As the subject of logic programming has grown, demand for more
expressive power and efficiency has led language designers to
import constructs from other programming paradigms. Given the
substantial gap between semantic methods in the functional,
imperative and declarative programming communities, it is hard to
evaluate the effectiveness of proposals to add imported features to
logic programming, unless there is an agreed-upon common framework.
A categorical foundation for logic programming is an essential tool
in this endeavour. In this work we show how to handle universal
quantification in categorical logic programming via indexed
categories. We define categorical syntax via tau-categories, and
resolution over such categories for hereditarily Harrop programs
and goals, and give a categorical operational semantics with
respect to which resolution is shown sound and complete. Our model
theory is a categorical generalization of the Kowalski-Van Emden
fixed point semantics based on indexing over programs in order to
capture program augmentation and state change. This framework is
sufficiently broad to handle constraint logic programming and also
a treatment of abstract datatypes.
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||Paperback - Trade
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