Type Inference - Example

Example

For example, let us consider the Haskell function map, which applies a function to each element of a list, and may be defined as:

map f = map f (first:rest) = f first : map f rest

From this, it is evident that the function map takes a list as its second argument, that its first argument f is a function that can be applied to the type of elements of that list, and that the result of map is constructed as a list with elements that are results of f. So assuming that a list contains elements of the same type, we can reliably construct a type signature

map :: (a -> b) -> ->

where the syntax "a -> b" denotes a function that takes an a as its parameter and produces a b. "a -> b -> c" is equivalent to "a -> (b -> c)".

Note that the inferred type of map is parametrically polymorphic: The type of the arguments and results of f are not inferred, but left as type variables, and so map can be applied to functions and lists of various types, as long as the actual types match in each invocation.