Fantasy Land Specification

(aka "Algebraic JavaScript Specification")

This project specifies interoperability of common algebraic structures:

• Functor
• Monad

General

An algebra is a set of values, a set of operators that it is closed under and some laws it must obey.

Terminology

1. "value" is any JavaScript value, including any which have the structures defined below.

Algebras

Functor

Functor values MUST implement map function that complies to a following rules:

1. map(u, function(a) { return a; }) equals u
2. map(u, function(x) { return f(g(x)); }) equals map(map(u, g), f)

map function

A value which has a functor must provide a map implementation. That takes functor value and f function:

map.define(u, function(u, f) {
  // ...
})

1. f must be a function,

   1. If f is not a function, the behaviour of map is unspecified.
   2. f can return any value.

2. map must return a value of the same functor

Monad

A value which satisfies the specification of a monad do not need to implement: Functor's map as it's defined by default:

map.define(Object, function(wrapped, f) {
   return flatMap(wrapped, function(unwrapped) {
      return derive(wrapped, f(unwrapped));
   });
});

1. of(a).then(f) equals f(a)
3. flatMap(m, function(u) { return derive(m, u) }) equals m
4. m.then(of) equals m
5. m.then(f).then(g) equals m.then(function(x) { return f(x).then(g); })

flatMap function

A value which is a monad must provide a flatMap implementation. The flatMap function takes m monad and f function as arguments:

flatMap(m, f)

1. f must be a function which returns a value

   1. If f is not a function, the behaviour of flatMap is unspecified.
   2. f must return a value of the same monad

2. flatMap must return a value of the same monad

derive function

A value which has a monad must provide derive implementation. Implementation must take source argument and value:

derive(m, a)

1. derive must provide a value of the same monad

   1. No parts of a should be checked