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src/Sequents/prover.ML

author | paulson |

Tue, 27 Jul 1999 19:01:46 +0200 | |

changeset 7097 | 5ab37ed3d53c |

parent 6054 | 4a4f6ad607a1 |

child 7122 | 87b233b31889 |

permissions | -rw-r--r-- |

moved the modal prover to modal.ML; installed the prover using TheoryDataFun

(* Title: LK/LK.ML ID: $Id$ Author: Lawrence C Paulson, Cambridge University Computer Laboratory Copyright 1992 University of Cambridge Simple classical reasoner for the sequent calculus, based on "theorem packs" *) (*Higher precedence than := facilitates use of references*) infix 4 add_safes add_unsafes; datatype pack = Pack of thm list * thm list; (*A theorem pack has the form (safe rules, unsafe rules) An unsafe rule is incomplete or introduces variables in subgoals, and is tried only when the safe rules are not applicable. *) fun less (rl1,rl2) = (nprems_of rl1) < (nprems_of rl2); val empty_pack = Pack([],[]); fun warn_duplicates [] = [] | warn_duplicates dups = (warning (String.concat ("Ignoring duplicate theorems:\n":: map (suffix "\n" o string_of_thm) dups)); dups); fun (Pack(safes,unsafes)) add_safes ths = let val dups = warn_duplicates (gen_inter eq_thm (ths,safes)) val ths' = gen_rems eq_thm (ths,dups) in Pack(sort (make_ord less) (ths'@safes), unsafes) end; fun (Pack(safes,unsafes)) add_unsafes ths = let val dups = warn_duplicates (gen_inter eq_thm (ths,unsafes)) val ths' = gen_rems eq_thm (ths,dups) in Pack(safes, sort (make_ord less) (ths'@unsafes)) end; fun merge_pack (Pack(safes,unsafes), Pack(safes',unsafes')) = Pack(sort (make_ord less) (safes@safes'), sort (make_ord less) (unsafes@unsafes')); fun print_pack (Pack(safes,unsafes)) = (writeln "Safe rules:"; print_thms safes; writeln "Unsafe rules:"; print_thms unsafes); (*Returns the list of all formulas in the sequent*) fun forms_of_seq (Const("SeqO'",_) $ P $ u) = P :: forms_of_seq u | forms_of_seq (H $ u) = forms_of_seq u | forms_of_seq _ = []; (*Tests whether two sequences (left or right sides) could be resolved. seqp is a premise (subgoal), seqc is a conclusion of an object-rule. Assumes each formula in seqc is surrounded by sequence variables -- checks that each concl formula looks like some subgoal formula. It SHOULD check order as well, using recursion rather than forall/exists*) fun could_res (seqp,seqc) = forall (fn Qc => exists (fn Qp => could_unify (Qp,Qc)) (forms_of_seq seqp)) (forms_of_seq seqc); (*Tests whether two sequents or pairs of sequents could be resolved*) fun could_resolve_seq (prem,conc) = case (prem,conc) of (_ $ Abs(_,_,leftp) $ Abs(_,_,rightp), _ $ Abs(_,_,leftc) $ Abs(_,_,rightc)) => could_res (leftp,leftc) andalso could_res (rightp,rightc) | (_ $ Abs(_,_,leftp) $ rightp, _ $ Abs(_,_,leftc) $ rightc) => could_res (leftp,leftc) andalso could_unify (rightp,rightc) | _ => false; (*Like filt_resolve_tac, using could_resolve_seq Much faster than resolve_tac when there are many rules. Resolve subgoal i using the rules, unless more than maxr are compatible. *) fun filseq_resolve_tac rules maxr = SUBGOAL(fn (prem,i) => let val rls = filter_thms could_resolve_seq (maxr+1, prem, rules) in if length rls > maxr then no_tac else (*((rtac derelict 1 THEN rtac impl 1 THEN (rtac identity 2 ORELSE rtac ll_mp 2) THEN rtac context1 1) ORELSE *) resolve_tac rls i end); (*Predicate: does the rule have n premises? *) fun has_prems n rule = (nprems_of rule = n); (*Continuation-style tactical for resolution. The list of rules is partitioned into 0, 1, 2 premises. The resulting tactic, gtac, tries to resolve with rules. If successful, it recursively applies nextac to the new subgoals only. Else fails. (Treatment of goals due to Ph. de Groote) Bind (RESOLVE_THEN rules) to a variable: it preprocesses the rules. *) (*Takes rule lists separated in to 0, 1, 2, >2 premises. The abstraction over state prevents needless divergence in recursion. The 9999 should be a parameter, to delay treatment of flexible goals. *) fun RESOLVE_THEN rules = let val [rls0,rls1,rls2] = partition_list has_prems 0 2 rules; fun tac nextac i state = state |> (filseq_resolve_tac rls0 9999 i ORELSE (DETERM(filseq_resolve_tac rls1 9999 i) THEN TRY(nextac i)) ORELSE (DETERM(filseq_resolve_tac rls2 9999 i) THEN TRY(nextac(i+1)) THEN TRY(nextac i))) in tac end; (*repeated resolution applied to the designated goal*) fun reresolve_tac rules = let val restac = RESOLVE_THEN rules; (*preprocessing done now*) fun gtac i = restac gtac i in gtac end; (*tries the safe rules repeatedly before the unsafe rules. *) fun repeat_goal_tac (Pack(safes,unsafes)) = let val restac = RESOLVE_THEN safes and lastrestac = RESOLVE_THEN unsafes; fun gtac i = restac gtac i ORELSE (print_tac "" THEN lastrestac gtac i) in gtac end; (*Tries safe rules only*) fun safe_tac (Pack(safes,unsafes)) = reresolve_tac safes; val safe_goal_tac = safe_tac; (*backwards compatibility*) (*Tries a safe rule or else a unsafe rule. Single-step for tracing. *) fun step_tac (thm_pack as Pack(safes,unsafes)) = safe_tac thm_pack ORELSE' filseq_resolve_tac unsafes 9999; (* Tactic for reducing a goal, using Predicate Calculus rules. A decision procedure for Propositional Calculus, it is incomplete for Predicate-Calculus because of allL_thin and exR_thin. Fails if it can do nothing. *) fun pc_tac thm_pack = SELECT_GOAL (DEPTH_SOLVE (repeat_goal_tac thm_pack 1)); (*The following two tactics are analogous to those provided by Provers/classical. In fact, pc_tac is usually FASTER than fast_tac!*) fun fast_tac thm_pack = SELECT_GOAL (DEPTH_SOLVE (step_tac thm_pack 1)); fun best_tac thm_pack = SELECT_GOAL (BEST_FIRST (has_fewer_prems 1, size_of_thm) (step_tac thm_pack 1)); structure ProverArgs = struct val name = "Sequents/prover"; type T = pack ref; val empty = ref empty_pack fun copy (ref pack) = ref pack; val prep_ext = copy; fun merge (ref pack1, ref pack2) = ref (merge_pack (pack1, pack2)); fun print _ (ref pack) = print_pack pack; end; structure ProverData = TheoryDataFun(ProverArgs); val prover_setup = [ProverData.init]; val print_thm_pack = ProverData.print; val thm_pack_ref_of_sg = ProverData.get_sg; val thm_pack_ref_of = ProverData.get; (* access global thm_pack *) val thm_pack_of_sg = ! o thm_pack_ref_of_sg; val thm_pack_of = thm_pack_of_sg o sign_of; val thm_pack = thm_pack_of o Context.the_context; val thm_pack_ref = thm_pack_ref_of_sg o sign_of o Context.the_context; (* change global thm_pack *) fun change_thm_pack f x = thm_pack_ref () := (f (thm_pack (), x)); val Add_safes = change_thm_pack (op add_safes); val Add_unsafes = change_thm_pack (op add_unsafes);