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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
Semantics for Local Computational Effects
, 2006
"... Starting with Moggi’s work on monads as refined to Lawvere theories, we give a general construct that extends denotational semantics for a global computational effect canonically to yield denotational semantics for a corresponding local computational effect. Our leading example yields a construction ..."
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Cited by 4 (0 self)
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Starting with Moggi’s work on monads as refined to Lawvere theories, we give a general construct that extends denotational semantics for a global computational effect canonically to yield denotational semantics for a corresponding local computational effect. Our leading example yields a construction of the usual denotational semantics for local state from that for global state. Given any Lawvere theory L, possibly countable and possibly enriched, we first give a universal construction that extends L, hence the global operations and equations of a given effect, to incorporate worlds of arbitrary finite size. Then, making delicate use of the final comodel of the ordinary Lawvere theory L, we give a construct that uniformly allows us to model block, the universality of the final comodel yielding a universal property of the construct. We illustrate both the universal extension of L and the canonical construction of block by seeing how they work in the case of state.