src/Provers/hypsubst.ML

+(*  Title: 	Provers/hypsubst
+    ID:         $Id$
+    Author: 	Lawrence C Paulson, Cambridge University Computer Laboratory
+    Copyright   1993  University of Cambridge
+
+Martin Coen's tactic for substitution in the hypotheses
+*)
+
+signature HYPSUBST_DATA =
+  sig
+  val dest_eq: term -> term*term
+  val imp_intr: thm	(* (P ==> Q) ==> P-->Q *)
+  val rev_cut_eq: thm	(* [| a=b;  a=b ==> R |] ==> R *)
+  val rev_mp: thm	(* [| P;  P-->Q |] ==> Q *)
+  val subst: thm	(* [| a=b;  P(a) |] ==> P(b) *)
+  val sym: thm		(* a=b ==> b=a *)
+  end;
+
+signature HYPSUBST =
+  sig
+  val bound_hyp_subst_tac : int -> tactic
+  val hyp_subst_tac       : int -> tactic
+    (*exported purely for debugging purposes*)
+  val eq_var              : bool -> term -> term * thm
+  val inspect_pair        : bool -> term * term -> term * thm
+  val liftvar             : int -> typ list -> term
+  end;
+
+functor HypsubstFun(Data: HYPSUBST_DATA): HYPSUBST = 
+struct
+
+local open Data in
+
+fun REPEATN 0 tac = all_tac
+  | REPEATN n tac = Tactic(fn state =>
+                           tapply(tac THEN REPEATN (n-1) tac,  state));
+
+local
+  val T = case #1 (types_sorts rev_cut_eq) ("a",0) of
+	      Some T => T
+   	    | None   => error"No such variable in rev_cut_eq"
+in
+  fun liftvar inc paramTs = Var(("a",inc), paramTs ---> incr_tvar inc T);
+end;
+
+exception EQ_VAR;
+
+fun loose (i,t) = 0 mem add_loose_bnos(t,i,[]);
+
+(*It's not safe to substitute for a constant; consider 0=1.
+  It's not safe to substitute for x=t[x] since x is not eliminated.
+  It's not safe to substitute for a variable free in the premises,
+    but how could we check for this?*)
+fun inspect_pair bnd (t,u) =
+  case (Pattern.eta_contract t, Pattern.eta_contract u) of
+       (Bound i, _) => if loose(i,u) then raise Match 
+		       else (t, asm_rl)
+     | (_, Bound i) => if loose(i,t) then raise Match 
+		       else (u, sym)
+     | (Free _, _) => if bnd orelse Logic.occs(t,u) then raise Match 
+		      else (t, asm_rl)
+     | (_, Free _) => if bnd orelse Logic.occs(u,t) then raise Match 
+		      else (u, sym) 
+     | _ => raise Match;
+
+ (* Extracts the name of the variable on the left (resp. right) of an equality
+   assumption.  Returns the rule asm_rl (resp. sym). *)
+fun eq_var bnd (Const("all",_) $ Abs(_,_,t)) = eq_var bnd t
+  | eq_var bnd (Const("==>",_) $ A $ B) = 
+	(inspect_pair bnd (dest_eq A) 
+	        (*Match comes from inspect_pair or dest_eq*)
+	 handle Match => eq_var bnd B)
+  | eq_var bnd _ = raise EQ_VAR;
+
+(*Lift and instantiate a rule wrt the given state and subgoal number *)
+fun lift_instpair (state, i, t, rule) =
+  let val {maxidx,sign,...} = rep_thm state
+      val (_, _, Bi, _) = dest_state(state,i)
+      val params = Logic.strip_params Bi
+      val var = liftvar (maxidx+1) (map #2 params)
+      and u   = Unify.rlist_abs(rev params, t)
+      and cterm = Sign.cterm_of sign
+  in cterm_instantiate [(cterm var, cterm u)] (lift_rule (state,i) rule)
+  end;
+
+fun eres_instpair_tac t rule i = STATE (fn state => 
+	   compose_tac (true, lift_instpair (state, i, t, rule),
+			length(prems_of rule)) i);
+
+val ssubst = sym RS subst;
+
+(*Select a suitable equality assumption and substitute throughout the subgoal
+  Replaces only Bound variables if bnd is true*)
+fun gen_hyp_subst_tac bnd i = DETERM (STATE(fn state =>
+      let val (_,_,Bi,_) = dest_state(state,i)
+	  val n = length(Logic.strip_assums_hyp Bi) - 1
+	  val (t,symopt) = eq_var bnd Bi
+      in eres_instpair_tac t (symopt RS rev_cut_eq) i  THEN
+         REPEATN n (etac rev_mp i) THEN
+	 etac ssubst i THEN REPEATN n (rtac imp_intr i)
+      end
+      handle THM _ => no_tac | EQ_VAR => no_tac));
+
+(*Substitutes for Free or Bound variables*)
+val hyp_subst_tac = gen_hyp_subst_tac false;
+
+(*Substitutes for Bound variables only -- this is always safe*)
+val bound_hyp_subst_tac = gen_hyp_subst_tac true;
+
+end
+end;
+