Описание тега coq-tactic

Tactics are programs written in Ltac, the untyped language used in the Coq proof assistant to transform goals and terms. In general, the aim of using tactics is to construct a proof or proof object for the theorem in question. Initially, the proof object contains a hole corresponding to the goal of the theorem in question. As the proof proceeds, tactics transform the current goal/sub-goal and hypotheses in the local proof context using established theorems in the global context as well as hypotheses in the local context. Some tactics can introduce new sub-goals corresponding to new holes in the proof object. For example, if the goal is a conjunction P /\ Q, can be decomposed into two sub-goals P and Q using the split tactic. Certain tactics can also reduce the number of sub-goals (or holes in the proof object). The theorem is proved when there is no more sub-goals to prove (i.e. no more holes to fill in the proof object).

Strictly speaking, tactics are not necessary to prove theorems in Coq. It is possible to construct a proof object directly. However, tactics provide an interactive way of constructing a proof, which are closer to the manner proofs are developed manually.

For a comprehensive documentation of tactics, see the Coq reference manual: https://coq.inria.fr/refman/tactic-index.html