author | blanchet |
Mon, 03 Feb 2014 10:14:18 +0100 | |
changeset 55263 | 4d63fffcde8d |
parent 55260 | ada3ae6458d4 |
child 55264 | 43473497fb65 |
permissions | -rw-r--r-- |
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(* Title: HOL/Tools/Sledgehammer/sledgehammer_isar.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_ISAR = |
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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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val trace : bool Config.T |
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type isar_params = |
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bool * (string option * string option) * Time.time * real * bool |
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* (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_Isar : SLEDGEHAMMER_ISAR = |
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struct |
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||
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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_Proof_Reconstruct |
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open Sledgehammer_Util |
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open Sledgehammer_Reconstructor |
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open Sledgehammer_Isar_Proof |
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open Sledgehammer_Isar_Preplay |
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open Sledgehammer_Isar_Compress |
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open Sledgehammer_Isar_Try0 |
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open Sledgehammer_Isar_Minimize |
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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 trace = Attrib.setup_config_bool @{binding sledgehammer_isar_trace} (K false) |
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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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fun add_lines_pass2 res [] = rev res |
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| add_lines_pass2 res ((name, role, t, rule, deps) :: lines) = |
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let |
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val is_last_line = null lines |
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fun looks_interesting () = |
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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 not (can the_single lines) |
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fun is_skolemizing_line (_, _, _, rule', deps') = |
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is_skolemize_rule rule' andalso member (op =) deps' name |
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fun is_before_skolemize_rule () = exists is_skolemizing_line lines |
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in |
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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 is_last_line orelse looks_interesting () orelse |
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is_before_skolemize_rule () then |
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add_lines_pass2 ((name, role, t, rule, deps) :: res) lines |
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else |
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add_lines_pass2 res (map (replace_dependencies_in_line (name, deps)) lines) |
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end |
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type isar_params = |
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bool * (string option * string option) * Time.time * real * bool * (term, string) atp_step list |
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* thm |
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val arith_methods = |
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[Arith_Method, Simp_Method, Auto_Method, Fastforce_Method, Blast_Method, Force_Method, |
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Algebra_Method, Metis_Method (NONE, NONE), Meson_Method] |
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val datatype_methods = [Simp_Method, Simp_Size_Method] |
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val metislike_methods0 = |
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[Metis_Method (NONE, NONE), Simp_Method, Auto_Method, Arith_Method, Blast_Method, |
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Fastforce_Method, Force_Method, Algebra_Method, Meson_Method] |
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val rewrite_methods = |
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[Auto_Method, Simp_Method, Fastforce_Method, Force_Method, Metis_Method (NONE, NONE), |
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Meson_Method] |
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val skolem_methods = [Metis_Method (NONE, NONE), Blast_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, alt_metis_args, preplay_timeout, compress_isar, try0_isar, atp_proof, |
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goal) = try isar_params () |
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val metislike_methods = insert (op =) (Metis_Method alt_metis_args) metislike_methods0 |
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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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val do_preplay = preplay_timeout <> Time.zeroTime |
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val try0_isar = try0_isar andalso do_preplay |
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val compress_isar = if isar_proofs = NONE andalso do_preplay then 1000.0 else compress_isar |
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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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fun get_role keep_role ((num, _), role, t, rule, _) = |
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if keep_role role then SOME ((raw_label_of_num num, t), rule) else NONE |
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val atp_proof = |
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atp_proof |
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|> rpair [] |-> fold_rev add_line_pass1 |
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|> add_lines_pass2 [] |
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val conjs = |
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map_filter (fn (name, role, _, _, _) => |
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if member (op =) [Conjecture, Negated_Conjecture] role then SOME name else NONE) |
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atp_proof |
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val assms = map_filter (Option.map fst o get_role (curry (op =) Hypothesis)) atp_proof |
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val lems = |
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map_filter (get_role (curry (op =) Lemma)) atp_proof |
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|> map (fn ((l, t), rule) => |
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let |
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val (skos, meths) = |
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if is_skolemize_rule rule then (skolems_of t, skolem_methods) |
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else if is_arith_rule rule then ([], arith_methods) |
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else ([], rewrite_methods) |
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in |
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Prove ([], skos, l, t, [], (([], []), meths)) |
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end) |
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val bot = atp_proof |> List.last |> #1 |
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val refute_graph = |
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atp_proof |
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|> map (fn (name, _, _, _, from) => (from, name)) |
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|> make_refute_graph bot |
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|> fold (Atom_Graph.default_node o rpair ()) conjs |
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val axioms = axioms_of_refute_graph refute_graph conjs |
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val tainted = tainted_atoms_of_refute_graph refute_graph conjs |
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val is_clause_tainted = exists (member (op =) tainted) |
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val steps = |
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Symtab.empty |
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|> fold (fn (name as (s, _), role, t, rule, _) => |
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Symtab.update_new (s, (rule, t |
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|> (if is_clause_tainted [name] then |
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HOLogic.dest_Trueprop |
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#> role <> Conjecture ? s_not |
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#> fold exists_of (map Var (Term.add_vars t [])) |
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#> HOLogic.mk_Trueprop |
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else |
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I)))) |
|
198 |
atp_proof |
|
54700 | 199 |
|
54755 | 200 |
val rule_of_clause_id = fst o the o Symtab.lookup steps o fst |
54700 | 201 |
|
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fun prop_of_clause [(num, _)] = Symtab.lookup steps num |> the |> snd |> close_form |
50016 | 203 |
| prop_of_clause names = |
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204 |
let |
54758 | 205 |
val lits = map (HOLogic.dest_Trueprop o snd) |
206 |
(map_filter (Symtab.lookup steps o fst) names) |
|
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|
207 |
in |
54754 | 208 |
(case List.partition (can HOLogic.dest_not) lits of |
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|
209 |
(negs as _ :: _, pos as _ :: _) => |
54507 | 210 |
s_imp (Library.foldr1 s_conj (map HOLogic.dest_not negs), Library.foldr1 s_disj pos) |
54754 | 211 |
| _ => fold (curry s_disj) lits @{term False}) |
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|
212 |
end |
50016 | 213 |
|> HOLogic.mk_Trueprop |> close_form |
54700 | 214 |
|
55169 | 215 |
fun maybe_show outer c = (outer andalso eq_set (op =) (c, conjs)) ? cons Show |
54700 | 216 |
|
217 |
fun isar_steps outer predecessor accum [] = |
|
218 |
accum |
|
219 |
|> (if tainted = [] then |
|
220 |
cons (Prove (if outer then [Show] else [], [], no_label, concl_t, [], |
|
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|
221 |
((the_list predecessor, []), metislike_methods))) |
54700 | 222 |
else |
223 |
I) |
|
224 |
|> rev |
|
54755 | 225 |
| isar_steps outer _ accum (Have (id, (gamma, c)) :: infs) = |
54700 | 226 |
let |
227 |
val l = label_of_clause c |
|
228 |
val t = prop_of_clause c |
|
54755 | 229 |
val rule = rule_of_clause_id id |
230 |
val skolem = is_skolemize_rule rule |
|
231 |
||
54700 | 232 |
fun prove sub by = Prove (maybe_show outer c [], [], l, t, sub, by) |
233 |
fun do_rest l step = isar_steps outer (SOME l) (step :: accum) infs |
|
54755 | 234 |
|
235 |
val deps = fold add_fact_of_dependencies gamma no_facts |
|
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|
236 |
val meths = |
55245 | 237 |
if skolem then skolem_methods |
238 |
else if is_arith_rule rule then arith_methods |
|
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|
239 |
else if is_datatype_rule rule then datatype_methods |
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|
240 |
else metislike_methods |
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|
241 |
val by = (deps, meths) |
54700 | 242 |
in |
243 |
if is_clause_tainted c then |
|
54712 | 244 |
(case gamma of |
54700 | 245 |
[g] => |
54755 | 246 |
if skolem andalso is_clause_tainted g then |
54751 | 247 |
let val subproof = Proof (skolems_of (prop_of_clause g), [], rev accum) in |
55245 | 248 |
isar_steps outer (SOME l) [prove [subproof] (no_facts, meths)] infs |
54700 | 249 |
end |
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|
250 |
else |
54700 | 251 |
do_rest l (prove [] by) |
54712 | 252 |
| _ => do_rest l (prove [] by)) |
54700 | 253 |
else |
54765 | 254 |
do_rest l (if skolem then Prove ([], skolems_of t, l, t, [], by) else prove [] by) |
54700 | 255 |
end |
256 |
| isar_steps outer predecessor accum (Cases cases :: infs) = |
|
257 |
let |
|
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|
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fun isar_case (c, subinfs) = |
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|
259 |
isar_proof false [] [(label_of_clause c, prop_of_clause c)] [] subinfs |
54700 | 260 |
val c = succedent_of_cases cases |
261 |
val l = label_of_clause c |
|
262 |
val t = prop_of_clause c |
|
263 |
val step = |
|
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|
264 |
Prove (maybe_show outer c [], [], l, t, |
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|
265 |
map isar_case (filter_out (null o snd) cases), |
55244
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|
266 |
((the_list predecessor, []), metislike_methods)) |
54700 | 267 |
in |
268 |
isar_steps outer (SOME l) (step :: accum) infs |
|
269 |
end |
|
270 |
and isar_proof outer fix assms lems infs = |
|
271 |
Proof (fix, assms, lems @ isar_steps outer NONE [] infs) |
|
272 |
||
55257 | 273 |
val string_of_isar_proof = string_of_isar_proof ctxt subgoal subgoal_count |
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changeset
|
274 |
|
55222 | 275 |
val trace = Config.get ctxt trace |
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changeset
|
276 |
|
55256 | 277 |
val canonical_isar_proof = |
51145 | 278 |
refute_graph |
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|
279 |
|> trace ? tap (tracing o prefix "Refute graph: " o string_of_refute_graph) |
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|
280 |
|> redirect_graph axioms tainted bot |
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|
281 |
|> trace ? tap (tracing o prefix "Direct proof: " o string_of_direct_proof) |
54754 | 282 |
|> isar_proof true params assms lems |
55213 | 283 |
|> postprocess_isar_proof_remove_unreferenced_steps I |
284 |
|> relabel_isar_proof_canonically |
|
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|
285 |
|
55256 | 286 |
val preplay_ctxt = ctxt |
287 |
|> enrich_context_with_local_facts canonical_isar_proof |
|
288 |
|> silence_reconstructors debug |
|
289 |
||
55260 | 290 |
val preplay_data = Unsynchronized.ref Canonical_Label_Tab.empty |
291 |
||
55263 | 292 |
fun init_preplay_outcomes (step as Prove (_, _, l, _, _, (_, meths))) = |
55260 | 293 |
set_preplay_outcomes_of_isar_step preplay_data l (map (fn meth => (meth, |
294 |
Lazy.lazy (fn () => preplay_isar_step preplay_ctxt preplay_timeout meth step))) |
|
295 |
meths) |
|
55263 | 296 |
| init_preplay_outcomes _ = () |
55260 | 297 |
|
55263 | 298 |
val _ = fold_isar_steps (K o init_preplay_outcomes) |
55260 | 299 |
(steps_of_isar_proof canonical_isar_proof) () |
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changeset
|
300 |
|
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|
301 |
fun str_of_preplay_outcome outcome = |
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|
302 |
if Lazy.is_finished outcome then string_of_play_outcome (Lazy.force outcome) else "?" |
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changeset
|
303 |
|
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parents:
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changeset
|
304 |
fun str_of_meth l meth = |
55260 | 305 |
string_of_proof_method meth ^ " " ^ |
306 |
str_of_preplay_outcome (preplay_outcome_of_isar_step (!preplay_data) l meth) |
|
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|
307 |
fun comment_of l = map (str_of_meth l) #> commas |
55222 | 308 |
|
55214
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changeset
|
309 |
fun trace_isar_proof label proof = |
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|
310 |
if trace then |
55222 | 311 |
tracing (timestamp () ^ "\n" ^ label ^ ":\n\n" ^ string_of_isar_proof comment_of proof ^ |
312 |
"\n") |
|
55214
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changeset
|
313 |
else |
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changeset
|
314 |
() |
54754 | 315 |
|
54828 | 316 |
val (play_outcome, isar_proof) = |
55256 | 317 |
canonical_isar_proof |
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|
318 |
|> tap (trace_isar_proof "Original") |
55258 | 319 |
|> compress_isar_proof preplay_ctxt compress_isar preplay_data |
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changeset
|
320 |
|> tap (trace_isar_proof "Compressed") |
55258 | 321 |
|> try0_isar ? try0_isar_proof preplay_ctxt preplay_timeout preplay_data |
55214
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changeset
|
322 |
|> tap (trace_isar_proof "Tried0") |
55213 | 323 |
|> postprocess_isar_proof_remove_unreferenced_steps |
55258 | 324 |
(try0_isar ? minimize_isar_step_dependencies preplay_ctxt preplay_data) |
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changeset
|
325 |
|> tap (trace_isar_proof "Minimized") |
55260 | 326 |
|> `(preplay_outcome_of_isar_proof (!preplay_data)) |
55220 | 327 |
||> chain_isar_proof |
328 |
||> kill_useless_labels_in_isar_proof |
|
329 |
||> relabel_isar_proof_finally |
|
49883 | 330 |
in |
55222 | 331 |
(case string_of_isar_proof (K (K "")) isar_proof of |
49883 | 332 |
"" => |
55213 | 333 |
if isar_proofs = SOME true then "\nNo structured proof available (proof too simple)." |
334 |
else "" |
|
55214
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changeset
|
335 |
| isar_text => |
50670
eaa540986291
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diff
changeset
|
336 |
let |
eaa540986291
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50557
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changeset
|
337 |
val msg = |
51203 | 338 |
(if verbose then |
55260 | 339 |
let val num_steps = add_isar_steps (steps_of_isar_proof isar_proof) 0 in |
55213 | 340 |
[string_of_int num_steps ^ " step" ^ plural_s num_steps] |
341 |
end |
|
51203 | 342 |
else |
343 |
[]) @ |
|
54828 | 344 |
(if do_preplay then [string_of_play_outcome play_outcome] else []) |
50277 | 345 |
in |
54507 | 346 |
"\n\nStructured proof" ^ (commas msg |> not (null msg) ? enclose " (" ")") ^ ":\n" ^ |
347 |
Active.sendback_markup [Markup.padding_command] isar_text |
|
54754 | 348 |
end) |
49883 | 349 |
end |
54760
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changeset
|
350 |
|
55168
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54838
diff
changeset
|
351 |
val one_line_proof = one_line_proof_text 0 one_line_params |
49883 | 352 |
val isar_proof = |
353 |
if debug then |
|
354 |
isar_proof_of () |
|
54754 | 355 |
else |
356 |
(case try isar_proof_of () of |
|
357 |
SOME s => s |
|
358 |
| NONE => |
|
359 |
if isar_proofs = SOME true then "\nWarning: The Isar proof construction failed." else "") |
|
49883 | 360 |
in one_line_proof ^ isar_proof end |
361 |
||
54824 | 362 |
fun isar_proof_would_be_a_good_idea (reconstr, play) = |
363 |
(case play of |
|
364 |
Played _ => reconstr = SMT |
|
54823 | 365 |
| Play_Timed_Out _ => true |
54824 | 366 |
| Play_Failed => true |
367 |
| 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
|
368 |
|
55168
948e8b7ea82f
correctly handle exceptions arising from (experimental) Isar proof code
blanchet
parents:
54838
diff
changeset
|
369 |
fun proof_text ctxt debug isar_proofs isar_params num_chained |
55256 | 370 |
(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
|
371 |
(if isar_proofs = SOME true orelse |
2654b3965c8d
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blanchet
parents:
51187
diff
changeset
|
372 |
(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
|
373 |
isar_proof_text ctxt debug isar_proofs isar_params |
49883 | 374 |
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
|
375 |
one_line_proof_text num_chained) one_line_params |
49883 | 376 |
|
377 |
end; |