src/Provers/typedsimp.ML

+(*  Title: 	typedsimp
+    ID:         $Id$
+    Author: 	Lawrence C Paulson, Cambridge University Computer Laboratory
+    Copyright   1993  University of Cambridge
+
+Functor for constructing simplifiers.  Suitable for Constructive Type
+Theory with its typed reflexivity axiom a:A ==> a=a:A.  For most logics try
+simp.ML.
+*)
+
+signature TSIMP_DATA =
+  sig
+  val refl: thm		(*Reflexive law*)
+  val sym: thm		(*Symmetric law*)
+  val trans: thm	(*Transitive law*)
+  val refl_red: thm	(* reduce(a,a) *)
+  val trans_red: thm	(* [|a=b; reduce(b,c) |] ==> a=c *)
+  val red_if_equal: thm (* a=b ==> reduce(a,b) *)
+  (*Built-in rewrite rules*)
+  val default_rls: thm list
+  (*Type checking or similar -- solution of routine conditions*)
+  val routine_tac: thm list -> int -> tactic
+  end;
+
+signature TSIMP =
+  sig
+  val asm_res_tac: thm list -> int -> tactic   
+  val cond_norm_tac: ((int->tactic) * thm list * thm list) -> tactic
+  val cond_step_tac: ((int->tactic) * thm list * thm list) -> int -> tactic
+  val norm_tac: (thm list * thm list) -> tactic
+  val process_rules: thm list -> thm list * thm list
+  val rewrite_res_tac: int -> tactic   
+  val split_eqn: thm
+  val step_tac: (thm list * thm list) -> int -> tactic
+  val subconv_res_tac: thm list -> int -> tactic   
+  end;
+
+
+functor TSimpFun (TSimp_data: TSIMP_DATA) : TSIMP = 
+struct
+local open TSimp_data
+in
+
+(*For simplifying both sides of an equation:
+      [| a=c; b=c |] ==> b=a
+  Can use resolve_tac [split_eqn] to prepare an equation for simplification. *)
+val split_eqn = standard (sym RSN (2,trans) RS sym);
+
+
+(*    [| a=b; b=c |] ==> reduce(a,c)  *)
+val red_trans = standard (trans RS red_if_equal);
+
+(*For REWRITE rule: Make a reduction rule for simplification, e.g.
+  [| a: C(0); ... ; a=c: C(0) |] ==> rec(0,a,b) = c: C(0) *)
+fun simp_rule rl = rl RS trans;
+
+(*For REWRITE rule: Make rule for resimplifying if possible, e.g.
+  [| a: C(0); ...; a=c: C(0) |] ==> reduce(rec(0,a,b), c)  *)
+fun resimp_rule rl = rl RS red_trans;
+
+(*For CONGRUENCE rule, like a=b ==> succ(a) = succ(b)
+  Make rule for simplifying subterms, e.g.
+  [| a=b: N; reduce(succ(b), c) |] ==> succ(a)=c: N   *)
+fun subconv_rule rl = rl RS trans_red;
+
+(*If the rule proves an equality then add both forms to simp_rls
+  else add the rule to other_rls*)
+fun add_rule (rl, (simp_rls, other_rls)) =
+    (simp_rule rl :: resimp_rule rl :: simp_rls, other_rls)
+    handle THM _ => (simp_rls, rl :: other_rls);
+
+(*Given the list rls, return the pair (simp_rls, other_rls).*)
+fun process_rules rls = foldr add_rule (rls, ([],[]));
+
+(*Given list of rewrite rules, return list of both forms, reject others*)
+fun process_rewrites rls = 
+  case process_rules rls of
+      (simp_rls,[])  =>  simp_rls
+    | (_,others) => raise THM 
+	("process_rewrites: Ill-formed rewrite", 0, others);
+
+(*Process the default rewrite rules*)
+val simp_rls = process_rewrites default_rls;
+
+(*If subgoal is too flexible (e.g. ?a=?b or just ?P) then filt_resolve_tac
+  will fail!  The filter will pass all the rules, and the bound permits
+  no ambiguity.*)
+
+(*Resolution with rewrite/sub rules.  Builds the tree for filt_resolve_tac.*)
+val rewrite_res_tac = filt_resolve_tac simp_rls 2;
+
+(*The congruence rules for simplifying subterms.  If subgoal is too flexible
+    then only refl,refl_red will be used (if even them!). *)
+fun subconv_res_tac congr_rls =
+  filt_resolve_tac (map subconv_rule congr_rls) 2
+  ORELSE'  filt_resolve_tac [refl,refl_red] 1;
+
+(*Resolve with asms, whether rewrites or not*)
+fun asm_res_tac asms =
+    let val (xsimp_rls,xother_rls) = process_rules asms
+    in 	routine_tac xother_rls  ORELSE'  
+	filt_resolve_tac xsimp_rls 2
+    end;
+
+(*Single step for simple rewriting*)
+fun step_tac (congr_rls,asms) =
+    asm_res_tac asms   ORELSE'  rewrite_res_tac  ORELSE'  
+    subconv_res_tac congr_rls;
+
+(*Single step for conditional rewriting: prove_cond_tac handles new subgoals.*)
+fun cond_step_tac (prove_cond_tac, congr_rls, asms) =
+    asm_res_tac asms   ORELSE'  rewrite_res_tac  ORELSE'  
+    (resolve_tac [trans, red_trans]  THEN'  prove_cond_tac)  ORELSE'  
+    subconv_res_tac congr_rls;
+
+(*Unconditional normalization tactic*)
+fun norm_tac arg = REPEAT_FIRST (step_tac arg)  THEN
+    TRYALL (resolve_tac [red_if_equal]);
+
+(*Conditional normalization tactic*)
+fun cond_norm_tac arg = REPEAT_FIRST (cond_step_tac arg)  THEN
+    TRYALL (resolve_tac [red_if_equal]);
+
+end;
+end;
+
+