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Type theory

In mathematical logic, and theoretical computer science, type theory is the study of formal systems that classify expressions or mathematical objects by their types. Roughly speaking, a type plays a similar role to that played by a data type in programming: it specifies what kind of thing an expression is and how it may be used. Type theories are used in…

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Differences from set theory

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Advanced material

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Type theory

Nodes200
Edges199
Triples145
Avg. degree1.99
Density0.01
Components1

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Type theory

Top relations

related to Advanced material · 19
Type theory → Computational, Constable, Implementing Mathematics, Introduction, Logic, Prentice-Hall, Programming Languages Summer School, Robert, Robert Harper's, Scholarpedia, Semantics, Summer, System, The Nuprl Proof Development, The TYPES Forum, Types, Types Project, VerificationAndrej Bauer's, YouTubeSummer
related to Differences from set theory · 15
Type theory → Church, Classical, Fraenkel, In, Moreover, Peano's, Set, The, There, Thus, Type, When, Where, Zermelo, ZFC
related to Proof assistants · 15
Type theory → Agda, Coq, HOL, Lean, LF, Luo's Unified Theory, Matita, Most, Much, NuPRL, PVS, Rocq, Twelf, Types, UTT
related to Mathematical foundations · 14
Type theory → Automath, Category, ETCS, Fraenkel, Homotopy, Lawvere's Elementary Theory, Martin-Löf, Mathematicians, Researchers, Sets, The, There, This, Zermelo
related to history · 11
Type theory → Bertrand Russell, Between, By, Entities, Russell, Russell's, Russell's Principia Mathematica, This, Type, Whitehead, Zermelo-Fraenkel
related to Introductory material · 10
Type theory → Constructions, Helmut BrandlIntuitionistic Type Theory, Henk BarendregtCalculus, Intuitionistic Type Theory, Martin-Löf's Type Theory, Per Martin-LöfProgramming, PhilosophyLambda Calculi, Stanford Encyclopedia, Typed Lambda Calculus, Types
related to Programming languages · 9
Type theory → Agda, Any, Computable Functions, Logic, Luo's Unified Theory, ML, The, Types, UTT
related to Rules of inference · 8
Type theory → Delta, For, Gamma, Gentzen-style, One, Rules, The, To
is a · 6
Type theory → active area of research, implementation of homotopy type theory MajorSimply typed lambda calculus which is a higher-order logicIntuitionistic type theorySystem FLF is often used to define other type the…, mathematical logic, notable area of research that mainly deals with equality in type theory, notable area of research that mainly deals with equality in type theory.Inductive typesInductive types are a general template for creating a large variety of types, study of formal systems that classify expressions or mathematical objects by their types
related to Axioms · 6
Type theory → An, Most, Set Theory, Sometimes, They, This

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Important terminology

type theory displaystyle types terms rules term function mathrm theories lambda logic functions set intuitionistic one mathsf may used also

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SubjectPredicateObjectConfidenceSrc
Type theoryis astudy of formal systems that classify expressions or mathematical objects by their types0.90text
Type theoryis aactive area of research0.90text
Type theoryis amathematical logic0.90text
Type theoryis anotable area of research that mainly deals with equality in type theory.Inductive typesInductive types are a general template for creating a large variety of types0.90text
Type theoryis anotable area of research that mainly deals with equality in type theory0.90text
Type theoryis aimplementation of homotopy type theory MajorSimply typed lambda calculus which is a higher-order logicIntuitionistic type theorySystem FLF is often used to define other type the…0.90text
Lawvere's Elementary Theory of the Category of Setsinstance ofThis led to proposals0.80text
the successor function Sinstance ofand functions0.80text
call with current continuationinstance ofThese include operators on continuations0.80text
canonicityinstance ofthese operators tend to break desirable properties0.80text
parametricity.Curryinstance ofthese operators tend to break desirable properties0.80text
parametricityinstance ofthese operators tend to break desirable properties0.80text

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