//[[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-UNYO (fullerenes (C60) etc.),
-those using LMNtal Java's GUI,

and so on, can be found in 
[[''this directory'' (click here)>http://www.ueda.info.waseda.ac.jp/lmntal/demo/]].

-The [[''ltl'' subdirectory>http://www.ueda.info.waseda.ac.jp/lmntal/demo/ltl/]] contains both programs and LTL formulas to model-check them.
-The [[''unyo'' subdirectory>http://www.ueda.info.waseda.ac.jp/lmntal/demo/unyo/]] contains programs to be run under the UNYO-UNYO visualizer.
//-The [[''wt'' subdirectory>http://www.ueda.info.waseda.ac.jp/lmntal/demo/wt/]] contains programs to be run with the LMNtal window toolkit of LMNtal Java.

All these programs are included in the latest distribution of [[LaViT>http://www.ueda.info.waseda.ac.jp/lmntal/lavit/index.php?Download]].

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, the list concatenation program 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, each with two free hands, are going to hold hands with others.
Is it possible that some agent is left alone?

 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, which can be computed by 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.


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