Editing Lambda Calculus (section)

== <span style="color: #FFFFFF;">Applying</span> ==
'''Modeling 'The Beta Reduction' (Simulating how a Lambda function runs):'''
<syntaxhighlight lang="python">
def simulate_lambda(func_body, input_val):
    """
    Shows the 'Substitution' logic of Lambda Calculus.
    """
    # Simple substitution: Replace 'x' in the body with the input
    result = func_body.replace("x", str(input_val))
    return f"STEP: λx.{func_body}({input_val}) -> {result}"

# Function: λx. x + 1 | Input: 5
print(simulate_lambda("x + 1", 5))
# Function: λx. x * x | Input: 10
print(simulate_lambda("x * x", 10))
</syntaxhighlight>

; Lambda Landmarks
: '''The 1936 Paper''' → Church's publication of "An Unsolvable Problem of Elementary Number Theory," which used Lambda Calculus to prove that some math questions have no answer.
: '''LISP (1958)''' → The first programming language based on Lambda Calculus, which became the standard for "Artificial Intelligence" for 40 years.
: '''The 'Typed' Lambda Calculus''' → Adding "Type Theory" (from Article 403) to Lambda Calculus, which created the foundation for modern safety-critical programming.
: '''The 'Lambda' Logo''' → How the Greek letter λ became the universal symbol for "Smart, Abstract Coding" and the mascot of the functional programming community.
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