87932f1c56
The following are accepted .(t) ._ We don't accept .t anymore because it will conflict with the field access notation.
83 lines
3.3 KiB
Text
83 lines
3.3 KiB
Text
universe variables u v
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inductive imf {A : Type u} {B : Type v} (f : A → B) : B → Type (max 1 u v)
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| mk : ∀ (a : A), imf (f a)
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definition inv_1 {A : Type u} {B : Type v} (f : A → B) : ∀ (b : B), imf f b → A
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| .(f a) (imf.mk .(f) a) := a
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definition inv_2 {A : Type u} {B : Type v} (f : A → B) : ∀ (b : B), imf f b → A
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| ._ (imf.mk ._ a) := a
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definition mk {A : Type u} {B : Type v} {f : A → B} (a : A) := imf.mk f a
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definition inv_3 {A : Type u} {B : Type v} (f : A → B) : ∀ (b : B), imf f b → A
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| .(f a) (mk a) := a -- Error, mk is not a constructor
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definition inv_4 {A : Type u} {B : Type v} (f : A → B) : ∀ (b : B), imf f b → A
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| .(f a) (.(mk) a) := a -- Error, we cannot use inaccessible annotation around functions in applications
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attribute [pattern] mk
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definition inv_5 {A : Type u} {B : Type v} (f : A → B) : ∀ (b : B), imf f b → A
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| .(f a) (mk a) := a
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definition inv_6 {A : Type u} {B : Type v} (f : A → B) : ∀ (b : B), imf f b → A
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| (f a) (mk a) := a -- Error, 'a' is being "declared" twice in the pattern
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definition inv_7 {A : Type u} {B : Type v} (f : A → B) : ∀ (b : B), imf f b → A
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| (f a) (mk b) := a -- Typing error, it would also fail when compiling the pattern
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definition g_1 : nat → nat → nat
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| a a := a -- Error, 'a' is being "declared" twice
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definition g_2 (a : nat) : nat → nat → nat
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| a b := a
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example (a b c : nat) : g_2 a b c = b :=
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rfl
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inductive vec1 (A : Type u) : nat → Type (max 1 u)
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| nil : vec1 0
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| cons : ∀ n, A → vec1 n → vec1 (n+1)
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section
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open vec1
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definition map_1 {A : Type u} (f : A → A → A) : Π {n}, vec1 A n → vec1 A n → vec1 A n
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| 0 (nil .(A)) (nil .(A)) := nil A
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| (n+1) (cons .(n) h₁ v₁) (cons .(n) h₂ v₂) := cons n (f h₁ h₂) (map_1 v₁ v₂)
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definition map_2 {A : Type u} (f : A → A → A) : Π {n}, vec1 A n → vec1 A n → vec1 A n
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| 0 (nil ._) (nil ._) := nil A
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| (n+1) (cons ._ h₁ v₁) (cons ._ h₂ v₂) := cons n (f h₁ h₂) (map_2 v₁ v₂)
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/- In map_3, we use the inaccessible terms to avoid pattern/matching on the first argument -/
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definition map_3 {A : Type u} (f : A → A → A) : Π {n}, vec1 A n → vec1 A n → vec1 A n
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| ._ (nil ._) (nil ._) := nil A
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| ._ (cons n h₁ v₁) (cons .(n) h₂ v₂) := cons n (f h₁ h₂) (map_3 v₁ v₂)
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end
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inductive vec2 (A : Type u) : nat → Type (max 1 u)
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| nil {} : vec2 0
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| cons : ∀ {n}, A → vec2 n → vec2 (n+1)
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section
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open vec2
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definition map_4 {A : Type u} (f : A → A → A) : Π {n}, vec2 A n → vec2 A n → vec2 A n
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| 0 nil nil := nil
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| (n+1) (cons h₁ v₁) (cons h₂ v₂) := cons (f h₁ h₂) (map_4 v₁ v₂)
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definition map_5 {A : Type u} (f : A → A → A) : Π {n}, vec2 A n → vec2 A n → vec2 A n
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| ._ nil nil := nil
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| ._ (@cons ._ n h₁ v₁) (cons h₂ v₂) := cons (f h₁ h₂) (map_5 v₁ v₂)
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/-
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The following variant will be rejected by the new equation compiler.
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In Lean2, the second equation is accepted because unassigned metavariables
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occurring in patterns become new variables. This feature is too hackish.
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-/
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definition map_6 {A : Type u} (f : A → A → A) : Π {n}, vec2 A n → vec2 A n → vec2 A n
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| ._ nil nil := nil
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| ._ (cons h₁ v₁) (cons h₂ v₂) := cons (f h₁ h₂) (map_6 v₁ v₂)
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end
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