src/Sequents/prover.ML
 changeset 2073 fb0655539d05 child 3538 ed9de44032e0
```--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/Sequents/prover.ML	Wed Oct 09 13:32:33 1996 +0200
@@ -0,0 +1,223 @@
+(*  Title:      LK/LK.ML
+    ID:         \$Id\$
+    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
+    Copyright   1992  University of Cambridge
+*)
+
+
+(**** Theorem Packs ****)
+
+(* based largely on LK *)
+
+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([],[]);
+
+
+    Pack(sort less (ths@safes), unsafes);
+
+    Pack(safes, sort less (ths@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 (fn 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_goal_tac (Pack(safes,unsafes)) = reresolve_tac safes;
+
+(*Tries a safe rule or else a unsafe rule.  Single-step for tracing. *)
+fun step_tac (thm_pack as Pack(safes,unsafes)) =
+    safe_goal_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));
+
+
+
+signature MODAL_PROVER_RULE =
+sig
+    val rewrite_rls      : thm list
+    val safe_rls         : thm list
+    val unsafe_rls       : thm list
+    val bound_rls        : thm list
+    val aside_rls        : thm list
+end;
+
+signature MODAL_PROVER =
+sig
+    val rule_tac   : thm list -> int ->tactic
+    val step_tac   : int -> tactic
+    val solven_tac : int -> int -> tactic
+    val solve_tac  : int -> tactic
+end;
+
+functor Modal_ProverFun (Modal_Rule: MODAL_PROVER_RULE) : MODAL_PROVER =
+struct
+local open Modal_Rule
+in
+
+(*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.*)
+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 G|-H could be resolved, comparing each side.*)
+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)
+    | _ => 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 resolve_tac rls i
+  end);
+
+fun fresolve_tac rls n = filseq_resolve_tac rls 999 n;
+
+(* NB No back tracking possible with aside rules *)
+
+fun aside_tac n = DETERM(REPEAT (filt_resolve_tac aside_rls 999 n));
+fun rule_tac rls n = fresolve_tac rls n THEN aside_tac n;
+
+val fres_safe_tac = fresolve_tac safe_rls;
+val fres_unsafe_tac = fresolve_tac unsafe_rls THEN' aside_tac;
+val fres_bound_tac = fresolve_tac bound_rls;
+
+fun UPTOGOAL n tf = let fun tac i = if i<n then all_tac
+                                    else tf(i) THEN tac(i-1)
+                    in STATE(fn state=> tac(nprems_of state)) end;
+
+(* Depth first search bounded by d *)
+fun solven_tac d n = STATE (fn state =>
+        if d<0 then no_tac
+        else if (nprems_of state = 0) then all_tac
+        else (DETERM(fres_safe_tac n) THEN UPTOGOAL n (solven_tac d)) ORELSE
+                 ((fres_unsafe_tac n  THEN UPTOGOAL n (solven_tac d)) APPEND
+                   (fres_bound_tac n  THEN UPTOGOAL n (solven_tac (d-1)))));
+
+fun solve_tac d = rewrite_goals_tac rewrite_rls THEN solven_tac d 1;
+
+fun step_tac n = STATE (fn state =>
+      if (nprems_of state = 0) then all_tac
+      else (DETERM(fres_safe_tac n)) ORELSE
+           (fres_unsafe_tac n APPEND fres_bound_tac n));
+
+end;
+end;```