16.4 An Overview of Logic Programming 735problem. Declarative semantics is considerably simpler than the semantics of
the imperative languages. For example, the meaning of a given proposition in a
logic programming language can be concisely determined from the statement
itself. In an imperative language, the semantics of a simple assignment statement
requires examination of local declarations, knowledge of the scoping rules of the
language, and possibly even examination of programs in other files just to deter-
mine the types of the variables in the assignment statement. Then, assuming the
expression of the assignment contains variables, the execution of the program
prior to the assignment statement must be traced to determine the values of those
variables. The resulting action of the statement, then, depends on its run-time
context. Comparing this semantics with that of a proposition in a logic language,
with no need to consider textual context or execution sequences, it is clear that
declarative semantics is far simpler than the semantics of imperative languages.
Thus, declarative semantics is often stated as one of the advantages that declara-
tive languages have over imperative languages (Hogger, 1984, pp. 240–241).
Programming in both imperative and functional languages is primarily pro-
cedural, which means that the programmer knows what is to be accomplished
by a program and instructs the computer on exactly how the computation is to
be done. In other words, the computer is treated as a simple device that obeys
orders. Everything that is computed must have every detail of that computation
spelled out. Some believe that this is the essence of the difficulty of program-
ming using imperative and functional languages.
Programming in a logic programming language is nonprocedural. Programs
in such languages do not state exactly how a result is to be computed but rather
describe the form of the result. The difference is that we assume the computer
system can somehow determine how the result is to be computed. What is needed
to provide this capability for logic programming languages is a concise means of
supplying the computer with both the relevant information and a method of infer-
ence for computing desired results. Predicate calculus supplies the basic form of
communication to the computer, and resolution provides the inference technique.
An example commonly used to illustrate the difference between procedural
and nonprocedural systems is sorting. In a language like Java, sorting is done
by explaining in a Java program all of the details of some sorting algorithm to
a computer that has a Java compiler. The computer, after translating the Java
program into machine code or some interpretive intermediate code, follows
the instructions and produces the sorted list.
In a nonprocedural language, it is necessary only to describe the character-
istics of the sorted list: It is some permutation of the given list such that for each
pair of adjacent elements, a given relationship holds between the two elements.
To state this formally, suppose the list to be sorted is in an array named list that
has a subscript range 1... n. The concept of sorting the elements of the given
list, named old_list, and placing them in a separate array, named new_list, can
then be expressed as follows:
sort(old_list, new_list) permute(old_list, new_list) x sorted(new_list)
sorted(list) 5 j such that 1...j 6 n, list(j)...list(j+1)