1(*  Title:      FOLP/hypsubst.ML
2    Author:     Martin D Coen, Cambridge University Computer Laboratory
3    Copyright   1995  University of Cambridge
4
5Original version of Provers/hypsubst.  Cannot use new version because it
6relies on the new simplifier!
7
8Martin Coen's tactic for substitution in the hypotheses
9*)
10
11signature HYPSUBST_DATA =
12  sig
13  val dest_eq   : term -> term*term
14  val imp_intr  : thm           (* (P ==> Q) ==> P-->Q *)
15  val rev_mp    : thm           (* [| P;  P-->Q |] ==> Q *)
16  val subst     : thm           (* [| a=b;  P(a) |] ==> P(b) *)
17  val sym       : thm           (* a=b ==> b=a *)
18  end;
19
20signature HYPSUBST =
21  sig
22  val bound_hyp_subst_tac : Proof.context -> int -> tactic
23  val hyp_subst_tac       : Proof.context -> int -> tactic
24    (*exported purely for debugging purposes*)
25  val eq_var              : bool -> term -> int * thm
26  val inspect_pair        : bool -> term * term -> thm
27  end;
28
29functor Hypsubst(Data: HYPSUBST_DATA): HYPSUBST =
30struct
31
32local open Data in
33
34exception EQ_VAR;
35
36(*It's not safe to substitute for a constant; consider 0=1.
37  It's not safe to substitute for x=t[x] since x is not eliminated.
38  It's not safe to substitute for a Var; what if it appears in other goals?
39  It's not safe to substitute for a variable free in the premises,
40    but how could we check for this?*)
41fun inspect_pair bnd (t, u) =
42  (case (Envir.eta_contract t, Envir.eta_contract u) of
43    (Bound i, _) =>
44      if loose_bvar1 (u, i) then raise Match
45      else sym         (*eliminates t*)
46   | (_, Bound i) =>
47      if loose_bvar (t, i) then raise Match
48      else asm_rl      (*eliminates u*)
49   | (Free _, _) =>
50      if bnd orelse Logic.occs (t, u) then raise Match
51      else sym          (*eliminates t*)
52   | (_, Free _) =>
53      if bnd orelse Logic.occs(u,t) then raise Match
54      else asm_rl       (*eliminates u*)
55   | _ => raise Match);
56
57(*Locates a substitutable variable on the left (resp. right) of an equality
58   assumption.  Returns the number of intervening assumptions, paried with
59   the rule asm_rl (resp. sym). *)
60fun eq_var bnd =
61  let fun eq_var_aux k (Const(\<^const_name>\<open>Pure.all\<close>,_) $ Abs(_,_,t)) = eq_var_aux k t
62        | eq_var_aux k (Const(\<^const_name>\<open>Pure.imp\<close>,_) $ A $ B) =
63              ((k, inspect_pair bnd (dest_eq A))
64                      (*Exception Match comes from inspect_pair or dest_eq*)
65               handle Match => eq_var_aux (k+1) B)
66        | eq_var_aux k _ = raise EQ_VAR
67  in  eq_var_aux 0  end;
68
69(*Select a suitable equality assumption and substitute throughout the subgoal
70  Replaces only Bound variables if bnd is true*)
71fun gen_hyp_subst_tac bnd ctxt = SUBGOAL(fn (Bi,i) =>
72      let val n = length(Logic.strip_assums_hyp Bi) - 1
73          val (k,symopt) = eq_var bnd Bi
74      in
75         DETERM
76           (EVERY [REPEAT_DETERM_N k (eresolve_tac ctxt [rev_mp] i),
77                   eresolve_tac ctxt [revcut_rl] i,
78                   REPEAT_DETERM_N (n-k) (eresolve_tac ctxt [rev_mp] i),
79                   eresolve_tac ctxt [symopt RS subst] i,
80                   REPEAT_DETERM_N n (resolve_tac ctxt [imp_intr] i)])
81      end
82      handle THM _ => no_tac | EQ_VAR => no_tac);
83
84(*Substitutes for Free or Bound variables*)
85val hyp_subst_tac = gen_hyp_subst_tac false;
86
87(*Substitutes for Bound variables only -- this is always safe*)
88val bound_hyp_subst_tac = gen_hyp_subst_tac true;
89
90end
91end;
92
93