Tagged unionIn computer science, a tagged union, also called a variant, variant record, choice type, discriminated union, disjoint union, sum type or coproduct, is a data structure used to hold a value that could take on several different, but fixed, types. Only one of the types can be in use at any one time, and a tag field explicitly indicates which one is in use. It can be thought of as a type that has several "cases", each of which should be handled correctly when that type is manipulated.
Functional programmingIn computer science, functional programming is a programming paradigm where programs are constructed by applying and composing functions. It is a declarative programming paradigm in which function definitions are trees of expressions that map values to other values, rather than a sequence of imperative statements which update the running state of the program. In functional programming, functions are treated as first-class citizens, meaning that they can be bound to names (including local identifiers), passed as arguments, and returned from other functions, just as any other data type can.
Union typeIn computer science, a union is a value that may have any of several representations or formats within the same position in memory; that consists of a variable that may hold such a data structure. Some programming languages support special data types, called union types, to describe such values and variables. In other words, a union type definition will specify which of a number of permitted primitive types may be stored in its instances, e.g., "float or long integer".
Kripke semanticsKripke semantics (also known as relational semantics or frame semantics, and often confused with possible world semantics) is a formal semantics for non-classical logic systems created in the late 1950s and early 1960s by Saul Kripke and André Joyal. It was first conceived for modal logics, and later adapted to intuitionistic logic and other non-classical systems. The development of Kripke semantics was a breakthrough in the theory of non-classical logics, because the model theory of such logics was almost non-existent before Kripke (algebraic semantics existed, but were considered 'syntax in disguise').
Top typeIn mathematical logic and computer science, some type theories and type systems include a top type that is commonly denoted with top or the symbol ⊤. The top type is sometimes called also universal type, or universal supertype as all other types in the type system of interest are subtypes of it, and in most cases, it contains every possible object of the type system. It is in contrast with the bottom type, or the universal subtype, which every other type is supertype of and it is often that the type contains no members at all.
Lambda cubeIn mathematical logic and type theory, the λ-cube (also written lambda cube) is a framework introduced by Henk Barendregt to investigate the different dimensions in which the calculus of constructions is a generalization of the simply typed λ-calculus. Each dimension of the cube corresponds to a new kind of dependency between terms and types. Here, "dependency" refers to the capacity of a term or type to bind a term or type. The respective dimensions of the λ-cube correspond to: x-axis (): types that can bind terms, corresponding to dependent types.
Unit typeIn the area of mathematical logic and computer science known as type theory, a unit type is a type that allows only one value (and thus can hold no information). The carrier (underlying set) associated with a unit type can be any singleton set. There is an isomorphism between any two such sets, so it is customary to talk about the unit type and ignore the details of its value. One may also regard the unit type as the type of 0-tuples, i.e. the of no types. The unit type is the terminal object in the of types and typed functions.
Type signatureIn computer science, a type signature or type annotation defines the inputs and outputs for a function, subroutine or method. A type signature includes the number, types, and order of the arguments contained by a function. A type signature is typically used during overload resolution for choosing the correct definition of a function to be called among many overloaded forms. In C and C++, the type signature is declared by what is commonly known as a function prototype.
Normal form (abstract rewriting)In abstract rewriting, an object is in normal form if it cannot be rewritten any further, i.e. it is irreducible. Depending on the rewriting system, an object may rewrite to several normal forms or none at all. Many properties of rewriting systems relate to normal forms. Stated formally, if (A,→) is an abstract rewriting system, x∈A is in normal form if no y∈A exists such that x→y, i.e. x is an irreducible term. An object a is weakly normalizing if there exists at least one particular sequence of rewrites starting from a that eventually yields a normal form.
Free variables and bound variablesIn mathematics, and in other disciplines involving formal languages, including mathematical logic and computer science, a variable may be said to be either free or bound. The terms are opposites. A free variable is a notation (symbol) that specifies places in an expression where substitution may take place and is not a parameter of this or any container expression. Some older books use the terms real variable and apparent variable for free variable and bound variable, respectively.
