Logic programming beyond Prolog
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by
M.H. van Emden
2014
Abstract
A logic program is an executable specification. For example, merge sort in
pure Prolog is a logical formula, yet shows creditable performance on long
linked lists. But such executable specifications are a compromise: the logic is
distorted by algorithmic considerations, yet only indirectly executable via an
abstract machine. This paper introduces relational programming, a method that
solves the difficulty with logic programming by a separation of concerns. It
requires three texts: (1) the axioms, a logical formula that specifies the
problem and is not compromised by algorithmic considerations, (2) the theorem,
a logical formula that expresses the idea of the algorithm and follows from the
axioms, and (3) the code, a transcription of the theorem to a procedural
language. Correctness of the code relies on the logical relationship of the
theorem with the axioms and relies on an accurate transcription of the theorem
to the procedural language. Sorting is an example where relational programming
has the advantage of a higher degree of abstractness: the data to be sorted can
be any data type in C++ (the procedural language we use in our examples) that
satisfies the axioms of linear order, while the pure-Prolog version is limited
to data structures in the form of linked cells. We show another advantage of
relational programs: they have a model-theoretic and fixpoint semantics
equivalent to each other and analogous to those of pure Prolog programs.
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