Quantitative Logics for Equivalence of Effectful Programs

Voorneveld, Niels

doi:10.1016/j.entcs.2019.09.015

Cited by 6 publications

(15 citation statements)

References 10 publications

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“…On the opposite side of equations, we have distinctions. We will use Eilenberg-Moore algebras to specify tests on algebraic expressions as done in [25]. If two expressions give us a different result for a test, we consider them to be distinct.…”

Section: Eilenberg-moore Algebrasmentioning

confidence: 99%

“…If moreover α is a morphism in the category of ω-cpos, then Γ α satisfies the additional properties required in [5] in order to use Howe's method and prove that applicative bisimilarity is compatible. As such, A is required to be a complete lattice by the theory developed in [25]. This is the case in all our examples.…”

Section: Relatorsmentioning

confidence: 99%

“…In [25], a quantitative logic is defined with the intention to specify a behavioural equivalence. One optional ingredient in that definition is the notion of negation, an involution on the carrier set A of the Eilenberg-Moore algebra.…”

Section: Involutionsmentioning

confidence: 99%

“…In [25], such logics were generalised to quantitative logics built using quantitative modalities. In most examples of effects, it is more natural to use a singular quantitative modality, given by Eilenberg-Moore algebras (e.g.…”

Section: Introductionmentioning

confidence: 99%

“…This definition varies slightly from effect trees used in [24,25], with the addition of a top element ⊤. We define a functor T Σ (−) on the category of sets, sending each set X to the set of trees T Σ X over X determined by Σ, and sending each function f : X → Y to the function T f : T Σ X → T Σ Y replacing each leaf x of its input by f (x) .…”

mentioning

confidence: 99%

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From Equations to Distinctions: Two Interpretations of Effectful Computations

Voorneveld¹

2020

Electron. Proc. Theor. Comput. Sci.

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There are several ways to define program equivalence for functional programs with algebraic effects. We consider two complementing ways to specify behavioural equivalence. One way is to specify a set of axiomatic equations, and allow proof methods to show that two programs are equivalent. Another way is to specify an Eilenberg-Moore algebra, which generate tests that could distinguish programs. These two methods are said to complement each other if any two programs can be shown to be equivalent if and only if there is no test to distinguish them.In this paper, we study a generic method to formulate from a set of axiomatic equations an Eilenberg-Moore algebra which complements it. We will look at an additional condition which must be satisfied for this to work. We then apply this method to a handful of examples of effects, including probability and global store, and show they coincide with the usual algebras from the literature. We will moreover study whether or not it is possible to specify a set of unary Boolean modalities which could function as distinction-tests complementing the equational theory.

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Section: Eilenberg-moore Algebrasmentioning

confidence: 99%

Section: Relatorsmentioning

confidence: 99%

Section: Involutionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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From Equations to Distinctions: Two Interpretations of Effectful Computations

Voorneveld¹

2020

Electron. Proc. Theor. Comput. Sci.

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Algebraic and Coalgebraic Perspectives on Interaction Laws

Uustalu

Voorneveld

2020

Programming Languages and Systems

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Monad algebras, turning computations over return values into values, are used to handle algebraic effects invoked by programs, whereas comonad coalgebras, turning initial states into environments ("cocomputations") over states, describe production of coalgebraic coeffects that can respond to effects. (Monad-comonad) interaction laws by Katsumata et al. describe interaction protocols between a computation and an environment. We show that any triple of those devices can be combined into a single algebra handling computations over state predicates. This method yields an isomorphism between the category of interaction laws, and the category of so-called merge functors which merge algebras and coalgebras to form combined algebras. In a similar vein, we can combine interaction laws with coalgebras only, retrieving Uustalu's stateful runners. If instead we combine interaction laws with algebras only, we get a novel concept of continuation-based runners that lift an environment of value predicates to a single predicate on computations of values. We use these notions to study different running examples of interactions of computations and environments.

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Combining Algebraic Effect Descriptions Using the Tensor of Complete Lattices

Voorneveld

2020

Electronic Notes in Theoretical Computer Science

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Quantitative Logics for Equivalence of Effectful Programs

Cited by 6 publications

References 10 publications

From Equations to Distinctions: Two Interpretations of Effectful Computations

From Equations to Distinctions: Two Interpretations of Effectful Computations

Algebraic and Coalgebraic Perspectives on Interaction Laws

Combining Algebraic Effect Descriptions Using the Tensor of Complete Lattices

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