Infinite executions of lazy and strict computations

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Highlights

  • We axiomatise the states from which a computation has infinite executions.

  • We uniformly cover relational and matrix-based models of non-strict and strict computations.

  • We give a new instance of binary iterings.

  • We verify all results in Isabelle, heavily using its automated theorem provers.

Abstract

We give axioms for an operation that describes the states from which a computation has infinite executions in several relational and matrix-based models. The models cover non-strict and strict computations which represent finite, infinite and aborting executions with varying precision. Based on the operation we provide an approximation order for a unified description of recursion. Least fixpoints in the approximation order are reduced to least and greatest fixpoints in the underlying semilattice order. We specialise this to a unified description of iteration which satisfies the axioms of a binary operation introduced in previous work. Previous consequences therefore generalise to all discussed computation models in a uniform way. All algebraic results are verified in Isabelle using its integrated automated theorem provers and SMT solvers.

Keywords

Axiomatic program semantics
Iteration algebras
Lazy execution
Non-strict computations
Relations
Sequential computations

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