Typed lambda calculusIn mathematics and computer science, a typed lambda calculus is a typed formalism that uses the lambda symbol (λ{\displaystyle \lambda }) to denote anonymous function abstraction. In this context, types are usually objects of a syntactic nature that are assigned to lambda terms; the exact nature of a type depends on the calculus considered (see kinds below).Simply typed lambda calculusThe simply typed lambda calculus ( λ → {\displaystyle \lambda ^{\to }} ), a form of type theory, is a typed interpretation of the lambda calculus with only one type constructor ( → {\displaystyle \to } ) that builds function types. It is the canonical and simplest example of a typed lambda calculus. The simply typed lambda calculus was originally introduced by Alonzo Church in 1940 as an attempt to avoid paradoxical use of the untyped lambda calculus.
Parametric polymorphismIn programming languages and type theory, parametric polymorphism allows a single piece of code to be given a "generic" type, using variables in place of actual types, and then instantiated with particular types as needed. Parametrically polymorphic functions and data types are sometimes called generic functions and generic datatypes, respectively, and they form the basis of generic programming. Parametric polymorphism may be contrasted with ad hoc polymorphism.
ML (programming language)ML (Meta Language) is the metalanguage developed for the Edinburgh LCF theorem prover in the 1970s. It is an early statically typed, functional language with polymorphictype inference in the Hindley–Milner style, and other features like exceptions and mutable variables. ML's design in LCF directly inspired the later ML family (notably Standard ML, Caml, and their derivatives) and influenced subsequent functional language development.
Type variableIn 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.
John C. ReynoldsJohn Charles Reynolds (June 1, 1935 – April 28, 2013) was an American computer scientist. Education and affiliationsJohn Reynolds studied at Purdue University and then earned a Doctor of Philosophy (Ph.D.) in theoretical physics from Harvard University in 1961. He was a professor of information science at Syracuse University from 1970 to 1986. From then until his death, he was a professor of computer science at Carnegie Mellon University.
Identity functionIn mathematics, an identity function, also called an identity relation, identity map or identity transformation, is a function that always returns the value that was used as its argument, unchanged. That is, when f{\displaystyle f} is the identity function, the equalityf(x)=x{\displaystyle f(x)=x} is true for all values of x{\displaystyle x} to which f{\displaystyle f} can be applied.
Jean-Yves GirardJean-Yves Girard (French:; born 1947) is a French logician working in proof theory. He is a research director (emeritus) at the mathematical institute of University of Aix-Marseille, at Luminy. BiographyJean-Yves Girard is an alumnus of the École normale supérieure de Saint-Cloud.
Universal quantificationIn mathematical logic, a universal quantification is a type of quantifier, a logical constant which is interpreted as "given any", "for all", "for every", or "given an arbitrary element". It expresses that a predicate can be satisfied by every member of a domain of discourse. In other words, it is the predication of a property or relation to every member of the domain.Computer scientistA computer scientist is a scientist who specializes in the academic study of computer science and technology. Computer scientists typically work on the theoretical side of computation.
Programming languageA programming language is an engineered language for expressing computer programs, typically allowing software to be written in a human readable manner. Execution of a program requires an implementation. There are two main approaches for implementing a programming language – compilation, where programs are translated ahead-of-time to machine code, and interpretation, where programs are directly executed.
LogicStudy of correct reasoningLogic studies valid forms of inference like modus ponens.Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical truths. It examines how conclusions follow from premises based on the structure of arguments alone, independent of their topic and content. Informal logic is associated with informal fallacies, critical thinking, and argumentation theory.*As an Amazon Associate I earn from qualifying purchases.