A monad for full ground reference cells

Kammar, Ohad; Levy, Paul Blain; Moss, Sean K.; Staton, Sam

doi:10.1109/lics.2017.8005109

Cited by 9 publications

(22 citation statements)

References 36 publications

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“…We would also like to relate Benton et al's [2] relational models to our construction. We want to apply this construction to more sophisticated computational effects, such as dynamic memory allocation [9]. Another application area to the free lifting is relational parametricity with effects -we have used it as a semantic precursor to the more syntactic work on analysing the value restriction [12], and we hope it applies more widely.…”

Section: Resultsmentioning

confidence: 99%

Factorisation Systems for Logical Relations and Monadic Lifting in Type-and-effect System Semantics

Kammar

McDermott

2018

Electronic Notes in Theoretical Computer Science

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Type-and-effect systems incorporate information about the computational effects, e.g., state mutation, probabilistic choice, or I/O, a program phrase may invoke alongside its return value. A semantics for type-and-effect systems involves a parameterised family of monads whose size is exponential in the number of effects. We derive such refined semantics from a single monad over a category, a choice of algebraic operations for this monad, and a suitable factorisation system over this category. We relate the derived semantics to the original semantics using fibrations for logical relations. Our proof uses a folklore technique for lifting monads with operations.

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Section: Resultsmentioning

confidence: 99%

Factorisation Systems for Logical Relations and Monadic Lifting in Type-and-effect System Semantics

Kammar

McDermott

2018

Electronic Notes in Theoretical Computer Science

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“…To set the context, we consider the following higher order language of programs with local references by slightly adapting the language of Kammar et al [9] to match with the fine-grain call-by-value perspective [11]. This allows us to formally distinguish pure and effectful judgements.…”

Section: A Call-by-value Language With Local Referencesmentioning

confidence: 99%

“…We proceed to present the full ground store monad by slightly tweaking the original construction [9] towards higher generality. The main distinction is that we do not recur to any specific program syntax and proceed in a completely axiomatic manner in terms of functors and natural transformations.…”

Section: Full Ground Store In the Abstractmentioning

confidence: 99%

“…Recently, Kammar et al [9] constructed an extensional monad-based denotational model of the full ground store, i.e. permitting not only memory allocation for discrete values, but also storing mutually linked data.…”

Section: Introductionmentioning

confidence: 99%

“…Hence, Θ is an internally complete Heyting algebra. From (9) and (10), we obtain the corresponding formulas for indexed meets and joins:…”

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confidence: 99%

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Local Local Reasoning: A BI-Hyperdoctrine for Full Ground Store

Polzer

Goncharov

2020

Lecture Notes in Computer Science

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Modelling and reasoning about dynamic memory allocation is one of the well-established strands of theoretical computer science, which is particularly well-known as a source of notorious challenges in semantics, reasoning, and proof theory. We capitalize on recent progress on categorical semantics of full ground store, in terms of a full ground store monad, to build a corresponding semantics of a higher order logic over the corresponding programs. Our main result is a construction of an (intuitionistic) BI-hyperdoctrine, which is arguably the semantic core of higher order logic over local store. Although we have made an extensive use of the existing generic tools, certain principled changes had to be made to enable the desired construction: while the original monad works over total heaps (to disable dangling pointers), our version involves partial heaps (heaplets) to enable compositional reasoning using separating conjunction. Another remarkable feature of our construction is that, in contrast to the existing generic approaches, our BI-algebra does not directly stem from an internal categorical partial commutative monoid. ‹ Sergey Goncharov acknowledges support by German Research Foundation (DFG) under project GO 2161/1-2.

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An Algebraic Theory for Shared-State Concurrency

Dvir

Kammar

Lahav

2022

Lecture Notes in Computer Science

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We present a monadic denotational semantics for a higherorder programming language with shared-state concurrency, i.e. globalstate in the presence of interleaving concurrency. Central to our approach is the use of Plotkin and Power's algebraic effect methodology: designing an equational theory that captures the intended semantics, and proving a monadic representation theorem for it. We use Hyland et al.'s equational theory of resumptions that extends non-deterministic global-state with an operator for yielding to the environment. The representation is based on Brookes-style traces. Based on this representation we define a denotational semantics that is directionally adequate with respect to a standard operational semantics. We use this semantics to justify compiler transformations of interest: redundant access eliminations, each following from a mundane algebraic calculation; while structural transformations follow from reasoning over the monad's interface.

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A monad for full ground reference cells

Cited by 9 publications

References 36 publications

Factorisation Systems for Logical Relations and Monadic Lifting in Type-and-effect System Semantics

Factorisation Systems for Logical Relations and Monadic Lifting in Type-and-effect System Semantics

Local Local Reasoning: A BI-Hyperdoctrine for Full Ground Store

An Algebraic Theory for Shared-State Concurrency

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