Union of Reducibility Candidates for Orthogonal Constructor Rewriting

Riba, Colin

doi:10.1007/978-3-540-69407-6_54

Cited by 4 publications

(5 citation statements)

References 17 publications

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“…We are also inspired by Riba's dissection of reducibility [Rib08], and refer to [Acc13] for extensive discussions and references about SN in linear logic.…”

Section: :42mentioning

confidence: 99%

Exponentials as Substitutions and the Cost of Cut Elimination in Linear Logic

Accattoli

2023

Logical Methods in Computer Science

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This paper introduces the exponential substitution calculus (ESC), a new presentation of cut elimination for IMELL, based on proof terms and building on the idea that exponentials can be seen as explicit substitutions. The idea in itself is not new, but here it is pushed to a new level, inspired by Accattoli and Kesner's linear substitution calculus (LSC). One of the key properties of the LSC is that it naturally models the sub-term property of abstract machines, that is the key ingredient for the study of reasonable time cost models for the $\lambda$-calculus. The new ESC is then used to design a cut elimination strategy with the sub-term property, providing the first polynomial cost model for cut elimination with unconstrained exponentials. For the ESC, we also prove untyped confluence and typed strong normalization, showing that it is an alternative to proof nets for an advanced study of cut elimination.

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“…We are also inspired by Riba's dissection of reducibility [Rib08], and refer to [Acc13] for extensive discussions and references about SN in linear logic.…”

Section: :42mentioning

confidence: 99%

Exponentials as Substitutions and the Cost of Cut Elimination in Linear Logic

Accattoli

2023

Logical Methods in Computer Science

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“…• In (Riba, 2007;Riba, 2008), Riba proves that his set of computability predicates is stable by union if R is an orthogonal constructor rewrite system. • In (Werner, 1994) (Lemma 4.14 p. 96), Werner proves that his set of computability predicates is stable by well-ordered union.…”

Section: Computabilitymentioning

confidence: 99%

Size-based termination of higher-order rewriting

Blanqui¹

2018

J. Funct. Prog.

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We provide a general and modular criterion for the termination of simply-typed λ -calculus extended with function symbols defined by user-defined rewrite rules. Following a work of Hughes, Pareto and Sabry for functions defined with a fixpoint operator and pattern-matching, several criteria use typing rules for bounding the height of arguments in function calls. In this paper, we extend this approach to rewriting-based function definitions and more general user-defined notions of size.

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“…Reducibility candidates, denoted by CR RE , form a reducibility family depending only on a rewrite relation → R and a set of elimination contexts E [15,16]. They come with an inherent notion of values V RE , which are the terms that interact with elimination contexts (see Def.…”

Section: Reducibility Candidatesmentioning

confidence: 99%

“…Our axiomatization of reducibility has been first presented in [15]. We use the version of [16] where details and proofs can be found.…”

Section: Reducibility Candidatesmentioning

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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Union of Reducibility Candidates for Orthogonal Constructor Rewriting

Cited by 4 publications

References 17 publications

Exponentials as Substitutions and the Cost of Cut Elimination in Linear Logic

Exponentials as Substitutions and the Cost of Cut Elimination in Linear Logic

Size-based termination of higher-order rewriting

On the Values of Reducibility Candidates

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