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(* Title: Provers/hypsubst
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ID: $Id$
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Author: Lawrence C Paulson, Cambridge University Computer Laboratory
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Copyright 1993 University of Cambridge
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Martin Coen's tactic for substitution in the hypotheses
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*)
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signature HYPSUBST_DATA =
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sig
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val dest_eq: term -> term*term
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val imp_intr: thm (* (P ==> Q) ==> P-->Q *)
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val rev_cut_eq: thm (* [| a=b; a=b ==> R |] ==> R *)
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val rev_mp: thm (* [| P; P-->Q |] ==> Q *)
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val subst: thm (* [| a=b; P(a) |] ==> P(b) *)
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val sym: thm (* a=b ==> b=a *)
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end;
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signature HYPSUBST =
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sig
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val bound_hyp_subst_tac : int -> tactic
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val hyp_subst_tac : int -> tactic
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(*exported purely for debugging purposes*)
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val eq_var : bool -> term -> term * thm
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val inspect_pair : bool -> term * term -> term * thm
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val liftvar : int -> typ list -> term
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end;
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functor HypsubstFun(Data: HYPSUBST_DATA): HYPSUBST =
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struct
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local open Data in
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fun REPEATN 0 tac = all_tac
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| REPEATN n tac = Tactic(fn state =>
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tapply(tac THEN REPEATN (n-1) tac, state));
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local
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val T = case #1 (types_sorts rev_cut_eq) ("a",0) of
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Some T => T
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| None => error"No such variable in rev_cut_eq"
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in
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fun liftvar inc paramTs = Var(("a",inc), paramTs ---> incr_tvar inc T);
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end;
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exception EQ_VAR;
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fun loose (i,t) = 0 mem add_loose_bnos(t,i,[]);
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(*It's not safe to substitute for a constant; consider 0=1.
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It's not safe to substitute for x=t[x] since x is not eliminated.
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It's not safe to substitute for a variable free in the premises,
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but how could we check for this?*)
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fun inspect_pair bnd (t,u) =
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case (Pattern.eta_contract t, Pattern.eta_contract u) of
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(Bound i, _) => if loose(i,u) then raise Match
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else (t, asm_rl)
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| (_, Bound i) => if loose(i,t) then raise Match
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else (u, sym)
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| (Free _, _) => if bnd orelse Logic.occs(t,u) then raise Match
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else (t, asm_rl)
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| (_, Free _) => if bnd orelse Logic.occs(u,t) then raise Match
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else (u, sym)
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| _ => raise Match;
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(* Extracts the name of the variable on the left (resp. right) of an equality
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assumption. Returns the rule asm_rl (resp. sym). *)
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fun eq_var bnd (Const("all",_) $ Abs(_,_,t)) = eq_var bnd t
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| eq_var bnd (Const("==>",_) $ A $ B) =
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(inspect_pair bnd (dest_eq A)
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(*Match comes from inspect_pair or dest_eq*)
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handle Match => eq_var bnd B)
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| eq_var bnd _ = raise EQ_VAR;
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(*Lift and instantiate a rule wrt the given state and subgoal number *)
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fun lift_instpair (state, i, t, rule) =
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let val {maxidx,sign,...} = rep_thm state
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val (_, _, Bi, _) = dest_state(state,i)
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val params = Logic.strip_params Bi
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val var = liftvar (maxidx+1) (map #2 params)
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and u = Unify.rlist_abs(rev params, t)
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231
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and cterm = cterm_of sign
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0
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in cterm_instantiate [(cterm var, cterm u)] (lift_rule (state,i) rule)
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end;
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fun eres_instpair_tac t rule i = STATE (fn state =>
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compose_tac (true, lift_instpair (state, i, t, rule),
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length(prems_of rule)) i);
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val ssubst = sym RS subst;
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(*Select a suitable equality assumption and substitute throughout the subgoal
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Replaces only Bound variables if bnd is true*)
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fun gen_hyp_subst_tac bnd i = DETERM (STATE(fn state =>
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let val (_,_,Bi,_) = dest_state(state,i)
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val n = length(Logic.strip_assums_hyp Bi) - 1
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val (t,symopt) = eq_var bnd Bi
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in eres_instpair_tac t (symopt RS rev_cut_eq) i THEN
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REPEATN n (etac rev_mp i) THEN
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etac ssubst i THEN REPEATN n (rtac imp_intr i)
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end
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handle THM _ => no_tac | EQ_VAR => no_tac));
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(*Substitutes for Free or Bound variables*)
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val hyp_subst_tac = gen_hyp_subst_tac false;
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(*Substitutes for Bound variables only -- this is always safe*)
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val bound_hyp_subst_tac = gen_hyp_subst_tac true;
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end
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end;
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