Arrow

Arrow<'T, 'U> represents a process that takes as input something of type 'T and outputs something of type 'U.

Minimal complete definition

• arr f and first f

static member Arr(f: 'T -> 'U) : 'Arrow<'T, 'U>
static member First (f: 'Arrow<'T, 'U>) : 'Arrow<('T * 'V),('U * 'V)>

Other operations

• second f

static member Second (f: 'Arrow<'T, 'U>) : 'Arrow<('V * 'T),('V * 'U)>

• (***) f g

static member ``***`` (f : 'Arrow<'T1,'U1>) (g : 'Arrow<'T2,'U2>) : 'Arrow<('T1 * 'T2),('U1 * 'U2)>

• (&&&) f g

static member  (&&&) (f : 'Arrow<'T,'U1>) (g : 'Arrow<'T,'U2>) : 'Arrow<'T,('U1 * 'U2)>

Rules

arr id = id
arr (f >>> g) = arr f >>> arr g
first (arr f) = arr (first f)
first (f >>> g) = first f >>> first g
first f >>> arr fst = arr fst >>> f
first f >>> arr (id *** g) = arr (id *** g) >>> first f
first (first f) >>> arr assoc = arr assoc >>> first f

where assoc ((a,b),c) = (a,(b,c))

Concrete implementations

From .Net/F#

• 'T->'U
• Func<'T,'U>

From F#+

• Kleisli<'T, 'Monad<'U>>

  Suggest another concrete implementation