calculus of constructions
E911973
formal system
foundational system for mathematics
higher-order typed lambda calculus
lambda calculus
type theory
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.
All labels observed (3)
| Label | Occurrences |
|---|---|
| calculus of constructions canonical | 3 |
| Calculus of Constructions | 2 |
| Calculus of Constructions (in terms of expressiveness hierarchy) | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T11210418 — 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: calculus of constructions Context triple: [Thierry Coquand, knownFor, calculus of constructions]
-
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.
lambda calculus
Lambda calculus is a formal system in mathematical logic and computer science that uses function abstraction and application to investigate computation and serves as a foundational model for programming languages.
-
C.
Coq
Coq is an interactive theorem prover and functional programming language based on dependent type theory, widely used for formally verifying mathematical proofs and software correctness.
-
D.
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.
-
E.
combinatory logic
Combinatory logic is a foundational formal system in mathematical logic and computer science that eliminates variables by expressing computation through the combination of a small set of primitive functions.
- 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: calculus of constructions Target entity description: 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.
-
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.
lambda calculus
Lambda calculus is a formal system in mathematical logic and computer science that uses function abstraction and application to investigate computation and serves as a foundational model for programming languages.
-
C.
Coq
Coq is an interactive theorem prover and functional programming language based on dependent type theory, widely used for formally verifying mathematical proofs and software correctness.
-
D.
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.
-
E.
combinatory logic
Combinatory logic is a foundational formal system in mathematical logic and computer science that eliminates variables by expressing computation through the combination of a small set of primitive functions.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
formal system
ⓘ
foundational system for mathematics ⓘ higher-order typed lambda calculus ⓘ lambda calculus ⓘ type theory ⓘ |
| allows |
encoding of mathematical theories
ⓘ
formal verification of programs ⓘ machine-checked proofs ⓘ |
| basedOn |
Curry–Howard correspondence
ⓘ
higher-order logic ⓘ typed lambda calculus ⓘ |
| creator |
Gérard Huet
NERFINISHED
ⓘ
Thierry Coquand ⓘ |
| extensionOf | simply typed lambda calculus ⓘ |
| field |
mathematical logic
ⓘ
proof theory ⓘ theoretical computer science ⓘ type theory ⓘ |
| generalizationOf |
System F
ⓘ
higher-order predicate logic ⓘ |
| hasFeature |
Pi types
ⓘ
confluence ⓘ constructive logic ⓘ dependent types ⓘ higher-order functions ⓘ impredicative quantification ⓘ lambda abstraction ⓘ polymorphism ⓘ proofs-as-programs interpretation ⓘ strong normalization ⓘ universal quantification as types ⓘ |
| hasJudgmentForm |
term has type
ⓘ
type is well-formed ⓘ |
| influenced |
Calculus of Inductive Constructions
ⓘ
Coq proof assistant ⓘ
linked to:
Coq
Epigram language design ⓘ LEGO proof assistant ⓘ Matita proof assistant ⓘ |
| logicalInterpretation | intuitionistic higher-order logic ⓘ |
| positionInLambdaCube | top corner ⓘ |
| relatedTo | lambda cube ⓘ |
| restriction | no general recursion in the pure system ⓘ |
| semantics |
Curry–Howard isomorphism
ⓘ
linked to:
Curry–Howard correspondence
proofs-as-programs semantics ⓘ |
| unifies |
higher-order logic
ⓘ
typed lambda calculus ⓘ |
| usedAs | foundation for proof assistants ⓘ |
| yearProposed | 1985 ⓘ |
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: calculus of constructions Description of subject: 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.
Referenced by (6)
Full triples — surface form annotated when it differs from this entity's canonical label.
subject linked to:
system F
linked to: calculus of constructions
linked to: calculus of constructions
linked to: calculus of constructions