coq - 将模式传递给战术

Question

我正在编写一种策略来查找与绑定(bind)列表中的键关联的值。就像是:

Require Import String List Program.

Ltac assoc needle haystack :=
  match haystack with
  | @nil (_ * ?T) => constr:(@None T)
  | cons (?k, ?v) ?t => let pr := constr:(eq_refl k : k = needle) in constr:(Some v)
  | cons _        ?t => let res := assoc needle t in constr:res
  end.

不幸的是，我不知道 key 的确切形式；相反，我知道一个与之匹配的模式。更准确地说，我正在寻找的关键是调用类型类方法的结果，但我事先不知道将使用哪个实例。在下面的示例中，我知道关键是调用 show "a" ，但我不知道用什么实例:

Open Scope string_scope.
Open Scope list_scope.

Class Show A := { show: A -> string }.
Instance Show1 : Show string := {| show := fun x => x |}.
Instance Show2 : Show string := {| show := fun x => x ++ x |}.

Goal True.
  (* Works (poses Some 1) *)
  let v := assoc (show "a") [(show (Show := Show2) "a", 1); ("b", 2)] in pose v.
  (* Does not work (poses None) *)
  let v := assoc (show "a") [(show (Show := Show1) "a", 1); ("b", 2)] in pose v.

有没有我可以在这里使用的技巧，没有通过 assoc检查匹配的ltac？理想情况下，它看起来像 (show (Show := _) "a") , 或者 (fun inst => show (Show := inst) "a") .

Answer 1

看起来传递一个函数效果很好，实际上:

Ltac assoc needlef haystack :=
  match haystack with
  | @nil (_ * ?T) => constr:(@None T)
  | cons (?k, ?v) ?t => let pr := constr:(eq_refl k : k = needlef _) in constr:(Some v)
  | cons _        ?t => let res := assoc needlef t in constr:res
  end.

Goal False.
  let v := assoc (fun i => show (Show := i) "a") [(show (Show := Show2) "a", 1); ("b", 2)] in pose v.
  let v := assoc (fun i => show (Show := i) "a") [(show (Show := Show1) "a", 1); ("b", 2)] in pose v.