49 lines
1.7 KiB
Text
49 lines
1.7 KiB
Text
Set: pp::colors
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Set: pp::unicode
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Assumed: N
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Assumed: lt
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Assumed: zero
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Assumed: one
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Assumed: two
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Assumed: three
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Assumed: two_lt_three
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Defined: vector
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Defined: const
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Defined: update
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Defined: select
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Defined: map
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variable one : N
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variable two : N
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variable three : N
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infix 50 < : lt
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axiom two_lt_three : two < three
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definition vector (A : Type) (n : N) : Type := ∀ (i : N), i < n → A
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definition const {A : Type} (n : N) (d : A) : vector A n := λ (i : N) (H : i < n), d
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definition update {A : Type} {n : N} (v : vector A n) (i : N) (d : A) : vector A n :=
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λ (j : N) (H : j < n), if j = i then d else v j H
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definition select {A : Type} {n : N} (v : vector A n) (i : N) (H : i < n) : A := v i H
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definition map {A B C : Type} {n : N} (f : A → B → C) (v1 : vector A n) (v2 : vector B n) : vector C n :=
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λ (i : N) (H : i < n), f (v1 i H) (v2 i H)
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select (update (const three ⊥) two ⊤) two two_lt_three : Bool
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eps (nonempty_intro ⊤) (λ r : Bool, ((two = two → r = ⊤) → ((two = two → ⊥) → r = ⊥) → ⊥) → ⊥)
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update (const three ⊥) two ⊤ : vector Bool three
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--------
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@select : ∀ (A : Type) (n : N) (v : vector A n) (i : N), i < n → A
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map type --->
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@map : ∀ (A B C : Type) (n : N), (A → B → C) → vector A n → vector B n → vector C n
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map normal form -->
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λ (A B C : Type)
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(n : N)
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(f : A → B → C)
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(v1 : ∀ (i : N), i < n → A)
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(v2 : ∀ (i : N), i < n → B)
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(i : N)
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(H : i < n),
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f (v1 i H) (v2 i H)
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update normal form -->
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λ (A : Type) (n : N) (v : ∀ (i : N), i < n → A) (i : N) (d : A) (j : N) (H : j < n),
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eps (nonempty_intro d) (λ r : A, ((j = i → r = d) → ((j = i → ⊥) → r = v j H) → ⊥) → ⊥)
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