Welcome to Fantasy Land

Unicorns and rainbows

Isn't that cute and wonderful? Fantasy Land is a specification for algebraic JavaScript, that is, the specification of how algebraic structures should be interoperable in the JavaScript environment. This means most part of JavaScript libraries and tools with focus in functional programming will follow these laws and specification, making them easily interoperable. This is the theory that will lead to a pragmatic and standardized practic.

But first, how can we define an algebra?

• A set of values: like primitive numbers, strings or even other data structures.
• A set of operators: that can be applied to values.
• A set of laws: the operations applied to these values must obey.

Each Fantasy Land algebra is a separate specification. Some algebras may depend on other algebras. The JavaScript primitives also have equivalents to some of these algebras, as we will see in some occasions. The specification warrants that values that satisfy to specific algebras can be safely replaced by other values that also respect them. For example, we can have:

• One list can be replaced by another if they have the same length.
• Two objects have the same keys and their values have the same or compatible types.
• Two functions have equivalent output types for equivalent input types.

Understanding type signatures

We'll be using a notation similar to Haskell type signatures to express the types that the algebras must satisfy, where:

• :: means "is a member of".
  • e :: t is the same as "the expression e is member of type t".
  • true :: Boolean means that "true is a member of type Boolean".
  • 42 :: Integer, Number means that "42 is a member of type Integer and type Number".
• New types can be created via type constructors.
  • Where type constructors can take zero or more parameters.
  • In Haskell, True is a type constructor that yields a Bool and takes no parameters.
  • Array is a type constructor that takes one parameter.
  • Array Number is the type of any array that holds only numbers, like [1, 2].
  • Types can be nested. Array (Array Boolean)) is the type of all arrays that have arrays of booleans, like [[true], [false, true], []], where [] can be seen as an array compatible to any type parameter.
• Lowercase letters stand for type variables:
  • Type variables can take any type unless they have constraint restrictions, as we'll see bellow.
  • [] can be seen as Array a for example, where a can be String, Number or any other type.
• ->, the arrow, stands for function type constructor.
  • -> is an infix binary type constructor that takes the input type on the left and output type on the right.
  • The left type of -> can be a grouping for functions that take more than one parameter, for example, (Number, Number) -> Number is a function that receives two numbers and returns another.
  • Parentheses on the left of -> are optional for unary functions and obligatory for the rest.
  • Functions that take no arguments can be represented by the unit type ().
  • a -> a is a function that receives a parameter and yields a value of the same type.
  • Array String -> Array Number is a function that receives an array of strings and yields an array of numbers.
  • (String, String) -> a is a function that receives two strings and yields anything.
  • () -> () is a function that takes no parameters and yields no results.
• ~>, the squiggly arrow, stands for method type constructor.
  • If a function is a property of an object, then it is a method. Methods have implicit type parameters that is the type of the object that holds the property.
  • Object ~> () ~> String is the signature satisfies by a method that, when applied to the object and without parameters, yields a string, such as Object.prototype.toString: (1).toString.
• =>, the fat arrow, stands for constraints in type variables.
  • Monoid a => a ~> a -> a stands for a method applied to an object of type a that receives another instance of a and yields also an a where all these values satisfy to the Monoid laws.