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.
Same as gazing avianly at the Smullyan book, which I got in ebook after buying it physically.