Subject: categories: typeful logic programming languages and categorical semantics/logic

From: Galchin Vasili <[email-masked]>
Date: Mon, 9 Feb 2004 20:52:12 -0800 (PST)

Hello,

  can somebody point to the application/research of
categorical semantics/logic to typeful logic
programming languages?

Thank you, Bill Halchin

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From: Jim Lipton <[email-masked]>
Date: Tue, 10 Feb 2004 14:35:28 -0500 (EST)

Papers I know of in Categorical Semantics of Logic Programming (and
related topics such as unification):
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-- Rydeheard, Burstall: A Categorical Unification Algorithm,
1986, LNCS 240, 1986.
  (This work also appeard in Rydeheard and Burstall's book:
"Computational Category Theory", Prentice-Hall, 1988)

-- Goguen: "What is Unification? A categorical View of Substitution,
Equations and Solution" CSLI-88 (Report) , 1988

-- Martini, Asperti: Projections instead of Variables, a
Category-Theoretic Interpretation of Logic Programs, Proc 6th ICLP,
MIT Press, 1989

-- Corradini, Asperti: A categorical Model for Logic Programs: Indexed
Monoidal Categories, 1992

-- Corradini, Montanari: An algebraic Semantics for Structured
Transition Systems and its applications to logic programs, TCS 1992

-- Finkelstein, Freyd, Lipton: Logic Programming in Tau Categories,
CSL 94, 1995 (LNCS 933)

-- Power, Kinoshita: A New Foundation for Logic Programming, ELP 96,
1996 (LNCS #?) Springer.

-- McGrail: "Monads and Control in Logic Programming",
Ph. D. Dissertation, Wesleyan University, 1997.

-- Lipton, McGrail: Encapsulating data in  Logic Programming via
Categorical Constraints, in Principles of Declarative Programming,
LNCS 1490, 1998.

-- Amato: Sequent Calculus and Indexed Categories as Foundations for
Logic Programming, P. D. Thesis, Univ. of Pisa, 2000

--Amato, Lipton: Indexed Categories and bottom-up semantics of Logic
Programming, Proceedings LPAR 01, Lecture Notes in Artifical
Intelligence 2250

-- Finkelstein, Freyd Lipton: A New Framework for Declarative
Programming, TCS 300, 2003.

The bibliography in the last paper cited contains more detailed
references.

There is a dissertation by Diaconescu, 1994, Oxford, on an
Institutions-and-categories-based approach to logic programming. I
regret not having the title and specifics with me at present.
Apologies for incomplete information, I am away from my files at
present. If anyone knows of publications that should be added to the
list I would appreciate hearing of them.

Regards,
--Jim Lipton

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> categorical semantics/logic to typeful logic

________________________________________________________________________
Jim Lipton [email-masked] [email-masked] |jlipton.web.wesleyan.edu
Math & Computer Science, Wesleyan University, Middletown CT 06459
Ramon y Cajal Visiting Researcher: Facultad de Informatica
Universidad Politecnica de Madrid, 28660-Boadilla del Monte, MADRID SPAIN
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