Apply the free variable substitution s to the given pattern

  • Syntax object for providing position information

  • idx : Nat

    Orginal alternative index. Alternatives can be split, this index is the original position of the alternative that generated this one.

  • rhs : Lean.Expr

    Right-hand-side of the alternative.

  • fvarDecls : List Lean.LocalDecl

    Alternative pattern variables.

  • Alternative patterns.

  • Pending constraints lhs ≋ rhs that need to be solved before the alternative is considered acceptable. We generate them when processing inaccessible patterns. Note that lhs and rhs often have different types. After we perform additional case analysis, their types become definitionally equal.

Match alternative

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    Return true if fvarId is one of the alternative pattern variables

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      Similar to checkAndReplaceFVarId, but ensures type of v is definitionally equal to type of fvarId. This extra check is necessary when performing dependent elimination and inaccessible terms have been used. For example, consider the following code fragment:

      inductive Vec (α : Type u) : Nat → Type u where
        | nil : Vec α 0
        | cons {n} (head : α) (tail : Vec α n) : Vec α (n+1)
      inductive VecPred {α : Type u} (P : α → Prop) : {n : Nat} → Vec α n → Prop where
        | nil   : VecPred P Vec.nil
        | cons  {n : Nat} {head : α} {tail : Vec α n} : P head → VecPred P tail → VecPred P (Vec.cons head tail)
      theorem ex {α : Type u} (P : α → Prop) : {n : Nat} → (v : Vec α (n+1)) → VecPred P v → Exists P
        | _, Vec.cons head _, VecPred.cons h (w : VecPred P Vec.nil) => ⟨head, h⟩

      Recall that _ in a pattern can be elaborated into pattern variable or an inaccessible term. The elaborator uses an inaccessible term when typing constraints restrict its value. Thus, in the example above, the _ at Vec.cons head _ becomes the inaccessible pattern .(Vec.nil) because the type ascription (w : VecPred P Vec.nil) propagates typing constraints that restrict its value to be Vec.nil. After elaboration the alternative becomes:

        | .(0), @Vec.cons .(α) .(0) head .(Vec.nil), @VecPred.cons .(α) .(P) .(0) .(head) .(Vec.nil) h w => ⟨head, h⟩


      (head : α), (h: P head), (w : VecPred P Vec.nil)

      Then, when we process this alternative in this module, the following check will detect that w has type VecPred P Vec.nil, when it is supposed to have type VecPred P tail. Note that if we had written

      theorem ex {α : Type u} (P : α → Prop) : {n : Nat} → (v : Vec α (n+1)) → VecPred P v → Exists P
        | _, Vec.cons head Vec.nil, VecPred.cons h (w : VecPred P Vec.nil) => ⟨head, h⟩

      we would get the easier to digest error message

      missing cases:
      _, (Vec.cons _ _ (Vec.cons _ _ _)), _
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        @[inline, reducible]
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            Convert a expression occurring as the argument of a match motive application back into a Pattern For example, we can use this method to convert x::y::xs at

            (motive : List Nat → Sort u_1) (xs : List Nat) (h_1 : (x y : Nat) → (xs : List Nat) → motive (x :: y :: xs))

            into a pattern object