27 lines
1.1 KiB
Text
27 lines
1.1 KiB
Text
import if_then_else
|
|
-- 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 := forall (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) then d else (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
|