
|
||||
parent_key = key_of step.parent;
|
||||
score = c.score;
|
||||
accepted = false;
|
||||
}
|
||||
:: !proposals
|
||||
| [] -> ())
|
||||
cands;
|
||||
if e.score > !best.score +. 1e-9 then begin
|
||||
best := e;
|
||||
(match e.hist with
|
||||
| step :: _ -> Hashtbl.replace accepted (transform_key step) ()
|
||||
| [] -> ());
|
||||
no_improve := 0
|
||||
end
|
||||
else incr no_improve;
|
||||
frontier := cands @ !frontier |> dedupe;
|
||||
let sorted = List.sort (fun a b -> compare b.score a.score) !frontier in
|
||||
frontier := List.filteri (fun i _ -> i < frontier_cap) sorted
|
||||
done;
|
||||
let steps = List.rev !best.hist in
|
||||
let proposals =
|
||||
List.rev !proposals
|
||||
|> List.map (fun p ->
|
||||
{
|
||||
p with
|
||||
accepted =
|
||||
Hashtbl.mem accepted
|
||||
(p.parent_key, Transform.describe p.transform);
|
||||
})
|
||||
in
|
||||
{
|
||||
best = !best.g;
|
||||
best_score = !best.score;
|
||||
initial_score = s0;
|
||||
steps;
|
||||
proposals;
|
||||
iterations = !iter;
|
||||
}
|
||||
|
||||
let proposals_to_tsv result =
|
||||
let header = "iteration\tparent_key\ttransform\tscore\taccepted" in
|
||||
let rows =
|
||||
List.map
|
||||
(fun p ->
|
||||
Printf.sprintf "%d\t%s\t%s\t%.10g\t%b" p.iteration
|
||||
(String.concat "\\n" (String.split_on_char '\n' p.parent_key))
|
||||
(Transform.describe p.transform)
|
||||
p.score p.accepted)
|
||||
result.proposals
|
||||
in
|
||||
String.concat "\n" (header :: rows)
|
||||
|
||||
let steps_to_tsv result =
|
||||
let header = "step\tparent_score\tscore\tdelta\ttransform" in
|
||||
let rows =
|
||||
List.mapi
|
||||
(fun i (s : step) ->
|
||||
Printf.sprintf "%d\t%.10g\t%.10g\t%.10g\t%s" (i + 1) s.parent_score
|
||||
s.score (s.score -. s.parent_score)
|
||||
(Transform.describe s.transform))
|
||||
result.steps
|
||||
in
|
||||
String.concat "\n" (header :: rows)
|
||||
@@ -0,0 +1,193 @@
|
||||
type t = Merge of string * string | Chunk of Grammar.symbol list
|
||||
|
||||
let describe = function
|
||||
| Merge (a, b) -> Printf.sprintf "merge %s,%s" a b
|
||||
| Chunk seq ->
|
||||
Printf.sprintf "chunk (%s)"
|
||||
(String.concat " " (List.map Grammar.symbol_to_string seq))
|
||||
|
||||
let starts_with seq lst =
|
||||
let m = List.length seq in
|
||||
let rec go i seq lst =
|
||||
if i = 0 then true
|
||||
else
|
||||
match (seq, lst) with
|
||||
| [], _ -> true
|
||||
| _, [] -> false
|
||||
| x :: xs, y :: ys -> Grammar.equal_symbol x y && go (i - 1) xs ys
|
||||
in
|
||||
List.length lst >= m && go m seq lst
|
||||
|
||||
let drop n lst =
|
||||
let rec go n lst = if n <= 0 then lst else match lst with [] -> [] | _ :: r -> go (n - 1) r in
|
||||
go n lst
|
||||
|
||||
let replace_all seq name rhs =
|
||||
let m = List.length seq in
|
||||
let rec go acc lst count =
|
||||
match lst with
|
||||
| _ when starts_with seq lst ->
|
||||
go (Grammar.Nonterm name :: acc) (drop m lst) (count + 1)
|
||||
| [] -> (List.rev acc, count)
|
||||
| x :: rest -> go (x :: acc) rest count
|
||||
in
|
||||
go [] rhs 0
|
||||
|
||||
let replace_first seq name rhs =
|
||||
let m = List.length seq in
|
||||
let rec go acc lst =
|
||||
match lst with
|
||||
| _ when starts_with seq lst -> (List.rev_append acc (Grammar.Nonterm name :: drop m lst), 1)
|
||||
| [] -> (List.rev acc, 0)
|
||||
| x :: rest -> go (x :: acc) rest
|
||||
in
|
||||
go [] rhs
|
||||
|
||||
let fresh_name (g : Grammar.t) _base =
|
||||
let existing = Grammar.nonterminals g in
|
||||
let candidates = [ "X"; "Y"; "Z"; "W"; "V"; "U"; "P"; "Q"; "R" ] in
|
||||
match List.find_opt (fun c -> not (List.mem c existing)) candidates with
|
||||
| Some c -> c
|
||||
| None ->
|
||||
let rec loop i =
|
||||
let c = "X" ^ string_of_int i in
|
||||
if List.mem c existing then loop (i + 1) else c
|
||||
in
|
||||
loop 1
|
||||
|
||||
let apply_merge (g : Grammar.t) a b =
|
||||
let survivor, removed =
|
||||
if String.equal a g.Grammar.start then (a, b)
|
||||
else if String.equal b g.Grammar.start then (b, a)
|
||||
else if String.compare a b <= 0 then (a, b)
|
||||
else (b, a)
|
||||
in
|
||||
let map_sym = function
|
||||
| Grammar.Nonterm x when String.equal x removed -> Grammar.Nonterm survivor
|
||||
| s -> s
|
||||
in
|
||||
let prods =
|
||||
List.map
|
||||
(fun (p : Grammar.production) ->
|
||||
let lhs = if String.equal p.lhs removed then survivor else p.lhs in
|
||||
{ p with lhs; rhs = List.map map_sym p.rhs })
|
||||
g.Grammar.productions
|
||||
in
|
||||
Grammar.copy_with g prods
|
||||
|
||||
let apply_chunk ?(occurrence = Scoring.All_occurrences) (g : Grammar.t) seq =
|
||||
if List.length seq < 2 then g
|
||||
else begin
|
||||
let name = fresh_name g "X" in
|
||||
let replace =
|
||||
match occurrence with
|
||||
| Scoring.All_occurrences -> replace_all
|
||||
| Scoring.First_occurrence -> replace_first
|
||||
in
|
||||
let total = ref 0 in
|
||||
let prods =
|
||||
List.map
|
||||
(fun (p : Grammar.production) ->
|
||||
let rhs, n = replace seq name p.rhs in
|
||||
total := !total + n;
|
||||
{ p with rhs })
|
||||
g.Grammar.productions
|
||||
in
|
||||
let newp =
|
||||
{
|
||||
Grammar.lhs = name;
|
||||
rhs = seq;
|
||||
count = float_of_int (max 1 !total);
|
||||
}
|
||||
in
|
||||
Grammar.copy_with g (prods @ [ newp ])
|
||||
end
|
||||
|
||||
let apply ?occurrence (g : Grammar.t) = function
|
||||
| Merge (a, b) -> apply_merge g a b
|
||||
| Chunk seq -> apply_chunk ?occurrence g seq
|
||||
|
||||
let candidates (g : Grammar.t) (config : Scoring.config) =
|
||||
let nts = Grammar.nonterminals g in
|
||||
let merges =
|
||||
let rec pairs = function
|
||||
| [] -> []
|
||||
| x :: rest -> List.map (fun y -> Merge (x, y)) rest @ pairs rest
|
||||
in
|
||||
pairs nts
|
||||
in
|
||||
let counts = Hashtbl.create 256 in
|
||||
let order = ref [] in
|
||||
List.iter
|
||||
(fun (p : Grammar.production) ->
|
||||
let arr = Array.of_list p.rhs in
|
||||
let n = Array.length arr in
|
||||
for len = 2 to min config.Scoring.max_chunk n do
|
||||
for i = 0 to n - len do
|
||||
let sub = Array.to_list (Array.sub arr i len) in
|
||||
match Hashtbl.find_opt counts sub with
|
||||
| Some c -> Hashtbl.replace counts sub (c + 1)
|
||||
| None ->
|
||||
Hashtbl.replace counts sub 1;
|
||||
order := sub :: !order
|
||||
done
|
||||
done)
|
||||
g.Grammar.productions;
|
||||
|
||||
let chunks =
|
||||
List.rev !order
|
||||
|> List.filter (fun k -> Hashtbl.find counts k >= 1)
|
||||
|> List.map (fun seq -> Chunk seq)
|
||||
in
|
||||
merges @ chunks
|
||||
|
||||
type change = {
|
||||
before_nts : string list;
|
||||
after_nts : string list;
|
||||
before_prods : Grammar.production list;
|
||||
after_prods : Grammar.production list;
|
||||
}
|
||||
|
||||
let change_of (before : Grammar.t) t (after : Grammar.t) =
|
||||
match t with
|
||||
| Merge (a, b) ->
|
||||
let survivor =
|
||||
if String.equal a before.Grammar.start then a
|
||||
else if String.equal b before.Grammar.start then b
|
||||
else if String.compare a b <= 0 then a
|
||||
else b
|
||||
in
|
||||
{
|
||||
before_nts = [ a; b ];
|
||||
after_nts = [ survivor ];
|
||||
before_prods =
|
||||
List.filter
|
||||
(fun p -> String.equal p.Grammar.lhs a || String.equal p.Grammar.lhs b)
|
||||
before.Grammar.productions;
|
||||
after_prods =
|
||||
List.filter
|
||||
(fun p -> String.equal p.Grammar.lhs survivor)
|
||||
after.Grammar.productions;
|
||||
}
|
||||
| Chunk seq ->
|
||||
let name = fresh_name before "X" in
|
||||
let affected_before =
|
||||
List.filter (fun p -> starts_with seq p.Grammar.rhs) before.Grammar.productions
|
||||
in
|
||||
let affected_after =
|
||||
List.filter
|
||||
(fun p ->
|
||||
String.equal p.Grammar.lhs name
|
||||
|| List.exists
|
||||
(function
|
||||
| Grammar.Nonterm x -> String.equal x name
|
||||
| Grammar.Term _ -> false)
|
||||
p.Grammar.rhs)
|
||||
after.Grammar.productions
|
||||
in
|
||||
{
|
||||
before_nts = name :: List.map (fun p -> p.Grammar.lhs) affected_before;
|
||||
after_nts = [ name ];
|
||||
before_prods = affected_before;
|
||||
after_prods = affected_after;
|
||||
}
|
||||
File diff suppressed because it is too large.
Load diff
|
After Width: | Height: | Size: 506 KiB |
@@ -0,0 +1,4 @@
|
||||
(test
|
||||
(name test_scfg)
|
||||
(flags (:standard -warn-error -a))
|
||||
(libraries scfg))
|
||||
@@ -0,0 +1,317 @@
|
||||
open Scfg
|
||||
|
||||
let failures = ref 0
|
||||
|
||||
let check name cond =
|
||||
if cond then Printf.printf "ok %s\n" name
|
||||
else begin
|
||||
incr failures;
|
||||
Printf.printf "FAIL %s\n" name
|
||||
end;
|
||||
flush stdout
|
||||
|
||||
let approx ?(tol = 1e-9) a b = abs_float (a -. b) < tol
|
||||
|
||||
let nt s = Grammar.Nonterm s
|
||||
let tm s = Grammar.Term s
|
||||
let prod lhs rhs = { Grammar.lhs; rhs; count = 1.0 }
|
||||
let g start ps = Grammar.make ~start ps
|
||||
|
||||
let has_prod g lhs rhs =
|
||||
List.exists
|
||||
(fun (p : Grammar.production) ->
|
||||
String.equal p.lhs lhs && Grammar.equal_rhs p.rhs rhs)
|
||||
g.Grammar.productions
|
||||
|
||||
let sample tokens count = { Corpus.tokens; count }
|
||||
|
||||
let () =
|
||||
check "log_gamma(1)=0" (approx (Scoring.log_gamma 1.0) 0.0);
|
||||
check "log_gamma(2)=0" (approx (Scoring.log_gamma 2.0) 0.0);
|
||||
check "log_gamma(1/2)=log sqrt pi"
|
||||
(approx (Scoring.log_gamma 0.5) (0.5 *. log Float.pi));
|
||||
check "log_gamma(3)=log 2"
|
||||
(approx (Scoring.log_gamma 3.0) (log 2.0))
|
||||
|
||||
let () =
|
||||
let amb = g "S" [ prod "S" [ nt "S"; nt "S" ]; prod "S" [ tm "a" ] ] in
|
||||
let prep = Parse.prepare amb in
|
||||
check "P(a) = 1/2" (approx (Parse.inside prep [ "a" ]) 0.5);
|
||||
check "P(aa) = 1/8" (approx (Parse.inside prep [ "a"; "a" ]) 0.125);
|
||||
check "P(aaa) = 1/16" (approx (Parse.inside prep [ "a"; "a"; "a" ]) 0.0625);
|
||||
let vp, vt = Parse.viterbi prep [ "a"; "a" ] in
|
||||
check "viterbi P(aa) = 1/8" (approx vp 0.125);
|
||||
check "viterbi tree exists" (vt <> None)
|
||||
|
||||
let () =
|
||||
let gr = g "S" [ prod "S" [ nt "A"; nt "B" ]; prod "A" [ tm "a" ]; prod "B" [ tm "b" ] ] in
|
||||
let prep = Parse.prepare gr in
|
||||
let cnt, p = Parse.expected_counts prep [ "a"; "b" ] in
|
||||
check "inside(ab)=1" (approx p 1.0);
|
||||
check "E[count S->AB]=1" (approx cnt.(0) 1.0);
|
||||
check "E[count A->a]=1" (approx cnt.(1) 1.0);
|
||||
check "E[count B->b]=1" (approx cnt.(2) 1.0)
|
||||
|
||||
let () =
|
||||
let amb = g "S" [ prod "S" [ nt "S"; nt "S" ]; prod "S" [ tm "a" ] ] in
|
||||
let prep = Parse.prepare amb in
|
||||
let cnt, _ = Parse.expected_counts prep [ "a"; "a" ] in
|
||||
check "E[count S->SS]=1" (approx cnt.(0) 1.0);
|
||||
check "E[count S->a]=2" (approx cnt.(1) 2.0)
|
||||
|
||||
let () =
|
||||
let gd =
|
||||
g "S"
|
||||
[ prod "S" [ tm "a" ];
|
||||
{ Grammar.lhs = "S"; rhs = [ tm "a" ]; count = 2.0 } ]
|
||||
in
|
||||
let gn = Grammar.normalize gd in
|
||||
check "dedupe keeps one production"
|
||||
(List.length gn.Grammar.productions = 1);
|
||||
check "dedupe sums counts"
|
||||
(approx (List.hd gn.Grammar.productions).Grammar.count 3.0)
|
||||
|
||||
let () =
|
||||
let gs = g "S" [ prod "S" [ nt "S" ]; prod "S" [ tm "a" ] ] in
|
||||
let gn = Grammar.normalize gs in
|
||||
check "self-loop removed"
|
||||
(not (has_prod gn "S" [ nt "S" ]));
|
||||
check "self-loop grammar keeps S->a" (has_prod gn "S" [ tm "a" ])
|
||||
|
||||
let () =
|
||||
let gc =
|
||||
Grammar.make ~start:"A"
|
||||
[ prod "A" [ nt "B" ]; prod "B" [ nt "A" ]; prod "A" [ tm "a" ] ]
|
||||
in
|
||||
let gn = Grammar.normalize gc in
|
||||
check "unit cycle removed" (not (has_prod gn "A" [ nt "B" ]));
|
||||
check "unit cycle grammar keeps A->a" (has_prod gn "A" [ tm "a" ])
|
||||
|
||||
let () =
|
||||
let gu =
|
||||
g "S" [ prod "S" [ nt "A" ]; prod "A" [ nt "B" ]; prod "B" [ tm "a" ] ]
|
||||
in
|
||||
let gn = Grammar.normalize gu in
|
||||
check "unit productions are preserved" (has_prod gn "S" [ nt "A" ]);
|
||||
check "unit productions chain preserved" (has_prod gn "A" [ nt "B" ])
|
||||
|
||||
let () =
|
||||
let cfg = { Scoring.default_config with alpha = 1.0; em_iters = 5 } in
|
||||
let g1 = g "S" [ prod "S" [ tm "a" ] ] in
|
||||
let m1, _, _, _ =
|
||||
Scoring.marginal_loglik ~config:cfg g1 [ sample [ "a" ] 1.0 ]
|
||||
in
|
||||
check "marginal(S->a, {a}, alpha=1) = 0" (approx m1 0.0);
|
||||
let g2 = g "S" [ prod "S" [ tm "a" ]; prod "S" [ tm "b" ] ] in
|
||||
let m2, _, _, _ =
|
||||
Scoring.marginal_loglik ~config:cfg g2 [ sample [ "a" ] 1.0 ]
|
||||
in
|
||||
check "marginal(S->a|b, {a}, alpha=1) = log 1/2"
|
||||
(approx m2 (log 0.5))
|
||||
|
||||
let paper_initial () =
|
||||
g "S"
|
||||
[
|
||||
prod "S" [ nt "A"; nt "B" ];
|
||||
prod "S" [ nt "A"; nt "A"; nt "B"; nt "B" ];
|
||||
prod "S" [ nt "A"; nt "A"; nt "A"; nt "B"; nt "B"; nt "B" ];
|
||||
prod "A" [ tm "a" ];
|
||||
prod "B" [ tm "b" ];
|
||||
]
|
||||
|
||||
let () =
|
||||
let g0 = paper_initial () in
|
||||
let gc1 = Grammar.normalize (Transform.apply g0 (Transform.Chunk [ nt "A"; nt "B" ])) in
|
||||
check "chunk(AB): S->X" (has_prod gc1 "S" [ nt "X" ]);
|
||||
check "chunk(AB): S->AXB" (has_prod gc1 "S" [ nt "A"; nt "X"; nt "B" ]);
|
||||
check "chunk(AB): S->AAXBB"
|
||||
(has_prod gc1 "S" [ nt "A"; nt "A"; nt "X"; nt "B"; nt "B" ]);
|
||||
check "chunk(AB): X->AB" (has_prod gc1 "X" [ nt "A"; nt "B" ]);
|
||||
check "chunk preserves language"
|
||||
(Grammar.language_up_to g0 6 = Grammar.language_up_to gc1 6)
|
||||
|
||||
let () =
|
||||
let g0 = paper_initial () in
|
||||
let gc1 = Grammar.normalize (Transform.apply g0 (Transform.Chunk [ nt "A"; nt "B" ])) in
|
||||
let gc2 =
|
||||
Grammar.normalize (Transform.apply gc1 (Transform.Chunk [ nt "A"; nt "X"; nt "B" ]))
|
||||
in
|
||||
check "chunk(AXB): S->Y" (has_prod gc2 "S" [ nt "Y" ]);
|
||||
check "chunk(AXB): S->AYB" (has_prod gc2 "S" [ nt "A"; nt "Y"; nt "B" ]);
|
||||
check "chunk(AXB): Y->AXB" (has_prod gc2 "Y" [ nt "A"; nt "X"; nt "B" ]);
|
||||
let gm = Grammar.normalize (Transform.apply gc2 (Transform.Merge ("S", "Y"))) in
|
||||
let gf = Grammar.normalize (Transform.apply gm (Transform.Merge ("S", "X"))) in
|
||||
check "final: S->AB" (has_prod gf "S" [ nt "A"; nt "B" ]);
|
||||
check "final: S->ASB" (has_prod gf "S" [ nt "A"; nt "S"; nt "B" ]);
|
||||
let expected =
|
||||
[
|
||||
[ "a"; "b" ];
|
||||
[ "a"; "a"; "b"; "b" ];
|
||||
[ "a"; "a"; "a"; "b"; "b"; "b" ];
|
||||
[ "a"; "a"; "a"; "a"; "b"; "b"; "b"; "b" ];
|
||||
]
|
||||
|> List.sort compare
|
||||
in
|
||||
check "final grammar generates a^n b^n"
|
||||
(Grammar.language_up_to gf 8 = expected)
|
||||
|
||||
let () =
|
||||
let g0 =
|
||||
g "S"
|
||||
[ prod "S" [ nt "A" ]; prod "S" [ nt "B" ]; prod "A" [ tm "a" ];
|
||||
prod "B" [ tm "b" ] ]
|
||||
in
|
||||
let gm = Grammar.normalize (Transform.apply g0 (Transform.Merge ("A", "B"))) in
|
||||
check "merge unifies terminals into one nonterminal"
|
||||
(List.length (Grammar.terminals gm) = 2
|
||||
&& List.length
|
||||
(List.filter (fun p -> Grammar.symbol_is_nonterm (List.hd p.Grammar.rhs))
|
||||
gm.Grammar.productions)
|
||||
>= 1);
|
||||
check "merge keeps both terminal productions" (has_prod gm "A" [ tm "a" ] && has_prod gm "A" [ tm "b" ])
|
||||
|
||||
let () =
|
||||
let cfg =
|
||||
{
|
||||
Scoring.default_config with
|
||||
em_iters = 5;
|
||||
max_chunk = 3;
|
||||
prior_weight = 1.0;
|
||||
}
|
||||
in
|
||||
let corpus = [ sample [ "a"; "b" ] 1.0; sample [ "a"; "a"; "b"; "b" ] 1.0; sample [ "a"; "a"; "a"; "b"; "b"; "b" ] 1.0 ] in
|
||||
let result =
|
||||
Search.run ~config:cfg ~beam_width:3 ~max_steps:12 ~patience:3
|
||||
(paper_initial ()) corpus
|
||||
in
|
||||
check "search improves the posterior"
|
||||
(result.Search.best_score > result.Search.initial_score);
|
||||
check "search returns accepted steps"
|
||||
(List.length result.Search.steps > 0);
|
||||
check "search output generates training strings"
|
||||
(List.for_all
|
||||
(fun s ->
|
||||
List.mem s (Grammar.language_up_to result.Search.best 8))
|
||||
[ [ "a"; "b" ]; [ "a"; "a"; "b"; "b" ]; [ "a"; "a"; "a"; "b"; "b"; "b" ] ])
|
||||
|
||||
let () =
|
||||
let g0 =
|
||||
g "S"
|
||||
[ prod "S" [ nt "A"; nt "S"; nt "A" ]; prod "S" [ tm "c" ];
|
||||
prod "S" [ nt "A"; nt "A"; nt "S"; nt "A"; nt "A" ];
|
||||
prod "A" [ tm "a" ] ]
|
||||
in
|
||||
let gn = Grammar.normalize g0 in
|
||||
check "redundant production pruned"
|
||||
(not (has_prod gn "S" [ nt "A"; nt "A"; nt "S"; nt "A"; nt "A" ]));
|
||||
check "recursive production kept" (has_prod gn "S" [ nt "A"; nt "S"; nt "A" ]);
|
||||
check "pruning preserves the language"
|
||||
(Grammar.language_up_to g0 5 = Grammar.language_up_to gn 5)
|
||||
|
||||
let () =
|
||||
let gr =
|
||||
g "S" [ prod "S" [ nt "A"; nt "B" ]; prod "A" [ tm "a" ]; prod "B" [ tm "b" ] ]
|
||||
in
|
||||
let prep = Parse.prepare gr in
|
||||
let _, tree = Parse.viterbi prep [ "a"; "b" ] in
|
||||
match tree with
|
||||
| Some t ->
|
||||
check "parse tree yield" (Parse.tree_yield t = [ "a"; "b" ]);
|
||||
check "parse tree root" (match t with Parse.Node ("S", _) -> true | _ -> false)
|
||||
| None -> check "parse tree yield" false
|
||||
|
||||
let () =
|
||||
let gr =
|
||||
g "S" [ prod "S" [ nt "A"; nt "B" ]; prod "A" [ tm "a" ]; prod "B" [ tm "b" ] ]
|
||||
in
|
||||
let corpus = [ sample [ "a"; "b" ] 1.0 ] in
|
||||
let avg, _, _, unp = Scoring.heldout gr ~train:corpus corpus in
|
||||
check "heldout loglik per token = 0" (approx avg 0.0);
|
||||
check "heldout parseable" (unp = 0)
|
||||
|
||||
let contains hay needle =
|
||||
let n = String.length hay and m = String.length needle in
|
||||
let rec go i = if i + m > n then false else if String.sub hay i m = needle then true else go (i + 1) in
|
||||
m = 0 || go 0
|
||||
|
||||
let () =
|
||||
let g0 = g "S" [ prod "S" [ nt "S"; nt "S" ]; prod "S" [ tm "a" ] ] in
|
||||
let d = Dot.dot_grammar g0 in
|
||||
check "dot numbers repeated rhs symbols in order"
|
||||
(contains d "pr_0 -> nt_S [label=\"1\"];"
|
||||
&& contains d "pr_0 -> nt_S [label=\"2\"];");
|
||||
check "dot labels production probability" (contains d "p=0.500");
|
||||
check "dot marks the start symbol" (contains d "shape=doublecircle");
|
||||
let tree_dot = Dot.dot_tree (Parse.Node ("S", [ Parse.Leaf "a" ])) in
|
||||
check "parse tree dot has an edge" (contains tree_dot "->")
|
||||
|
||||
let () =
|
||||
check "digamma(1)" (approx (Scoring.digamma 1.0) (-0.5772156649015329) ~tol:1e-9);
|
||||
check "digamma(2)" (approx (Scoring.digamma 2.0) 0.42278433509846713 ~tol:1e-9)
|
||||
|
||||
let () =
|
||||
let mk mode =
|
||||
{ Scoring.default_config with alpha = 1.0; em_iters = 10; mode }
|
||||
in
|
||||
let corpus = [ sample [ "a" ] 1.0 ] in
|
||||
let g1 = g "S" [ prod "S" [ tm "a" ] ] in
|
||||
let d1 = Scoring.details ~config:(mk Scoring.Variational) g1 corpus in
|
||||
check "variational ELBO (single production) = 0"
|
||||
(approx d1.Scoring.posterior 0.0 ~tol:1e-6);
|
||||
let g2 = g "S" [ prod "S" [ tm "a" ]; prod "S" [ tm "b" ] ] in
|
||||
let dm = Scoring.details ~config:(mk Scoring.Marginal) g2 corpus in
|
||||
let dv = Scoring.details ~config:(mk Scoring.Variational) g2 corpus in
|
||||
check "variational matches marginal (unambiguous)"
|
||||
(approx dv.Scoring.posterior dm.Scoring.posterior ~tol:1e-6)
|
||||
|
||||
let () =
|
||||
let g0 =
|
||||
g "S"
|
||||
[ prod "S" [ nt "A"; nt "B"; nt "A"; nt "B" ]; prod "A" [ tm "a" ];
|
||||
prod "B" [ tm "b" ] ]
|
||||
in
|
||||
let all =
|
||||
Grammar.normalize (Transform.apply g0 (Transform.Chunk [ nt "A"; nt "B" ]))
|
||||
in
|
||||
let first =
|
||||
Grammar.normalize
|
||||
(Transform.apply ~occurrence:Scoring.First_occurrence g0
|
||||
(Transform.Chunk [ nt "A"; nt "B" ]))
|
||||
in
|
||||
check "chunk all replaces every occurrence"
|
||||
(has_prod all "S" [ nt "X"; nt "X" ]);
|
||||
check "chunk first replaces only the leftmost"
|
||||
(has_prod first "S" [ nt "X"; nt "A"; nt "B" ])
|
||||
|
||||
let () =
|
||||
let g0 =
|
||||
g "S"
|
||||
[ prod "S" [ nt "A"; nt "S"; nt "A" ]; prod "S" [ tm "c" ];
|
||||
prod "S" [ nt "A"; nt "A"; nt "A"; nt "S"; nt "A"; nt "A"; nt "A" ];
|
||||
prod "A" [ tm "a" ] ]
|
||||
in
|
||||
let gn = Grammar.normalize g0 in
|
||||
check "deeply redundant production pruned"
|
||||
(not
|
||||
(has_prod gn "S"
|
||||
[ nt "A"; nt "A"; nt "A"; nt "S"; nt "A"; nt "A"; nt "A" ]));
|
||||
check "deep redundancy preserves language"
|
||||
(Grammar.language_up_to g0 7 = Grammar.language_up_to gn 7)
|
||||
|
||||
let () =
|
||||
let g0 =
|
||||
g "S"
|
||||
[ prod "S" [ nt "A"; nt "B" ]; prod "S" [ nt "A"; nt "S"; nt "B" ];
|
||||
prod "S" [ nt "A"; nt "A"; nt "B" ]; prod "A" [ tm "a" ];
|
||||
prod "B" [ tm "b" ] ]
|
||||
in
|
||||
let gn = Grammar.normalize g0 in
|
||||
check "non-redundant production kept"
|
||||
(has_prod gn "S" [ nt "A"; nt "A"; nt "B" ])
|
||||
|
||||
let () =
|
||||
if !failures = 0 then Printf.printf "\nAll tests passed.\n"
|
||||
else begin
|
||||
Printf.printf "\n%d test(s) failed.\n" !failures;
|
||||
exit 1
|
||||
end
|
||||
Reference in new issue
Block a user