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

Kammar, Ohad; McDermott, Dylan

doi:10.1016/j.entcs.2018.11.012

Cited by 10 publications

(6 citation statements)

References 26 publications

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“…The proof follows that of Theorem 2, replacing the monadic lifting with a folklore monadic lifting for algebraic effects (Kammar, 2014;Kammar & McDermott, 2018).…”

Section: Operational Metatheorymentioning

confidence: 90%

On the expressive power of user-defined effects: Effect handlers, monadic reflection, delimited control

Forster

Kammar²,

Lindley

et al. 2019

J. Funct. Prog.

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We compare the expressive power of three programming abstractions for user-defined computational effects: Plotkin and Pretnar’s effect handlers, Filinski’s monadic reflection, and delimited control. This comparison allows a precise discussion about the relative expressiveness of each programming abstraction. It also demonstrates the sensitivity of the relative expressiveness of user-defined effects to seemingly orthogonal language features. We present three calculi, one per abstraction, extending Levy’s call-by-push-value. For each calculus, we present syntax, operational semantics, a natural type-and-effect system, and, for effect handlers and monadic reflection, a set-theoretic denotational semantics. We establish their basic metatheoretic properties: safety, termination, and, where applicable, soundness and adequacy. Using Felleisen’s notion of a macro translation, we show that these abstractions can macro express each other, and show which translations preserve typeability. We use the adequate finitary set-theoretic denotational semantics for the monadic calculus to show that effect handlers cannot be macro expressed while preserving typeability either by monadic reflection or by delimited control. Our argument fails with simple changes to the type system such as polymorphism and inductive types. We supplement our development with a mechanised Abella formalisation.

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“…The proof follows that of Theorem 2, replacing the monadic lifting with a folklore monadic lifting for algebraic effects (Kammar, 2014;Kammar & McDermott, 2018).…”

Section: Operational Metatheorymentioning

confidence: 90%

On the expressive power of user-defined effects: Effect handlers, monadic reflection, delimited control

Forster

Kammar²,

Lindley

et al. 2019

J. Funct. Prog.

Self Cite

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“…Our characterisation of definability will rely on the semantic ⊤⊤-lifting of Katsumata [2005]. Alternative liftings include the free lifting [Kammar and McDermott 2018] and the monadic lifting of Goubault-Larrecq et al [2008]. We choose Katsumata's approach because it interacts well with the extra structure we shall need at sum types (see Def.…”

Section: Monad Liftings and Generalised ⊤⊤-Liftingmentioning

confidence: 99%

Fully abstract models for effectful λ-calculi via category-theoretic logical relations

Kammar

Katsumata

Saville

2022

Proc. ACM Program. Lang.

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We present a construction which, under suitable assumptions, takes a model of Moggi’s computational λ-calculus with sum types, effect operations and primitives, and yields a model that is adequate and fully abstract. The construction, which uses the theory of fibrations, categorical glueing, ⊤⊤-lifting, and ⊤⊤-closure, takes inspiration from O’Hearn & Riecke’s fully abstract model for PCF. Our construction can be applied in the category of sets and functions, as well as the category of diffeological spaces and smooth maps and the category of quasi-Borel spaces, which have been studied as semantics for differentiable and probabilistic programming.

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“…In the future we plan to refine the type system into a type-and-effect system [18,20,22,29,39,40], by annotating the typing judgments with the allowed effects. The denotations then depend on the effect annotations, with each annotation having its own associated equational theory.…”

Section: Conclusion Related Work and Future Workmentioning

confidence: 99%

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

Cited by 10 publications

References 26 publications

On the expressive power of user-defined effects: Effect handlers, monadic reflection, delimited control

On the expressive power of user-defined effects: Effect handlers, monadic reflection, delimited control

Fully abstract models for effectful λ-calculi via category-theoretic logical relations

An Algebraic Theory for Shared-State Concurrency

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