26 lines
1.1 KiB
Text
26 lines
1.1 KiB
Text
(* Define a "fake" type to simulate the natural numbers. This is just a test. *)
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Variable N : Type
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Variable lt : N -> N -> Bool
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Variable zero : N
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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 := Pi (i : N) (H : i < n), A
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Definition const {A : Type} (n : N) (d : A) : vector A n := fun (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 := fun (j : N) (H : j < n), if (j = i) d (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 := fun (i : N) (H : i < n), f (v1 i H) (v2 i H)
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Show Environment 10
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Check select (update (const three false) two true) two two_lt_three
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Eval select (update (const three false) two true) two two_lt_three
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Check update (const three false) two true
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Echo "\n--------"
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Check @select
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Echo "\nmap type ---> "
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Check @map
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Echo "\nmap normal form --> "
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Eval @map
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Echo "\nupdate normal form --> "
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Eval @update
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