Coq CompCert中的EvalOp是什么？附其定义解析

EvalOp is a custom Ltac tactic in the CompCert verified compiler, defined in the compcert.backend.SplitLongproof module. Its core purpose is to automate the process of proving goals related to expression evaluation in CompCert's intermediate representations.

Here's the snippet of its definition you provided, formatted as Coq code:

Ltac EvalOp := eauto; match goal with 
  | [ |- eval_exprlist _ _ _ _ _ Enil _ ] => constructor 
  | [ |- eval_exprlist _ _ _ _ _ (_:::_) _ ] => econstructor; EvalOp 
  | [ |- eval_expr _ _ _ _ _ (Eletvar _) _ ] => constructor; simpl; eauto 
  | [ |- eval_expr _ _ _ _ _ (Elet _ _) _ ] => econstructor; EvalOp 
  | [ |- eval_expr _ _ _ _ _ (lift _) _ ] => apply eval_lift; EvalOp 
  | [ |- eval_expr _ _ _ _ _ _ _ ] => eapply eval_Eop;...

Let's break down how this tactic works step by step:

• Initial eauto: First, it tries to automatically discharge any simple subgoals using Coq's built-in automated proof search, handling trivial cases upfront.
• Pattern matching on goal shapes:
  • For goals involving evaluating an empty expression list (eval_exprlist with Enil): Uses constructor directly to build the proof, since empty list evaluation is a base case.
  • For goals involving evaluating a non-empty expression list (_:::_): Uses econstructor to start the proof, then recursively calls EvalOp to handle the remaining elements of the list.
  • For evaluating an Eletvar (let variable) expression: Constructs the base proof case, simplifies the goal with simpl, then uses eauto to clean up any remaining trivial subgoals.
  • For evaluating an Elet (let binding) expression: Starts the proof with econstructor, then recurses with EvalOp to handle the bound expression and the body.
  • For evaluating a lift expression (used to shift variable indices): Applies the pre-proven eval_lift lemma, then recurses with EvalOp to handle the underlying expression.
  • For other general eval_expr goals (like operator applications): Attempts to apply the eval_Eop lemma, with the omitted ... likely covering additional expression types (like constants, variables, or other operations) common in CompCert's IR.

In short, EvalOp is a domain-specific tactic tailored to streamline proofs about expression evaluation in CompCert's backend, reducing the manual effort needed to construct these often repetitive proof steps.

内容的提问来源于stack exchange，提问作者Jian Wang