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(* Title: Provers/clasimp.ML
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ID: $Id$
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Author: David von Oheimb, TU Muenchen
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Combination of classical reasoner and simplifier (depends on
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simplifier.ML, classical.ML, blast.ML).
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*)
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infix 4 addSIs2 addSEs2 addSDs2 addIs2 addEs2 addDs2 addsimps2 delsimps2;
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infix 4 addSss addss;
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signature CLASIMP_DATA =
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sig
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structure Simplifier: SIMPLIFIER
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structure Classical: CLASSICAL
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structure Blast: BLAST
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sharing type Classical.claset = Blast.claset
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end
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signature CLASIMP =
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sig
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include CLASIMP_DATA
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type claset
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type simpset
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type clasimpset
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val addSIs2 : clasimpset * thm list -> clasimpset
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val addSEs2 : clasimpset * thm list -> clasimpset
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val addSDs2 : clasimpset * thm list -> clasimpset
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val addIs2 : clasimpset * thm list -> clasimpset
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val addEs2 : clasimpset * thm list -> clasimpset
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val addDs2 : clasimpset * thm list -> clasimpset
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val addsimps2 : clasimpset * thm list -> clasimpset
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val delsimps2 : clasimpset * thm list -> clasimpset
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val addSss : claset * simpset -> claset
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val addss : claset * simpset -> claset
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val CLASIMPSET :(clasimpset -> tactic) -> tactic
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val CLASIMPSET' :(clasimpset -> 'a -> tactic) -> 'a -> tactic
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val clarsimp_tac: clasimpset -> int -> tactic
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val Clarsimp_tac: int -> tactic
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val mk_auto_tac : clasimpset -> int -> int -> tactic
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val auto_tac : clasimpset -> tactic
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val Auto_tac : tactic
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val auto : unit -> unit
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val force_tac : clasimpset -> int -> tactic
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val Force_tac : int -> tactic
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val force : int -> unit
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end;
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functor ClasimpFun(Data: CLASIMP_DATA): CLASIMP =
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struct
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open Data;
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type claset = Classical.claset;
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type simpset = Simplifier.simpset;
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type clasimpset = claset * simpset;
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(* clasimpset operations *)
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(*this interface for updating a clasimpset is rudimentary and just for
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convenience for the most common cases*)
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fun pair_upd1 f ((a,b),x) = (f(a,x), b);
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fun pair_upd2 f ((a,b),x) = (a, f(b,x));
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fun op addSIs2 arg = pair_upd1 Classical.addSIs arg;
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fun op addSEs2 arg = pair_upd1 Classical.addSEs arg;
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fun op addSDs2 arg = pair_upd1 Classical.addSDs arg;
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fun op addIs2 arg = pair_upd1 Classical.addIs arg;
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fun op addEs2 arg = pair_upd1 Classical.addEs arg;
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fun op addDs2 arg = pair_upd1 Classical.addDs arg;
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fun op addsimps2 arg = pair_upd2 Simplifier.addsimps arg;
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fun op delsimps2 arg = pair_upd2 Simplifier.delsimps arg;
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(*Add a simpset to a classical set!*)
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(*Caution: only one simpset added can be added by each of addSss and addss*)
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fun cs addSss ss = op Classical.addSaltern (cs, ("safe_asm_full_simp_tac",
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CHANGED o Simplifier.safe_asm_full_simp_tac ss));
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fun cs addss ss = op Classical.addbefore (cs, ("asm_full_simp_tac",
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CHANGED o Simplifier.asm_full_simp_tac ss));
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(* tacticals *)
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fun CLASIMPSET tacf state =
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Classical.CLASET (fn cs => Simplifier.SIMPSET (fn ss => tacf (cs, ss))) state;
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fun CLASIMPSET' tacf i state =
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Classical.CLASET (fn cs => Simplifier.SIMPSET (fn ss => tacf (cs, ss) i)) state;
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fun clarsimp_tac (cs, ss) = Simplifier.safe_asm_full_simp_tac ss THEN_MAYBE'
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Classical.clarify_tac (cs addSss ss);
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fun Clarsimp_tac i = clarsimp_tac (Classical.claset(), Simplifier.simpset()) i;
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(* auto_tac *)
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fun blast_depth_tac cs m i thm =
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Blast.depth_tac cs m i thm
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handle Blast.TRANS s => (warning ("Blast_tac: " ^ s); Seq.empty);
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(* a variant of depth_tac that avoids interference of the simplifier
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with dup_step_tac when they are combined by auto_tac *)
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fun nodup_depth_tac cs m i state = CHANGED (SELECT_GOAL
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(REPEAT_DETERM1 (COND (has_fewer_prems 1) no_tac
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(Classical.safe_step_tac cs 1))
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THEN_ELSE (DEPTH_SOLVE (nodup_depth_tac cs m 1),
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Classical.appWrappers cs (fn i => Classical.inst0_step_tac cs i APPEND
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COND (K(m=0)) no_tac
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((Classical.instp_step_tac cs i APPEND Classical.step_tac cs i)
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THEN DEPTH_SOLVE (nodup_depth_tac cs (m-1) i))) 1))
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i) state;
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(*Designed to be idempotent, except if best_tac instantiates variables
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in some of the subgoals*)
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fun mk_auto_tac (cs, ss) m n =
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let val cs' = cs addss ss
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val maintac =
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blast_depth_tac cs m (* fast but can't use addss *)
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ORELSE'
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nodup_depth_tac cs' n; (* slower but more general *)
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in EVERY [ALLGOALS (Simplifier.asm_full_simp_tac ss),
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TRY (Classical.safe_tac cs),
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REPEAT (FIRSTGOAL maintac),
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TRY (Classical.safe_tac (cs addSss ss)),
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prune_params_tac]
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end;
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fun auto_tac (cs,ss) = mk_auto_tac (cs,ss) 4 2;
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fun Auto_tac st = auto_tac (Classical.claset(), Simplifier.simpset()) st;
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fun auto () = by Auto_tac;
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(* force_tac *)
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(* aimed to solve the given subgoal totally, using whatever tools possible *)
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fun force_tac (cs,ss) = let val cs' = cs addss ss in SELECT_GOAL (EVERY [
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Classical.clarify_tac cs' 1,
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IF_UNSOLVED (Simplifier.asm_full_simp_tac ss 1),
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ALLGOALS (Classical.best_tac cs')]) end;
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fun Force_tac i = force_tac (Classical.claset(), Simplifier.simpset()) i;
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fun force i = by (Force_tac i);
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end;
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