Tactical.POP

STRUCTURE

SYNOPSIS

Applies tactic generated from the first element of a goal’s assumption list.

DESCRIPTION

When applied to a theorem-tactic and a goal, POP_ASSUM applies the theorem-tactic to the ASSUMEd first element of the assumption list, and applies the resulting tactic to the goal without the first assumption in its assumption list:

   POP_ASSUM f ({A1,...,An} ?- t) = f (A1 |- A1) ({A2,...,An} ?- t)

FAILURE

Fails if the assumption list of the goal is empty, or the theorem-tactic fails when applied to the popped assumption, or if the resulting tactic fails when applied to the goal (with depleted assumption list).

COMMENTS

It is possible simply to use the theorem ASSUME A1 as required rather than use POP_ASSUM; this will also maintain A1 in the assumption list, which is generally useful. In addition, this approach can equally well be applied to assumptions other than the first.

There are admittedly times when POP_ASSUM is convenient, but it is most unwise to use it if there is more than one assumption in the assumption list, since this introduces a dependency on the ordering, which is vulnerable to changes in the HOL system.

Another point to consider is that if the relevant assumption has been obtained by DISCH_TAC, it is often cleaner to use DISCH_THEN with a theorem-tactic. For example, instead of:

   DISCH_TAC THEN POP_ASSUM (SUBST1_TAC o SYM)

one might use

   DISCH_THEN (SUBST1_TAC o SYM)

The tactical POP_ASSUM is also available under the lower-case version of the name, pop_assum.

EXAMPLE

The goal:

   {4 = SUC x} ?- x = 3

can be solved by:

   POP_ASSUM
    (fn th => REWRITE_TAC[REWRITE_RULE[num_CONV “4”, INV_SUC_EQ] th])

USES

Making more delicate use of an assumption than rewriting or resolution using it.

SEEALSO

ASSUM_LIST, EVERY_ASSUM, IMP_RES_TAC, POP_ASSUM_LIST, POP_LAST_ASSUM, REWRITE_TAC