A Generic Operational Metatheory for Algebraic Effects

Johann, Patricia; Simpson, Alex; Voigtländer, Janis

doi:10.1109/lics.2010.29

Cited by 44 publications

(53 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…More recently, Johann et al (2010) have proposed a generic framework for operational reasoning about algebraic effects. Their work is complementary to ours: they develop effect-independent proof principles, whereas we develop effect-specific proof principles.…”

Section: Logical Relationsmentioning

confidence: 99%

The impact of higher-order state and control effects on local relational reasoning

2012

View full text Add to dashboard Cite

Reasoning about program equivalence is one of the oldest problems in semantics. In recent years, useful techniques have been developed, based on bisimulations and logical relations, for reasoning about equivalence in the setting of increasingly realistic languages-languages nearly as complex as ML or Haskell. Much of the recent work in this direction has considered the interesting representation independence principles enabled by the use of local state, but it is also important to understand the principles that powerful features like higher-order state and control effects disable. This latter topic has been broached extensively within the framework of game semantics, resulting in what Abramsky dubbed the "semantic cube": fully abstract game-semantic characterizations of various axes in the design space of ML-like languages. But when it comes to reasoning about many actual examples, game semantics does not yet supply a useful technique for proving equivalences.In this paper, we marry the aspirations of the semantic cube to the powerful proof method of step-indexed Kripke logical relations. Building on recent work of Ahmed et al. (2009), we define the first fully abstract logical relation for an ML-like language with recursive types, abstract types, general references and call/cc. We then show how, under orthogonal restrictions to the expressive power of our language-namely, the restriction to first-order state and/or the removal of call/cc-we can enhance the proving power of our possibleworlds model in correspondingly orthogonal ways, and we demonstrate this proving power on a range of interesting examples. Central to our story is the use of state transition systems to model the way in which properties of local state evolve over time.

show abstract

Section: Logical Relationsmentioning

confidence: 99%

The impact of higher-order state and control effects on local relational reasoning

2012

View full text Add to dashboard Cite

show abstract

“…More recently, Johann, Simpson, and Voigtländer [14] have proposed a generic framework for operational reasoning about algebraic effects. Their work is complementary to ours: they develop effect-independent proof principles, whereas we develop effectspecific proof principles.…”

Section: Logical Relationsmentioning

confidence: 99%

The impact of higher-order state and control effects on local relational reasoning

2010

View full text Add to dashboard Cite

Reasoning about program equivalence is one of the oldest problems in semantics. In recent years, useful techniques have been developed, based on bisimulations and logical relations, for reasoning about equivalence in the setting of increasingly realistic languages-languages nearly as complex as ML or Haskell. Much of the recent work in this direction has considered the interesting representation independence principles enabled by the use of local state, but it is also important to understand the principles that powerful features like higher-order state and control effects disable. This latter topic has been broached extensively within the framework of game semantics, resulting in what Abramsky dubbed the "semantic cube": fully abstract game-semantic characterizations of various axes in the design space of ML-like languages. But when it comes to reasoning about many actual examples, game semantics does not yet supply a useful technique for proving equivalences.In this paper, we marry the aspirations of the semantic cube to the powerful proof method of step-indexed Kripke logical relations. Building on recent work of Ahmed, Dreyer, and Rossberg, we define the first fully abstract logical relation for an ML-like language with recursive types, abstract types, general references and call/cc. We then show how, under orthogonal restrictions to the expressive power of our language-namely, the restriction to first-order state and/or the removal of call/cc-we can enhance the proving power of our possible-worlds model in correspondingly orthogonal ways, and we demonstrate this proving power on a range of interesting examples. Central to our story is the use of state transition systems to model the way in which properties of local state evolve over time.

show abstract

“…One way to do this is to directly allow the is_trace predicate to allow a choice of possible refinements, effectively interpreting away some events in the refinement definition. A second option is to introduce a more sophisticated version of refinement that uses both the definition above and an event interpreter as described in Section 3-the resulting relations should be quite similar to those studied by Johann et al [2010].…”

Section: Relating Itrees and Trace-based Semanticsmentioning

confidence: 99%

Interaction trees: representing recursive and impure programs in Coq

Xia

Zakowski

et al. 2019

Proc. ACM Program. Lang.

View full text Add to dashboard Cite

We present interaction trees (ITrees), a general-purpose data structure in Coq for formalizing the behaviors of recursive programs that interact with their environment. ITrees are built of uninterpreted events and their continuations-a coinductive variant of a "free monad. " We study the compositional properties of interpreters built from event handlers and show how to use them to implement a general mutual recursion operator. The resulting theory enables equational reasoning about ITrees up to weak bisimulation. Using this theory, we prove the termination-sensitive correctness of a compiler from a simple imperative source language to an assembly-like target whose meanings are given as an ITree-based denotational semantics. Crucially, the correctness proof follows entirely by structural induction and the equational theory of combinators for control-flow graphs, which are built on top of the mutual recursion operator. ITrees are also executable, e.g. through extraction, making them suitable for debugging, testing, and implementing executable artifacts.

show abstract

A Generic Operational Metatheory for Algebraic Effects

Cited by 44 publications

References 22 publications

The impact of higher-order state and control effects on local relational reasoning

The impact of higher-order state and control effects on local relational reasoning

The impact of higher-order state and control effects on local relational reasoning

Interaction trees: representing recursive and impure programs in Coq

Contact Info

Product

Resources

About