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169
Lectures on the curry-howard isomorphism
, 1998
"... The Curry-Howard 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 λ-calculus, first-order logic corresponds to dependent ..."
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Cited by 13 (0 self)
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The Curry-Howard 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 λ-calculus, first-order logic corresponds
The limits of the Curry-Howard isomorphism
, 2013
"... The well-known Curry-Howard isomorphism relates functions with proofs and can be considered as one of the conceptional bases of Martin-Löf’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 well-known Curry-Howard isomorphism relates functions with proofs and can be considered as one of the conceptional bases of Martin-Löf’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 Curry-Howard 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 Curry-Howard Isomorphism is used to represent proof constructions in a term-functional language and to specify analogies by transformation rules on these ter ..."
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Cited by 1 (0 self)
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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 Curry-Howard Isomorphism is used to represent proof constructions in a term-functional language and to specify analogies by transformation rules
Curry-Howard Isomorphism and Intuitionistic Linear Logic
, 1996
"... The notion of Curry-Howard 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 Curry-Howard 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 Curry-Howard Isomorphism for Compilation and Program Execution (Extended Abstract)
- In Proc. Typed Lambda Calculi and Applications, Springer LNCS 1581
, 1999
"... This paper establishes a Curry-Howard isomorphism for compilation and program execution by showing the following facts. (1) The set of A-normal forms, which is often used as an intermediate language for compilation, corresponds to a subsystem of Kleene's contraction-free variant of Gentzen&apos ..."
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Cited by 5 (4 self)
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This paper establishes a Curry-Howard isomorphism for compilation and program execution by showing the following facts. (1) The set of A-normal forms, which is often used as an intermediate language for compilation, corresponds to a subsystem of Kleene's contraction-free variant of Gentzen
The Logical Abstract Machine: a Curry-Howard 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 low-level ma-chine code and code generation. We first define a calculus, called sequen-tial sequent calculus, of intuitionistic propositional logic. A proof of the calculus only contains left rules and has a linear (non-branching) struc-ture, 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 Curry-Howard 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
Type-Free Curry-Howard Isomorphisms (A Proof-Theory Inspired Exposition of the Isomorphism between the Untyped -Calculus with Variable Names and à la de Bruijn)
"... We give an alternative, proof-theory inspired proof of the well-known 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 Curry-Howard correspondence is formulaindependent. We identify the exchange rule as the the proof-theoretical difference between the two representations of the systems. 1 Introduction The Curry-Howard correspondence relates formal inference systems of symbolic logic to typed -like calculi
Proofs as Cryptography: a new interpretation
"... of the Curry-Howard isomorphism for software certificates ..."
References
"... [19] L. Roversi. Curry-howard isomorphism for intuitionistic linear logic: proof-theorist's ..."
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[19] L. Roversi. Curry-howard isomorphism for intuitionistic linear logic: proof-theorist's
Putting Curry-Howard to work
- In Proceedings of ACM Workshop on
, 2005
"... Abstract The Curry-Howard 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 Curry-Howard 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
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