General Computer Science 320201 GenCS I & II Lecture ... - Kwarc

GAs = evolution: e.g., real genes encode replication machinery!
4.2 Logic Programming
c○: Michael Kohlhase 502
We will now learn a new programming paradigm: “logic programming” (also called “Declarative
Programming”), which is an application of the search techniques we looked at last, and the logic
techniques. We are going to study ProLog (the oldest and most widely used) as a concrete example
of the ideas behind logic programming.
4.2.1 Introduction to Logic Programming and PROLOG
Logic Programming is a programming style that differs from functional and imperative programming
in the basic procedural intuition. Instead of transforming the state of the memory by issuing
instructions (as in imperative programming), or computing the value of a function on some arguments,
logic programming interprets the program as a body of knowledge about the respective
situation, which can be queried for consequences. This is actually a very natural intuition; after
all we only run (imperative or functional) programs if we want some question answered.
Logic Programming
Idea: Use logic as a programming language!
We state what we know about a problem (the program) and then ask for results (what the
program would compute)
Example 623
Program Leibniz is human x + 0 = x
Sokrates is is human If x + y = z then x + s(y) = s(z)
Sokrates is a greek 3 is prime
Every human is fallible
Query Are there fallible greeks? is there a z with s(s(0)) + s(0) = z
Answer Yes, Sokrates! yes s(s(s(0)))
How to achieve this?: Restrict the logic calculus sufficiently that it can be used as computational
procedure.
Slogan: Computation = Logic + Control ([Kowalski ’73])
We will use the programming language ProLog as an example
c○: Michael Kohlhase 503
Of course, this the whole point of writing down a knowledge base (a program with knowledge
about the situation), if we do not have to write down all the knowledge, but a (small) subset,
from which the rest follows. We have already seen how this can be done: with logic. For logic
programming we will use a logic called “first-order logic” which we will not formally introduce
here. We have already seen that we can formulate propositional logic using terms from an abstract
data type instead of propositional variables – recall Definition 2.6.1. For our purposes, we will
just use terms with variables instead of the ground terms used there.
Representing a Knowledge base in ProLog
Definition 624 Fix an abstract data type 〈{B, . . .}, {, . . .}〉, then we call all constructor
terms of sort B ProLog terms.
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