File hypsubst.ML (Isabelle2005: October 2005)

# File hypsubst.ML

    (*  Title:      FOLP/hypsubst
        ID:         $Id: hypsubst.ML,v 1.4 1997/07/22 09:12:58 paulson Exp $
        Author:     Martin D Coen, Cambridge University Computer Laboratory
        Copyright   1995  University of Cambridge

    Original version of Provers/hypsubst.  Cannot use new version because it
    relies on the new simplifier!

    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_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 -> int * thm
      val inspect_pair        : bool -> term * term -> thm
      end;

    functor HypsubstFun(Data: HYPSUBST_DATA): HYPSUBST =
    struct

    local open Data in

    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 Var; what if it appears in other goals?
      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_atom t, Pattern.eta_contract_atom u) of
           (Bound i, _) => if loose(i,u) then raise Match
                           else sym         (*eliminates t*)
         | (_, Bound i) => if loose(i,t) then raise Match
                           else asm_rl      (*eliminates u*)
         | (Free _, _) => if bnd orelse Logic.occs(t,u) then raise Match
                          else sym          (*eliminates t*)
         | (_, Free _) => if bnd orelse Logic.occs(u,t) then raise Match
                          else asm_rl       (*eliminates u*)
         | _ => raise Match;

    (*Locates a substitutable variable on the left (resp. right) of an equality
       assumption.  Returns the number of intervening assumptions, paried with
       the rule asm_rl (resp. sym). *)
    fun eq_var bnd =
      let fun eq_var_aux k (Const("all",_) $ Abs(_,_,t)) = eq_var_aux k t
            | eq_var_aux k (Const("==>",_) $ A $ B) =
                  ((k, inspect_pair bnd (dest_eq A))
                          (*Exception Match comes from inspect_pair or dest_eq*)
                   handle Match => eq_var_aux (k+1) B)
            | eq_var_aux k _ = raise EQ_VAR
      in  eq_var_aux 0  end;

    (*Select a suitable equality assumption and substitute throughout the subgoal
      Replaces only Bound variables if bnd is true*)
    fun gen_hyp_subst_tac bnd = SUBGOAL(fn (Bi,i) =>
          let val n = length(Logic.strip_assums_hyp Bi) - 1
              val (k,symopt) = eq_var bnd Bi
          in
             DETERM
               (EVERY [REPEAT_DETERM_N k (etac rev_mp i),
    		   etac revcut_rl i,
    		   REPEAT_DETERM_N (n-k) (etac rev_mp i),
    		   etac (symopt RS subst) i,
    		   REPEAT_DETERM_N 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;