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Lectures on the curryhoward isomorphism
, 1998
"... The CurryHoward isomorphism states an amazing correspondence between systems of formal logic as encountered in proof theory and computational calculi as found in type theory. For instance, minimal propositional logic corresponds to simply typed λcalculus, firstorder logic corresponds to dependent ..."
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Cited by 13 (0 self)
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The CurryHoward isomorphism states an amazing correspondence between systems of formal logic as encountered in proof theory and computational calculi as found in type theory. For instance, minimal propositional logic corresponds to simply typed λcalculus, firstorder logic corresponds
The limits of the CurryHoward isomorphism
, 2013
"... The wellknown CurryHoward isomorphism relates functions with proofs and can be considered as one of the conceptional bases of MartinLöf’s type theory. For our considerations, the crucial correspondence is the one between (intuitionistic) proofs of an implication A → B and functions of the type A ..."
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The wellknown CurryHoward isomorphism relates functions with proofs and can be considered as one of the conceptional bases of MartinLöf’s type theory. For our considerations, the crucial correspondence is the one between (intuitionistic) proofs of an implication A → B and functions of the type
Building Proofs by Analogy via the CurryHoward Isomorphism
, 1992
"... We present a formal method for building proofs by analogy and its implementation as a proof tactic for the NuPRL proof development system. The CurryHoward Isomorphism is used to represent proof constructions in a termfunctional language and to specify analogies by transformation rules on these ter ..."
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We present a formal method for building proofs by analogy and its implementation as a proof tactic for the NuPRL proof development system. The CurryHoward Isomorphism is used to represent proof constructions in a termfunctional language and to specify analogies by transformation rules
CurryHoward Isomorphism and Intuitionistic Linear Logic
, 1996
"... The notion of CurryHoward Isomorphism (CHI) was originally introduced for formalizing to which extent the computational behavior of the typed calculus (fi t ) is joined at the semantics of the natural deduction for Intuitionistic Logic (IL). The introduction of the Intuitionistic Linear Logic ..."
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Cited by 3 (3 self)
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The notion of CurryHoward Isomorphism (CHI) was originally introduced for formalizing to which extent the computational behavior of the typed calculus (fi t ) is joined at the semantics of the natural deduction for Intuitionistic Logic (IL). The introduction of the Intuitionistic Linear Logic
A CurryHoward Isomorphism for Compilation and Program Execution (Extended Abstract)
 In Proc. Typed Lambda Calculi and Applications, Springer LNCS 1581
, 1999
"... This paper establishes a CurryHoward isomorphism for compilation and program execution by showing the following facts. (1) The set of Anormal forms, which is often used as an intermediate language for compilation, corresponds to a subsystem of Kleene's contractionfree variant of Gentzen&apos ..."
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Cited by 5 (4 self)
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This paper establishes a CurryHoward isomorphism for compilation and program execution by showing the following facts. (1) The set of Anormal forms, which is often used as an intermediate language for compilation, corresponds to a subsystem of Kleene's contractionfree variant of Gentzen
The Logical Abstract Machine: a CurryHoward isomorphism for machine code
 In A. Middeldorp and T. Sato, Eds., Proc. Fuji International Symposium on Functional and Logic Programming (FLOPS ’01), LNCS 1722
, 1999
"... Abstract. This paper presents a logical framework for lowlevel machine code and code generation. We first define a calculus, called sequential sequent calculus, of intuitionistic propositional logic. A proof of the calculus only contains left rules and has a linear (nonbranching) structure, whi ..."
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Cited by 11 (6 self)
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ture, which reflects the properties of sequential machine code. We then establish a CurryHoward isomorphism between this proof system and machine code based on the following observation. An ordinary machine instruction corresponds to a polymorphic proof transformer that extends a given proof with one
TypeFree CurryHoward Isomorphisms (A ProofTheory Inspired Exposition of the Isomorphism between the Untyped Calculus with Variable Names and à la de Bruijn)
"... We give an alternative, prooftheory inspired proof of the wellknown result that the untyped calculus presented with variable names and `a la de Bruijn are isomorphic. The two presentations of the calculus come about from two isomorphic logic formalisations by observing that, for the logic in ..."
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in question, the CurryHoward correspondence is formulaindependent. We identify the exchange rule as the the prooftheoretical difference between the two representations of the systems. 1 Introduction The CurryHoward correspondence relates formal inference systems of symbolic logic to typed like calculi
Proofs as Cryptography: a new interpretation
"... of the CurryHoward isomorphism for software certificates ..."
References
"... [19] L. Roversi. Curryhoward isomorphism for intuitionistic linear logic: prooftheorist's ..."
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[19] L. Roversi. Curryhoward isomorphism for intuitionistic linear logic: prooftheorist's
Putting CurryHoward to work
 In Proceedings of ACM Workshop on
, 2005
"... Abstract The CurryHoward isomorphism states that types are propositionsand that programs are proofs. This allows programmers to state and enforce invariants of programs by using types. Unfortunately,the type systems of today's functional languages cannot directly express interesting properties ..."
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Cited by 26 (2 self)
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Abstract The CurryHoward isomorphism states that types are propositionsand that programs are proofs. This allows programmers to state and enforce invariants of programs by using types. Unfortunately,the type systems of today's functional languages cannot directly express interesting
Results 1  10
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