The GAMBOL package is a trivially modified extraction of the logic programming portion of the Frolic system written at the University of Utah. I have made a few changes to get it to compile under a modern Common Lisp, in addition to a few style changes that don't alter any functionality.

Using Gambol

Gambol is basic logic programming system written in pure Lisp, using Lisp-like syntax. Most of it will seem familiar to people who know Prolog, but apart from core functionality it is nowhere near a complete system — i.e., it doesn't provide the mass of built-in operations and predicates of an ISO-compliant Prolog. The semantics of some operations (like retract, for example) differ from a compliant Prolog, too.

Gambol is heavy conser.

The Package

The package name is :gambol. There are no nicknames.

It depends on no other libraries.

Note that because Gambol is just working with ordinary Lisp symbols most of the time you have to keep in mind what package you define facts and rules in. Except for core operators (is, assertz, etc.) you'll have to state the package on terms if you define rules in a different package from where you'll be querying the database.

Logic Programming

Like Prolog, Gambol deals with facts, rules, procedures and queries.

Facts are represented so:

(*- (mortal socrates))
(*- (eat cats mice))

The *- macro adds new facts and rules to the database. A predicate may have an arbitrary number of arguments.

Rules are represented so:

(*- head b,,1,, b,,2,, ... b,,n,,)

Where the b,,n,, terms are called the body of the rule. Within rules (and facts) you can use logical variables. These are simply lisp symbols that start with a question mark. This represents, "if something is human, it is mortal" —

(*- (mortal ?x) (human ?x))

Notice that a fact is just a degenerate sort of rule which is always true.

If you don't care about the term in a particular rule you can use ?? as a special placeholder variable.

Procedures are collections of rules which all have the same predicate:

(*- (append (?x . ?xs) ?ys (?x . ?zs))
    (append ?xs ?ys ?zs))
(*- (append nil ?ys ?ys))

Notice that the Gambol unifier understands Lisp lists. Where Prolog uses | to separate the head from the rest of the list, Gambol uses the usual Lispy dotted-pair notation.

Interactive queries are called with one of the ?- or ??- macros. ?- will present one answer after the other, asking you if you wish to continue after each. ??- will find all solutions immediately.

None of the macros presented so far gives you a way to pass Lisp values into the database of facts and rules. See the API section below for function calls to interact with the database.

Special Predicates and Operators

(cut)
Is equivalent to the Prolog cut (!) operator.

(fail)
is an immediate fail. Combined with (cut) this can be used to implement the usual Prolog negation as failure:

(*- (not ?p)
    ?p
    (cut)
    (fail))

(= ?x ?x)
Performs unification.

(asserta ?p)
Adds a new fact to the head of the database. pl-asserta is the function equivalent. Always succeeds.

(assertz ?p)
Adds a new fact to the end of the database, as though via the **- macro pl-assert. These three Lisp expressions will accomplish the same thing:

(*- (fibonacci 0 1))
(?- (assert (fibonacci 0 1)))
(pl-assert '((fibonacci 0 1)))

Always succeeds.

(retract ?p) removes a fact from the database. It is not currently smart enough to remove rules. It will retract a fact that matches perfectly, or, if logical variables are in the expression, the first solution found. If it finds a fact to remove, it succeeds. If it finds nothing, it fails.

(is logical-variable(s) (lop (lisp-expression)))
binds one or more logical variables to the result of a lisp expression:

GAMBOL> (*- (1- ?n ?result)
            (is ?result (lop (1- ?n))))
((1- ?N ?RESULT) (IS ?RESULT (LOP (1- ?N))))
GAMBOL> (??- (1- 3 ?result))

?RESULT = 2

Several logical variables may come between is and the lisp expression if that lisp expression will return multiple values.

(lop (lisp-expression))
allows Gambol to invoke arbitrary Lisp functions. Any logical variables in the expression will be correctly substituted before the function is evaluated. Note that the lisp expression must be an applyable function, not a macro or special form. If the lisp expression returns non-nil the term is counted as a success.

GAMBOL> (*- (greater-than ?x ?y) (lop (> ?x ?y)))
((GREATER-THAN ?X ?Y) (LOP (> ?X ?Y)))
GAMBOL> (??- (greater-than 5 7))
NO
GAMBOL> (??- (greater-than 7 5))
YES

(lisp (lisp-expression))
evaluates the lisp expression, but the term always counts as a success. This is used to get Lisp side-effects:

GAMBOL> (*- (write ?x) (lisp (format t "~A" ?x)))
((WRITE ?X) (LISP (FORMAT T "~A" ?X)))
GAMBOL> (?- (write (tasty pizza)))
(TASTY PIZZA)
YES
More?  (y or n) n

NIL

API

special variable
*TRACING*
if set to t will cause queries to print out trace information.

special variable
*LIPS*
keeps track of how many logical inferences have been performed. You reset this and combine it with timing output to assess how quickly Gambol's doing its work.

macro
*- rule
adds new rules and facts to the database. They are inserted in the order they arrive.

macro
?- goal
interactively tries to solve the goal, asking you if you want to continue after each solution found.

macro
??- goal
immediately finds all solutions to the goal.

function
pl-assert rule
is the function counterpart to the **- macro. The rule must therefore be quoted (or constructed). Also, keep in mind that a fact is a rule missing a body. This results in extra list embedding:

(pl-assert '((mortal socrates)))         ; same as: (**- (mortal socrates))
(pl-assert '((mortal ?x) (human ?x)))    ; same as: (**- (mortal ?x) (human ?x))

function
pl-asserta rule
adds a new rule to the database. If the predicate already exists the new rule goes at the head of the list of rules for that predicate.

function
pl-retract rule
removes a fact from the database. The fact may be literal or contain logical variables. In all cases, it only removes the first matching fact it finds. Like pl-assert, take care with the list form:

(pl-retract '((mortal socrates)))

function
pl-solve-one goals
returns the first set of bindings (an association list) which satisfies the goal. If there are no variables necessary to satisfy the goal, then t is simply returned. nil is returned if the goal cannot be satisfied.

function
pl-solve-next
returns the next set of bindings which satisfy the goal set in the last pl-solve-one call.

function
pl-solve-rest
returns a list of bindings of the remaining solutions to the last pl-solve-one call.

function
pl-solve-all goals
immediately returns all bindings that satisfy the goal.

macro
do-solve-all (bindings) goals
is a convenience wrapper around pl-solve-all which iterates over all the solutions. The bindings should be the logical variables you're interested in. These will be successively bound to the values returned by pl-solve-all:

GAMBOL> (do-solve-all (?who) '((mortal ?who))
          (format t "~A is mortal~%" ?who))
SOCRATES is mortal
GERTRUDE.STEIN is mortal
NIL
GAMBOL>

function
clear-rules &optional (predicates nil)
with no arguments empties the rules database. Or you may specify a list of predicates to clear.

function
print-rules &optional (predicates nil)
with no arguments prints out all rules. Or you may specify a list of predicates.

function
print-rule predicate
prints all the rules for predicate.

Multiple Rulebases

As of the 0.03 release it is possible to have multiple, independent rulebases.

function
current-rulebase
returns a reference to the current rulebase. This is useful if you want to keep the current global rulebase before wiping it.

function
make-rulebase
creates a new, blank rulebase.

macro
with-rulebase rulebase &body body
all prolog operations in the body will work with the given rulebase instead of the default. Because Gambol's rulebase and state are contained in a bunch of special variables, you can nest this macro safely. Given a blank default rulebase, this should return nil:

   (let ((default-rulebase (current-rulebase)))
     (with-rulebase (make-rulebase)
       (*- (fibonacci 0 1))
       (*- (fibonacci 1 1))
       (with-rulebase default-rulebase
         (pl-solve-one '((fibonacci 0 1))))))

What I changed to turn Frolic into Gambol

Logical variables were converted from _var to ?var (a more common representation).
The ^ read macro was yanked, and replaced with predicate operators, LOP and LISP.
References to 'frobs' removed.
The operation of LOP and LISP was switched from using EVAL to using APPLY. This somewhat restricts how these can be used, but I don't think that's really a problem.
The "I don't care" variable is ?? instead of __. I might yet change this to just ? which is somewhat common.
Several unused global variables were removed, including the state storage which would have allowed the HOW function to explain how a solution was reached. It looks like that was never completed.
The code exhibits a preoccupation with performance, which often takes the form of macros where functions would do just as well. You can't trace macros, so I converted some of these back to normal functions.
I added a macro to iterate over solutions from PL-SOLVE-ALL, DO-SOLVE-ALL.

I contacted one of the authors to verify the licensing — "we always operated under the BSD license ideas." My trivial modifications are under MIT out of habit. Since these two license schemes are kissing cousins, I doubt this is really a problem.

wmannis/cl-gambol

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