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.
|
|
Variable N : Type
|
|
Variable lt : N -> N -> Bool
|
|
Variable zero : N
|
|
Variable one : N
|
|
Variable two : N
|
|
Variable three : N
|
|
Infix 50 < : lt
|
|
Axiom two_lt_three : two < three
|
|
Definition vector (A : Type) (n : N) : Type := Pi (i : N) (H : i < n), A
|
|
Definition const {A : Type} (n : N) (d : A) : vector A n := fun (i : N) (H : i < n), d
|
|
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)
|
|
Definition select {A : Type} {n : N} (v : vector A n) (i : N) (H : i < n) : A := v i H
|
|
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)
|
|
print Environment 10
|
|
Check select (update (const three false) two true) two two_lt_three
|
|
Eval select (update (const three false) two true) two two_lt_three
|
|
Check update (const three false) two true
|
|
print "\n--------"
|
|
Check @select
|
|
print "\nmap type ---> "
|
|
Check @map
|
|
print "\nmap normal form --> "
|
|
Eval @map
|
|
print "\nupdate normal form --> "
|
|
Eval @update
|