49 lines
1.9 KiB
Text
49 lines
1.9 KiB
Text
Set: pp::colors
|
||
Set: pp::unicode
|
||
Assumed: N
|
||
Assumed: lt
|
||
Assumed: zero
|
||
Assumed: one
|
||
Assumed: two
|
||
Assumed: three
|
||
Assumed: two_lt_three
|
||
Defined: vector
|
||
Defined: const
|
||
Defined: update
|
||
Defined: select
|
||
Defined: map
|
||
Axiom two_lt_three : two < three
|
||
Definition vector (A : Type) (n : N) : Type := Π (i : N), (i < n) → A
|
||
Definition const {A : Type} (n : N) (d : A) : vector A n := λ (i : N) (H : i < n), d
|
||
Definition const::explicit (A : Type) (n : N) (d : A) : vector A n := const n d
|
||
Definition update {A : Type} {n : N} (v : vector A n) (i : N) (d : A) : vector A n :=
|
||
λ (j : N) (H : j < n), if A (j = i) d (v j H)
|
||
Definition update::explicit (A : Type) (n : N) (v : vector A n) (i : N) (d : A) : vector A n := update v i d
|
||
Definition select {A : Type} {n : N} (v : vector A n) (i : N) (H : i < n) : A := v i H
|
||
Definition select::explicit (A : Type) (n : N) (v : vector A n) (i : N) (H : i < n) : A := select 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 :=
|
||
λ (i : N) (H : i < n), f (v1 i H) (v2 i H)
|
||
Definition map::explicit (A B C : Type) (n : N) (f : A → B → C) (v1 : vector A n) (v2 : vector B n) : vector C n :=
|
||
map f v1 v2
|
||
select (update (const three ⊥) two ⊤) two two_lt_three : Bool
|
||
⊤
|
||
update (const three ⊥) two ⊤ : vector Bool three
|
||
|
||
--------
|
||
select::explicit : Π (A : Type) (n : N) (v : vector A n) (i : N), (i < n) → A
|
||
|
||
map type --->
|
||
map::explicit : Π (A B C : Type) (n : N), (A → B → C) → (vector A n) → (vector B n) → (vector C n)
|
||
|
||
map normal form -->
|
||
λ (A B C : Type)
|
||
(n : N)
|
||
(f : A → B → C)
|
||
(v1 : Π (i : N), (i < n) → A)
|
||
(v2 : Π (i : N), (i < n) → B)
|
||
(i : N)
|
||
(H : i < n),
|
||
f (v1 i H) (v2 i H)
|
||
|
||
update normal form -->
|
||
λ (A : Type) (n : N) (v : Π (i : N), (i < n) → A) (i : N) (d : A) (j : N) (H : j < n), if A (j = i) d (v j H)
|