Help Sample lambda calculus programming

[Well1AmNichtDiePerson]

Sample lambda calculus programming or code in C/C++, Visual Basic, C#, PHP, Java, Python

 

[🤖]

Here's an example of a lambda calculus expression implemented in 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 the 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).

We can then test these lambda expressions by applying them to arguments using the app function. The output of the above code demonstrates the behavior of logical operations in lambda calculus.

 

[Well1AmNichtDiePerson]

Here's an example of a lambda calculus expression implemented in 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 the 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).

We can then test these lambda expressions by applying them to arguments using the app function. The output of the above code demonstrates the behavior of logical operations in lambda calculus.

functional programming in PHP, lambda calculus

 

[🤖]

functional programming in PHP, 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:

<?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 the 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).

We can then test these lambda expressions by applying them to arguments using the app function. The output of the above code demonstrates the behavior of logical operations in lambda calculus.

 

[Well1AmNichtDiePerson]

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:

<?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 the 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).

We can then test these lambda expressions by applying them to arguments using the app function. The output of the above code demonstrates the behavior of logical operations in lambda calculus.

functional programming in C#, lambda calculus

 

[🤖]

functional programming in C#, 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#:

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 the 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).

We can then test these lambda expressions by applying them to arguments using the app function. The output of the above code demonstrates the behavior of logical operations in lambda calculus.

 

[Well1AmNichtDiePerson]

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#:

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 the 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).

We can then test these lambda expressions by applying them to arguments using the app function. The output of the above code demonstrates the behavior of logical operations in lambda calculus.

functional programming in Visual Basic, lambda calculus

 

[Well1AmNichtDiePerson]

Here's an example of a lambda calculus expression implemented in 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 the 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).

We can then test these lambda expressions by applying them to arguments using the app function. The output of the above code demonstrates the behavior of logical operations in lambda calculus.

functional programming in Java, lambda calculus

 

[Well1AmNichtDiePerson]

Here's an example of a lambda calculus expression implemented in 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 the 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).

We can then test these lambda expressions by applying them to arguments using the app function. The output of the above code demonstrates the behavior of logical operations in lambda calculus.

OOP programming in PHP, lambda calculus