blanketglossary

Type theory

Definition

In mathematics, 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 the study of programming languages, formal logic, and the formalization of mathematics.

Related concepts

ACM Computing Classification System Abstract logic Ackermann set theory Agda (programming language)Aleph number Alfred North Whitehead Algebraic logic Algebraic topology Algorithm Algorithm design Algorithmic efficiency Alonzo Church Alphabet (formal languages)Alternative semantics Ambiguity Analysis of algorithms Anaphora (linguistics)And (logic)Annals of Mathematics Anonymous function Antecedent-contained deletion Application security Argument Argument of a function Arity Artificial intelligence Atomic formula Atomic model (mathematical logic)Atomic sentence Augmented reality Automata theory Automated planning and scheduling Automated proof checking Automated theorem proving Automath Autonomy of syntax Axiom Axiom of choice Axiom of reducibility Axiom schema Axiomatic system Axiomatization of Boolean algebras BHK interpretation Banach–Tarski paradox Bertrand Russell Bijection Binary operation Binding (linguistics)Boolean Logic Boolean algebra Boolean algebra (structure)Boolean algebras canonically defined Boolean function Brouwer–Heyting–Kolmogorov interpretation C-monoid Calculus of constructions Calculus of inductive constructions Call/cc Canonicity (type theory)Cantor's diagonal argument Cantor's paradox Cantor's theorem Cardinality Cartesian closed category Cartesian product Cataphora Categorial grammar Categorical logic Categorical semantics Categorical theory Category (mathematics)Category of sets Category theory Church encoding Church–Turing thesis Class (set theory)Classical logic Codomain Coercion (linguistics)Cognitive semantics Combinatory categorial grammar Combinatory logic Communication protocol Compactness theorem Compiler Compiler construction Complement (set theory)Complete theory Computability theory Computable function Computable set Computably enumerable set Computational biology Computational chemistry Computational complexity Computational complexity theory Computational engineering Computational geometry Computational intelligence Computational mathematics Computational physics Computational problem Computational semantics Computational social science Computer accessibility Computer animation Computer architecture Computer data storage Computer graphics Computer hardware Computer network Computer programming Computer science Computer security Computer vision Computing Computing platform Concrete category Concurrency (computer science)Concurrent computing Conditional operator Conditional sentence Conservative extension Conservativity Consistency Constructible universe Construction of the real numbers Constructive mathematics Constructive set theory Constructivism (mathematics)Constructor (programming)Context set Continuation Continuum hypothesis Control flow Control theory Conversational scoreboard Countable set Counterfactuals Cross-validation (statistics)Crossover effects Cryptography Cubical type theory Cumulativity (linguistics)Curry–Howard correspondence Curry–Howard isomorphism Cyber-physical system Cyberwarfare Dana Scott Data mining Data type Database De dicto and de re De se Decidability (logic)Decision problem Decision support system Deduction system Deductive system Definiteness Denotation Deontic modality Dependability Dependent type Dependent type theory Diagram (mathematical logic)Dialogue systems Digital art Digital library Digital marketing Discourse relation Discourse representation theory Discrete mathematics Disjoint union Disjunction Distributed artificial intelligence Distributed computing Distributional semantics Document management system Domain-specific language Domain of a function Donkey anaphora Dot product Double bind Double negation Downward entailing Dynamic semantics E-commerce Educational technology Electronic design automation Electronic publishing Electronic voting Element (mathematics)Elementary Theory of the Category of Sets Elementary diagram Elementary equivalence Elementary function arithmetic Embedded system Empty set Empty type Enterprise information system Enterprise software Enumeration Epistemic modality Equality (mathematics)Equiconsistency Equivalence relation Euclid's Elements Euclidean geometry Evidentiality Exhaustivity Existential closure Existential quantification Expression (mathematics)Expressive power (computer science)Extension (semantics)Extension by definitions Extension by new constant and function names Extensionality Fault tolerance Faultless disagreement Finitary relation Finite-valued logic Finite model theory Finite set First-order logic Fixed-point logic Focus (linguistics)Forcing (mathematics)Form (architecture)Form factor (design)Formal grammar Formal language Formal logic Formal methods Formal proof Formal semantics (linguistics)Formal semantics (logic)Formal semantics (natural language)Formal system Formalization of mathematics Formation rule Foundations of geometry Foundations of mathematics Free choice inference Free logic Free variables and bound variables Function (mathematics)Function application Functional predicate Fuzzy set Gamma General set theory Generalized quantifier Generative grammar Geographic information system Girard's paradox Givenness Glue semantics Graphics processing unit Green computing Gregory Bateson Grothendieck universe Ground expression Ground formula Gödel's completeness theorem Gödel's incompleteness theorems Gödel numbering HOL (proof assistant)Halting problem Hardware acceleration Hardware security Health informatics Henk Barendregt Hereditary set Higher-order logic Hilbert's axioms Hilbert system History of logic History of mathematical logic History of type theory Homogeneity (linguistics)Homotopy Homotopy type theory Human-centered computing Human–computer interaction Hurford disjunction Identity type Image (mathematics)Image compression Inaccessible cardinal Inalienable possession Independence (mathematical logic)Indexicality Indicator function Induction-induction Induction-recursion Industrial process control Inference Inferentialism Infinite-valued logic Infinite set Information retrieval Information security Information system Information theory Inhabited set Injective function Inquisitive semantics Integrated circuit Integrated development environment Intension Intensional logic Interaction design Interpretation (logic)Interpretation (model theory)Interpretation function Interpreter (computing)Intersection Intersection (set theory)Intersective modifier Intrinsic and extrinsic properties Intrusion detection system Intuitionistic logic Intuitionistic type theory Isabelle (proof assistant)Isomorphism J. Roger Hindley John Lane Bell Jon Barwise Journal of Functional Programming Judgment (mathematical logic)Julia (programming language)Kind (type theory)Kleene–Rosser paradox Knowledge representation and reasoning Kolmogorov complexity Kripke's theory of truth Kripke–Platek set theory LEGO (proof assistant)Lambda calculus Lambda cube Lambek Large cardinal Law of excluded middle Lean (proof assistant)Left associative Lemma (mathematics)Lexical semantics Library (computing)Lindström's theorem Linguistic entailment Linguistics wars List (abstract data type)List of Hilbert systems List of axioms List of computer size categories List of first-order theories List of formal systems List of mathematical theories List of set identities and relations List of statements independent of ZFC Locally cartesian closed category Logic Logic for Computable Functions Logic in computer science Logic translation Logical biconditional Logical conjunction Logical connective Logical consequence Logical constant Logical disjunction Logical equality Logical equivalence Logical form (linguistics)Logical framework Logical or Logical truth Logicism Logophoricity Löwenheim–Skolem theorem ML (programming language)Machine learning Many-valued logic Map (mathematics)Martin-Löf type theory Material conditional Mathematical analysis Mathematical logic Mathematical object Mathematical optimization Mathematical software Mathematics Matita Meaning postulate Mereology Metalanguage Metavariable Middleware Minimal axioms for Boolean algebra Mirativity Mizar system Mobile computing Modal subordination Modality (semantics)Model complete theory Model of computation Model theory Modeling language Mogensen–Scott encoding Monad (functional programming)Monadic predicate calculus Monadic second-order logic Montague grammar Morse–Kelley set theory Multi-task learning Multimedia database Multiprocessing Multithreading (computer architecture)NLab NP (complexity)Naive Set Theory (book)Naive set theory Natural deduction Natural language Natural language processing Natural number Negation Network architecture Network performance Network scheduler Network security Network service Networking hardware New Foundations Non-Euclidean geometry Non-logical symbol Non-standard model Non-standard model of arithmetic Normal form (abstract rewriting)Not (logic)NuPRL Numerical analysis Opaque context Open formula Open source Operating system Operation (mathematics)Operations research Operator associativity Or (logic)Order of operations Ordered pair Ordinal analysis Ordinal number Outline of computer science P (complexity)P versus NP problem Paradox Paradoxes of set theory Parallel computing Parameter Parametricity Partition of a set Paul Halmos Peano arithmetic Peano axioms Per Martin-Löf Performative utterance Peripheral Philosophy of artificial intelligence Philosophy of language Philosophy of mathematics Photograph manipulation Plural quantification Polarity item Possible world Power set Pragmatics Predicate (mathematical logic)Predicate logic Predicate variable Pregroup grammar Presupposition Prime model Primitive recursive arithmetic Primitive recursive function Principia Mathematica Principle of compositionality Printed circuit board Privative adjective Probability Processor (computing)Program synthesis Programming language Programming language theory Programming paradigm Programming team Programming tool Proof assistant Proof by contradiction Proof of impossibility Proof theory Proposition Propositional attitudes Propositional calculus Propositional formula Propositional logic Propositional variable Propositions Prototype Verification System Pure type system Quantification (logic)Quantificational variability effect Quantifier (logic)Quantifier raising Quantifier rank Quantization (linguistics)Quantum computing Question under discussion Randomized algorithm Real-time computing Record (computer science)Recursion Recursive definition Recursive set Reference Reflexive relation Reinforcement learning Relation (mathematics)Rendering (computer graphics)Requirements analysis Responsive predicate Reverse mathematics Rewriting Richard Montague Rising declarative Robert Lee Constable Robinson arithmetic Rocq Rocq (software)Rule of inference Russell's paradox ST type theory Satisfiability Saturated model Scalar implicature Scholarpedia Schröder–Bernstein theorem Scope (formal semantics)Second-order arithmetic Second-order logic Security hacker Security service (telecommunication)Segmented discourse representation theory Self-verifying theories Semantic analysis (compilers)Semantic parsing Semantic theory of truth Semantics (computer science)Semantics (logic)Semantics of logic Sentence (mathematical logic)Sequent calculus Set-theoretic definition of natural numbers Set (mathematics)Set theory Signature (logic)Simply typed lambda calculus Singleton (mathematics)Situation semantics Skolem arithmetic Sloppy identity Social computing Social software Software configuration management Software construction Software deployment Software design Software development Software development process Software engineering Software framework Software maintenance Software quality Software repository Solid modeling Soundness Spectrum of a sentence Spectrum of a theory Speech act Square of opposition Squiggle operator Stanford Encyclopedia of Philosophy Static program analysis Statistics Stochastic computing Strawson entailment Strength (mathematical logic)Strict conditional String (formal languages)Strongly normalizing Structural rule Structure (mathematical logic)Subsective modifier Substitution (logic)Substructure (mathematics)Subtrigging Subtyping Successor function Supertask Supervaluationism Supervised learning Surjective function Syllogism Symbol (formal)Symmetric relation Syntax (logic)Syntax–semantics interface System F System U System on a chip T-schema Tagged union Tarski's axiomatization of the reals Tarski's axioms Tarski's theory of truth Tarski's undefinability theorem Tarski–Grothendieck set theory Tautology (logic)Telicity Temperature paradox Tense–aspect–mood Term (logic)Term logic Theorem Theoretical computer science Theories of truth Theory (mathematical logic)Theory of computation Thierry Coquand Three-valued logic Timeline of mathematical logic Transfer principle Transitive relation Transitive set True arithmetic Truth-conditional semantics Truth-value Truth predicate Truth table Truth value Turing machine Turnstile (symbol)Twelf Type (model theory)Type inference Type inhabitation Type safety Type shifter Type system Type theory with records Typed lambda calculus Type–token distinction Ubiquitous computing Ultrafilter (set theory)Ultraproduct Uncountable set Undecidable problem Uninterpreted function Union (set theory)Uniqueness quantification Unit type Universal grinder Universal quantification Universal set Universe (mathematics)Unsupervised learning Urelement Vagueness Validity (logic)Variable (mathematics)Vector space Venn diagram Veridicality Very-large-scale integration Video game Virtual machine Virtual reality Visualization (graphics)Von Neumann universe Von Neumann–Bernays–Gödel set theory Well-formed formula Wireless sensor network Word processor World Wide Web Zermelo–Fraenkel set theory

159 concepts already in your glossary