Simple Saturated Sets for Disjunction and Second-Order Existential Quantification

Tatsuta, Makoto

doi:10.1007/978-3-540-73228-0_26

Cited by 13 publications

(13 citation statements)

References 10 publications

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“…5.7). This prevents us from the counter example of [18] (Ex. 2.1): we can type (let w = Ixy in zww) but this term does not reduce to u 1 since Ixy is not a value.…”

Section: ⊓ ⊔mentioning

confidence: 99%

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On the Values of Reducibility Candidates

Riba

2009

Lecture Notes in Computer Science

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Abstract. The straightforward elimination of union types is known to break subject reduction, and for some extensions of the lambda-calculus, to break strong normalization as well. Similarly, the straightforward elimination of implicit existential types breaks subject reduction. We propose elimination rules for union types and implicit existential quantification which use a form call-by-value issued from Girard's reducibility candidates. We show that these rules remedy the above mentioned difficulties, for strong normalization and, for the existential quantification, for subject reduction as well. Moreover, for extensions of the lambda-calculus based on intuitionistic logic, we show that the obtained existential quantification is equivalent to its usual impredicative encoding w.r.t. provability in realizability models built from reducibility candidates and biorthogonals.

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“…5.7). This prevents us from the counter example of [18] (Ex. 2.1): we can type (let w = Ixy in zww) but this term does not reduce to u 1 since Ixy is not a value.…”

Section: ⊓ ⊔mentioning

confidence: 99%

“…The counter example for subject reduction given in [1] has been adapted to implicit existential types in [18]. Concerning strong normalization, the difficulties are related to type interpretations in reducibility.…”

Section: Introductionmentioning

confidence: 99%

On the Values of Reducibility Candidates

Riba

2009

Lecture Notes in Computer Science

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“…It means that terms contain no explicit type annotations. For the notation of terms for (∃E), we will follow [13].…”

Section: Introductionmentioning

confidence: 99%

Untitled

Nakazawa¹,

Tatsutay²

2010

Chicago J. of Theoretical Comp. Sci.

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A multiple quantifier is a quantifier having inference rules that introduce or eliminate arbitrary number of quantifiers by one inference. This paper introduces the lambda calculus with negation, conjunction, and multiple existential quantifiers, and the lambda calculus with implication and multiple universal quantifiers. Their type checking and type inference are proved to be undecidable. This paper also shows that the undecidability of type checking and type inference in the type-free-style lambda calculus with negation, conjunction, and existence is reduced to the undecidability of type checking and type inference in the type-free-style polymorphic lambda calculus.

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“…3) are stable by union and lead to an adequate type interpretation. This has been exploited for instance in [2,21].…”

Section: Stability By Unionmentioning

confidence: 99%

“…An interesting way to compare different type interpretations is to study their stability by union. This is even a necessary property in some cases [2,7,21].…”

Section: Introductionmentioning

confidence: 96%

Union of Reducibility Candidates for Orthogonal Constructor Rewriting

Riba

Logic and Theory of Algorithms

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Simple Saturated Sets for Disjunction and Second-Order Existential Quantification

Cited by 13 publications

References 10 publications

On the Values of Reducibility Candidates

On the Values of Reducibility Candidates

Untitled

Union of Reducibility Candidates for Orthogonal Constructor Rewriting

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