Article

A framework for typed HOAS and semantics

Authors:

Marino Miculan,

Ivan ScagnettoAuthors Info & Claims

PPDP '03: Proceedings of the 5th ACM SIGPLAN international conference on Principles and practice of declaritive programming

Pages 184 - 194

https://doi.org/10.1145/888251.888269

Published: 27 August 2003 Publication History

Abstract

We investigate a framework for representing and reasoning about syntactic and semantic aspects of typed languages with variable binders.First, we introduce typed binding signatures and develop a theory of typed abstract syntax with binders. Each signature is associated to a category of "presentation" models, where the language of the typed signature is the initial model.At the semantic level, types can be given also a computational meaning in a (possibly different) semantic category. We observe that in general, semantic aspects of terms and variables can be reflected in the presentation category by means of an adjunction. Therefore, the category of presentation models is expressive enough to represent both the syntactic and the semantic aspects of languages.We introduce then a metalogical system, inspired by the internal languages of the presentation category, which can be used for reasoning on both the syntax and the semantics of languages. This system is composed by a core equational logic tailored for reasoning on the syntactic aspects; when a specific semantics is chosen, the system can be modularly extended with further "semantic" notions, as needed.

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Cited By

Ahrens BMatthes RMörtberg APopescu AZdancewic S(2022)Implementing a category-theoretic framework for typed abstract syntaxProceedings of the 11th ACM SIGPLAN International Conference on Certified Programs and Proofs10.1145/3497775.3503678(307-323)Online publication date: 17-Jan-2022
https://dl.acm.org/doi/10.1145/3497775.3503678
Hamana M(2022)Complete algebraic semantics for second-order rewriting systems based on abstract syntax with variable bindingMathematical Structures in Computer Science10.1017/S0960129522000287(1-32)Online publication date: 14-Oct-2022
https://doi.org/10.1017/S0960129522000287
Fiore MHamana M(2013)Multiversal Polymorphic Algebraic TheoriesProceedings of the 2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science10.5555/2591370.2591395(520-529)Online publication date: 25-Jun-2013
https://dl.acm.org/doi/10.5555/2591370.2591395
Show More Cited By

Index Terms

A framework for typed HOAS and semantics
1. Software and its engineering
  1. Software notations and tools
    1. Formal language definitions
      1. Semantics
      2. Syntax
2. Theory of computation
  1. Formal languages and automata theory
    1. Formalisms
      1. Algebraic language theory
  2. Semantics and reasoning
    1. Program semantics
      1. Algebraic semantics
      2. Denotational semantics

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cover image ACM Conferences

PPDP '03: Proceedings of the 5th ACM SIGPLAN international conference on Principles and practice of declaritive programming

August 2003

292 pages

ISBN:1581137052

DOI:10.1145/888251

Conference Chair:
Konstantinos Sagonas
Uppsala University, SW
,
Program Chair:
Dale Miller
INRIA/Futurs & Ecole Polytechnique, France

Copyright © 2003 ACM.

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Published: 27 August 2003

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PPDP03: 5th International Conference on Principles and Practice of Declarative Programming 2003

August 27 - 29, 2003

Uppsala, Sweden

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PPDP '03 Paper Acceptance Rate 24 of 48 submissions, 50%;

Overall Acceptance Rate 230 of 486 submissions, 47%

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Cited By

Ahrens BMatthes RMörtberg APopescu AZdancewic S(2022)Implementing a category-theoretic framework for typed abstract syntaxProceedings of the 11th ACM SIGPLAN International Conference on Certified Programs and Proofs10.1145/3497775.3503678(307-323)Online publication date: 17-Jan-2022
https://dl.acm.org/doi/10.1145/3497775.3503678
Hamana M(2022)Complete algebraic semantics for second-order rewriting systems based on abstract syntax with variable bindingMathematical Structures in Computer Science10.1017/S0960129522000287(1-32)Online publication date: 14-Oct-2022
https://doi.org/10.1017/S0960129522000287
Fiore MHamana M(2013)Multiversal Polymorphic Algebraic TheoriesProceedings of the 2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science10.5555/2591370.2591395(520-529)Online publication date: 25-Jun-2013
https://dl.acm.org/doi/10.5555/2591370.2591395
Fiore MHamana M(2013)Multiversal Polymorphic Algebraic Theories: Syntax, Semantics, Translations, and Equational Logic2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science10.1109/LICS.2013.59(520-529)Online publication date: Jun-2013
https://doi.org/10.1109/LICS.2013.59
Ahrens B(2012)Extended Initiality for Typed Abstract SyntaxLogical Methods in Computer Science10.2168/LMCS-8(2:1)20128:2Online publication date: 6-Apr-2012
https://doi.org/10.2168/LMCS-8(2:1)2012
Hamana M(2011)Polymorphic abstract syntax via Grothendieck constructionProceedings of the 14th international conference on Foundations of software science and computational structures: part of the joint European conferences on theory and practice of software10.5555/1987171.1987203(381-395)Online publication date: 26-Mar-2011
https://dl.acm.org/doi/10.5555/1987171.1987203
Gabbay MCiancia V(2011)Freshness and name-restriction in sets of traces with namesProceedings of the 14th international conference on Foundations of software science and computational structures: part of the joint European conferences on theory and practice of software10.5555/1987171.1987202(365-380)Online publication date: 26-Mar-2011
https://dl.acm.org/doi/10.5555/1987171.1987202
Hamana M(2010)Initial Algebra Semantics for Cyclic Sharing Tree StructuresLogical Methods in Computer Science10.2168/LMCS-6(3:15)20106:3Online publication date: 3-Sep-2010
https://doi.org/10.2168/LMCS-6(3:15)2010
Fiore M(2008)Second-Order and Dependently-Sorted Abstract SyntaxProceedings of the 2008 23rd Annual IEEE Symposium on Logic in Computer Science10.1109/LICS.2008.38(57-68)Online publication date: 24-Jun-2008
https://dl.acm.org/doi/10.1109/LICS.2008.38
Hamana MLeuschel MPodelski A(2007)Higher-order semantic labelling for inductive datatype systemsProceedings of the 9th ACM SIGPLAN international conference on Principles and practice of declarative programming10.1145/1273920.1273933(97-108)Online publication date: 14-Jul-2007
https://dl.acm.org/doi/10.1145/1273920.1273933
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