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.
All labels observed (6)
| Label | Occurrences |
|---|---|
| Martin-Löf type theory canonical | 2 |
| Martin-Löf dependent type theory | 1 |
| constructive type theory | 1 |
| extensional Martin-Löf type theory | 1 |
| intensional Martin-Löf type theory | 1 |
| intuitionistic type theory | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T13444188 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Martin-Löf type theory Context triple: [Per Martin-Löf, knownFor, Martin-Löf type theory]
-
A.
Curry–Howard correspondence
The Curry–Howard correspondence is a foundational principle in logic and computer science that establishes a deep analogy between proofs and programs, and between logical propositions and types in programming languages.
-
B.
univalent foundations program
The univalent foundations program is a research initiative that redefines the foundations of mathematics using homotopy type theory, emphasizing computationally verifiable proofs and new connections between logic, topology, and category theory.
-
C.
Brouwer–Heyting–Kolmogorov interpretation
The Brouwer–Heyting–Kolmogorov interpretation is a foundational explanation of intuitionistic logic that interprets logical connectives and proofs in terms of explicit constructions and algorithms rather than classical truth values.
-
D.
calculus of constructions
The calculus of constructions is a powerful type theory and foundational formal system that unifies higher-order logic and typed lambda calculus, serving as the basis for several modern proof assistants.
-
E.
Per Martin-Löf
Per Martin-Löf is a Swedish logician and philosopher known for developing intuitionistic type theory, a foundational system that underpins much of modern constructive mathematics and type theory in computer science.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Martin-Löf type theory Target entity description: 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.
-
A.
Curry–Howard correspondence
The Curry–Howard correspondence is a foundational principle in logic and computer science that establishes a deep analogy between proofs and programs, and between logical propositions and types in programming languages.
-
B.
univalent foundations program
The univalent foundations program is a research initiative that redefines the foundations of mathematics using homotopy type theory, emphasizing computationally verifiable proofs and new connections between logic, topology, and category theory.
-
C.
Brouwer–Heyting–Kolmogorov interpretation
The Brouwer–Heyting–Kolmogorov interpretation is a foundational explanation of intuitionistic logic that interprets logical connectives and proofs in terms of explicit constructions and algorithms rather than classical truth values.
-
D.
calculus of constructions
The calculus of constructions is a powerful type theory and foundational formal system that unifies higher-order logic and typed lambda calculus, serving as the basis for several modern proof assistants.
-
E.
Per Martin-Löf
Per Martin-Löf is a Swedish logician and philosopher known for developing intuitionistic type theory, a foundational system that underpins much of modern constructive mathematics and type theory in computer science.
- F. None of above. chosen
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 ⓘ |
| developmentPeriod | 1970s ⓘ |
| formalizes | Brouwer–Heyting–Kolmogorov interpretation ⓘ |
| 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
ⓘ
linked to:
Martin-Löf type theory
intensional Martin-Löf type theory ⓘ
linked to:
Martin-Löf type theory
|
| influenced |
Agda
ⓘ
Coq ⓘ Curry–Howard correspondence developments ⓘ Epigram ⓘ Homotopy type theory ⓘ
linked to:
homotopy type theory
Idris ⓘ NuPRL ⓘ |
| namedAfter | Per Martin-Löf ⓘ |
| provides | internal language for constructive mathematics ⓘ |
| rejects |
unrestricted axiom of choice
ⓘ
unrestricted law of excluded middle ⓘ |
| relatedTo |
Curry–Howard correspondence
ⓘ
lambda calculus ⓘ |
| supports |
interactive theorem proving
ⓘ
program extraction from proofs ⓘ |
| usedIn |
constructive mathematics
ⓘ
formalization of mathematics ⓘ functional programming languages ⓘ program verification ⓘ proof assistants ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Martin-Löf type theory Description of subject: 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.
Referenced by (7)
Full triples — surface form annotated when it differs from this entity's canonical label.
subject linked to:
Jan
linked to: Martin-Löf type theory
linked to: Martin-Löf type theory
linked to: Martin-Löf type theory
linked to: Martin-Löf type theory
linked to: Martin-Löf type theory