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Curry–Howard correspondence
In
programming language theory
and
proof theory
, the
Curry–Howard correspondence
(also known as the
Curry–Howard isomorphism
or
equivalence
, or the
proofs-as-programs
and
propositions-
or
formulae-as-types interpretation
) is the direct relationship between
computer programs
and
mathematical proofs
. It is a generalization of a syntactic
analogy
between systems of formal logic and computational calculi that was first discovered by the American
mathematician
Haskell Curry
and
logician
William Alvin Howard
. It is the link between logic and computation that is usually attributed to Curry and Howard, although the idea is related to the operational interpretation of
intuitionistic logic
given in various formulations by
L. E. J. Brouwer
,
Arend Heyting
and
Andrey Kolmogorov
(see
Brouwer–Heyting–Kolmogorov interpretation
) and
Stephen Kleene
(see
Realizability
). The relationship has been extended to include
category theory
as the three-way
Curry–Howard–Lambek correspondence
.
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