mathlib documentation

tactic.simp_result

simp_result

dsimp_result and simp_result are a pair of tactics for applying dsimp or simp to the result produced by other tactics.

As examples, tactics which use revert and intro may insert additional id terms in the result they produce. If there is some reason these are undesirable (e.g. the result term needs to be human-readable, or satisfying syntactic rather than just definitional properties), wrapping those tactics in dsimp_result can remove the id terms "after the fact".

Similarly, tactics using subst and rw will nearly always introduce eq.rec terms, but sometimes these will be easy to remove, for example by simplifying using eq_rec_constant. This is a non-definitional simplification lemma, and so wrapping these tactics in simp_result will result in a definitionally different result.

There are several examples in the associated test file, demonstrating these interactions with revert and subst.

These tactics should be used with some caution. You should consider whether there is any real need for the simplification of the result, and whether there is a more direct way of producing the result you wanted, before relying on these tactics.

Both are implemented in terms of a generic intercept_result tactic, which allows you to run an arbitrary tactic and modify the returned results.

meta def tactic.intercept_result {α : Type} :
(exprtactic expr)tactic αtactic α

intercept_result m t attempts to run a tactic t, intercepts any results t assigns to the goals, and runs m : exprtactic expr on each of the expressions before assigning the returned values to the original goals.

Because intercept_result uses unsafe.type_context.assign rather than unify, if the tactic m does something unreasonable you may produce terms that don't typecheck, possibly with mysterious error messages. Be careful!

dsimp_result t attempts to run a tactic t, intercepts any results it assigns to the goals, and runs dsimp on those results before assigning the simplified values to the original goals.

simp_result t attempts to run a tactic t, intercepts any results t assigns to the goals, and runs simp on those results before assigning the simplified values to the original goals.

dsimp_result { tac } attempts to run a tactic block tac, intercepts any results the tactic block would have assigned to the goals, and runs dsimp on those results before assigning the simplified values to the original goals.

You can use the usual interactive syntax for dsimp, e.g. dsimp_result only [a, b, c] with attr { tac }.

simp_result { tac } attempts to run a tactic block tac, intercepts any results the tactic block would have assigned to the goals, and runs simp on those results before assigning the simplified values to the original goals.

You can use the usual interactive syntax for simp, e.g. simp_result only [a, b, c] with attr { tac }.