Ramified Corecurrence and Logspace

Ramyaa, Ramyaa; Leivant, Daniel

doi:10.1016/j.entcs.2011.09.025

Cited by 12 publications

(10 citation statements)

References 15 publications

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“…They used such a framework to obtain an ICC characterization of primitive corecurrence (a weak form of productivity). Ramyaa and Leivant [36] also shows that a ramified version of corecurrence gives an ICC characterization of the class of functions over streams working in logarithmic space. Leivant and Ramyaa [30] further studied the correspondence between ramified recurrence and ramified corecurrence.…”

Section: Related Workmentioning

confidence: 95%

Algebras and coalgebras in the light affine Lambda calculus

GaboardiMarco

PéchouxRomain

2015

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Algebra and coalgebra are widely used to model data types in functional programming languages and proof assistants. Their use permits to better structure the computations and also to enhance the expressivity of a language or of a proof system. Interestingly, parametric polymorphismà la System F provides a way to encode algebras and coalgebras in strongly normalizing languages without loosing the good logical properties of the calculus. Even if these encodings are sometimes unsatisfying because they provide only limited forms of algebras and coalgebras, they give insights on the expressivity of System F in terms of functions that we can program in it. With the goal of contributing to a better understanding of the expressivity of Implicit Computational Complexity systems, we study the problem of defining algebras and coalgebras in the Light Affine Lambda Calculus, a system characterizing the complexity class FPTIME. In this system, the principle of stratification limits the ways we can use parametric polymorphism, and in general the way we can write our programs. We show here that while stratification poses some issues to the standard System F encodings, it still permits to encode some weak form of algebra and coalgebra. Using the algebra encoding one can define in the Light Affine Lambda Calculus the traditional inductive types. Unfortunately, the corresponding coalgebra encoding permits only a very limited form of coinductive data types. To extend this class we study an extension of the Light Affine Lambda Calculus by distributive laws for the modality §. This extension has been discussed but not studied before.

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Section: Related Workmentioning

confidence: 95%

Algebras and coalgebras in the light affine Lambda calculus

GaboardiMarco

PéchouxRomain

2015

SIGPLAN Not.

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“…The work in this paper builds on earlier work on implicit characterisations of logarithmic space complexity classes. While implicit characterisations of complexity classes often focus on minimal formal systems, such as function algebras [36,38,39] or while-languages [26], the results are useful in obtaining a better understanding of the resource usage properties of programming languages. Bonfante [8] shows how to capture logspace by a firstorder functional language.…”

Section: Implicit Characterisations Of Logarithmic Spacementioning

confidence: 99%

“…An intml program for this can be found as an example in the experimental implementation of intml 1 . An interesting direction for further work is to consider lazy data structures and corecursion in intml and the relation to the work of Ramyaa and Leivant [39]. Where we use functions to represent long strings, Ramyaa and Leivant use streams.…”

Section: Implicit Characterisations Of Logarithmic Spacementioning

confidence: 99%

Computation by interaction for space-bounded functional programming

Lago

Schöpp

2016

Information and Computation

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We consider the problem of supporting sublinear space programming in a functional programming language. Writing programs with sublinear space usage often requires one to use special implementation techniques for otherwise easy tasks, e.g. one cannot compose functions directly for lack of space for the intermediate result, but must instead compute and recompute small parts of the intermediate result on demand. In this paper, we study how the implementation of such techniques can be supported by functional programming languages. Our approach is based on modelling computation by interaction using the Int construction of Joyal, Street & Verity. We derive functional programming constructs from the structure obtained by applying the Int construction to a term model of a given functional language. The thus derived core functional language intml is formulated by means of a type system inspired by Baillot & Terui's Dual Light Affine Logic. It can be understood as a programming language simplification of Stratified Bounded Affine Logic. We show that it captures the classes flogspace and nflogspace of the functions computable in deterministic logarithmic space and in non-deterministic logarithmic space, respectively. We illustrate the expressiveness of intml by showing how typical graph algorithms, such a test for acyclicity in undirected graphs, can be represented in it.

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“…They used such a framework to obtain an implicit characterization of primitive corecurrence (a weak form of productivity). More recently, in [36] they have also shown that a ramified version of co-recurrence gives an implicit characterization of the class of functions over streams working in logarithmic space. In contrast to our approach considering functions working on data types, their characterization deals with functions working on streams of digits; however, they consider the complexity of a stream program as a function of the output.…”

Section: Related Workmentioning

confidence: 99%

On bounding space usage of streams using interpretation analysis

Gaboardi

Péchoux

2015

Science of Computer Programming

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Interpretation methods are important tools in implicit computational complexity. They have been proved particularly useful to statically analyze and to limit the complexity of programs. However, most of these studies have been so far applied in the context of term rewriting systems over finite data.In this paper, we show how interpretations can also be used to study properties of lazy first-order functional programs over streams. In particular, we provide some interpretation criteria useful to ensure two kinds of stream properties: space upper bounds and input/output upper bounds. Our space upper bounds criteria ensures global and local upper bounds on the size of each output stream element expressed in terms of the maximal size of the input stream elements. The input/output upper bounds criteria consider instead the relations between the number of elements read from the input stream and the number of elements produced on the output stream.This contribution can be seen as a first step in the development of a methodology aiming at using interpretation properties to ensure space safety properties of programs working on streams.

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Ramified Corecurrence and Logspace

Cited by 12 publications

References 15 publications

Algebras and coalgebras in the light affine Lambda calculus

Algebras and coalgebras in the light affine Lambda calculus

Computation by interaction for space-bounded functional programming

On bounding space usage of streams using interpretation analysis

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