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Principal Type
In type theory, a type system is said to have the principal type property if, given a term and an environment, there exists a principal type for this term in this environment, i.e. a type such that all other types for this term in this environment are an instance of the principal type. The principal type property is a desirable one for a type system, as it provides a way to type expressions in a given environment with a type which encompasses all of the expressions' possible types, instead of having several incomparable possible types. Type inference for systems with the principal type property will usually attempt to infer the principal type. For instance, the ML system has the principal type property and principal types for an expression can be computed by Robinson's unification algorithm, which is used by the Hindley–Milner type inference algorithm. However, many extensions to the type system of ML, such as polymorphic recursion, can make the inference of the principal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Type Theory
In mathematics, logic, and computer science, a type theory is the formal presentation of a specific type system, and in general type theory is the academic study of type systems. Some type theories serve as alternatives to set theory as a foundation of mathematics. Two influential type theories that were proposed as foundations are Alonzo Church's typed λ-calculus and Per Martin-Löf's intuitionistic type theory. Most computerized proof-writing systems use a type theory for their foundation. A common one is Thierry Coquand's Calculus of Inductive Constructions. History Type theory was created to avoid a paradox in a mathematical foundation based on naive set theory and formal logic. Russell's paradox, which was discovered by Bertrand Russell, existed because a set could be defined using "all possible sets", which included itself. Between 1902 and 1908, Bertrand Russell proposed various "theories of type" to fix the problem. By 1908 Russell arrived at a "ramified" ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Type System
In computer programming, a type system is a logical system comprising a set of rules that assigns a property called a type to every "term" (a word, phrase, or other set of symbols). Usually the terms are various constructs of a computer program, such as variables, expressions, functions, or modules. A type system dictates the operations that can be performed on a term. For variables, the type system determines the allowed values of that term. Type systems formalize and enforce the otherwise implicit categories the programmer uses for algebraic data types, data structures, or other components (e.g. "string", "array of float", "function returning boolean"). Type systems are often specified as part of programming languages and built into interpreters and compilers, although the type system of a language can be extended by optional tools that perform added checks using the language's original type syntax and grammar. The main purpose of a type system in a programming langua ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Instance (type Theory)
Instantiation or instance may refer to: Philosophy * A modern concept similar to ''participation'' in classical Platonism; see the Theory of Forms * The instantiation principle, the idea that in order for a property to exist, it must be had by some object or substance; the instance being a specific object rather than the idea of it * Universal instantiation * An instance (predicate logic), a statement produced by applying universal instantiation to a universal statement * Existential fallacy, also called existential instantiation * A substitution instance, a formula of mathematical logic that can be produced by substituting certain strings of symbols for others in formula, also can be used as the mathematical order to represent the data in an algorithm Computing * Instance (computer science), referring to any running process, or specifically to an object as an instance of a class * Table instance (or database instance), a concept in database design; see Row (database) * Creati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Type Inference
Type inference refers to the automatic detection of the type of an expression in a formal language. These include programming languages and mathematical type systems, but also natural languages in some branches of computer science and linguistics. Nontechnical explanation Types in a most general view can be associated to a designated use suggesting and restricting the activities possible for an object of that type. Many nouns in language specify such uses. For instance, the word leash indicates a different use than the word line. Calling something a table indicates another designation than calling it firewood, though it might be materially the same thing. While their material properties make things usable for some purposes, they are also subject of particular designations. This is especially the case in abstract fields, namely mathematics and computer science, where the material is finally only bits or formulas. To exclude unwanted, but materially possible uses, the concept ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
ML (programming Language)
ML (Meta Language) is a general-purpose functional programming language. It is known for its use of the polymorphic Hindley–Milner type system, which automatically assigns the types of most expressions without requiring explicit type annotations, and ensures type safetythere is a formal proof that a well-typed ML program does not cause runtime type errors. ML provides pattern matching for function arguments, garbage collection, imperative programming, call-by-value and currying. It is used heavily in programming language research and is one of the few languages to be completely specified and verified using formal semantics. Its types and pattern matching make it well-suited and commonly used to operate on other formal languages, such as in compiler writing, automated theorem proving, and formal verification. Overview Features of ML include a call-by-value evaluation strategy, first-class functions, automatic memory management through garbage collection, parametric poly ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robinson's Unification Algorithm
In logic and computer science, unification is an algorithmic process of solving equations between symbolic expressions. Depending on which expressions (also called ''terms'') are allowed to occur in an equation set (also called ''unification problem''), and which expressions are considered equal, several frameworks of unification are distinguished. If higher-order variables, that is, variables representing functions, are allowed in an expression, the process is called higher-order unification, otherwise first-order unification. If a solution is required to make both sides of each equation literally equal, the process is called syntactic or free unification, otherwise semantic or equational unification, or E-unification, or unification modulo theory. A ''solution'' of a unification problem is denoted as a substitution, that is, a mapping assigning a symbolic value to each variable of the problem's expressions. A unification algorithm should compute for a given problem a ''complete ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polymorphic Recursion
In computer science, polymorphic recursion (also referred to as Milner– Mycroft typability or the Milner–Mycroft calculus) refers to a recursive parametrically polymorphic function where the type parameter changes with each recursive invocation made, instead of staying constant. Type inference for polymorphic recursion is equivalent to semi-unification and therefore undecidable and requires the use of a semi-algorithm or programmer-supplied type annotations. Example Nested datatypes Consider the following nested datatype: data Nested a = a :<: (Nested , Epsilon infixr 5 :<: nested = 1 :<: ,3,4:<: 5,6 ,9 :<: Epsilon [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Haskell (programming Language)
Haskell () is a general-purpose, statically-typed, purely functional programming language with type inference and lazy evaluation. Designed for teaching, research and industrial applications, Haskell has pioneered a number of programming language features such as type classes, which enable type-safe operator overloading, and monadic IO. Haskell's main implementation is the Glasgow Haskell Compiler (GHC). It is named after logician Haskell Curry. Haskell's semantics are historically based on those of the Miranda programming language, which served to focus the efforts of the initial Haskell working group. The last formal specification of the language was made in July 2010, while the development of GHC continues to expand Haskell via language extensions. Haskell is used in academia and industry. , Haskell was the 28th most popular programming language by Google searches for tutorials, and made up less than 1% of active users on the GitHub source code repository. His ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Generalized Algebraic Data Type
In functional programming, a generalized algebraic data type (GADT, also first-class phantom type, guarded recursive datatype, or equality-qualified type) is a generalization of parametric algebraic data types. Overview In a GADT, the product constructors (called data constructors in Haskell) can provide an explicit instantiation of the ADT as the type instantiation of their return value. This allows defining functions with a more advanced type behaviour. For a data constructor of Haskell 2010, the return value has the type instantiation implied by the instantiation of the ADT parameters at the constructor's application. -- A parametric ADT that is not a GADT data List a = Nil , Cons a (List a) integers = Cons 12 (Cons 107 Nil) -- the type of integers is List Int strings = Cons "boat" (Cons "dock" Nil) -- the type of strings is List String -- A GADT data Expr a where EBool :: Bool -> Expr Bool EInt :: Int -> Expr Int EEqual :: Expr Int -> Expr I ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Type Annotation
In 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. Examples C/C++ In C and C++, the type signature is declared by what is commonly known as a function prototype. In C/C++, a function declaration reflects its use; for example, a function pointer with the signature would be called as: char c; double d; int retVal = (*fPtr)(c, d); Erlang In Erlang, type signatures may be optionally declared, as: -spec(function_name(type1(), type2(), ...) -> out_type()). For example: -spec(is_even(number()) -> boolean()). Haskell A type signature in Haskell generally takes the following form: functionName :: arg1Type -> arg2Type -> ... -> argNType Notice that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Type Theory
In mathematics, logic, and computer science, a type theory is the formal presentation of a specific type system, and in general type theory is the academic study of type systems. Some type theories serve as alternatives to set theory as a foundation of mathematics. Two influential type theories that were proposed as foundations are Alonzo Church's typed λ-calculus and Per Martin-Löf's intuitionistic type theory. Most computerized proof-writing systems use a type theory for their foundation. A common one is Thierry Coquand's Calculus of Inductive Constructions. History Type theory was created to avoid a paradox in a mathematical foundation based on naive set theory and formal logic. Russell's paradox, which was discovered by Bertrand Russell, existed because a set could be defined using "all possible sets", which included itself. Between 1902 and 1908, Bertrand Russell proposed various "theories of type" to fix the problem. By 1908 Russell arrived at a "ramified" ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
