Results 1  10
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10
A syntactical analysis of nonsizeincreasing polynomial time computation
, 2002
"... A syntactical proof is given that all functions definable in a certain affine linear typed λcalculus with iteration in all types are polynomial time computable. The proof provides explicit polynomial bounds that can easily be calculated. ..."
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Cited by 11 (2 self)
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A syntactical proof is given that all functions definable in a certain affine linear typed λcalculus with iteration in all types are polynomial time computable. The proof provides explicit polynomial bounds that can easily be calculated.
Validity concepts in prooftheoretic semantics
 ProofTheoretic Semantics. Special issue of Synthese
"... Abstract. The standard approach to what I call “prooftheoretic semantics”, which is mainly due to Dummett and Prawitz, attempts to give a semantics of proofs by defining what counts as a valid proof. After a discussion of the general aims of prooftheoretic semantics, this paper investigates in det ..."
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Cited by 5 (4 self)
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Abstract. The standard approach to what I call “prooftheoretic semantics”, which is mainly due to Dummett and Prawitz, attempts to give a semantics of proofs by defining what counts as a valid proof. After a discussion of the general aims of prooftheoretic semantics, this paper investigates in detail various notions of prooftheoretic validity and offers certain improvements of the definitions given by Prawitz. Particular emphasis is placed on the relationship between semantic validity concepts and validity concepts used in normalization theory. It is argued that these two sorts of concepts must be kept strictly apart. 1. Introduction: Prooftheoretic
An isomorphism between cutelimination procedure and proof reduction
 In S. Ronchi Della Rocca, Ed., Typed Lambda Calculi and Applications (TLCA ’07), LNCS 4583
, 2007
"... proof reduction ..."
Extracting a normalization algorithm in Isabelle/HOL
 TYPES FOR PROOFS AND PROGRAMS, INTERNATIONAL WORKSHOP, TYPES 2004, JOUYENJOSAS
, 2004
"... We present a formalization of a constructive proof of weak normalization for the simplytyped λcalculus in the theorem prover Isabelle/HOL, and show how a program can be extracted from it. Unlike many other proofs of weak normalization based on Tait’s strong computability predicates, which require ..."
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Cited by 2 (1 self)
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We present a formalization of a constructive proof of weak normalization for the simplytyped λcalculus in the theorem prover Isabelle/HOL, and show how a program can be extracted from it. Unlike many other proofs of weak normalization based on Tait’s strong computability predicates, which require a logic supporting strong eliminations and can give rise to dependent types in the extracted program, our formalization requires only relatively simple proof principles. Thus, the program obtained from this proof is typable in simplytyped higherorder logic as implemented in Isabelle/HOL, and a proof of its correctness can automatically be derived within the system.
On Zucker's isomorphism for LJ and its extension to Pure Type Systems
, 2003
"... It is shown how the sequent calculus LJ can be embedded into a simple extension of the calculus by generalized applications, called J. The reduction rules of cut elimination and normalization can be precisely correlated, if explicit substitutions are added to J. The resulting system J2 is prove ..."
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Cited by 1 (0 self)
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It is shown how the sequent calculus LJ can be embedded into a simple extension of the calculus by generalized applications, called J. The reduction rules of cut elimination and normalization can be precisely correlated, if explicit substitutions are added to J. The resulting system J2 is proved strongly normalizing, thus showing strong normalization for Gentzen's cut elimination steps. This re nes previous results by Zucker, Pottinger and Herbelin on the isomorphism between natural deduction and sequent calculus.
Short proofs of strong normalization
"... Abstract. This paper presents simple, syntactic strong normalization proofs for the simplytyped λcalculus and the polymorphic λcalculus (system F) with the full set of logical connectives, and all the permutative reductions. The normalization proofs use translations of terms and types of λ→,∧,∨, ..."
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Abstract. This paper presents simple, syntactic strong normalization proofs for the simplytyped λcalculus and the polymorphic λcalculus (system F) with the full set of logical connectives, and all the permutative reductions. The normalization proofs use translations of terms and types of λ→,∧,∨, ⊥ to terms and types of λ → and from F∀,∃,→,∧,∨, ⊥ to F∀,→. 1
unknown title
, 905
"... Arithmetical proofs of strong normalization results for symmetric λcalculi ..."
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Arithmetical proofs of strong normalization results for symmetric λcalculi
Strong normalization of classical natural deduction with disjunctions
"... This paper proves strong normalization of classical natural deduction with disjunction and permutative conversions, by using CPStranslation and augmentations. By them, this paper also proves strong normalization of classical natural deduction with general elimination rules for implication and conju ..."
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This paper proves strong normalization of classical natural deduction with disjunction and permutative conversions, by using CPStranslation and augmentations. By them, this paper also proves strong normalization of classical natural deduction with general elimination rules for implication and conjunction, and their permutative conversions. This paper also proves natural deduction can be embedded into natural deduction with general elimination rules, strictly preserving proof normalization.
Proving Strong Normalisation via Nondeterministic Translations into Klop’s Extended λCalculus
"... In this paper we present strong normalisation proofs using a technique of nondeterministic translations into Klop’s extended λcalculus. We first illustrate the technique by showing strong normalisation of a typed calculus that corresponds to natural deduction with general elimination rules. Then w ..."
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In this paper we present strong normalisation proofs using a technique of nondeterministic translations into Klop’s extended λcalculus. We first illustrate the technique by showing strong normalisation of a typed calculus that corresponds to natural deduction with general elimination rules. Then we study its explicit substitution version, the typefree calculus of which does not satisfy PSN with respect to reduction of the original calculus; nevertheless it is shown that typed terms are strongly normalising with respect to reduction of the explicit substitution calculus. In the same framework we prove strong normalisation of Sørensen and Urzyczyn’s cutelimination system in intuitionistic sequent calculus.