24 lines
1.2 KiB
Text
24 lines
1.2 KiB
Text
(* Define a "fake" type to simulate the natural numbers. This is just a test. *)
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Variable Natural : Type
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Variable lt : Natural -> Natural -> Bool
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Variable zero : Natural
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Variable one : Natural
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Variable two : Natural
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Variable three : Natural
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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 : Natural) : Type := Pi (i : Natural) (H : i < n), A
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Definition const (A : Type) (n : Natural) (d : A) : vector A n := fun (i : Natural) (H : i < n), d
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Definition update (A : Type) (n : Natural) (v : vector A n) (i : Natural) (d : A) : vector A n := fun (j : Natural) (H : j < n), if A (j = i) d (v j H)
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Definition select (A : Type) (n : Natural) (v : vector A n) (i : Natural) (H : i < n) : A := v i H
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Definition map (A B C : Type) (n : Natural) (f : A -> B -> C) (v1 : vector A n) (v2 : vector B n) : vector C n := fun (i : Natural) (H : i < n), f (v1 i H) (v2 i H)
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Show Environment
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Check select Bool three (update Bool three (const Bool three false) two true) two two_lt_three
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Eval select Bool three (update Bool three (const Bool three false) two true) two two_lt_three
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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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