```//[[Documentation]]

*Example Programs

A number of example programs, including

-those with just one or a few rules,
-encodings of various calculi (propositional logic, Petri Nets, lambda calculus, ambient calculus, etc.),
-state-space search using SLIM's nondeterministic execution (typical AI problems etc.),
-model checking (distributed and concurrent algorithms, protocol verification, etc.),
-graph visualization using UNYO (fullerenes (C60) etc.),
-those using LMNtal Java's GUI,

and so on, can be found
[['''''HERE'''''>http://www.ueda.info.waseda.ac.jp/lmntal/demo/]].  Those programs are included in the latest distribution of [[LaViT>http://www.ueda.info.waseda.ac.jp/lmntal/lavit/index.php?Download]] also.

Let us introduce some simple examples below.

**List Concatenation

Lists formed with c(cons) and n(il) constructors can be concatenated using the following two rules:

append(X,Y,Z), n(X)      :- Y=Z.
append(X,Y,Z), c(A,X1,X) :- c(A,Z1,Z), append(X1,Y,Z1).

Enter those rules with the following initial state:

append(c(1,c(2,c(3,n))),c(4,c(5,n)),result).

RESULT: result(c(1,c(2,c(3,c(4,c(5,n)))))) with the two rules above.

The above initial state is written using the '''term abbreviation scheme''' explained [[here>Syntax]].  By further applying the term abbreviation scheme and the Prolog-like list syntax, list concatenation can be written also as:

Z=append([],    Y) :- Z=Y.
Z=append([A|X1],Y) :- Z=[A|append(X1,Y)].

result = append([1,2,3],[4,5]).

RESULT: result=[1,2,3,4,5] with the two rules above.

**Self-Organizing Loops

Ten agents with two free hands are going to hold hands with others.

a(free,free),a(free,free),a(free,free),a(free,free),a(free,free),
a(free,free),a(free,free),a(free,free),a(free,free),a(free,free).

a(X,free),a(free,Y) :- a(X,C),a(C,Y).

RESULT: Twenty possible final configurations.  You can randomly compute them by running the program using LMNtal Java with the ''-s'' (shuffle) option, or running SLIM with the ''-nd'' (nondeterministic execution) option.  LaViT's ''StateViewer'' will show you a state transition diagram of the problem.

**Vending Machine

Two customers with different amounts of coins and hunger
are buying chocolates from a vending machine.
Each chocolate costs three
and only two kinds of coins are considered: one and five.

{customer,a,five,one,one,hunger,hunger}.  % Customer a has \$7, buying 2 chocolates
{customer,b,five,hunger}.                 % Customer b has \$5, buying 1 chocolate
{vending,choco,choco,choco,one,one}.      % Vending machine has 3 chocolates

{customer,\$c,hunger,five}, {vending,\$v,choco,one,one} :-
{customer,\$c,choco,one,one}, {vending,\$v,five}.
{customer,\$c,hunger,one,one,one}, {vending,\$v,choco} :-
{customer,\$c,choco}, {vending,\$v,one,one,one}.

LaViT with ''-nd'' will compute two possible final states:

RESULT 1:
{customer,a,choco,choco,one},
{customer,b,choco,one,one},
{vending,five,five,one}, <RULES>
RESULT 2:
{customer,a,hunger,hunger,five,one,one},
{customer,b,choco,one,one},
{vending,choco,choco,five}, <RULES>

Observe that applying each rule preserves
the total amount of coins and chocos within the system.
```