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Parametricity and local variables
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FoSSaCS '02 Proceedings of the 5th International Conference on Foundations of Software Science and Computation Structures
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Term Equational Systems and Logics
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Electronic Notes in Theoretical Computer Science (ENTCS)
Semantics for Local Computational Effects
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Information and Computation - Special issue: Seventh workshop on coalgebraic methods in computer science 2004
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TLCA'05 Proceedings of the 7th international conference on Typed Lambda Calculi and Applications
A Nominal Relational Model for Local Store
Electronic Notes in Theoretical Computer Science (ENTCS)
Comodels and effects in mathematical operational semantics
FOSSACS'13 Proceedings of the 16th international conference on Foundations of Software Science and Computation Structures
Instances of Computational Effects: An Algebraic Perspective
LICS '13 Proceedings of the 2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science
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Every algebraic theory gives rise to a monad, and monads allow a meta-language which is a basic programming language with side-effects. Equations in the algebraic theory give rise to equations between programs in the meta-language. An interesting question is this: to what extent can we put equational reasoning for programs into the algebraic theory for the monad? In this paper I focus on local state, where programs can allocate, update and read the store. Plotkin and Power (FoSSaCS'02) have proposed an algebraic theory of local state, and they conjectured that the theory is complete, in the sense that every consistent equation is already derivable. The central contribution of this paper is to confirm this conjecture. To establish the completeness theorem, it is necessary to reformulate the informal theory of Plotkin and Power as an enriched algebraic theory in the sense of Kelly and Power (JPAA, 89:163–179). The new presentation can be read as 14 program assertions about three effects. The completeness theorem for local state is dependent on certain conditions on the type of storable values. When the set of storable values is finite, there is a subtle additional axiom regarding quotient types.