Math 156
Discrete Mathematics for Computer Science
Fall 1999

Intro to Prolog

More information about the Toy Prolog interpreter can be found at

Here is a short example:

Press 'Run' and see what happens.

Ingredient	Syntax Rules	Example(s)
Predicates	begin with lower case letter followed by parenthesized parameter list	`prof()`, `inClass()`, `teaches()`, `isStudent()`
Constants	begin with lower case letter	`pruim`, `math221`, `math156`, `joeSchmo`, `janeDoe`
Variables	begin with capital letter	`P`, `Stud`, `S`
Logical operators	`<=`, `and`, `not`	Examples are obvious, but see below for restrictions on `<=`. Notice, there is no "or".
Implied quantifiers	Invisible	See below for explanation

Note: all names (of variables, constants, and predicates) are case sensitive, but are internally truncated at 10 characters.

There are three kinds of lines in a prolog program. (Note that each is ended by a period.)

Facts: A fact consists of a predicate followed by its paramter list. The paramters may be either constants or variables. Variables are quantified by an implied universal quantifier (forall). They are called facts becuase they state a fact about some object or collection of objects.
In the example above, each of the first four lines is a fact stating a certain relationship between two constant objects. The line equal(X,X) is universally quantified and means that for every X, X is equal to X.
Query: A Toy Prolog program can only have one of these, and it must be the last line. (Some other flavors of prolog allow for multiple queries in one program.) Queries are indicated by an initial ? followed by a predicate (or a conjuction of predicates and negated predicates). You can think of any variables appearing in the query as being quantified by an implied existential quantifier, or a "search quantifier". Toy Prolog will search for all the ways it can find to satisfy the predicate by trying different settings of the variables. (Actually, prolog uses some logical rules, most importantly resolution, so that it can deal with the rules as well as the facts.)

Using just facts and a query, we can can already do some interesting things.

Rules. It is the rules that make Prolog interesting. Rules have the form A <= B, where A is a predicate and B is a conjuction of predicates and negated predicates. The paramters may be either constants or variables. Variables are quantified by an implied universal quantifier (forall).
In the Example 1, the line
teaches(P,Stud) <= prof(P,X) and inClass(Stud,X). is a rule. It is equivalent to forall Stud forall P forall X [prof(P,X) and inClass(Stud,X) -> teach(P,Stud) ]. That is, for any course, student and professor, if the professor teaches the course and the student is in the course, then the professor teaches the student.
Now let's look at the query in Example 1. That query is equivalent to asking "Do there exist any students that pruim teaches?" The result of running the program is to display all the students taught by pruim. Prolog uses the facts and rules to see when in can conclude of a student that pruim teaches the student. Notice again the order in which things appear. In particular, if there is more than one way to conclude that pruim teaches some student, that student appears twice in the list.
Note: It is also possible to query predicates with more than one variable paramter or none (all constants). For example,
? teaches(pruim,janeDoe). will see if pruim teaches janeDoe.

Write Prolog Queries that do the following: