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.
Mots clés : functional programming languages, lambda calculus, strictness analysis, set constraints, tree automata
@article{ITA_2007__41_2_225_0,
author = {Schmidt-Schauss, Manfred and Sabel, David and Sch\"utz, Marko},
title = {Deciding inclusion of set constants over infinite non-strict data structures},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
pages = {225--241},
publisher = {EDP-Sciences},
volume = {41},
number = {2},
year = {2007},
doi = {10.1051/ita:2007010},
mrnumber = {2350646},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ita:2007010/}
}
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 - Informatique Théorique et Applications PY - 2007 SP - 225 EP - 241 VL - 41 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ita:2007010/ DO - 10.1051/ita:2007010 LA - en ID - ITA_2007__41_2_225_0 ER -
%0 Journal Article %A Schmidt-Schauss, Manfred %A Sabel, David %A Schütz, Marko %T Deciding inclusion of set constants over infinite non-strict data structures %J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications %D 2007 %P 225-241 %V 41 %N 2 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ita:2007010/ %R 10.1051/ita:2007010 %G en %F ITA_2007__41_2_225_0
Schmidt-Schauss, Manfred; Sabel, David; Schütz, Marko. Deciding inclusion of set constants over infinite non-strict data structures. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 41 (2007) no. 2, pp. 225-241. doi : 10.1051/ita:2007010. http://www.numdam.org/articles/10.1051/ita:2007010/
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