Example Programs †

A number of example programs, including

and so on, can be found in this directory (click here).

All these programs are included in the latest distribution of LaViT.

Let us introduce some simple examples below.

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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).

Let them rewrite 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. By using the term abbreviation scheme and the Prolog-like list syntax, the list concatenation program can be written also in a functional style 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.

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Greatest Common Divisor †

The following program computes the GCD of two numbers using one rule, based on the fact that the GCD won't change by replacing the larger number with the difference between the two numbers:

n=100, n=72;
n=$x, n=$y :- $x>$y | n=$x-$y, n=$y.

RESULT: n=4, n=4.

How to handle numbers in LMNtal is not detailed here but is described in Built-in Types and Guards.

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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.

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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 and wants to buy two chocolates
{customer,b,five,hunger}.                 % Customer b has $5 and wants to buy one 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},   // Oops!
          {customer,b,choco,one,one}, 
          {vending,choco,choco,five}, <RULES>

Observe that applying each rule preserves the total number of coins and chocolates within the system.

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