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CurryHoward
"... for incomplete firstorder logic derivations using oneandahalf level terms ..."
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for incomplete firstorder logic derivations using oneandahalf level terms
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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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
Oneandahalfth order terms: CurryHoward and incomplete derivations
"... Abstract. The CurryHoward correspondence connects Natural Deduction derivation with the lambdacalculus. Predicates are types, derivations are terms. This supports reasoning from assumptions to conclusions, but we may want to reason ‘backwards ’ from the desired conclusion towards the assumptions. ..."
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Cited by 5 (4 self)
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. At intermediate stages we may have an ‘incomplete derivation’, with ‘holes’. This is natural in informal practice; the challenge is to formalise it. To this end we use a oneandahalfth order technique based on nominal terms, with two levels of variable. Predicates are types, derivations are terms — and the two
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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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
CurryHoward Term Calculi for GentzenStyle Classical Logic
, 2008
"... This thesis is concerned with the extension of the CurryHoward Correspondence to classical logic. Although much progress has been made in this area since the seminal paper by Griffin, we believe that the question of finding canonical calculi corresponding to classical logics has not yet been resolv ..."
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This thesis is concerned with the extension of the CurryHoward Correspondence to classical logic. Although much progress has been made in this area since the seminal paper by Griffin, we believe that the question of finding canonical calculi corresponding to classical logics has not yet been
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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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
CurryHoward terms for Linear Logic
 In Logic Colloquium
, 1994
"... In this paper we 1. provide a natural deduction system for full firstorder linear logic, 2. introduce CurryHowardstyle terms for this version of linear logic, 3. extend the notion of substitution of CurryHoward terms for term variables, 4. define the reduction rules for the CurryHoward terms ..."
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In this paper we 1. provide a natural deduction system for full firstorder linear logic, 2. introduce CurryHowardstyle terms for this version of linear logic, 3. extend the notion of substitution of CurryHoward terms for term variables, 4. define the reduction rules for the CurryHoward
CurryHoward terms for Linear Logic
 IN LOGIC COLLOQUIUM
, 1994
"... In this paper we 1. provide a natural deduction system for full firstorder linear logic, 2. prove its equivalence to Girard's original system, 3. introduce CurryHowardstyle terms for this version of linear logic, 4. extend the notion of substitution of CurryHoward terms for term variables a ..."
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In this paper we 1. provide a natural deduction system for full firstorder linear logic, 2. prove its equivalence to Girard's original system, 3. introduce CurryHowardstyle terms for this version of linear logic, 4. extend the notion of substitution of CurryHoward terms for term variables
An Analysis of FirstOrder Logics of Probability
 Artificial Intelligence
, 1990
"... : We consider two approaches to giving semantics to firstorder logics of probability. The first approach puts a probability on the domain, and is appropriate for giving semantics to formulas involving statistical information such as "The probability that a randomly chosen bird flies is greater ..."
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Cited by 316 (18 self)
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: We consider two approaches to giving semantics to firstorder logics of probability. The first approach puts a probability on the domain, and is appropriate for giving semantics to formulas involving statistical information such as "The probability that a randomly chosen bird flies
Extending the CurryHoward interpretation to linear, relevance and other resource logics
 JOURNAL OF SYMBOLIC LOGIC
, 1992
"... ..."
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