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Calculus of constructions and Typed lambda calculus

Shortcuts: Differences, Similarities, Jaccard Similarity Coefficient, References.

Difference between Calculus of constructions and Typed lambda calculus

Calculus of constructions vs. Typed lambda calculus

In mathematical logic and computer science, the calculus of constructions (CoC) is a type theory created by Thierry Coquand. A typed lambda calculus is a typed formalism that uses the lambda-symbol (\lambda) to denote anonymous function abstraction.

Similarities between Calculus of constructions and Typed lambda calculus

Calculus of constructions and Typed lambda calculus have 10 things in common (in Unionpedia): Dependent type, Henk Barendregt, Intuitionistic type theory, Lambda cube, Mathematical logic, Normal form (abstract rewriting), Programming language, Pure type system, System F, Type system.

Dependent type

In computer science and logic, a dependent type is a type whose definition depends on a value.

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Henk Barendregt

Hendrik Pieter (Henk) Barendregt (born 18 December 1947, Amsterdam) is a Dutch logician, known for his work in lambda calculus and type theory.

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Intuitionistic type theory

Intuitionistic type theory (also known as constructive type theory, or Martin-Löf type theory, the latter abbreviated as MLTT) is a type theory and an alternative foundation of mathematics.

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Lambda cube

In mathematical logic and type theory, the λ-cube (also written lambda cube) is a framework introduced by Henk Barendregt to investigate the different dimensions in which the calculus of constructions is a generalization of the simply typed λ-calculus.

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Mathematical logic

Mathematical logic is the study of formal logic within mathematics.

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Normal form (abstract rewriting)

In abstract rewriting, an object is in normal form if it cannot be rewritten any further, i.e. it is irreducible.

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Programming language

A programming language is a system of notation for writing computer programs.

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Pure type system

In the branches of mathematical logic known as proof theory and type theory, a pure type system (PTS), previously known as a generalized type system (GTS), is a form of typed lambda calculus that allows an arbitrary number of sorts and dependencies between any of these.

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System F

System F (also polymorphic lambda calculus or second-order lambda calculus) is a typed lambda calculus that introduces, to simply typed lambda calculus, a mechanism of universal quantification over types.

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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).

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The list above answers the following questions

Calculus of constructions and Typed lambda calculus Comparison

Calculus of constructions has 34 relations, while Typed lambda calculus has 41. As they have in common 10, the Jaccard index is 13.33% = 10 / (34 + 41).

References

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