What are the two types of recursive types?
There are two forms of recursive types: so-called isorecursive types and equirecursive types. The two forms differ in how recursively typed terms are introduced and eliminated. μα.
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How do you define a recursive data type in ML?
In Standard ML, the tree and forest data types can be mutually defined recursively as follows, which allows for empty trees: In Haskell, the tree and forest data types can be defined in a similar way: In type theory, a recursive type has the general form μα.T where the variable of type α can appear in the type T and represents the entire type itself.
Can a recursive type be used in Haskell?
In functional programming languages, isorecursive types (in the form of data types) are much more common. Recursion is not allowed in type synonyms in Miranda, OCaml (unless the -rectypes flag is used or it is a register or variant), and Haskell; so, for example, the following Haskell types are illegal:
How are equicursive types used in functional programming?
Equirecursive types capture the form of self-referential (or mutually referential) type definitions seen in procedural and object-oriented programming languages, and also arise in class and object type-theoretic semantics. In functional programming languages, isorecursive types (in the form of data types) are much more common.
How are recursive data types defined in Haskell?
In Haskell, the data types of trees and forests can be defined in a similar way: in type theory, a recursive type has the general form μα.T where the variable of type α can appear in the type T and represents the type complete. For example, natural numbers (see Peano arithmetic) can be defined by the Haskell data type:
How are recursive data structures used in computer science?
An important application of recursion in computing is the definition of dynamic data structures, such as lists and trees. Recursive data structures can dynamically grow to an arbitrarily large size in response to runtime requirements; rather, the size requirements of a static array must be set at compile time.
How are recursive data types used in Lisp?
They are fundamental to the list processing languages Lisp and Scheme (where for historical reasons they are called nil, cons, car, and cdr, respectively). They are widely used in functional programming, where first and rest are sometimes called the head and tail.