author | blanchet |
Wed, 29 Jan 2014 23:24:34 +0100 | |
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parent 55168 | 948e8b7ea82f |
child 55183 | 17ec4a29ef71 |
permissions | -rw-r--r-- |
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(* Title: HOL/Tools/Sledgehammer/sledgehammer_reconstruct.ML |
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Author: Jasmin Blanchette, TU Muenchen |
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Author: Steffen Juilf Smolka, TU Muenchen |
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Isar proof reconstruction from ATP proofs. |
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*) |
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signature SLEDGEHAMMER_RECONSTRUCT = |
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sig |
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type atp_step_name = ATP_Proof.atp_step_name |
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type ('a, 'b) atp_step = ('a, 'b) ATP_Proof.atp_step |
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type 'a atp_proof = 'a ATP_Proof.atp_proof |
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type stature = ATP_Problem_Generate.stature |
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type one_line_params = Sledgehammer_Reconstructor.one_line_params |
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type isar_params = |
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bool * string * string * Time.time * real * bool * (term, string) atp_step list * thm |
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val proof_text : Proof.context -> bool -> bool option -> (unit -> isar_params) -> int -> |
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one_line_params -> string |
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end; |
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structure Sledgehammer_Reconstruct : SLEDGEHAMMER_RECONSTRUCT = |
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struct |
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open ATP_Util |
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open ATP_Problem |
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open ATP_Proof |
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open ATP_Problem_Generate |
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open ATP_Proof_Reconstruct |
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open Sledgehammer_Util |
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open Sledgehammer_Reconstructor |
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open Sledgehammer_Proof |
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open Sledgehammer_Annotate |
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open Sledgehammer_Print |
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open Sledgehammer_Preplay |
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open Sledgehammer_Compress |
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open Sledgehammer_Try0 |
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open Sledgehammer_Minimize_Isar |
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structure String_Redirect = ATP_Proof_Redirect( |
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type key = atp_step_name |
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val ord = fn ((s, _ : string list), (s', _)) => fast_string_ord (s, s') |
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val string_of = fst) |
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open String_Redirect |
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val e_skolemize_rules = ["skolemize", "shift_quantors"] |
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val spass_pirate_datatype_rule = "DT" |
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val vampire_skolemisation_rule = "skolemisation" |
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(* TODO: Use "Z3_Proof.string_of_rule" once it is moved to Isabelle *) |
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val z3_skolemize_rule = "sk" |
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val z3_th_lemma_rule = "th-lemma" |
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val skolemize_rules = |
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e_skolemize_rules @ [spass_skolemize_rule, vampire_skolemisation_rule, z3_skolemize_rule] |
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val is_skolemize_rule = member (op =) skolemize_rules |
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val is_arith_rule = String.isPrefix z3_th_lemma_rule |
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val is_datatype_rule = String.isPrefix spass_pirate_datatype_rule |
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fun raw_label_of_num num = (num, 0) |
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fun label_of_clause [(num, _)] = raw_label_of_num num |
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| label_of_clause c = (space_implode "___" (map (fst o raw_label_of_num o fst) c), 0) |
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fun add_fact_of_dependencies [(_, ss as _ :: _)] = apsnd (union (op =) ss) |
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| add_fact_of_dependencies names = apfst (insert (op =) (label_of_clause names)) |
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(* No "real" literals means only type information (tfree_tcs, clsrel, or clsarity). *) |
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fun is_only_type_information t = t aconv @{prop True} |
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(* Discard facts; consolidate adjacent lines that prove the same formula, since they differ only in |
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type information. *) |
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fun add_line_pass1 (line as (name, role, t, rule, [])) lines = |
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(* No dependencies: lemma (for Z3), fact, conjecture, or (for Vampire) internal facts or |
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definitions. *) |
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if role = Lemma orelse role = Conjecture orelse role = Negated_Conjecture orelse |
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role = Hypothesis orelse is_arith_rule rule then |
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line :: lines |
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else if role = Axiom then |
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(* Facts are not proof lines. *) |
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lines |> is_only_type_information t ? map (replace_dependencies_in_line (name, [])) |
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else |
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map (replace_dependencies_in_line (name, [])) lines |
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| add_line_pass1 line lines = line :: lines |
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(* Recursively delete empty lines (type information) from the proof. |
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(FIXME: needed? And why is "delete_dependency" so complicated?) *) |
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fun add_line_pass2 (line as (name, _, t, _, [])) lines = |
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if is_only_type_information t then delete_dependency name lines else line :: lines |
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| add_line_pass2 line lines = line :: lines |
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and delete_dependency name lines = |
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fold_rev add_line_pass2 (map (replace_dependencies_in_line (name, [])) lines) [] |
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fun add_lines_pass3 res [] = rev res |
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| add_lines_pass3 res ((name, role, t, rule, deps) :: lines) = |
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if role <> Plain orelse is_skolemize_rule rule orelse is_arith_rule rule orelse |
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is_datatype_rule rule orelse |
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(* the last line must be kept *) |
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null lines orelse |
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(not (is_only_type_information t) andalso null (Term.add_tvars t []) |
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andalso length deps >= 2 andalso |
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(* don't keep next to last line, which usually results in a trivial step *) |
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not (can the_single lines)) then |
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add_lines_pass3 ((name, role, t, rule, deps) :: res) lines |
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else |
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add_lines_pass3 res (map (replace_dependencies_in_line (name, deps)) lines) |
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val add_labels_of_proof = |
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steps_of_proof |
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#> fold_isar_steps (byline_of_step #> (fn SOME ((ls, _), _) => union (op =) ls | _ => I)) |
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fun kill_useless_labels_in_proof proof = |
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let |
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val used_ls = add_labels_of_proof proof [] |
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fun kill_label l = if member (op =) used_ls l then l else no_label |
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fun kill_assms assms = map (apfst kill_label) assms |
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fun kill_step (Prove (qs, xs, l, t, subproofs, by)) = |
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Prove (qs, xs, kill_label l, t, map kill_proof subproofs, by) |
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| kill_step step = step |
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and kill_proof (Proof (fix, assms, steps)) = |
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Proof (fix, kill_assms assms, map kill_step steps) |
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in |
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kill_proof proof |
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end |
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val assume_prefix = "a" |
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val have_prefix = "f" |
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val relabel_proof = |
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let |
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fun fresh_label depth prefix (accum as (l, subst, next)) = |
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if l = no_label then |
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accum |
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else |
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let val l' = (replicate_string (depth + 1) prefix, next) in |
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(l', (l, l') :: subst, next + 1) |
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end |
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fun relabel_facts subst = apfst (maps (the_list o AList.lookup (op =) subst)) |
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fun relabel_assm depth (l, t) (subst, next) = |
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let val (l, subst, next) = (l, subst, next) |> fresh_label depth assume_prefix in |
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((l, t), (subst, next)) |
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end |
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fun relabel_assms subst depth assms = fold_map (relabel_assm depth) assms (subst, 1) ||> fst |
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fun relabel_steps _ _ _ [] = [] |
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| relabel_steps subst depth next (Prove (qs, xs, l, t, sub, by) :: steps) = |
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let |
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val (l, subst, next) = (l, subst, next) |> fresh_label depth have_prefix |
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val sub = relabel_proofs subst depth sub |
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val by = apfst (relabel_facts subst) by |
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in |
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Prove (qs, xs, l, t, sub, by) :: relabel_steps subst depth next steps |
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end |
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| relabel_steps subst depth next (step :: steps) = |
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step :: relabel_steps subst depth next steps |
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and relabel_proof subst depth (Proof (fix, assms, steps)) = |
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let val (assms, subst) = relabel_assms subst depth assms in |
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Proof (fix, assms, relabel_steps subst depth 1 steps) |
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end |
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and relabel_proofs subst depth = map (relabel_proof subst (depth + 1)) |
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in |
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relabel_proof [] 0 |
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end |
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val chain_direct_proof = |
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let |
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fun chain_qs_lfs NONE lfs = ([], lfs) |
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| chain_qs_lfs (SOME l0) lfs = |
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if member (op =) lfs l0 then ([Then], lfs |> remove (op =) l0) else ([], lfs) |
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fun chain_step lbl (Prove (qs, xs, l, t, subproofs, ((lfs, gfs), methss))) = |
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let val (qs', lfs) = chain_qs_lfs lbl lfs in |
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Prove (qs' @ qs, xs, l, t, chain_proofs subproofs, ((lfs, gfs), methss)) |
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end |
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| chain_step _ step = step |
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and chain_steps _ [] = [] |
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| chain_steps (prev as SOME _) (i :: is) = |
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chain_step prev i :: chain_steps (label_of_step i) is |
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| chain_steps _ (i :: is) = i :: chain_steps (label_of_step i) is |
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and chain_proof (Proof (fix, assms, steps)) = |
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Proof (fix, assms, chain_steps (try (List.last #> fst) assms) steps) |
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and chain_proofs proofs = map (chain_proof) proofs |
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in |
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chain_proof |
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end |
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type isar_params = |
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bool * string * string * Time.time * real * bool * (term, string) atp_step list * thm |
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val arith_methodss = |
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[[Arith_Method, Simp_Method, Auto_Method, Fastforce_Method, Blast_Method, Force_Method, |
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Metis_Method], [Meson_Method]] |
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val datatype_methodss = [[Simp_Size_Method, Simp_Method]] |
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val metislike_methodss = |
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[[Metis_Method, Simp_Method, Auto_Method, Arith_Method, Blast_Method, Fastforce_Method, |
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Force_Method], [Meson_Method]] |
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val rewrite_methodss = |
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[[Auto_Method, Simp_Method, Fastforce_Method, Force_Method, Metis_Method], [Meson_Method]] |
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val skolem_methodss = [[Metis_Method, Blast_Method], [Metis_New_Skolem_Method], [Meson_Method]] |
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fun isar_proof_text ctxt debug isar_proofs isar_params |
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(one_line_params as (_, _, _, _, subgoal, subgoal_count)) = |
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let |
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fun isar_proof_of () = |
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let |
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val SOME (verbose, metis_type_enc, metis_lam_trans, preplay_timeout, isar_compress, |
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isar_try0, atp_proof, goal) = try isar_params () |
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val (params, _, concl_t) = strip_subgoal goal subgoal ctxt |
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val (_, ctxt) = |
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params |
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|> map (fn (s, T) => (Binding.name s, SOME T, NoSyn)) |
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|> (fn fixes => ctxt |> Variable.set_body false |> Proof_Context.add_fixes fixes) |
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|
220 |
|
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221 |
val do_preplay = preplay_timeout <> Time.zeroTime |
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222 |
val isar_try0 = isar_try0 andalso do_preplay |
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223 |
|
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224 |
val is_fixed = Variable.is_declared ctxt orf can Name.dest_skolem |
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fun skolems_of t = Term.add_frees t [] |> filter_out (is_fixed o fst) |> rev |
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226 |
|
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|
227 |
fun get_role keep_role ((num, _), role, t, rule, _) = |
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228 |
if keep_role role then SOME ((raw_label_of_num num, t), rule) else NONE |
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|
229 |
|
49883 | 230 |
val atp_proof = |
231 |
atp_proof |
|
54755 | 232 |
|> rpair [] |-> fold_rev add_line_pass1 |
233 |
|> rpair [] |-> fold_rev add_line_pass2 |
|
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|
234 |
|> add_lines_pass3 [] |
54700 | 235 |
|
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|
236 |
val conjs = |
54700 | 237 |
map_filter (fn (name, role, _, _, _) => |
238 |
if member (op =) [Conjecture, Negated_Conjecture] role then SOME name else NONE) |
|
239 |
atp_proof |
|
54751 | 240 |
val assms = map_filter (Option.map fst o get_role (curry (op =) Hypothesis)) atp_proof |
54700 | 241 |
val lems = |
242 |
map_filter (get_role (curry (op =) Lemma)) atp_proof |
|
54751 | 243 |
|> map (fn ((l, t), rule) => |
54753 | 244 |
let |
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245 |
val (skos, methss) = |
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|
246 |
if is_skolemize_rule rule then (skolems_of t, skolem_methodss) |
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|
247 |
else if is_arith_rule rule then ([], arith_methodss) |
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248 |
else ([], rewrite_methodss) |
54753 | 249 |
in |
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|
250 |
Prove ([], skos, l, t, [], (([], []), methss)) |
54753 | 251 |
end) |
54700 | 252 |
|
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|
253 |
val bot = atp_proof |> List.last |> #1 |
54700 | 254 |
|
51145 | 255 |
val refute_graph = |
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256 |
atp_proof |
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257 |
|> map (fn (name, _, _, _, from) => (from, name)) |
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|
258 |
|> make_refute_graph bot |
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|
259 |
|> fold (Atom_Graph.default_node o rpair ()) conjs |
54700 | 260 |
|
51145 | 261 |
val axioms = axioms_of_refute_graph refute_graph conjs |
54700 | 262 |
|
51145 | 263 |
val tainted = tainted_atoms_of_refute_graph refute_graph conjs |
51156 | 264 |
val is_clause_tainted = exists (member (op =) tainted) |
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|
265 |
val steps = |
49883 | 266 |
Symtab.empty |
51201 | 267 |
|> fold (fn (name as (s, _), role, t, rule, _) => |
54758 | 268 |
Symtab.update_new (s, (rule, t |
269 |
|> (if is_clause_tainted [name] then |
|
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|
270 |
HOLogic.dest_Trueprop |
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|
271 |
#> role <> Conjecture ? s_not |
54758 | 272 |
#> fold exists_of (map Var (Term.add_vars t [])) |
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|
273 |
#> HOLogic.mk_Trueprop |
54758 | 274 |
else |
275 |
I)))) |
|
276 |
atp_proof |
|
54700 | 277 |
|
54755 | 278 |
val rule_of_clause_id = fst o the o Symtab.lookup steps o fst |
54700 | 279 |
|
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|
280 |
fun prop_of_clause [(num, _)] = Symtab.lookup steps num |> the |> snd |> close_form |
50016 | 281 |
| prop_of_clause names = |
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282 |
let |
54758 | 283 |
val lits = map (HOLogic.dest_Trueprop o snd) |
284 |
(map_filter (Symtab.lookup steps o fst) names) |
|
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|
285 |
in |
54754 | 286 |
(case List.partition (can HOLogic.dest_not) lits of |
50018
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|
287 |
(negs as _ :: _, pos as _ :: _) => |
54507 | 288 |
s_imp (Library.foldr1 s_conj (map HOLogic.dest_not negs), Library.foldr1 s_disj pos) |
54754 | 289 |
| _ => fold (curry s_disj) lits @{term False}) |
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|
290 |
end |
50016 | 291 |
|> HOLogic.mk_Trueprop |> close_form |
54700 | 292 |
|
55169 | 293 |
fun maybe_show outer c = (outer andalso eq_set (op =) (c, conjs)) ? cons Show |
54700 | 294 |
|
295 |
fun isar_steps outer predecessor accum [] = |
|
296 |
accum |
|
297 |
|> (if tainted = [] then |
|
298 |
cons (Prove (if outer then [Show] else [], [], no_label, concl_t, [], |
|
54767
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|
299 |
((the_list predecessor, []), metislike_methodss))) |
54700 | 300 |
else |
301 |
I) |
|
302 |
|> rev |
|
54755 | 303 |
| isar_steps outer _ accum (Have (id, (gamma, c)) :: infs) = |
54700 | 304 |
let |
305 |
val l = label_of_clause c |
|
306 |
val t = prop_of_clause c |
|
54755 | 307 |
val rule = rule_of_clause_id id |
308 |
val skolem = is_skolemize_rule rule |
|
309 |
||
54700 | 310 |
fun prove sub by = Prove (maybe_show outer c [], [], l, t, sub, by) |
311 |
fun do_rest l step = isar_steps outer (SOME l) (step :: accum) infs |
|
54755 | 312 |
|
313 |
val deps = fold add_fact_of_dependencies gamma no_facts |
|
54836 | 314 |
val methss = |
315 |
if is_arith_rule rule then arith_methodss |
|
316 |
else if is_datatype_rule rule then datatype_methodss |
|
317 |
else metislike_methodss |
|
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|
318 |
val by = (deps, methss) |
54700 | 319 |
in |
320 |
if is_clause_tainted c then |
|
54712 | 321 |
(case gamma of |
54700 | 322 |
[g] => |
54755 | 323 |
if skolem andalso is_clause_tainted g then |
54751 | 324 |
let val subproof = Proof (skolems_of (prop_of_clause g), [], rev accum) in |
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|
325 |
isar_steps outer (SOME l) [prove [subproof] (no_facts, skolem_methodss)] [] |
54700 | 326 |
end |
51148
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|
327 |
else |
54700 | 328 |
do_rest l (prove [] by) |
54712 | 329 |
| _ => do_rest l (prove [] by)) |
54700 | 330 |
else |
54765 | 331 |
do_rest l (if skolem then Prove ([], skolems_of t, l, t, [], by) else prove [] by) |
54700 | 332 |
end |
333 |
| isar_steps outer predecessor accum (Cases cases :: infs) = |
|
334 |
let |
|
335 |
fun isar_case (c, infs) = |
|
336 |
isar_proof false [] [(label_of_clause c, prop_of_clause c)] [] infs |
|
337 |
val c = succedent_of_cases cases |
|
338 |
val l = label_of_clause c |
|
339 |
val t = prop_of_clause c |
|
340 |
val step = |
|
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|
341 |
Prove (maybe_show outer c [], [], l, t, |
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|
342 |
map isar_case (filter_out (null o snd) cases), |
54767
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changeset
|
343 |
((the_list predecessor, []), metislike_methodss)) |
54700 | 344 |
in |
345 |
isar_steps outer (SOME l) (step :: accum) infs |
|
346 |
end |
|
347 |
and isar_proof outer fix assms lems infs = |
|
348 |
Proof (fix, assms, lems @ isar_steps outer NONE [] infs) |
|
349 |
||
54831 | 350 |
val (preplay_interface as {overall_preplay_outcome, ...}, isar_proof) = |
51145 | 351 |
refute_graph |
54699 | 352 |
(* |
54751 | 353 |
|> tap (tracing o prefix "Refute graph: " o string_of_refute_graph) |
54699 | 354 |
*) |
51031
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changeset
|
355 |
|> redirect_graph axioms tainted bot |
54699 | 356 |
(* |
54751 | 357 |
|> tap (tracing o prefix "Direct proof: " o string_of_direct_proof) |
54699 | 358 |
*) |
54754 | 359 |
|> isar_proof true params assms lems |
54712 | 360 |
|> postprocess_remove_unreferenced_steps I |
52556
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completely rewrote SH compress; added two parameters for experimentation/fine grained control
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changeset
|
361 |
|> relabel_proof_canonically |
54500 | 362 |
|> `(proof_preplay_interface debug ctxt metis_type_enc metis_lam_trans do_preplay |
53761
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use configuration mechanism for low-level tracing
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53586
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changeset
|
363 |
preplay_timeout) |
54754 | 364 |
|
54828 | 365 |
val (play_outcome, isar_proof) = |
52556
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completely rewrote SH compress; added two parameters for experimentation/fine grained control
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changeset
|
366 |
isar_proof |
54501 | 367 |
|> compress_proof (if isar_proofs = SOME true then isar_compress else 1000.0) |
53762 | 368 |
preplay_interface |
52632
23393c31c7fe
added sledgehammer parameters isar_try0 and isar_minimize and their negative aliases
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diff
changeset
|
369 |
|> isar_try0 ? try0 preplay_timeout preplay_interface |
54712 | 370 |
|> postprocess_remove_unreferenced_steps (isar_try0 ? min_deps_of_step preplay_interface) |
54831 | 371 |
|> `overall_preplay_outcome |
54758 | 372 |
||> (chain_direct_proof #> kill_useless_labels_in_proof #> relabel_proof) |
54754 | 373 |
|
54500 | 374 |
val isar_text = |
375 |
string_of_proof ctxt metis_type_enc metis_lam_trans subgoal subgoal_count isar_proof |
|
49883 | 376 |
in |
54754 | 377 |
(case isar_text of |
49883 | 378 |
"" => |
51190
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made "isar_proofs" a 3-way option, to provide a way to totally disable isar_proofs if desired
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changeset
|
379 |
if isar_proofs = SOME true then |
50671 | 380 |
"\nNo structured proof available (proof too simple)." |
49883 | 381 |
else |
382 |
"" |
|
383 |
| _ => |
|
50670
eaa540986291
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changeset
|
384 |
let |
eaa540986291
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diff
changeset
|
385 |
val msg = |
51203 | 386 |
(if verbose then |
54828 | 387 |
let val num_steps = add_proof_steps (steps_of_proof isar_proof) 0 in |
388 |
[string_of_int num_steps ^ " step" ^ plural_s num_steps] |
|
389 |
end |
|
51203 | 390 |
else |
391 |
[]) @ |
|
54828 | 392 |
(if do_preplay then [string_of_play_outcome play_outcome] else []) |
50277 | 393 |
in |
54507 | 394 |
"\n\nStructured proof" ^ (commas msg |> not (null msg) ? enclose " (" ")") ^ ":\n" ^ |
395 |
Active.sendback_markup [Markup.padding_command] isar_text |
|
54754 | 396 |
end) |
49883 | 397 |
end |
54760
a1ac3eaa0d11
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diff
changeset
|
398 |
|
55168
948e8b7ea82f
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blanchet
parents:
54838
diff
changeset
|
399 |
val one_line_proof = one_line_proof_text 0 one_line_params |
49883 | 400 |
val isar_proof = |
401 |
if debug then |
|
402 |
isar_proof_of () |
|
54754 | 403 |
else |
404 |
(case try isar_proof_of () of |
|
405 |
SOME s => s |
|
406 |
| NONE => |
|
407 |
if isar_proofs = SOME true then "\nWarning: The Isar proof construction failed." else "") |
|
49883 | 408 |
in one_line_proof ^ isar_proof end |
409 |
||
54824 | 410 |
fun isar_proof_would_be_a_good_idea (reconstr, play) = |
411 |
(case play of |
|
412 |
Played _ => reconstr = SMT |
|
54823 | 413 |
| Play_Timed_Out _ => true |
54824 | 414 |
| Play_Failed => true |
415 |
| Not_Played => false) |
|
51187
c344cf148e8f
avoid using "smt" for minimization -- better use the prover itself, since then Sledgehammer gets to try metis again and gives the opportunity to output an Isar proof -- and show Isar proof as fallback for SMT proofs
blanchet
parents:
51179
diff
changeset
|
416 |
|
55168
948e8b7ea82f
correctly handle exceptions arising from (experimental) Isar proof code
blanchet
parents:
54838
diff
changeset
|
417 |
fun proof_text ctxt debug isar_proofs isar_params num_chained |
49883 | 418 |
(one_line_params as (preplay, _, _, _, _, _)) = |
51190
2654b3965c8d
made "isar_proofs" a 3-way option, to provide a way to totally disable isar_proofs if desired
blanchet
parents:
51187
diff
changeset
|
419 |
(if isar_proofs = SOME true orelse |
2654b3965c8d
made "isar_proofs" a 3-way option, to provide a way to totally disable isar_proofs if desired
blanchet
parents:
51187
diff
changeset
|
420 |
(isar_proofs = NONE andalso isar_proof_would_be_a_good_idea preplay) then |
55168
948e8b7ea82f
correctly handle exceptions arising from (experimental) Isar proof code
blanchet
parents:
54838
diff
changeset
|
421 |
isar_proof_text ctxt debug isar_proofs isar_params |
49883 | 422 |
else |
53052
a0db255af8c5
sledgehammer sendback always uses Markup.padding_command: sensible default for most practical applications -- old-style in-line replacement is superseded by auto mode or panel;
wenzelm
parents:
53047
diff
changeset
|
423 |
one_line_proof_text num_chained) one_line_params |
49883 | 424 |
|
425 |
end; |