Tactic.FILTER_STRIP

STRUCTURE

SYNOPSIS

Conditionally strips apart a goal by eliminating the outermost connective.

DESCRIPTION

Stripping apart a goal in a more careful way than is done by STRIP_TAC may be necessary when dealing with quantified terms and implications. FILTER_STRIP_TAC behaves like STRIP_TAC, but it does not strip apart a goal if it contains a given term.

If u is a term, then FILTER_STRIP_TAC u is a tactic that removes one outermost occurrence of one of the connectives !, ==>, ~ or /\ from the conclusion of the goal t, provided the term being stripped does not contain u. A negation ~t is treated as the implication t ==> F. FILTER_STRIP_TAC u also breaks apart conjunctions without applying any filtering.

If t is a universally quantified term, FILTER_STRIP_TAC u strips off the quantifier:

      A ?- !x.v
   ================  FILTER_STRIP_TAC ``u``       [where x is not u]
     A ?- v[x'/x]

where x' is a primed variant that does not appear free in the assumptions A. If t is a conjunction, no filtering is done and FILTER_STRIP_TAC u simply splits the conjunction:

      A ?- v /\ w
   =================  FILTER_STRIP_TAC ``u``
    A ?- v   A ?- w

If t is an implication and the antecedent does not contain a free instance of u, then FILTER_STRIP_TAC u moves the antecedent into the assumptions and recursively splits the antecedent according to the following rules (see STRIP_ASSUME_TAC):

    A ?- v1 /\ ... /\ vn ==> v            A ?- v1 \/ ... \/ vn ==> v
   ============================        =================================
       A u {v1,...,vn} ?- v             A u {v1} ?- v ... A u {vn} ?- v

     A ?- ?x.w ==> v
   ====================
    A u {w[x'/x]} ?- v

where x' is a variant of x.

FAILURE

FILTER_STRIP_TAC u (A,t) fails if t is not a universally quantified term, an implication, a negation or a conjunction; or if the term being stripped contains u in the sense described above (conjunction excluded).

EXAMPLE

When trying to solve the goal

   ?- !n. m <= n /\ n <= m ==> (m = n)

the universally quantified variable n can be stripped off by using

   FILTER_STRIP_TAC ``m:num``

and then the implication can be stripped apart by using

   FILTER_STRIP_TAC ``m:num = n``

USES

FILTER_STRIP_TAC is used when stripping outer connectives from a goal in a more delicate way than STRIP_TAC. A typical application is to keep stripping by using the tactic REPEAT (FILTER_STRIP_TAC u) until one hits the term u at which stripping is to stop.

SEEALSO

CONJ_TAC, FILTER_DISCH_TAC, FILTER_DISCH_THEN, FILTER_GEN_TAC, STRIP_ASSUME_TAC, STRIP_TAC