On the algebraic structure of declarative programming languages

被引:14
作者
Amato, Gianluca [1 ]
Lipton, James [2 ]
McGrail, Robert [3 ]
机构
[1] Univ G dAnnunzio, Dipartimento Sci, I-65127 Pescara, Italy
[2] Wesleyan Univ, Dept Math, Middletown, CT 06459 USA
[3] Bard Coll, Annandale on Hudson, NY USA
关键词
Categorical logic; Indexed categories; Logic programming; Abstract data types; Constraint logic programming; ABSTRACT INTERPRETATION; LOGIC; SEMANTICS; SPECIFICATION; FRAMEWORK; PROLOG;
D O I
10.1016/j.tcs.2009.07.038
中图分类号
TP301 [理论、方法];
学科分类号
081202 ;
摘要
We develop an algebraic framework, Logic Programming Doctrines, for the syntax, proof theory, operational semantics and model theory of Horn Clause logic programming based on indexed premonoidal categories. Our aim is to provide a uniform framework for logic programming and its extensions capable of incorporating constraints, abstract data types, features imported from other programming language paradigms and a mathematical description of the state space in a declarative manner. We define a new way to embed information about data into logic programming derivations by building a sketch-like description of data structures directly into an indexed category of proofs. We give an algebraic axiomatization of bottom-up semantics in this general setting, describing categorical models as fixed points of a continuous operator. (C) 2009 Elsevier B.V. All rights reserved.
引用
收藏
页码:4626 / 4671
页数:46
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