Data.SnocList.Elem

Definitions

data Elem : a -> SnocList a -> Type

  A proof that some element is found in a list.

Totality: total
Visibility: public export
Constructors:

Here : Elem x (sx :< x)

  A proof that the element is at the head of the list

There : Elem x sx -> Elem x (sx :< y)

  A proof that the element is in the tail of the list

Hints:

DecEq (Elem x sx)

Injective There

Uninhabited (Here = There e)

Uninhabited (There e = Here)

Uninhabited (Elem x [<])

neitherHereNorThere : Not (x = y) -> Not (Elem x sx) -> Not (Elem x (sx :< y))

  An item not in the head and not in the tail is not in the list at all.

Visibility: public export

isElem : DecEq a => (x : a) -> (sx : SnocList a) -> Dec (Elem x sx)

  Check whether the given element is a member of the given list.

Visibility: public export

get : (sx : SnocList a) -> Elem x sx -> a

  Get the element at the given position.

Visibility: public export

lookup : (sx : SnocList a) -> Elem x sx -> Singleton x

  Get the element at the given position, with proof that it is the desired element.

Visibility: public export

dropElem : (sx : SnocList a) -> Elem x sx -> SnocList a

  Remove the element at the given position.

Visibility: public export

elemToNat : Elem x sx -> Nat

  Erase the indices, returning the numeric position of the element

Visibility: public export

indexElem : Nat -> (sx : SnocList a) -> Maybe (x : a ** Elem x sx)

  Find the element with a proof at a given position (in reverse), if it is valid

Visibility: public export

elemMap : (0 f : (a -> b)) -> Elem x sx -> Elem (f x) (map f sx)

  Lift the membership proof to a mapped list

Visibility: export