Productivity of Stream Definitions

Endrullis, Jörg; Grabmayer, Clemens; Hendriks, Dimitri; Isihara, Ariya; Klop, Jan Willem

doi:10.1007/978-3-540-74240-1_24

Cited by 26 publications

(43 citation statements)

References 11 publications

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“…The notion of productivity given in [14,42] is equivalent to our notion of weak normalisation. The notion of productivity is defined as weak normalisation but excluding terms that do not contain constructors such as (tl (tl (tl .…”

Section: Conclusion and Related Workmentioning

confidence: 99%

Pure type systems with corecursion on streams

Severi

Vries

2012

SIGPLAN Not.

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In this paper, we use types for ensuring that programs involving streams are well-behaved. We extend pure type systems with a type constructor for streams, a modal operator next and a fixed point operator for expressing corecursion. This extension is called Pure Type Systems with Corecursion (CoPTS). The typed lambda calculus for reactive programs defined by Krishnaswami and Benton can be obtained as a CoPTS. CoPTSs allow us to study a wide range of typed lambda calculi extended with corecursion using only one framework. In particular, we study this extension for the calculus of constructions which is the underlying formal language of Coq. We use the machinery of infinitary rewriting and formalise the idea of well-behaved programs using the concept of infinitary normalisation. The set of finite and infinite terms is defined as a metric completion. We establish a precise connection between the modal operator (•A) and the metric at a syntactic level by relating a variable of type (•A) with the depth of all its occurrences in a term. This syntactic connection between the modal operator and the depth is the key to the proofs of infinitary weak and strong normalisation.

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Section: Conclusion and Related Workmentioning

confidence: 99%

Pure type systems with corecursion on streams

Severi

Vries

2012

SIGPLAN Not.

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“…Productive streams are defined in the literature [6] as terms weakly normalizing to infinite lists, which is in our case equivalent to: a stream s is productive if for all n :: Nat, s !! n evaluates to a strict value.…”

Section: Lemmamentioning

confidence: 99%

Interpretation of Stream Programs: Characterizing Type 2 Polynomial Time Complexity

Férée

Hainry

Hoyrup

et al. 2010

Algorithms and Computation

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Abstract. We study polynomial time complexity of type 2 functionals. For that purpose, we introduce a first order functional stream language. We give criteria, named well-founded, on such programs relying on second order interpretation that characterize two variants of type 2 polynomial complexity including the Basic Feasible Functions (BFF). These characterizations provide a new insight on the complexity of stream programs. Finally, we adapt these results to functions over the reals, a particular case of type 2 functions, and we provide a characterization of polynomial time complexity in Recursive Analysis.

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“…The start language S can be specified by providing a tree automaton T that generates S; the program then searches an extension of T which fulfills the requirements of Theorem 6.3. Note that with the productivity tool of [3] we could already prove productivity of this specification fully automatically. a(b(c)))), and 2 < 3.…”

Section: Examples and Toolmentioning

confidence: 99%

Proving Infinitary Normalization

Endrullis

Grabmayer

Hendriks

et al. 2009

Lecture Notes in Computer Science

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Abstract. We investigate the notion of 'infinitary strong normalization' (SN ∞ ), introduced in [6], the analogue of termination when rewriting infinite terms. A (possibly infinite) term is SN ∞ if along every rewrite sequence each fixed position is rewritten only finitely often. In [9], SN ∞ has been investigated as a system-wide property, i.e. SN ∞ for all terms of a given rewrite system. This global property frequently fails for trivial reasons. For example, in the presence of the collapsing rule tail(x:σ) → σ, the infinite term t = tail(0:t) rewrites to itself only. Moreover, in practice one usually is interested in SN ∞ of a certain set of initial terms. We give a complete characterization of this (more general) 'local version' of SN ∞ using interpretations into weakly monotone algebras (as employed in [9]). Actually, we strengthen this notion to continuous weakly monotone algebras (somewhat akin to [5]). We show that tree automata can be used as an automatable instance of our framework; an actual implementation is made available along with this paper.

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Productivity of Stream Definitions

Cited by 26 publications

References 11 publications

Pure type systems with corecursion on streams

Pure type systems with corecursion on streams

Interpretation of Stream Programs: Characterizing Type 2 Polynomial Time Complexity

Proving Infinitary Normalization

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