MATCH_ABBREV_TAC

Q.MATCH_ABBREV_TAC : term quotation -> tactic

Introduces abbreviations by matching a pattern against the goal statement.

When applied to the goal (asl, w), the tactic Q.MATCH_ABBREV_TAC q parses the quotation q in the context of the goal, producing a term to use as a pattern. The tactic then attempts a (first order) match of the pattern against the term w. Variables that occur in both the pattern and the goal are treated as “local constants”, and will not acquire instantiations.

For each variable v in the pattern that has not been treated as a local constant, there will be an instantiation term t, such that the substitution pattern [v1 |-> t1, v2 |-> t2, ...] produces w. The effect of the tactic is to then perform abbreviations in the goal, replacing each t with the corresponding v (as long as v does not have a name beginning with an underscore character), and adding assumptions of the form Abbrev(v = t) to the goal.

Because the tactic ignores underscore variables, the user can abbreviate just those parts of the goal that are particularly relevant. Note also that the standard parser treats variables consisting of entirely underscores specially: each is expanded to a fresh name. This means that a pattern can use _ repeatedly, and it will not cause the match to look for the same instantiation for each occurrence. Nor it will require corresponding sub-terms to have the same type.

Failure

MATCH_ABBREV_TAC fails if the pattern provided does not match the goal, or if variables from the goal are used in the pattern in ways that make the pattern fail to type-check.

Example

If the current goal is

   ?- (n + 10) * y <= 42315 /\ (!x y. x < y ==> f x < f y)

then applying the tactic Q.MATCH_ABBREV_TAC `X <= Y /\ P` results in the goal

   Abbrev(X = (n + 10) * y),
   Abbrev(Y = 42315),
   Abbrev(P = !x y. x < y ==> f x < f y)
      ?-
   X <= Y /\ P

If the current goal is

   ?- (n + 10) * y <= 42315 /\ (!x y. x < y ==> f x < f y)

then applying the tactic Q.MATCH_ABBREV_TAC `a * _ <= b /\ _` results in the goal

   Abbrev (a = n + 10)
   Abbrev (b = 42315)
     ?-
   a * y <= b /\ !x y. x < y ==> f x < f y

See also

Q.ABBREV_TAC, Q.HO_MATCH_ABBREV_TAC