Program Equivalence is Coinductive

We describe computational models, notably Turing and counter machines, as state transition systems with side effects. Side effects are expressed via an algebraic signature and interpreted over comodels for that signature: comodels describe the memory model while the transition system captures the co...

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Published in:Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science pp. 337 - 346
Main Authors: Pattinson, Dirk, Schröder, Lutz
Format: Conference Proceeding
Language:English
Published: New York, NY, USA ACM 05.07.2016
Series:ACM Conferences
Subjects:
Theory of computation > Logic
Theory of computation > Logic > Programming logic
Theory of computation > Models of computation
Theory of computation > Semantics and reasoning > Program reasoning
Models of computation
non-wellfounded proofs
program equivalence
comodels
algebraic theories
ISBN:9781450343916, 1450343910
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Abstract We describe computational models, notably Turing and counter machines, as state transition systems with side effects. Side effects are expressed via an algebraic signature and interpreted over comodels for that signature: comodels describe the memory model while the transition system captures the control structure. Equational reasoning over comodels is known to be subtle. We identify a criterion on equational theories and classes of comodels that guarantees completeness, over the given class of comodels, of the standard equational calculus, and show that this criterion is satisfied in our leading examples. Based on a complete equational axiomatization of the memory (co)model, we then give a complete inductive-coinductive calculus for simulation between states, where a state simulates another if it has at least the same terminating computations, with the same cumulative effect on global state. Extensional equivalence of computations can then be expressed as mutual simulation. The crucial use of coinduction is to deal with non-termination of the simulated computation where the coinductive rule permits infinite unfolding.
AbstractList We describe computational models, notably Turing and counter machines, as state transition systems with side effects. Side effects are expressed via an algebraic signature and interpreted over comodels for that signature: comodels describe the memory model while the transition system captures the control structure. Equational reasoning over comodels is known to be subtle. We identify a criterion on equational theories and classes of comodels that guarantees completeness, over the given class of comodels, of the standard equational calculus, and show that this criterion is satisfied in our leading examples. Based on a complete equational axiomatization of the memory (co)model, we then give a complete inductive-coinductive calculus for simulation between states, where a state simulates another if it has at least the same terminating computations, with the same cumulative effect on global state. Extensional equivalence of computations can then be expressed as mutual simulation. The crucial use of coinduction is to deal with non-termination of the simulated computation where the coinductive rule permits infinite unfolding.
Author Pattinson, Dirk
Schröder, Lutz
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  givenname: Lutz
  surname: Schröder
  fullname: Schröder, Lutz
  organization: Friedrich-Alexander-Universität Erlangen-Nürnberg
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DOI 10.1145/2933575.2934506
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Keywords Models of computation
non-wellfounded proofs
program equivalence
comodels
algebraic theories
Language English
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Snippet We describe computational models, notably Turing and counter machines, as state transition systems with side effects. Side effects are expressed via an...
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StartPage 337
SubjectTerms Theory of computation -- Logic
Theory of computation -- Logic -- Programming logic
Theory of computation -- Models of computation
Theory of computation -- Semantics and reasoning -- Program reasoning
Title Program Equivalence is Coinductive
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