Name | # | Haskell | Ramda | Sanctuary | Signature |
---|---|---|---|---|---|
identity | I | id |
identity |
I |
a → a |
constant | K | const |
always |
K |
a → b → a |
apply | A | ($) |
call |
I ¹ |
(a → b) → a → b |
thrush | T | (&) |
applyTo |
T |
a → (a → b) → b |
duplication | W | join ² |
unnest ² |
join ² |
(a → a → b) → a → b |
flip | C | flip |
flip |
flip |
(a → b → c) → b → a → c |
compose | B | (.) , fmap ² |
map ² |
compose , map ² |
(b → c) → (a → b) → a → c |
substitution | S | (<*>) ² |
ap ² |
ap ² |
(a → b → c) → (a → b) → a → c |
chain | S_³ | (=<<) ² |
chain ² |
chain ² |
(a → b → c) → (b → a) → b → c |
converge | S2³ | apply2way , liftA2 ², liftM2 ² |
lift2 ² |
(b → c → d) → (a → b) → (a → c) → a → d |
|
psi | P | on |
on |
on |
(b → b → c) → (a → b) → a → a → c |
fix-point⁴ | Y | fix |
(a → a) → a |
¹) The A-combinator can be implemented as an alias of the I-combinator. Its implementation in Haskell exists because the infix nature gives it some utility. Its implementation in Ramda exists because it is overloaded with additional functionality.
²) Algebras like ap
have different implementations for different types.
They work like Function combinators only for Function inputs.
³) I could not find a consistent name for these combinators, but they are common enough in the JavaScript ecosystem to justify their inclusion. I named them myself in order to refer to their implementation.
⁴) In JavaScript and other non-lazy languages, it is impossible to
implement the Y-combinator. Instead a variant known as the applicative or
strict fix-point combinator is implemented. This variant is sometimes
rererred to as the Z-combinator. The implementation found in combinators.js
is the strictly evaluated "Z" combinator, which needs the extra wrapper
around g (g)
on the right hand side.
@Avaq: sorry, I wasn't suggesting that, only responding to something @JohanWiltink said.
And yes, it's not an implementation of that pattern, although the first argument can in fact be a curried function. The next functions, though, cannot be supplied separately. So you can do
But not
So it's more like
(although as usual with Ramda functions, the first argument can be uncurried or curried.)