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.
Observed surface forms (1)
| Surface form | Occurrences |
|---|---|
| Calculus of Constructions | 0 |
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
NERFINISHED
ⓘ
higher-order logic ⓘ typed lambda calculus ⓘ |
| creator |
Gérard Huet
NERFINISHED
ⓘ
Thierry Coquand NERFINISHED ⓘ |
| extensionOf | simply typed lambda calculus ⓘ |
| field |
mathematical logic
ⓘ
proof theory ⓘ theoretical computer science ⓘ type theory ⓘ |
| generalizationOf |
System F
NERFINISHED
ⓘ
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
NERFINISHED
ⓘ
Coq proof assistant NERFINISHED ⓘ Epigram language design ⓘ LEGO proof assistant NERFINISHED ⓘ Matita proof assistant NERFINISHED ⓘ |
| logicalInterpretation | intuitionistic higher-order logic ⓘ |
| positionInLambdaCube | top corner ⓘ |
| relatedTo | lambda cube ⓘ |
| restriction | no general recursion in the pure system ⓘ |
| semantics |
Curry–Howard isomorphism
NERFINISHED
ⓘ
proofs-as-programs semantics ⓘ |
| unifies |
higher-order logic
ⓘ
typed lambda calculus ⓘ |
| usedAs | foundation for proof assistants ⓘ |
| yearProposed | 1985 ⓘ |
Referenced by (3)
Full triples — surface form annotated when it differs from this entity's canonical label.