The Coinductive Resumption Monad

Piróg, Maciej; Gibbons, Jeremy

doi:10.1016/j.entcs.2014.10.015

Cited by 21 publications

(13 citation statements)

References 31 publications

(49 reference statements)

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“…It is an interesting challenge for future work to describe the 'coinductive' list monad transformer, given by carriers of final coalgebras. In such a case, the free monad becomes the free completely iterative monad introduced by Aczel et al [1], and the resumption monad becomes the coinductive resumption monad described by Piróg and Gibbons [26]. The universal properties of both constructions are similar to those of their inductive counterparts, but considerably more complicated (see Adámek et al [2] for the case of the free completely iterative monad).…”

Section: Discussionmentioning

confidence: 97%

Eilenberg–Moore Monoids and Backtracking Monad Transformers

Piróg

2016

Electron. Proc. Theor. Comput. Sci.

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We develop an algebraic underpinning of backtracking monad transformers in the general setting of monoidal categories. As our main technical device, we introduce Eilenberg-Moore monoids, which combine monoids with algebras for strong monads. We show that Eilenberg-Moore monoids coincide with algebras for the list monad transformer ('done right') known from Haskell libraries. From this, we obtain a number of results, including the facts that the list monad transformer is indeed a monad, a transformer, and an instance of the MonadPlus class. Finally, we construct an Eilenberg-Moore monoid of endomorphisms, which, via the codensity monad construction, yields a continuation-based implementationà la Hinze.

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Section: Discussionmentioning

confidence: 97%

Eilenberg–Moore Monoids and Backtracking Monad Transformers

Piróg

2016

Electron. Proc. Theor. Comput. Sci.

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“…We would like to explore temporal specification of general, effectful programs. To do so, we wish to develop the treatment of the coinductive resumptions monad [55], that provides a general framework to reason on effectful computations, as shown by interaction trees [70]. It would be interesting to study temporal specifications we could give to effectful programs encoded in this setting.…”

Section: Discussionmentioning

confidence: 99%

Temporal Refinements for Guarded Recursive Types

Jaber

Riba

2021

Programming Languages and Systems

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We propose a logic for temporal properties of higher-order programs that handle infinite objects like streams or infinite trees, represented via coinductive types. Specifications of programs use safety and liveness properties. Programs can then be proven to satisfy their specification in a compositional way, our logic being based on a type system.The logic is presented as a refinement type system over the guarded $$\lambda $$ λ -calculus, a $$\lambda $$ λ -calculus with guarded recursive types. The refinements are formulae of a modal $$\mu $$ μ -calculus which embeds usual temporal modal logics such as and . The semantics of our system is given within a rich structure, the topos of trees, in which we build a realizability model of the temporal refinement type system.

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“…Also in this case a big-step trace semantics is defined with two mutually recursive coinductive judgments, and weak bisimilarity is needed; however, the definition of the observational equivalence is more involved, since it requires nesting inductive definitions in coinductive ones. A generalised notion of resumption has been introduced later by Piróg and Gibbons [44] in a category-theoretic and coalgebraic context.…”

Section: Concluding Discussionmentioning

confidence: 99%

A framework for big-step semantics

Dagnino

2019

Proceedings of the Conference Companion of the 3rd International Conference on Art, Science, and Engineering of Programming

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It is well-known that big-step semantics is not able to distinguish stuck and non-terminating computations. This is a strong limitation as it makes very difficult to reason about properties involving infinite computations, such as type soundness, which cannot even be expressed. To face this problem, we develop a systematic study of big-step semantics: we introduce an abstract definition of what a big-step semantics is, we formalise the evaluation algorithm implicitly associated with any big-step semantics and we identify computations with executions of such an algorithm, thus recovering the distinction between stuckness an non-termination. Then, we define constructions yielding an extended version of a given arbitrary big-step semantics, where such a difference is made explicit. Building on such constructions, we describe a general proof technique to show that a predicate is sound, that is, prevents stuck computation, with respect to a big-step semantics. The extended semantics are exploited in the meta-theory, notably they are necessary to show that the proof technique works. However, they remain transparent when using the proof technique, since it consists in checking three conditions on the original rules only. We illustrate the technique by several examples, showing that it is applicable also in cases where subject reduction does not hold, hence the standard technique for small-step semantics cannot be used.

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The Coinductive Resumption Monad

Cited by 21 publications

References 31 publications

Eilenberg–Moore Monoids and Backtracking Monad Transformers

Eilenberg–Moore Monoids and Backtracking Monad Transformers

Temporal Refinements for Guarded Recursive Types

A framework for big-step semantics

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