Curry–Howard correspondence

E588866
concept in mathematical logic concept in theoretical computer science correspondence between logic and computation

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.

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Observed surface forms (3)

Surface form Occurrences
Curry–Howard–Lambek correspondence 2
Curry–Howard correspondence (foundational ideas) 1
“Propositions as Types” 1

Statements (48)

Predicate Object
instanceOf concept in mathematical logic ⓘ
concept in theoretical computer science ⓘ
correspondence between logic and computation ⓘ
alsoKnownAs Curry–Howard isomorphism NERFINISHED ⓘ
proofs-as-programs ⓘ
propositions-as-types NERFINISHED ⓘ
appliesTo constructive type theory ⓘ
intuitionistic logic NERFINISHED ⓘ
natural deduction systems ⓘ
sequent calculi ⓘ
simply typed lambda calculus ⓘ
typed lambda calculi ⓘ
coreClaim proof normalization corresponds to program evaluation ⓘ
proofs correspond to programs ⓘ
propositions correspond to types ⓘ
developedBy Haskell Curry NERFINISHED ⓘ
William Alvin Howard NERFINISHED ⓘ
field logic in computer science ⓘ
programming language theory ⓘ
proof theory ⓘ
type theory ⓘ
formalizedIn Howard 1969 paper "The formulae-as-types notion of construction" NERFINISHED ⓘ
formalizesRelationBetween constructive proofs ⓘ
programs with types ⓘ
historicalRoot combinatory logic NERFINISHED ⓘ
intuitionistic proof theory ⓘ
lambda calculus ⓘ
implies every constructive proof can be seen as a program ⓘ
program extraction from proofs ⓘ
type checking corresponds to proof checking ⓘ
inspired dependently typed programming languages ⓘ
design of functional programming languages ⓘ
proof assistants ⓘ
type systems in programming languages ⓘ
namedAfter Haskell Curry NERFINISHED ⓘ
William Alvin Howard NERFINISHED ⓘ
relatedConcept Brouwer–Heyting–Kolmogorov interpretation NERFINISHED ⓘ
constructive mathematics ⓘ
dependent types ⓘ
homotopy type theory NERFINISHED ⓘ
relatesConcept computer programs ⓘ
formal proofs ⓘ
logical propositions ⓘ
types in programming languages ⓘ
usedIn Agda NERFINISHED ⓘ
Coq NERFINISHED ⓘ
Idris programming language NERFINISHED ⓘ
Lean theorem prover NERFINISHED ⓘ

Referenced by (7)

Full triples — surface form annotated when it differs from this entity's canonical label.

Curry encoding → influencedBy → Curry–Howard correspondence ⓘ
Haskell Curry → notableWork → Curry–Howard correspondence ⓘ
this entity surface form: Curry–Howard correspondence (foundational ideas)
Haskell Curry → knownFor → Curry–Howard correspondence ⓘ
Haskell Curry → knownFor → Curry–Howard correspondence ⓘ
this entity surface form: Curry–Howard–Lambek correspondence
Haskell Curry → hasConceptNamedAfter → Curry–Howard correspondence ⓘ
Haskell Curry → hasConceptNamedAfter → Curry–Howard correspondence ⓘ
this entity surface form: Curry–Howard–Lambek correspondence
Philip Wadler → coAuthored → Curry–Howard correspondence ⓘ
this entity surface form: “Propositions as Types”