Lvc.IL.Patterns

Require Import List.
Require Export Util Relations Get Drop Var Val Exp Env Map CSet AutoIndTac MoreList.

Set Implicit Arguments.

Inductive pattern :=
  | PatternScore
  | PatternVar (x:var)
  | PatternList (Z:list var).

Fixpoint patternVars (p:pattern) : set var :=
  match p with
    | PatternScore ⇒ ∅
    | PatternVar x ⇒ {{x}}
    | PatternList Z ⇒ of_list Z
  end.

Definition patternMatchList
         (patternMatch: pattern → val → option (list var × list val)) :=
  fix patternMatchList (Z:list pattern) (vl:list val) {struct Z} : option (list var × list val) :=
  match Z, vl with
    | p::Z´, v::vl ⇒
      mdo l <- patternMatch p v;
        let (varl, vall) := l in
        mdo l´ <- patternMatchList Z´ vl;
          let (varl´, vall´) := l´ in
          Some ((varl++varl´)%list, (vall++vall´)%list)
    | nil, nil ⇒ Some (nil, nil)
  | _, _ ⇒ None
  end.

Fixpoint patternMatch (p:pattern) (v:val) {struct p} : option (list var × list val) :=
  match p, v with
    | PatternScore, _ ⇒ Some (nil, nil)
    | PatternVar x, v ⇒ Some (x::nil, v::nil)

    | _, _ ⇒ None
  end.

Definition patterneq (p q:pattern)
  := ∀ v, patternMatch p v ≠ None ↔ patternMatch q v ≠ None.

Instance patterneq_Equivalence_instance : Equivalence patterneq.
constructor; firstorder.
Defined.

Lemma patterneq_some p q v ZVL
: patterneq p q → patternMatch p v = Some ZVL → ∃ ZVL, patternMatch q v = Some ZVL.
Proof.
  intros. specialize (H v).
  destruct (patternMatch q v).
  - eexists; eauto.
  - exfalso; firstorder. eapply H; congruence.
Qed.