Lecture

Types in Lambda Calculus

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In course

CS-452: Foundations of software

The course introduces the foundations on which programs and programming languages are built. It introduces syntax, types and semantics as building blocks that together define the properties of a program part or a language. Students will learn how to apply ...

Description

This lecture introduces the concept of types in lambda calculus, focusing on two example languages: typing arithmetic expressions and simply typed lambda calculus. The instructor explains how to define types, specify typing rules, and prove soundness. The lecture covers topics such as evaluation rules, type safety, typechecking algorithm, canonical forms, progress, preservation, and properties of the typing relation.

Instructors (2)

Martin Odersky

Martin Odersky heads the programming research group at EPFL. His research interests cover fundamental as well as applied aspects of programming languages. They include semantics, type systems, programming language design, and compiler construction. The main focus if his work lies in the integration of object-oriented and functional programming. His research thesis is that the two paradigms are just two sides of the same coin and should be unified as much as possible. To prove this he has experimented a number of language designs, from Pizza to GJ to Functional Nets. He has also influenced the development of Java as a co-designer of Java generics and as the original author of the current javac reference compiler. His current work concentrates on the Scala programming language, which unifies FP and OOP, while staying completely interoperable with Java and .NET. Martin Odersky got his doctorate from ETHZ, in 1989. He held research positions at the IBM T.J. Watson Research Center from 1989 and at Yale University from 1991. He was then a professor at the University of Karlsruhe from 1993 and at the University of South Australia from 1997. He joined EPFL as full professor in 1999. He is associate editor of the Journal of Functional Programming and member of IFIP WG 2.8. He was conference chair for ICFP 2000, and program chair for ECOOP 2004 as well as ETAPS/CC 2007.

Sébastien Jean Robert Doeraene

Expertise Language design, compilers, virtual machines.Pedagogy in computer science. Current Work Scala.js, the dialect of Scala for JavaScript and WebAssembly Sébastien Doeraene is a compiler/runtime systems hacker and a Scala enthusiast. Best known as the author of Scala.js, he is now lecturer at EPFL. He holds a PhD from EPFL, having worked under the supervision of Prof. Martin Odersky, and a master's degree in computer science engineering from Université catholique de Louvain in Belgium. When he is not

Official source

Ontological neighbourhood

Theoretical computer science

Programming language theory: High-level programming languages

Related concepts (32)

Type system

In computer programming, a type system is a logical system comprising a set of rules that assigns a property called a type (for example, integer, floating point, string) 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.

Simply typed lambda calculus

The simply typed lambda calculus (), a form of type theory, is a typed interpretation of the lambda calculus with only one type constructor () 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. The term simple type is also used to refer extensions of the simply typed lambda calculus such as products, coproducts or natural numbers (System T) or even full recursion (like PCF).

Typed lambda calculus

A typed lambda calculus is a typed formalism that uses the lambda-symbol () 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). From a certain point of view, typed lambda calculi can be seen as refinements of the untyped lambda calculus, but from another point of view, they can also be considered the more fundamental theory and untyped lambda calculus a special case with only one type.

Lambda calculus

Lambda calculus (also written as λ-calculus) is a formal system in mathematical logic for expressing computation based on function abstraction and application using variable binding and substitution. It is a universal model of computation that can be used to simulate any Turing machine. It was introduced by the mathematician Alonzo Church in the 1930s as part of his research into the foundations of mathematics. Lambda calculus consists of constructing lambda terms and performing reduction operations on them.

Type safety

In computer science, type safety and type soundness are the extent to which a programming language discourages or prevents type errors. Type safety is sometimes alternatively considered to be a property of facilities of a computer language; that is, some facilities are type-safe and their usage will not result in type errors, while other facilities in the same language may be type-unsafe and a program using them may encounter type errors.

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