Types
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Although functional programming can be done in a dynamically typed language (Lisp, the functional programming language forerunner, had no types), strong static type adds a very natural complement to functional programming.
From a mathematical point of view, a function sets a relationship between the set defined by the function argument (domain in math speaking) and the corresponding results (co-domain). Algebra studies exactly these relationships and may help the programmer in proving certain properties of the functions composing the programs.
Algebraic Data Types (ADT) are aggregated types in the algebra context. Two ADTs are of particular interest – sum types and product types. With sum and product referring to the resulting number of possible values (i.e. cardinality of sets).
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