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Adequacy for algebraic effects
 In 4th FoSSaCS
, 2001
"... We present a logic for algebraic effects, based on the algebraic representation of computational effects by operations and equations. We begin with the acalculus, a minimal calculus which separates values, effects, and computations and thereby canonises the order of evaluation. This is extended to ..."
Abstract

Cited by 30 (16 self)
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We present a logic for algebraic effects, based on the algebraic representation of computational effects by operations and equations. We begin with the acalculus, a minimal calculus which separates values, effects, and computations and thereby canonises the order of evaluation. This is extended to obtain the logic, which is a classical firstorder multisorted logic with higherorder value and computation types, as in Levy’s callbypushvalue, a principle of induction over computations, a free algebra principle, and predicate fixed points. This logic embraces Moggi’s computational λcalculus, and also, via definable modalities, HennessyMilner logic, and evaluation logic, though Hoare logic presents difficulties. 1
Linearlyused state in models of callbyvalue
"... Abstract. We investigate the phenomenon that every monad is a linear state monad. We do this by studying a fullycomplete statepassing translation from an impure callbyvalue language to a new linear type theory: the enriched callbyvalue calculus. The results are not specific to store, but can b ..."
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Cited by 5 (5 self)
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Abstract. We investigate the phenomenon that every monad is a linear state monad. We do this by studying a fullycomplete statepassing translation from an impure callbyvalue language to a new linear type theory: the enriched callbyvalue calculus. The results are not specific to store, but can be applied to any computational effect expressible using algebraic operations, even to effects that are not usually thought of as stateful. There is a bijective correspondence between generic effects in the source language and state access operations in the enriched callbyvalue calculus. From the perspective of categorical models, the enriched callbyvalue calculus suggests a refinement of the traditional Kleisli models of effectful callbyvalue languages. The new models can be understood as enriched adjunctions. 1
Handlers in Action
"... We lay operational foundations for effect handlers. Introduced by Plotkin and Pretnar, effect handlers are a novel programming construct that generalises exception handlers, handling a range of computational effects, such as I/O, state, and nondeterminism. We propose a smallstep structural operatio ..."
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Cited by 3 (0 self)
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We lay operational foundations for effect handlers. Introduced by Plotkin and Pretnar, effect handlers are a novel programming construct that generalises exception handlers, handling a range of computational effects, such as I/O, state, and nondeterminism. We propose a smallstep structural operational semantics for a higherorder calculus of effect handlers, along with a sound type and effect system. We explore two alternative effect handler implementation techniques: free monads, and delimited continuations. Finally, we show that Filinski’s monadic reflection can be straightforwardly simulated by effect handlers. 1.
Towards Effects in Mathematical Operational Semantics
"... In this paper, we study extensions of mathematical operational semantics with algebraic effects. Our starting point is an effectfree coalgebraic operational semantics, given by a natural transformation of syntax over behaviour. The operational semantics of the extended language arises by distributi ..."
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In this paper, we study extensions of mathematical operational semantics with algebraic effects. Our starting point is an effectfree coalgebraic operational semantics, given by a natural transformation of syntax over behaviour. The operational semantics of the extended language arises by distributing program syntax over effects, again inducing a coalgebraic operational semantics, but this time in the Kleisli category for the monad derived from the algebraic effects. The final coalgebra in this Kleisli category then serves as the denotational model. For it to exist, we ensure that the the Kleisli category is enriched over CPOs by considering the monad of possibly infinite terms, extended with a bottom element. Unlike the effectless setting, not all operational specifications give rise to adequate and compositional semantics. We give a proof of adequacy and compositionality provided the specifications can be described by evaluationincontext. We illustrate our techniques with a simple extension of (stateless) while programs with global store, i.e. variable lookup.