DeepAI
Log In Sign Up

Polymorphic Iterable Sequential Effect Systems

08/06/2018
by   Colin S. Gordon, et al.
0

Effect systems are lightweight extensions to type systems that can verify a wide range of important properties with modest developer burden. But our general understanding of effect systems is limited primarily to systems where the order of effects is irrelevant. Understanding such systems in terms of a semilattice of effects grounds understanding of the essential issues, and provides guidance when designing new effect systems. By contrast, sequential effect systems --- where the order of effects is important --- lack an established algebraic characterization. We derive an algebraic characterization from the shape of prior concrete sequential effect systems. We present an abstract polymorphic effect system with singleton effects parameterized by an effect quantale --- an algebraic structure with well-defined properties that can model a range of existing sequential effect systems. We define effect quantales, derive useful properties, and show how they cleanly model a variety of known sequential effect systems. We show that for most effect quantales, there is a free, general notion of iterating a sequential effect, and that for systems we consider the derived iteration agrees with the manually designed iteration operators in prior work. Identifying and applying the right algebraic structure led us to subtle insights into the design of sequential effect systems, which provides guidance on non-obvious points of designing sequential effect systems. We also position effect quantales with respect to work on categorical semantics for sequential effect systems, clarifying the distinctions between these systems and our own. In addition, our derived iteration construct should generalize to these semantic structures, addressing limitations of that work.

READ FULL TEXT

page 1

page 2

page 3

page 4

11/29/2018

Sequential Effect Systems with Control Operators

Sequential effect systems are a class of effect system that exploits inf...
04/10/2018

Factorisation systems for logical relations and monadic lifting in type-and-effect system semantics

Type-and-effect systems incorporate information about the computational ...
03/04/2021

Contextual Modal Types for Algebraic Effects and Handlers

Programming languages with algebraic effects often rely on effect annota...
03/07/2022

Handling Higher-Order Effects

Algebraic effect handlers is a programming paradigm where programmers ca...
02/10/2021

Designing group sequential clinical trials when a delayed effect is anticipated: A practical guidance

A common feature of many recent trials evaluating the effects of immunot...
03/11/2009

Free actions and Grassmanian variety

An algebraic notion of representational consistency is defined. A theore...
03/04/2019

Dijkstra Monads for All

This paper proposes a general semantic framework for verifying programs ...