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Computational types from a logical perspective
 Journal of Functional Programming
, 1998
"... Moggi’s computational lambda calculus is a metalanguage for denotational semantics which arose from the observation that many different notions of computation have the categorical structure of a strong monad on a cartesian closed category. In this paper we show that the computational lambda calculus ..."
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Cited by 60 (6 self)
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Moggi’s computational lambda calculus is a metalanguage for denotational semantics which arose from the observation that many different notions of computation have the categorical structure of a strong monad on a cartesian closed category. In this paper we show that the computational lambda calculus also arises naturally as the term calculus corresponding (by the CurryHoward correspondence) to a novel intuitionistic modal propositional logic. We give natural deduction, sequent calculus and Hilbertstyle presentations of this logic and prove strong normalisation and confluence results. 1
Parameterised notions of computation
 In MSFP 2006: Workshop on mathematically structured functional programming, ed. Conor McBride and Tarmo Uustalu. Electronic Workshops in Computing, British Computer Society
, 2006
"... Moggi’s Computational Monads and Power et al’s equivalent notion of Freyd category have captured a large range of computational effects present in programming languages such as exceptions, sideeffects, input/output and continuations. We present generalisations of both constructs, which we call para ..."
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Cited by 52 (3 self)
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Moggi’s Computational Monads and Power et al’s equivalent notion of Freyd category have captured a large range of computational effects present in programming languages such as exceptions, sideeffects, input/output and continuations. We present generalisations of both constructs, which we call parameterised monads and parameterised Freyd categories, that also capture computational effects with parameters. Examples of such are composable continuations, sideeffects where the type of the state varies and input/output where the range of inputs and outputs varies. By also considering monoidal parameterisation, we extend the range of effects to cover separated sideeffects and multiple independent streams of I/O. We also present two typed λcalculi that soundly and completely model our categorical definitions — with and without monoidal parameterisation — and act as prototypical languages with parameterised effects.
Monadic Encapsulation of Effects: A Revised Approach (Extended Version)
 Journal of Functional Programming
, 1999
"... Launchbury and Peyton Jones came up with an ingenious idea for embedding regions of imperative programming in a pure functional language like Haskell. The key idea was based on a simple modification of HindleyMilner's type system. Our first contribution is to propose a more natural encapsulati ..."
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Cited by 30 (5 self)
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Launchbury and Peyton Jones came up with an ingenious idea for embedding regions of imperative programming in a pure functional language like Haskell. The key idea was based on a simple modification of HindleyMilner's type system. Our first contribution is to propose a more natural encapsulation construct exploiting higherorder kinds, which achieves the same encapsulation effect, but avoids the ad hoc type parameter of the original proposal. The second contribution is a type safety result for encapsulation of strict state using both the original encapsulation construct and the newly introduced one. We establish this result in a more expressive context than the original proposal, namely in the context of the higherorder lambdacalculus. The third contribution is a type safety result for encapsulation of lazy state in the higherorder lambdacalculus. This result resolves an outstanding open problem on which previous proof attempts failed. In all cases, we formalize the intended implementations as simple bigstep operational semantics on untyped terms, which capture interesting implementation details not captured by the reduction semantics proposed previously. 1
Under consideration for publication in J. Functional Programming 1 Notions of Computation as Monoids
, 2014
"... There are different notions of computation, the most popular being monads, applicative functors, and arrows. In this article we show that these three notions can be seen as monoids in a monoidal category. We demonstrate that at this level of abstraction one can obtain useful results which can be ins ..."
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There are different notions of computation, the most popular being monads, applicative functors, and arrows. In this article we show that these three notions can be seen as monoids in a monoidal category. We demonstrate that at this level of abstraction one can obtain useful results which can be instantiated to the different notions of computation. In particular, we show how free constructions and Cayley representations for monoids translate into useful constructions for monads, applicative functors, and arrows. Moreover, the uniform presentation of all three notions helps in the analysis of the relation between them. 1
Under consideration for publication in J. Functional Programming 1 Monadic Regions∗
"... Regionbased type systems provide programmer control over memory management without sacrificing typesafety. However, the type systems for regionbased languages, such as the MLKit or Cyclone, are relatively complicated, and proving their soundness is nontrivial. This paper shows that the complicat ..."
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Regionbased type systems provide programmer control over memory management without sacrificing typesafety. However, the type systems for regionbased languages, such as the MLKit or Cyclone, are relatively complicated, and proving their soundness is nontrivial. This paper shows that the complication is in principle unnecessary. In particular, we show that plain old parametric polymorphism, as found in Haskell, is all that is needed. We substantiate this claim by giving a type and meaningpreserving translation from a variation of the region calculus of Tofte and Talpin to a monadic variant of System F with region primitives whose types and operations are inspired by (and generalize) the ST monad of Launchbury and Peyton Jones. Capsule Review
Under consideration for publication in J. Functional Programming 1 Transactional Events∗
"... Concurrent programs require highlevel abstractions in order to manage complexity and enable compositional reasoning. In this paper, we introduce a novel concurrency abstraction, dubbed transactional events, which combines firstclass synchronous messagepassing events with allornothing transactio ..."
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Concurrent programs require highlevel abstractions in order to manage complexity and enable compositional reasoning. In this paper, we introduce a novel concurrency abstraction, dubbed transactional events, which combines firstclass synchronous messagepassing events with allornothing transactions. This combination enables simple solutions to interesting problems in concurrent programming. For example, guarded synchronous receive can be implemented as an abstract transactional event, whereas in other languages it requires a nonabstract, nonmodular protocol. As another example, threeway rendezvous can be implemented as an abstract transactional event, which is impossible using firstclass events alone. Both solutions are easy to code and easy to reason about. The expressive power of transactional events arises from a sequencing combinator whose semantics enforces an allornothing transactional property – either both of the constituent events synchronize in sequence or neither of them synchronizes. This sequencing combinator, along with a nondeterministic choice combinator, gives transactional events the compositional structure of a monadwithplus. We provide a formal semantics for transactional events and give a detailed account of an implementation. 1
Under consideration for publication in J. Functional Programming 1 Delimited control and computational effects
"... We give a framework for delimited control with multiple prompts, in the style of Parigot’s λµcalculus, through a series of incremental extensions by starting with the pure λcalculus. Each language inherits the semantics and reduction theory of its parent, giving a systematic way to describe each l ..."
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We give a framework for delimited control with multiple prompts, in the style of Parigot’s λµcalculus, through a series of incremental extensions by starting with the pure λcalculus. Each language inherits the semantics and reduction theory of its parent, giving a systematic way to describe each level of control. For each language of interest, we fully characterize its semantics in terms machine. Furthermore, the control operations are expressed in terms of finegrained primitives that can be used to build wellknown, higherlevel control operators. In order to illustrate the expressive power provided by the various languages, we show how other computational effects can be encoded in terms of these control operators.