Effectful program distancing

Lago, Ugo Dal; Gavazzo, Francesco

doi:10.1145/3498680

Cited by 7 publications

(19 citation statements)

References 71 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Further examples of logical relations that can be described in our framework include classic Kripke logical relations [Mit96] (take fibrations of poset-indexed relations) as well as logical relations for information flow (the latter could be approached both as suitable Kripke logical relations or by considering a shallow semantics on the category of classified sets [Kav19]). Additionally, since differential logical relations can be used to reason about nontrivial notions such as program sensitivity and cost analysis [DLG22a], our framework can be used for reasoning about the same notions too. Even if general, the vehicle calculus of this work lacks some important programming language features, such as recursive types and polymorphism.…”

Section: Discussionmentioning

confidence: 99%

“…Here, we show how our general notion of an operational logical relation subsumes the one of a DLR (and, consequently, that the fundamental lemma of DLRs is an instance of Theorem 3.15). Additionally, we show how differential extensions are precisely liftings of monads to the fibration of differential relations and how the so-called coupling-based differential extension [DLG22a] is an instance of a general monadic lifting to such a fibration, viz. the well-known Barr lifting properly fitted to a differential setting.…”

Section: The Fibration Of Differential Relationsmentioning

confidence: 99%

“…The most famous one is perhaps the so-called Barr extension [Bar70] of a Set -monad to the category of (endo)relations, which is fibred over Set (other notions of lifting include ⊤⊤-and codensity lifting [KSU18,Kat13]). In the differential setting, the notion of a differential extension has been recently proposed [DLG22a] as a way to lift monads to generalised distance spaces. To what extent such a construction is canonical and whether it defines an actual monadic lifting, however, have been left as open questions.…”

Section: The Fibration Of Differential Relationsmentioning

confidence: 99%

“…DLRs are a new form logical relations introduced to define higher-order distances between programs, such distances being abstract notions reflecting the interactive complexity of the programs compared. DLRs have been studied operationally and on specific calculi only, oftentimes introducing new notionssuch as the one of a differential extension of a monad [DLG22a] -whose mathematical status is still not well understood. The main consequence of that is that a general, structural account of pure and effectful DLRs is still missing.…”

Section: Introductionmentioning

confidence: 99%

“…Whether differential extensions indeed define a monadic lifting is left as an open problem in[DLG22a].…”

mentioning

confidence: 99%

See 4 more Smart Citations

A Fibrational Tale of Operational Logical Relations: Pure, Effectful and Differential

Dagnino¹,

Gavazzo²

2023

Preprint

View full text Add to dashboard Cite

Logical relations built on top of an operational semantics are one of the most successful proof methods in programming language semantics. In recent years, more and more expressive notions of operationally-based logical relations have been designed and applied to specific families of languages. However, a unifying abstract framework for operationally-based logical relations is still missing. We show how fibrations can provide a uniform treatment of operational logical relations, using as reference example a λ-calculus with generic effects endowed with a novel, abstract operational semantics defined on a large class of categories. Moreover, this abstract perspective allows us to give a solid mathematical ground also to differential logical relations -a recently introduced notion of higher-order distance between programs -both pure and effectful, bringing them back to a common picture with traditional ones.

show abstract

Section: Discussionmentioning

confidence: 99%

Section: The Fibration Of Differential Relationsmentioning

confidence: 99%

Section: The Fibration Of Differential Relationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…Whether differential extensions indeed define a monadic lifting is left as an open problem in[DLG22a].…”

mentioning

confidence: 99%

See 3 more Smart Citations

A Fibrational Tale of Operational Logical Relations: Pure, Effectful and Differential

Dagnino¹,

Gavazzo²

2023

Preprint

View full text Add to dashboard Cite

show abstract

Logical Predicates in Higher-Order Mathematical Operational Semantics

Goncharov,

Santamaria,

Schröder

et al. 2024

Lecture Notes in Computer Science

View full text Add to dashboard Cite

We present a systematic approach to logical predicates based on universal coalgebra and higher-order abstract GSOS, thus making a first step towards a unifying theory of logical relations. We start with the observation that logical predicates are special cases of coalgebraic invariants on mixed-variance functors. We then introduce the notion of a locally maximal logical refinement of a given predicate, with a view to enabling inductive reasoning, and identify sufficient conditions on the overall setup in which locally maximal logical refinements canonically exist. Finally, we develop induction-up-to techniques that simplify inductive proofs via logical predicates on systems encoded as (certain classes of) higher-order GSOS laws by identifying and abstracting away from their boiler-plate part.

show abstract

A relational theory of effects and coeffects

Lago

Gavazzo

2022

Proc. ACM Program. Lang.

Self Cite

View full text Add to dashboard Cite

Graded modal types systems and coeffects are becoming a standard formalism to deal with context-dependent, usage-sensitive computations, especially when combined with computational effects. From a semantic perspective, effectful and coeffectful languages have been studied mostly by means of denotational semantics and almost nothing has been done from the point of view of relational reasoning. This gap in the literature is quite surprising, since many cornerstone results — such as non-interference , metric preservation , and proof irrelevance — on concrete coeffects are inherently relational. In this paper, we fill this gap by developing a general theory and calculus of program relations for higher-order languages with combined effects and coeffects. The relational calculus builds upon the novel notion of a corelator (or comonadic lax extension ) to handle coeffects relationally. Inside such a calculus, we define three notions of effectful and coeffectful program refinements: contextual approximation , logical preorder , and applicative similarity . These are the first operationally-based notions of program refinement (and, consequently, equivalence) for languages with combined effects and coeffects appearing in the literature. We show that the axiomatics of a corelator (together with the one of a relator) is precisely what is needed to prove all the aforementioned program refinements to be precongruences, this way obtaining compositional relational techniques for reasoning about combined effects and coeffects.

show abstract

Effectful program distancing

Cited by 7 publications

References 71 publications

A Fibrational Tale of Operational Logical Relations: Pure, Effectful and Differential

A Fibrational Tale of Operational Logical Relations: Pure, Effectful and Differential

Logical Predicates in Higher-Order Mathematical Operational Semantics

A relational theory of effects and coeffects

Contact Info

Product

Resources

About