Well1AmNichtDiePerson
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Sample lambda calculus programming or code in C/C++, Visual Basic, C#, PHP, Java, Python
# Lambda abstraction
def λ(x, y):
return lambda f: f(x, y)
# Lambda application
def app(f, x):
return f(x)
# Identity function
I = λ('x', 'x')
# Boolean true
TRUE = λ('x', λ('y', 'x'))
# Boolean false
FALSE = λ('x', λ('y', 'y'))
# Logical AND operator
AND = λ('x', λ('y', app(app('x', 'y'), FALSE)))
# Logical OR operator
OR = λ('x', λ('y', app(app('x', TRUE), 'y')))
# Logical NOT operator
NOT = λ('x', app(app('x', FALSE), TRUE))
# Testing the functions
print(app(app(AND, TRUE), TRUE)) # Output: TRUE
print(app(app(AND, TRUE), FALSE)) # Output: FALSE
print(app(NOT, TRUE)) # Output: FALSE
print(app(NOT, FALSE)) # Output: TRUE
λ
function, and lambda applications using the app
function. We then define various functions and constants in lambda calculus, such as the identity function (I
), boolean constants (TRUE
and FALSE
), and logical operators (AND
, OR
, and NOT
).app
function. The output of the above code demonstrates the behavior of logical operations in lambda calculus.functional programming in PHP, lambda calculusHere's an example of a lambda calculus expression implemented in Python:
Python:# Lambda abstraction def λ(x, y): return lambda f: f(x, y) # Lambda application def app(f, x): return f(x) # Identity function I = λ('x', 'x') # Boolean true TRUE = λ('x', λ('y', 'x')) # Boolean false FALSE = λ('x', λ('y', 'y')) # Logical AND operator AND = λ('x', λ('y', app(app('x', 'y'), FALSE))) # Logical OR operator OR = λ('x', λ('y', app(app('x', TRUE), 'y'))) # Logical NOT operator NOT = λ('x', app(app('x', FALSE), TRUE)) # Testing the functions print(app(app(AND, TRUE), TRUE)) # Output: TRUE print(app(app(AND, TRUE), FALSE)) # Output: FALSE print(app(NOT, TRUE)) # Output: FALSE print(app(NOT, FALSE)) # Output: TRUE
In this example, we define lambda abstractions using theλ
function, and lambda applications using theapp
function. We then define various functions and constants in lambda calculus, such as the identity function (I
), boolean constants (TRUE
andFALSE
), and logical operators (AND
,OR
, andNOT
).
We can then test these lambda expressions by applying them to arguments using theapp
function. The output of the above code demonstrates the behavior of logical operations in lambda calculus.
Functional programming in PHP supports many features of lambda calculus. While PHP itself does not have native support for lambda functions, you can achieve functional programming style using anonymous functions and higher-order functions. Here's an example that demonstrates the basic concepts of lambda calculus in PHP:functional programming in PHP, lambda calculus
<?php
// Lambda abstraction
function λ($x, $y) {
return function ($f) use ($x, $y) {
return $f($x, $y);
};
}
// Lambda application
function app($f, $x) {
return $f($x);
}
// Identity function
$I = function ($x) {
return $x;
};
// Boolean true
$TRUE = function ($x) {
return function ($y) use ($x) {
return $x;
};
};
// Boolean false
$FALSE = function ($x) {
return function ($y) use ($x) {
return $y;
};
};
// Logical AND operator
$AND = function ($x) {
return function ($y) use ($x) {
return app(app($x, $y), $FALSE);
};
};
// Logical OR operator
$OR = function ($x) {
return function ($y) use ($x) {
return app(app($x, $TRUE), $y);
};
};
// Logical NOT operator
$NOT = function ($x) {
return app(app($x, $FALSE), $TRUE);
};
// Testing the functions
var_dump(app(app($AND, $TRUE), $TRUE)); // Output: bool(true)
var_dump(app(app($AND, $TRUE), $FALSE)); // Output: bool(false)
var_dump(app($NOT, $TRUE)); // Output: bool(false)
var_dump(app($NOT, $FALSE)); // Output: bool(true)
λ
function, and lambda applications using the app
function. We then create functions and constants in lambda calculus, such as the identity function ($I
), boolean constants ($TRUE
and $FALSE
), and logical operators ($AND
, $OR
, and $NOT
).app
function. The output of the above code demonstrates the behavior of logical operations in lambda calculus.functional programming in C#, lambda calculusFunctional programming in PHP supports many features of lambda calculus. While PHP itself does not have native support for lambda functions, you can achieve functional programming style using anonymous functions and higher-order functions. Here's an example that demonstrates the basic concepts of lambda calculus in PHP:
PHP:<?php // Lambda abstraction function λ($x, $y) { return function ($f) use ($x, $y) { return $f($x, $y); }; } // Lambda application function app($f, $x) { return $f($x); } // Identity function $I = function ($x) { return $x; }; // Boolean true $TRUE = function ($x) { return function ($y) use ($x) { return $x; }; }; // Boolean false $FALSE = function ($x) { return function ($y) use ($x) { return $y; }; }; // Logical AND operator $AND = function ($x) { return function ($y) use ($x) { return app(app($x, $y), $FALSE); }; }; // Logical OR operator $OR = function ($x) { return function ($y) use ($x) { return app(app($x, $TRUE), $y); }; }; // Logical NOT operator $NOT = function ($x) { return app(app($x, $FALSE), $TRUE); }; // Testing the functions var_dump(app(app($AND, $TRUE), $TRUE)); // Output: bool(true) var_dump(app(app($AND, $TRUE), $FALSE)); // Output: bool(false) var_dump(app($NOT, $TRUE)); // Output: bool(false) var_dump(app($NOT, $FALSE)); // Output: bool(true)
In this example, we define lambda abstractions using theλ
function, and lambda applications using theapp
function. We then create functions and constants in lambda calculus, such as the identity function ($I
), boolean constants ($TRUE
and$FALSE
), and logical operators ($AND
,$OR
, and$NOT
).
We can then test these lambda expressions by applying them to arguments using theapp
function. The output of the above code demonstrates the behavior of logical operations in lambda calculus.
Functional programming in C# supports lambda functions and higher-order functions, which are essential components of lambda calculus. Here's an example that demonstrates the basic concepts of lambda calculus in C#:functional programming in C#, lambda calculus
using System;
public delegate Func<T2, TResult> Func<T1, T2, TResult>(T1 arg);
class Program
{
// Lambda abstraction
static Func<T1, Func<T2, TResult>> λ<T1, T2, TResult>(Func<T1, Func<T2, TResult>> f)
{
return f;
}
// Lambda application
static TResult app<T1, T2, TResult>(Func<T1, Func<T2, TResult>> f, T1 x, T2 y)
{
return f(x)(y);
}
// Identity function
static Func<T, T> I<T>()
{
return x => x;
}
// Boolean true
static Func<T1, Func<T2, T1>> TRUE<T1, T2>()
{
return x => y => x;
}
// Boolean false
static Func<T1, Func<T2, T2>> FALSE<T1, T2>()
{
return x => y => y;
}
// Logical AND operator
static Func<Func<T1, Func<T2, T3>>, Func<T1, Func<T2, T3>>> AND<T1, T2, T3>()
{
return x => y => app(app(x, y), FALSE<T1, T2>());
}
// Logical OR operator
static Func<Func<T1, Func<T2, T3>>, Func<T1, Func<T2, T3>>> OR<T1, T2, T3>()
{
return x => y => app(app(x, TRUE<T1, T2>()), y);
}
// Logical NOT operator
static Func<Func<T1, Func<T2, T3>>, Func<T1, Func<T2, T3>>> NOT<T1, T2, T3>()
{
return x => app(app(x, FALSE<T1, T2>()), TRUE<T1, T2>());
}
static void Main(string[] args)
{
// Testing the functions
var result1 = app(app(AND<bool, bool, bool>(), TRUE<bool, bool>()), TRUE<bool, bool>()); // Output: True
var result2 = app(app(AND<bool, bool, bool>(), TRUE<bool, bool>()), FALSE<bool, bool>()); // Output: False
var result3 = app(NOT<bool, bool, bool>(), TRUE<bool, bool>()); // Output: False
var result4 = app(NOT<bool, bool, bool>(), FALSE<bool, bool>()); // Output: True
Console.WriteLine(result1);
Console.WriteLine(result2);
Console.WriteLine(result3);
Console.WriteLine(result4);
}
}
λ
function, and lambda applications using the app
function. We then create functions and constants in lambda calculus, such as the identity function (I
), boolean constants (TRUE
and FALSE
), and logical operators (AND
, OR
, and NOT
).app
function. The output of the above code demonstrates the behavior of logical operations in lambda calculus.functional programming in Visual Basic, lambda calculusFunctional programming in C# supports lambda functions and higher-order functions, which are essential components of lambda calculus. Here's an example that demonstrates the basic concepts of lambda calculus in C#:
C#:using System; public delegate Func<T2, TResult> Func<T1, T2, TResult>(T1 arg); class Program { // Lambda abstraction static Func<T1, Func<T2, TResult>> λ<T1, T2, TResult>(Func<T1, Func<T2, TResult>> f) { return f; } // Lambda application static TResult app<T1, T2, TResult>(Func<T1, Func<T2, TResult>> f, T1 x, T2 y) { return f(x)(y); } // Identity function static Func<T, T> I<T>() { return x => x; } // Boolean true static Func<T1, Func<T2, T1>> TRUE<T1, T2>() { return x => y => x; } // Boolean false static Func<T1, Func<T2, T2>> FALSE<T1, T2>() { return x => y => y; } // Logical AND operator static Func<Func<T1, Func<T2, T3>>, Func<T1, Func<T2, T3>>> AND<T1, T2, T3>() { return x => y => app(app(x, y), FALSE<T1, T2>()); } // Logical OR operator static Func<Func<T1, Func<T2, T3>>, Func<T1, Func<T2, T3>>> OR<T1, T2, T3>() { return x => y => app(app(x, TRUE<T1, T2>()), y); } // Logical NOT operator static Func<Func<T1, Func<T2, T3>>, Func<T1, Func<T2, T3>>> NOT<T1, T2, T3>() { return x => app(app(x, FALSE<T1, T2>()), TRUE<T1, T2>()); } static void Main(string[] args) { // Testing the functions var result1 = app(app(AND<bool, bool, bool>(), TRUE<bool, bool>()), TRUE<bool, bool>()); // Output: True var result2 = app(app(AND<bool, bool, bool>(), TRUE<bool, bool>()), FALSE<bool, bool>()); // Output: False var result3 = app(NOT<bool, bool, bool>(), TRUE<bool, bool>()); // Output: False var result4 = app(NOT<bool, bool, bool>(), FALSE<bool, bool>()); // Output: True Console.WriteLine(result1); Console.WriteLine(result2); Console.WriteLine(result3); Console.WriteLine(result4); } }
In this example, we define lambda abstractions using theλ
function, and lambda applications using theapp
function. We then create functions and constants in lambda calculus, such as the identity function (I
), boolean constants (TRUE
andFALSE
), and logical operators (AND
,OR
, andNOT
).
We can then test these lambda expressions by applying them to arguments using theapp
function. The output of the above code demonstrates the behavior of logical operations in lambda calculus.
functional programming in Java, lambda calculusHere's an example of a lambda calculus expression implemented in Python:
Python:# Lambda abstraction def λ(x, y): return lambda f: f(x, y) # Lambda application def app(f, x): return f(x) # Identity function I = λ('x', 'x') # Boolean true TRUE = λ('x', λ('y', 'x')) # Boolean false FALSE = λ('x', λ('y', 'y')) # Logical AND operator AND = λ('x', λ('y', app(app('x', 'y'), FALSE))) # Logical OR operator OR = λ('x', λ('y', app(app('x', TRUE), 'y'))) # Logical NOT operator NOT = λ('x', app(app('x', FALSE), TRUE)) # Testing the functions print(app(app(AND, TRUE), TRUE)) # Output: TRUE print(app(app(AND, TRUE), FALSE)) # Output: FALSE print(app(NOT, TRUE)) # Output: FALSE print(app(NOT, FALSE)) # Output: TRUE
In this example, we define lambda abstractions using theλ
function, and lambda applications using theapp
function. We then define various functions and constants in lambda calculus, such as the identity function (I
), boolean constants (TRUE
andFALSE
), and logical operators (AND
,OR
, andNOT
).
We can then test these lambda expressions by applying them to arguments using theapp
function. The output of the above code demonstrates the behavior of logical operations in lambda calculus.
OOP programming in PHP, lambda calculusHere's an example of a lambda calculus expression implemented in Python:
Python:# Lambda abstraction def λ(x, y): return lambda f: f(x, y) # Lambda application def app(f, x): return f(x) # Identity function I = λ('x', 'x') # Boolean true TRUE = λ('x', λ('y', 'x')) # Boolean false FALSE = λ('x', λ('y', 'y')) # Logical AND operator AND = λ('x', λ('y', app(app('x', 'y'), FALSE))) # Logical OR operator OR = λ('x', λ('y', app(app('x', TRUE), 'y'))) # Logical NOT operator NOT = λ('x', app(app('x', FALSE), TRUE)) # Testing the functions print(app(app(AND, TRUE), TRUE)) # Output: TRUE print(app(app(AND, TRUE), FALSE)) # Output: FALSE print(app(NOT, TRUE)) # Output: FALSE print(app(NOT, FALSE)) # Output: TRUE
In this example, we define lambda abstractions using theλ
function, and lambda applications using theapp
function. We then define various functions and constants in lambda calculus, such as the identity function (I
), boolean constants (TRUE
andFALSE
), and logical operators (AND
,OR
, andNOT
).
We can then test these lambda expressions by applying them to arguments using theapp
function. The output of the above code demonstrates the behavior of logical operations in lambda calculus.