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 := forall (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) 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 := fun (i : N) (H : i < n), f (v1 i H) (v2 i H)
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print 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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print "\n--------"
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check @select
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print "\nmap type ---> "
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check @map
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print "\nmap normal form --> "
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eval @map
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print "\nupdate normal form --> "
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eval @update
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