In type theory, a type system is said to have the princial type property if, given a term and an environment, there exists a principal type for this term in this environment, ie. a type such that all other types for this term in this environment are an instance of the principal type.
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Type variable
In type theory and programming languages, a type variable is a mathematical variable ranging over types. Even in programming languages that allow mutable variables, a type variable remains an abstraction, in the sense that it does not correspond to some memory locations. Programming languages that support parametric polymorphism make use of universally quantified type variables. Languages that support existential types make use of existentially quantified type variables.
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Type inference
Type inference refers to the automatic deduction of the type of an expression in a programming language. If some, but not all, type annotations are already present it is referred to as type reconstruction. It is a feature present in some strongly statically typed languages. It is often characteristic of ¿ but not limited to ¿ functional programming languages in general. Some languages that include type inference are ML, OCaml, Haskell, Scala, D, Clean, Opa and Go.
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Polymorphism (computer science)
In computer science, polymorphism is a programming language feature that allows values of different data types to be handled using a uniform interface. The concept of parametric polymorphism applies to both data types and functions. A function that can evaluate to or be applied to values of different types is known as a polymorphic function. A data type that can appear to be of a generalized type (e.g.
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Type theory
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 programming language theory, a branch of computer science, type theory can refer to the design, analysis and study of type systems, although some computer scientists limit the term's meaning to the study of abstract formalisms such as typed ¿-calculi.
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Type system
A type system associates a type with each computed value. By examining the flow of these values, a type system attempts to ensure or prove that no type errors can occur. The particular type system in question determines exactly what constitutes a type error, but in general the aim is to prevent operations expecting a certain kind of value being used with values for which that operation does not make sense; memory errors will also be prevented.
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Satisfiability
In mathematical logic, satisfiability and validity are elementary concepts of semantics. A formula is satisfiable if it is possible to find an interpretation that makes the formula true. A formula is valid if all interpretations make the formula true. The opposites of these concepts are unsatisfiability and invalidity, that is, a formula is unsatisfiable if none of the interpretations make the formula true, and invalid if some such interpretation makes the formula false.
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Soundness
In mathematical logic, a logical system has the soundness property if and only if its inference rules prove only formulas that are valid with respect to its semantics. In most cases, this comes down to its rules having the property of preserving truth, but this is not the case in general. The word derives from the Germanic 'Sund' as in Gesundheit, meaning health. Thus to say that an argument is sound means, following the etymology, to say that the argument is healthy.
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