Transformation of Strictness-Related Analyses Based on Abstract Interpretation

Mizuhito OGAWA; Satoshi ONO

Transformation of Strictness-Related Analyses Based on Abstract Interpretation

Mizuhito OGAWA, Satoshi ONO

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This paper newly proposes HOMomorphic Transformer (HOMT) in order to formalize relations among strictness-related analyses (SRAs) on first-order functional programs. A HOMT is defined to be a composition of special instances of abstract interpretation, and has enough ability to treat known SRAs including head/tail/total strictness detection on nonflat domains. A set of HOMTs, furthermore, is an algebraic space such that some composition of HOMTs can be reduced to a simpler HOMT. This structure gives a transformational mechanism between various SRAs, and further clarifies the equivalence and the hierarchy among them. First, we show a construction of a HOMT as a composition of Unit-HOMTs (U-HOMTs) which are specified by quadruplet representations. Second, algebraic relations among HOMTs are shown as reduction rules among specific pairs of quadruplet representations. Thus, hierarchy among HOMTs can be clarified by finding some adequate quadruplet representation which bridges a HOMT to the other. Third, various SRAs are formalized as HOMTs in either forward or back-ward manners. They are also shown to be safe under unified discussions. Finally, their equivalence and hierarchy are examined in terms of an algebraic structure of HOMTs.

Publication: IEICE TRANSACTIONS on Information Vol.E74-D No.2 pp.406-416

Publication Date: 1991/02/25

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Type of Manuscript: PAPER

Category: Bio-Cybernetics

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Mizuhito OGAWA
Satoshi ONO

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Mizuhito OGAWA, Satoshi ONO, "Transformation of Strictness-Related Analyses Based on Abstract Interpretation" in IEICE TRANSACTIONS on Information, vol. E74-D, no. 2, pp. 406-416, February 1991, doi: .
Abstract: This paper newly proposes HOMomorphic Transformer (HOMT) in order to formalize relations among strictness-related analyses (SRAs) on first-order functional programs. A HOMT is defined to be a composition of special instances of abstract interpretation, and has enough ability to treat known SRAs including head/tail/total strictness detection on nonflat domains. A set of HOMTs, furthermore, is an algebraic space such that some composition of HOMTs can be reduced to a simpler HOMT. This structure gives a transformational mechanism between various SRAs, and further clarifies the equivalence and the hierarchy among them. First, we show a construction of a HOMT as a composition of Unit-HOMTs (U-HOMTs) which are specified by quadruplet representations. Second, algebraic relations among HOMTs are shown as reduction rules among specific pairs of quadruplet representations. Thus, hierarchy among HOMTs can be clarified by finding some adequate quadruplet representation which bridges a HOMT to the other. Third, various SRAs are formalized as HOMTs in either forward or back-ward manners. They are also shown to be safe under unified discussions. Finally, their equivalence and hierarchy are examined in terms of an algebraic structure of HOMTs.
URL: https://global.ieice.org/en_transactions/information/10.1587/e74-d_2_406/_p

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@ARTICLE{e74-d_2_406,
author={Mizuhito OGAWA, Satoshi ONO, },
journal={IEICE TRANSACTIONS on Information},
title={Transformation of Strictness-Related Analyses Based on Abstract Interpretation},
year={1991},
volume={E74-D},
number={2},
pages={406-416},
abstract={This paper newly proposes HOMomorphic Transformer (HOMT) in order to formalize relations among strictness-related analyses (SRAs) on first-order functional programs. A HOMT is defined to be a composition of special instances of abstract interpretation, and has enough ability to treat known SRAs including head/tail/total strictness detection on nonflat domains. A set of HOMTs, furthermore, is an algebraic space such that some composition of HOMTs can be reduced to a simpler HOMT. This structure gives a transformational mechanism between various SRAs, and further clarifies the equivalence and the hierarchy among them. First, we show a construction of a HOMT as a composition of Unit-HOMTs (U-HOMTs) which are specified by quadruplet representations. Second, algebraic relations among HOMTs are shown as reduction rules among specific pairs of quadruplet representations. Thus, hierarchy among HOMTs can be clarified by finding some adequate quadruplet representation which bridges a HOMT to the other. Third, various SRAs are formalized as HOMTs in either forward or back-ward manners. They are also shown to be safe under unified discussions. Finally, their equivalence and hierarchy are examined in terms of an algebraic structure of HOMTs.},
keywords={},
doi={},
ISSN={},
month={February},}

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TY - JOUR
TI - Transformation of Strictness-Related Analyses Based on Abstract Interpretation
T2 - IEICE TRANSACTIONS on Information
SP - 406
EP - 416
AU - Mizuhito OGAWA
AU - Satoshi ONO
PY - 1991
DO -
JO - IEICE TRANSACTIONS on Information
SN -
VL - E74-D
IS - 2
JA - IEICE TRANSACTIONS on Information
Y1 - February 1991
AB - This paper newly proposes HOMomorphic Transformer (HOMT) in order to formalize relations among strictness-related analyses (SRAs) on first-order functional programs. A HOMT is defined to be a composition of special instances of abstract interpretation, and has enough ability to treat known SRAs including head/tail/total strictness detection on nonflat domains. A set of HOMTs, furthermore, is an algebraic space such that some composition of HOMTs can be reduced to a simpler HOMT. This structure gives a transformational mechanism between various SRAs, and further clarifies the equivalence and the hierarchy among them. First, we show a construction of a HOMT as a composition of Unit-HOMTs (U-HOMTs) which are specified by quadruplet representations. Second, algebraic relations among HOMTs are shown as reduction rules among specific pairs of quadruplet representations. Thus, hierarchy among HOMTs can be clarified by finding some adequate quadruplet representation which bridges a HOMT to the other. Third, various SRAs are formalized as HOMTs in either forward or back-ward manners. They are also shown to be safe under unified discussions. Finally, their equivalence and hierarchy are examined in terms of an algebraic structure of HOMTs.
ER -