48 lines
1.5 KiB
Text
48 lines
1.5 KiB
Text
def f : List Int → Bool := fun _ => true
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def ex1 : Bool :=
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f [1, 2, 3] -- Works
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def ex2 : Bool :=
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let xs := [1, 2, 3];
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/- The following application fails.
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In the Lean3 elaborator, the `;` after `have` and `let` expressions is a "check-point".
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The elaborator will resolve type class instances and force pending numeral types to `Nat` if they
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have not been assigned yet.
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So, `xs` will have type `List Nat`.
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Solution: remove "check-point" from `let`, but keep the one on `have`. We use `have` expressions
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when proving, and it is nice to make sure the proposition does not have meta-variables before continuing. -/
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f xs
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def ex3 : IO Bool :=
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do
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xs ← pure [1, 2, 3];
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pure $ f xs -- Works
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def ex4 :=
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[1, 2, 3].map $ fun x => x+1
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def ex5 (xs : List String) :=
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/- `r.push x` fails because we don't know the type of `r`.
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Potential solution: the elaborator should suspend the elaboration of `fun r x => r.push x`,
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elaborate `Array.empty`, and then resume the suspension.
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-/
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xs.foldl (fun r x => r.push x) Array.empty
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inductive Expr
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| val : Nat → Expr
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| app : Expr → Expr → Expr
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instance : HasCoe Nat Expr := ⟨Expr.val⟩
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def foo : Expr → Expr := fun e => e
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def ex6 :=
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/- `1` is elaborated to `HasOne.one ?A ?S : ?A`.
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Typing constraints unify `?A =?= Expr`, and
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we fail to synthesize `HasOne Expr`.
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Users get confused since they have defined `HasCoe Nat Expr`.
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Solution: elaborate `1` into `Expr.lit (Literal.natVal 1) : Nat`,
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and rely on coercions.
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-/
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foo 1
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