In mathematics, logic and computer science, type theory is any of several formal systems that can serve as alternatives to naive set theory, or the study of such formalisms in general...
In computer science, functional programming is a programming paradigm that treats computation as the evaluation of mathematical functions and avoids state and mutable data. It emphasizes the application of functions, in contrast to the imperative programming style, which emphasizes changes in state...
In computer programming, particularly functional programming and type theory, an algebraic data type is a datatype each of whose values is data from other datatypes wrapped in one of the constructors of the datatype. Any wrapped datum is an argument to the constructor...
:
data Stream a =
Cons a (Stream a)
Generating and computing with streams requires lazy evaluation
Lazy evaluation
In programming language theory, lazy evaluation or call-by-need is an evaluation strategy which delays the evaluation of an expression until the value of this is actually required and which also avoids repeated evaluations...
, either implicitly in a lazily evaluated language or by creating and forcing thunk
Thunk (functional programming)
In computer science, a thunk is a parameterless closure created to prevent the evaluation of an expression until forced at a later time. In lazy languages thunks are created and forced implicitly...
s in an eager language. In total languages they must be defined as codata and can be iterated over using (guarded) corecursion
Corecursion
In computer science, corecursion is a type of operation that is dual to recursion. Corecursion and codata allow total languages to work with infinite data structures such as streams. Corecursion is often used in conjunction with lazy evaluation. Corecursion can produce both finite and infinite data...
.
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