Martin-Löf type theory
E1041769
Martin-Löf type theory is a foundational system for constructive mathematics and computer science that integrates logic and computation through dependent types and serves as a basis for proof assistants and functional programming languages.
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
dependent type theory
ⓘ
foundational system for constructive mathematics ⓘ type theory ⓘ |
| aimsAt | unifying logic and computation ⓘ |
| basedOn | intuitionistic logic ⓘ |
| developedBy | Per Martin-Löf NERFINISHED ⓘ |
| developmentPeriod | 1970s ⓘ |
| formalizes | Brouwer–Heyting–Kolmogorov interpretation NERFINISHED ⓘ |
| foundationFor | constructive set-free foundations of mathematics ⓘ |
| hasComponent |
W-types
ⓘ
finite types ⓘ natural number type ⓘ universe hierarchy ⓘ Π-types ⓘ Σ-types ⓘ |
| hasKeyFeature |
constructive logic
ⓘ
constructive semantics ⓘ dependent types ⓘ identity types ⓘ inductive types ⓘ intensional equality ⓘ proofs as programs ⓘ propositions as types ⓘ universes ⓘ |
| hasSemantics |
categorical semantics
ⓘ
computational semantics ⓘ |
| hasVariant |
extensional Martin-Löf type theory
NERFINISHED
ⓘ
intensional Martin-Löf type theory NERFINISHED ⓘ |
| influenced |
Agda
NERFINISHED
ⓘ
Coq NERFINISHED ⓘ Curry–Howard correspondence developments ⓘ Epigram NERFINISHED ⓘ Homotopy type theory NERFINISHED ⓘ Idris NERFINISHED ⓘ NuPRL NERFINISHED ⓘ |
| namedAfter | Per Martin-Löf NERFINISHED ⓘ |
| provides | internal language for constructive mathematics ⓘ |
| rejects |
unrestricted axiom of choice
ⓘ
unrestricted law of excluded middle ⓘ |
| relatedTo |
Curry–Howard correspondence
NERFINISHED
ⓘ
lambda calculus NERFINISHED ⓘ |
| supports |
interactive theorem proving
ⓘ
program extraction from proofs ⓘ |
| usedIn |
constructive mathematics
ⓘ
formalization of mathematics ⓘ functional programming languages ⓘ program verification ⓘ proof assistants ⓘ |
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.