Open AccessBook Chapter10.1007/978-3-540-27764-4_2

Constructing Polymorphic Programs with Quotient Types

- 12 Jul 2004

- pp 2-15

TL;DR: This paper provides the basis for writing polymorphic programs over quotient datatypes by extending the recently developed theory of containers.

Abstract: The efficient representation and manipulation of data is one of the fundamental tasks in the construction of large software systems. Parametric polymorphism has been one of the most successful approaches to date but, as of yet, has not been applicable to programming with quotient datatypes such as unordered pairs, cyclic lists, bags etc. This paper provides the basis for writing polymorphic programs over quotient datatypes by extending our recently developed theory of containers.

AI Agents for this Paper

Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps

Most frequently asked questions

1. What are the contributions in "Constructing polymorphic programs with quotient types" ?

This paper provides the basis for writing polymorphic programs over quotient datatypes by extending their recently developed theory of containers.

2. What future works have the authors mentioned in the paper "Constructing polymorphic programs with quotient types" ?

As for further work, the authors believe containers are an excellent platform for generic program and they wish to develop this application of containers.

Citations

•Journal Article•10.1016/J.TCS.2005.06.002

Containers: constructing strictly positive types

Michael Abbott, +2 more

- 06 Sep 2005

- Theoretical Computer Science

TL;DR: It is shown that morphisms between containers can be full and faithfully interpreted as polymorphic functions (i.e. natural transformations) and that, in the presence of W-types, all strictly positive types give rise to containers.

...read moreread less

228

•Journal Article•10.1016/J.ENTCS.2009.07.081

Continuous Functions on Final Coalgebras

Neil Ghani, +2 more

- 01 Aug 2009

- Electronic Notes in Theoretical Computer...

TL;DR: This work extends its previous results to cover the case of final coalgebras for a broader class of functors than that giving rise to streams, including those that arise from countable signatures of finite-place untyped operators.

...read moreread less

•Journal Article•10.4204/EPTCS.76.5

An Investigation of the Laws of Traversals

Mauro Jaskelioff, +1 more

- 14 Feb 2012

- arXiv: Programming Languages

TL;DR: This article proves that finitary containers are traversable in the authors' sense and argues that elements in a traversable structure are visited exactly once.

...read moreread less

•Dissertation

Quotient types in type theory

Nuo Li

- 15 Jul 2015

TL;DR: The expected syntax of quotient types is investigated and an algebraic structure of quotients called definable quotients is proposed to define, which relates the setoid interpretation and the set definition via a normalisation function which returns a normal form (canonical choice) for each equivalence class.

...read moreread less

•Journal Article•10.2168/LMCS-10(3:14)2014

When is a container a comonad

Danel Ahman, +2 more

- 25 Aug 2014

- arXiv: Programming Languages

TL;DR: In this paper, directed containers are introduced to capture the common situation where every position in a data structure determines another data structure, informally, the sub-data-structure rooted by that position.

...read moreread less

...

Expand

References

•Book

Categories for the Working Mathematician

Saunders Mac Lane

- 01 Jan 1971

TL;DR: In this article, the authors present a table of abstractions for categories, including Axioms for Categories, Functors, Natural Transformations, and Adjoints for Preorders.

...read moreread less

10.5K

Monograph•10.1017/CBO9780511525858

Handbook of Categorical Algebra

Francis Borceux

- 26 Aug 1994

TL;DR: The Handbook of Categorical Algebra is intended to give, in three volumes, a rather detailed account of what, ideally, everybody working in category theory should know, whatever the specific topic of research they have chosen.

...read moreread less

1.4K

•Book

Categorical Logic and Type Theory

Bart Jacobs

- 28 Jan 1999

TL;DR: This chapter discusses fibred category theory, which is concerned with the role of type theory in the development of categorical identity and its role in the construction of types.

...read moreread less

749

Book Chapter•10.1007/BFB0072514

Foncteurs analytiques et espèces de structures

André Joyal

- 01 Jan 1986

327

...

Expand

Constructing Polymorphic Programs with Quotient Types

Chat with Paper

AI Agents for this Paper

Most frequently asked questions

1. What are the contributions in "Constructing polymorphic programs with quotient types" ?

2. What future works have the authors mentioned in the paper "Constructing polymorphic programs with quotient types" ?

Citations

Containers: constructing strictly positive types

Continuous Functions on Final Coalgebras

An Investigation of the Laws of Traversals

Quotient types in type theory

When is a container a comonad

References

Categories for the Working Mathematician

Graduate Texts in Mathematics

Handbook of Categorical Algebra

Categorical Logic and Type Theory

Foncteurs analytiques et espèces de structures

Related Papers (5)

Containers: constructing strictly positive types

Foncteurs analytiques et espèces de structures

The cartesian closed bicategory of generalised species of structures

Towards a practical programming language based on dependent type theory

Une théorie combinatoire des séries formelles