On the Significance of the Collapse Operation

Parys, Paweł

doi:10.1109/lics.2012.62

Cited by 29 publications

(25 citation statements)

References 10 publications

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“…Bibliographic Note. As already mentioned in the introduction, the idea of the type system presented above originates from Parys [23]. In that paper, a similar type system was introduced for configurations of collapsible pushdown systems.…”

Section: Deterministic Quantitiesmentioning

confidence: 99%

“…Intersection type systems were intensively used in the context of recursion schemes, for several purposes like model-checking [18,21,5,29], pumping [19,2], transformations of HORSes [20,1,8], etc. Interestingly, constructions very similar to intersection types were used also on the side of collapsible pushdown systems; they were alternating stack automata [4], and types of stacks [23,16]. The type systems are also closely connected to linear logic [14,13].…”

Section: Introductionmentioning

confidence: 99%

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Intersection Types for Unboundedness Problems

Parys

2019

Electron. Proc. Theor. Comput. Sci.

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Intersection types have been originally developed as an extension of simple types, but they can also be used for refining simple types. In this survey we concentrate on the latter option; more precisely, on the use of intersection types for describing quantitative properties of simply typed lambda-terms. We present two type systems. The first allows to estimate (by appropriately defined value of a derivation) the number of appearances of a fixed constant a in the beta-normal form of a considered lambdaterm. The second type system is more complicated, and allows to estimate the maximal number of appearances of the constant a on a single branch. * Work supported by the National Science Centre, Poland (grant no. 2016/22/E/ST6/00041). 1 Following the convention in this area, we use the word "sort" for simple types, and the word "type" for intersection types refining them.

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Section: Deterministic Quantitiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Intersection Types for Unboundedness Problems

Parys

2019

Electron. Proc. Theor. Comput. Sci.

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“…Intersection type systems were intensively used in the context of HORSes, for several purposes like model-checking [13,16,5,21], pumping [14], transformations of HORSes [15,6], etc. Interestingly, constructions very similar to intersection types were used also on the side of collapsible pushdown systems; they were alternating stack automata [4], and types of stacks [19,11].…”

Section: Introductionmentioning

confidence: 99%

Intersection Types and Counting

Parys

2017

Electron. Proc. Theor. Comput. Sci.

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We present a new approach to the following meta-problem: given a quantitative property of trees, design a type system such that the desired property for the tree generated by an infinitary ground λ -term corresponds to some property of a derivation of a type for this λ -term, in this type system.Our approach is presented in the particular case of the language finiteness problem for nondeterministic higher-order recursion schemes (HORSes): given a nondeterministic HORS, decide whether the set of all finite trees generated by this HORS is finite. We give a type system such that the HORS can generate a tree of an arbitrarily large finite size if and only if in the type system we can obtain derivations that are arbitrarily large, in an appropriate sense; the latter condition can be easily decided.

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“…The safety restriction has been shown to be a real restriction by Parys [29]. Nevertheless, concerning the IO and OI hierarchies, the question as to whether safety is a genuine restriction in terms of the definable languages is still an open problem.…”

Section: Introductionmentioning

confidence: 99%

The IO and OI Hierarchies Revisited

Kobele

Salvati

2013

Automata, Languages, and Programming

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We study languages of λ-terms generated by IO and OI unsafe grammars. These languages can be used to model meaning representations in the formal semantics of natural languages following the tradition of Montague [25]. Using techniques pertaining to the denotational semantics of the simply typed λ-calculus, we show that the emptiness and membership problems for both types of grammars are decidable. In the course of the proof of the decidability results for OI, we identify a decidable variant of the λ-definability problem, and prove a stronger form of Statman's finite completeness Theorem [35].

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On the Significance of the Collapse Operation

Cited by 29 publications

References 10 publications

Intersection Types for Unboundedness Problems

Intersection Types for Unboundedness Problems

Intersection Types and Counting

The IO and OI Hierarchies Revisited

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