Functional Programming in the Fantasy Land
Marius Jurgelenas & Karolis Masiulis
VilniusJs
2018
(x) => x
Fantasy Land
- Method Signatures
- Laws
- Constraints
https://github.com/fantasyland/fantasy-land
Specified in JavaScript by Fantasy Land spec
Functor
Applicative
Apply
Chain
Monad
Method signatures
Laws
map :: Functor f => f a ~> (a -> b) -> f b
u.map(a => a) === u
u.map(x => f(g(x))) === u.map(g).map(f)
Identity
Composition
Functor
Extended Hindley-Milner type system
[1,2,3].map(x => x + 1) // [2,3,4]
Constraints
- f must be a function,
- If f is not a function, the behaviour of map is unspecified.
- f can return any value.
- No parts of f's return value should be checked.
- map must return a value of the same Functor
u.map(f)
Functor
Functor
Applicative
Apply
Chain
Monad
Method signature
of :: Applicative f => a -> f a
A value which has an Applicative must provide an of function on its type representative. The of function takes one argument:
F.of(a)
Applicative
Functor
Applicative
Apply
Chain
Monad
Method signature
ap :: Apply f => f a ~> f (a -> b) -> f b
Apply
map :: Functor f => f a ~> (a -> b) -> f b
ap :: Apply f => f a ~> f (a -> b) -> f b
Functor vs Apply
Functor
Applicative
Apply
Chain
Monad
Method signature
chain :: Chain f => f a ~> (a -> f b) -> f b
Chain
map :: Functor f => f a ~> (a -> b) -> f b
ap :: Apply f => f a ~> f (a -> b) -> f b
Functor vs Apply vs Chain
chain :: Chain f => f a ~> (a -> f b) -> f b
Functor
Applicative
Apply
Chain
Monad
Monad
A Monad must implement the Applicative and Chain specifications.
There is one operation to manipulate values of the monad (chain), and an operation to put values into a monad (of)