(* Title: FOLP/hypsubst
ID: $Id$
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 t, Pattern.eta_contract 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 i = DETERM (STATE(fn state =>
let val (_,_,Bi,_) = dest_state(state,i)
val n = length(Logic.strip_assums_hyp Bi) - 1
val (k,symopt) = eq_var bnd Bi
in
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;