Deciding inclusion of set constants over infinite non-strict data structures

Manfred Schmidt-Schauss; David Sabel; Marko Schütz

RAIRO - Theoretical Informatics and Applications (2007)

  • Volume: 41, Issue: 2, page 225-241
  • ISSN: 0988-3754

Abstract

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Various static analyses of functional programming languages that permit infinite data structures make use of set constants like Top, Inf, and Bot, denoting all terms, all lists not eventually ending in Nil, and all non-terminating programs, respectively. We use a set language that permits union, constructors and recursive definition of set constants with a greatest fixpoint semantics in the set of all, also infinite, computable trees, where all term constructors are non-strict. This paper proves decidability, in particular DEXPTIME-completeness, of inclusion of co-inductively defined sets by using algorithms and results from tree automata and set constraints. The test for set inclusion is required by certain strictness analysis algorithms in lazy functional programming languages and could also be the basis for further set-based analyses.

How to cite

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Schmidt-Schauss, Manfred, Sabel, David, and Schütz, Marko. "Deciding inclusion of set constants over infinite non-strict data structures." RAIRO - Theoretical Informatics and Applications 41.2 (2007): 225-241. <http://eudml.org/doc/250016>.

@article{Schmidt2007,
abstract = { Various static analyses of functional programming languages that permit infinite data structures make use of set constants like Top, Inf, and Bot, denoting all terms, all lists not eventually ending in Nil, and all non-terminating programs, respectively. We use a set language that permits union, constructors and recursive definition of set constants with a greatest fixpoint semantics in the set of all, also infinite, computable trees, where all term constructors are non-strict. This paper proves decidability, in particular DEXPTIME-completeness, of inclusion of co-inductively defined sets by using algorithms and results from tree automata and set constraints. The test for set inclusion is required by certain strictness analysis algorithms in lazy functional programming languages and could also be the basis for further set-based analyses. },
author = {Schmidt-Schauss, Manfred, Sabel, David, Schütz, Marko},
journal = {RAIRO - Theoretical Informatics and Applications},
keywords = {Functional programming languages; lambda calculus; strictness analysis; set constraints; tree automata; DEXPTIME-completeness; lazy functional programming languages},
language = {eng},
month = {7},
number = {2},
pages = {225-241},
publisher = {EDP Sciences},
title = {Deciding inclusion of set constants over infinite non-strict data structures},
url = {http://eudml.org/doc/250016},
volume = {41},
year = {2007},
}

TY - JOUR
AU - Schmidt-Schauss, Manfred
AU - Sabel, David
AU - Schütz, Marko
TI - Deciding inclusion of set constants over infinite non-strict data structures
JO - RAIRO - Theoretical Informatics and Applications
DA - 2007/7//
PB - EDP Sciences
VL - 41
IS - 2
SP - 225
EP - 241
AB - Various static analyses of functional programming languages that permit infinite data structures make use of set constants like Top, Inf, and Bot, denoting all terms, all lists not eventually ending in Nil, and all non-terminating programs, respectively. We use a set language that permits union, constructors and recursive definition of set constants with a greatest fixpoint semantics in the set of all, also infinite, computable trees, where all term constructors are non-strict. This paper proves decidability, in particular DEXPTIME-completeness, of inclusion of co-inductively defined sets by using algorithms and results from tree automata and set constraints. The test for set inclusion is required by certain strictness analysis algorithms in lazy functional programming languages and could also be the basis for further set-based analyses.
LA - eng
KW - Functional programming languages; lambda calculus; strictness analysis; set constraints; tree automata; DEXPTIME-completeness; lazy functional programming languages
UR - http://eudml.org/doc/250016
ER -

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