Supercompilation of the interpreter of Lambda-numeration
Functions of logic of the expressions
index.htm - Russian text
lambda.zip - archived directory.
The software package accessible to addresses is used
Lambda calculus interpreter ( http://drcjt.freeyellow.com/Lambda.html ) - head page,
Download the source code ( http://drcjt.freeyellow.com/lambda-1.00.tar.gz ) - software package.
The software package is aplet, therefore head program Lambda.java was reworked.
Here we consider supercompilation of the lagic formulas written in Lambdas - nomenclatures. Actually, the compiler of the logical Lambdas - formulas in Java-programs is obtained.
We compile a method test () in the program lambda.java.
The specialization happens till two variables:
The following logic operations are used: implication, negation, conjunction and disjunction. Their description
let true = \x. \y. x
let false = \x. \y. y
let impl = \x. \y. x y true
let not = \x. x false true
let or = \x. \y. impl (not x) y
let and = \x. \y. not (or (not x) (not y))
We have used that property, that conjunction and disjunction express through implication and negation.
Lambda is meant by the character "\", in text constants she is doubled.
The residual program calculates value of the formula for any set of values of arguments.
Let's pass with the description 14 examples.
All examples are made out on one template:
The residual program, откопированная from an output file of the supercompiler together with the lines - comments, on first of which is indicated time of supercompilation up to постпроцессинга, and on last - complete time. "
Example 1. x & (y | z)
strStart = "\\x. \\y. \\z. and x (or y z)"; int nVar = 3;
//-------------------------------------- 25 sec - postprocessing...
public static boolean test (final boolean[] param_18)
{
if (param_18[0]
&& (param_18[1] || param_18[2])) {
return true;}
else {
return false;}
}
//-------------------------------------- 27 sec - JScp version 0.0.72
Example 2. x | (y & z)
strStart = "\\x. \\y. \\z. or x (and y z)"; nVar = 3;
//-------------------------------------- 24 sec - postprocessing...
public static boolean test (final boolean[] param_18)
{
if (param_18[0]
|| param_18[1] && param_18[2]) {
return true;}
else {
return false;}
}
//-------------------------------------- 26 sec - JScp version 0.0.72
Example 3. Implication
strStart = "\\x. \\y. impl x y"; nVar = 2;
//-------------------------------------- 8 sec - postprocessing...
public static boolean test (final boolean[] param_18)
{
if (param_18[0]
&& !param_18[1]) {
return false;}
else {
return true;}
}
//-------------------------------------- 9 sec - JScp version 0.0.72
Example 4. Identically true function
strStart = "\\x. \\y. impl x (impl y x)"; nVar = 2;
//-------------------------------------- 10 sec - postprocessing...
public static boolean test (final boolean[] param_18)
{
return true;
}
//-------------------------------------- 10 sec - JScp version 0.0.72
Example 5. Implication (3 variable)
strStart = "\\x. \\y. \\z. impl x y"; nVar = 3;
//-------------------------------------- 17 sec - postprocessing...
public static boolean test (final boolean[] param_18)
{
if (param_18[0]
&& !param_18[1]) {
return false;}
else {
return true;}
}
//-------------------------------------- 18 sec - JScp version 0.0.72
Example 6. Identically true function
strStart = "\\x. \\y. \\z. impl x (impl y x)"; nVar = 3;
//-------------------------------------- 20 sec - postprocessing...
public static boolean test (final boolean[] param_18)
{
return true;
}
//-------------------------------------- 21 sec - JScp version 0.0.72
Example 7. Other identically true function
\\x. \\y. \\z. impl (impl x (impl y z)) (impl (impl x y) (impl x z)) nVar = 3;
//-------------------------------------- 39 sec - postprocessing...
public static boolean test (final boolean[] param_18)
{
return true;
}
//-------------------------------------- 41 sec - JScp version 0.0.72
Example 8. Implication (4 variable)
strStart = "\\x. \\y. \\z. \\u. impl x y"; nVar = 4;
//-------------------------------------- 37 sec - postprocessing...
public static boolean test (final boolean[] param_18)
{
if (param_18[0]
&& !param_18[1]) {
return false;}
else {
return true;}
}
//-------------------------------------- 39 sec - JScp version 0.0.72
Example 9. True only in two cases
\\x. \\y. \\z. or (and x (and y z)) (and (not x) (and (not y) (not z))) nVar = 3;
//-------------------------------------- 59 sec - postprocessing...
public static boolean test (final boolean[] param_18)
{
if (param_18[0]) {
if (param_18[1]
&& param_18[2]) {
return true;}
else {
return false;}}
else {
if (param_18[1]
|| param_18[2]) {
return false;}
else {
return true;}}
}
//-------------------------------------- 65 sec - JScp version 0.0.72
Example 10. (x & y) | (z & u)
strStart = "\\x. \\y. \\z. \\u. or (and x y ) (and z u)"; nVar = 4;
//-------------------------------------- 75 sec - postprocessing...
public static boolean test (final boolean[] param_18)
{
if (param_18[0]) {
if (param_18[1]
|| param_18[2] && param_18[3]) {
return true;}
else {
return false;}}
else {
if (param_18[2]
&& param_18[3]) {
return true;}
else {
return false;}}
}
//-------------------------------------- 82 sec - JScp version 0.0.72
Example 11. (x | not x) & (y | not y) & z = true & true & z = z
strStart = "\\x. \\y. \\z. and (and (or x (not x)) (or y (not y))) z"; nVar = 3;
//-------------------------------------- 50 sec - postprocessing...
public static boolean test (final boolean[] param_18)
{
if (param_18[2]) {
return true;}
else {
return false;}
}
//-------------------------------------- 55 sec - JScp version 0.0.72
Example 12. Max True - (x & y) | (y & z) | (x & z)
strStart = "\\x. \\y. \\z. or (and x y) (or (and y z) (and x z))"; int nVar = 3;
//-------------------------------------- 47 sec - postprocessing...
public static boolean test (final boolean[] param_18)
{
if (param_18[0]) {
if (param_18[1]
|| param_18[2]) {
return true;}
else {
return false;}}
else {
if (param_18[1]
&& param_18[2]) {
return true;}
else {
return false;}}
}
//-------------------------------------- 52 sec - JScp version 0.0.72
Example 13. Mostik
\\x. \\y. \\z. \\u. \\v.
or (or (and x y) (and z u)) (or (and x (and v u)) (and z (and v y)))
nVar = 5;
//-------------------------------------- 340 sec - postprocessing...
public static boolean test (final boolean[] param_18)
{
if (param_18[0]) {
if (param_18[1]) {
return true;}
else {
if (param_18[2]) {
if (param_18[3]) {
return true;}
else {
return false;}}
else {
if (param_18[3]
&& param_18[4]) {
return true;}
else {
return false;}}}}
else {
if (param_18[1]) {
if (param_18[2]
&& (param_18[3] || param_18[4])) {
return true;}
else {
return false;}}
else {
if (param_18[2]
&& param_18[3]) {
return true;}
else {
return false;}}}
}
//-------------------------------------- 379 sec - JScp version 0.0.72
Example 14. Equality
strStart = "\\x. \\y. and (impl x y) (impl y x)"; nVar = 2;
//-------------------------------------- 14 sec - postprocessing...
public static boolean test (final boolean[] param_18)
{
if (param_18[0]) {
if (param_18[1]) {
return true;}
else {
return false;}}
else {
if (param_18[1]) {
return false;}
else {
return true;}}
}
//-------------------------------------- 16 sec - JScp version 0.0.72