FREEZE_THEN : thm_tactical

SYNOPSIS

`Freezes' a theorem to prevent instantiation of its free variables.

DESCRIBE

FREEZE_THEN expects a tactic-generating function f:thm->tactic and a theorem (A1 |- w) as arguments. The tactic-generating function f is applied to the theorem (w |- w). If this tactic generates the subgoal:

    A ?- t
   =========  f (w |- w)
    A ?- t1

then applying FREEZE_THEN f (A1 |- w) to the goal (A ?- t) produces the subgoal:

    A ?- t
   =========  FREEZE_THEN f (A1 |- w)
    A ?- t1

Since the term w is a hypothesis of the argument to the function f, none of the free variables present in w may be instantiated or generalized. The hypothesis is discharged by PROVE_HYP upon the completion of the proof of the subgoal.

FAILURE

Failures may arise from the tactic-generating function. An invalid tactic arises if the hypotheses of the theorem are not alpha-convertible to assumptions of the goal.

EXAMPLE

Given the goal ([ "b < c"; "a < b" ], "(SUC a) <= c"), and the specialized variant of the theorem LESS_TRANS:

   th = |- !p. a < b /\ b < p ==> a < p

IMP_RES_TAC th will generate several unneeded assumptions:

   {b < c, a < b, a < c, !p. c < p ==> b < p, !a'. a' < a ==> a' < b}
       ?- (SUC a) <= c

which can be avoided by first `freezing' the theorem, using the tactic

   FREEZE_THEN IMP_RES_TAC th

This prevents the variables a and b from being instantiated.

   {b < c, a < b, a < c} ?- (SUC a) <= c

USES

Used in serious proof hacking to limit the matches achievable by resolution and rewriting.

SEEALSO  ASSUME,   IMP_RES_TAC,   PROVE_HYP,   RES_TAC,   REWR_CONV