Type system and Type theory

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Difference between Type system and Type theory

Type system vs. Type theory

In programming languages, a type system is a set of rules that assigns a property called type to the various constructs of a computer program, such as variables, expressions, functions or modules. In mathematics, logic, and computer science, a type theory is any of a class of formal systems, some of which can serve as alternatives to set theory as a foundation for all mathematics.

Compiler

A compiler is computer software that transforms computer code written in one programming language (the source language) into another programming language (the target language).

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Data type

In computer science and computer programming, a data type or simply type is a classification of data which tells the compiler or interpreter how the programmer intends to use the data.

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Epigram (programming language)

Epigram is a functional programming language with dependent types.

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ML (programming language)

ML (Meta Language) is a general-purpose functional programming language.

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Programming language

A programming language is a formal language that specifies a set of instructions that can be used to produce various kinds of output.

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Software bug

A software bug is an error, flaw, failure or fault in a computer program or system that causes it to produce an incorrect or unexpected result, or to behave in unintended ways.

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System F

System F, also known as the (Girard–Reynolds) polymorphic lambda calculus or the second-order lambda calculus, is a typed lambda calculus that differs from the simply typed lambda calculus by the introduction of a mechanism of universal quantification over types.

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Type system

In programming languages, a type system is a set of rules that assigns a property called type to the various constructs of a computer program, such as variables, expressions, functions or modules.

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Type theory

In mathematics, logic, and computer science, a type theory is any of a class of formal systems, some of which can serve as alternatives to set theory as a foundation for all mathematics.

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Typed lambda calculus

A typed lambda calculus is a typed formalism that uses the lambda-symbol (\lambda) to denote anonymous function abstraction.

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