Checking equivalence of corecursive streams: An inductive procedure

In recent work, non-periodic streams have been defined corecursively, by representing them with finitary equational systems built on top of various operators, besides the standard constructor. When only the stream constructor is allowed in equations, only periodic streams can be represented, and the...

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Published in:Theoretical computer science Vol. 1009; p. 114680
Main Authors: Ancona, Davide, Barbieri, Pietro, Zucca, Elena
Format: Journal Article
Language:English
Published: Elsevier B.V 12.09.2024
Subjects:
Operational semantics
Regular trees
Stream programming
Stream programming
Operational semantics
Regular trees
ISSN:0304-3975, 1879-2294
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Abstract In recent work, non-periodic streams have been defined corecursively, by representing them with finitary equational systems built on top of various operators, besides the standard constructor. When only the stream constructor is allowed in equations, only periodic streams can be represented, and the structures of periodic streams and infinite regular trees are isomorphic. Therefore, one can use the theory of regular trees to get a sound and complete procedure to decide whether two equational systems are equivalent, that is, define the same streams. However, such an isomorphism no longer exists if one allows other operators in equations; in particular, there exist systems of equations which have the same unique solution as streams, but not as regular trees. Hence, equality of regular trees becomes stronger then equality of streams, with a negative impact on termination of functions whose definition is based on the equivalence of the representation of streams as finitary equational systems. To overcome this problem, we provide a weaker definition of equivalence, and prove its soundness and relative completeness. This definition is coinductive, hence non-algorithmic. However, we show that it can be turned into an equivalent inductive procedure.
AbstractList In recent work, non-periodic streams have been defined corecursively, by representing them with finitary equational systems built on top of various operators, besides the standard constructor. When only the stream constructor is allowed in equations, only periodic streams can be represented, and the structures of periodic streams and infinite regular trees are isomorphic. Therefore, one can use the theory of regular trees to get a sound and complete procedure to decide whether two equational systems are equivalent, that is, define the same streams. However, such an isomorphism no longer exists if one allows other operators in equations; in particular, there exist systems of equations which have the same unique solution as streams, but not as regular trees. Hence, equality of regular trees becomes stronger then equality of streams, with a negative impact on termination of functions whose definition is based on the equivalence of the representation of streams as finitary equational systems. To overcome this problem, we provide a weaker definition of equivalence, and prove its soundness and relative completeness. This definition is coinductive, hence non-algorithmic. However, we show that it can be turned into an equivalent inductive procedure.
ArticleNumber 114680
Author Barbieri, Pietro
Ancona, Davide
Zucca, Elena
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  email: elena.zucca@unige.it
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Keywords Stream programming
Operational semantics
Regular trees
Language English
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Snippet In recent work, non-periodic streams have been defined corecursively, by representing them with finitary equational systems built on top of various operators,...
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SubjectTerms Operational semantics
Regular trees
Stream programming
Title Checking equivalence of corecursive streams: An inductive procedure
URI https://dx.doi.org/10.1016/j.tcs.2024.114680
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