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This work introduces λsc, a calculus unifying algebraic and scoped effects, providing support for modular composition of different effects through handlers.

Abstract

The content discusses the challenges and design choices in creating a calculus that supports both algebraic and scoped effects. It presents operational semantics, type-and-effect systems, and examples to illustrate the concepts.
Algebraic effects & handlers offer structured composition of effects, while scoped effects introduce additional complexity due to delimited scopes. The paper aims to bridge these two approaches with λsc, enabling modular handling of various types of effects.
The calculus extends existing models with row polymorphism and explicit forwarding clauses for scoped operations. It addresses the limitations of monomorphic handlers by introducing polymorphic handling capabilities.
The operational semantics demonstrate how computations are reduced based on handler clauses for both algebraic and scoped operations. The type-and-effect system ensures correct typing of values, computations, and handlers in the unified calculus.

Stats

Algebraic eﬀects & handlers have been adopted in several libraries such as fused-eﬀects [RTWS18], extensible-eﬀects [KSSF19], Eﬀ in OCaml [KS18].
Languages like Eﬀ [Pre15], Links [HL16], Koka [Lei17], Eﬀekt [BSO20] utilize algebraic eﬀects & handlers.
Examples include catch for exceptions, local for state variables, call for nondeterministic programs with cut operation.
The calculus introduces λsc with native support for both algebraic and scoped eﬀects & handlers.
Polymorphic handlers enable handling of scoped operations with varying result types.

Quotes

"Algebraic eﬀects & handlers provide structured composition of eﬀects."
"Some eﬀects require special care due to their delimited scope."
"The goal is to unify algebraic and scoped effects in a single calculus."

Key Insights Distilled From

by Roger Bosman... at **arxiv.org** 03-07-2024

Deeper Inquiries

The introduction of polymorphic handlers in the calculus impacts the expressiveness of handling different types of effects by allowing for more flexibility and generality in handling operations. With polymorphic handlers, a single handler can handle a wide range of effect types, as it abstracts over the value type of computations. This means that handlers are no longer limited to handling specific types of effects but can be applied to a broader set of effectful computations.
Polymorphic handlers enable the handling of scoped effects with varying scoped result types, which would not be possible with monomorphic handlers. By abstracting over the value type, polymorphic handlers can adapt to different scenarios where the handled computation may have different result types based on its context or operation.
Overall, polymorphic handlers enhance the modularity and reusability of handler functions by making them more adaptable to diverse effect types and scoped result types.

The implications of explicit forwarding clauses for unknown scoped operations on modularity are significant in terms of maintaining control over how unhandled operations are passed along in a computation chain. Explicit forwarding clauses ensure that each handler explicitly defines how it forwards any unknown scoped operations that it does not handle itself.
This approach enhances modularity by providing clear guidelines on how unhandled operations should be treated within a computational context. It allows for precise control over how these operations are propagated through different parts of a program, ensuring consistency and predictability in their treatment.
Explicit forwarding clauses also promote code clarity and maintainability by clearly delineating responsibilities between different parts of a program that handle various effects. By explicitly defining forwarding behavior, developers can easily understand how unhandled operations will be managed without ambiguity or unexpected behavior.

The concept of unified calculi can be applied beyond computer science to other areas such as mathematics, physics, engineering, and social sciences. In mathematics, unified calculi could provide a common framework for expressing mathematical concepts across different branches like algebra, geometry, calculus, etc., leading to better integration and understanding among various mathematical theories.
In physics, unified calculi could help streamline calculations and modeling across different physical phenomena by providing consistent rules and structures for representing complex systems. This could lead to more efficient problem-solving techniques and enhanced predictive capabilities in scientific research.
In engineering fields like mechanical engineering or electrical engineering, unified calculi could offer standardized methods for analyzing systems and designing solutions across diverse applications. This would facilitate interdisciplinary collaboration and innovation within engineering disciplines.
In social sciences such as economics or psychology, unified calculi could aid in developing comprehensive models for understanding human behavior or economic trends by establishing common frameworks for analysis and interpretation. This could lead to more robust theories and methodologies in social science research.

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