Editing Type Theory (section)

== <span style="color: #FFFFFF;">Applying</span> ==
'''Modeling 'The Type Checker' (Visualizing how code prevents errors):'''
<syntaxhighlight lang="python">
def add_values(val_a, val_b):
    """
    A simple Python version of a type-checking logic.
    """
    type_a = type(val_a)
    type_b = type(val_b)
    
    if type_a != type_b:
        return f"TYPE ERROR: Cannot add {type_a.__name__} to {type_b.__name__}!"
    
    return f"RESULT: {val_a + val_b} (Type: {type_a.__name__})"

# Success Case:
print(add_values(10, 20))
# Error Case:
print(add_values(10, "Hello"))
</syntaxhighlight>

; Type Landmarks
: '''The Principia Mathematica (1910)''' → The birth of "Simple Type Theory," where Bertrand Russell used "Levels" (Types) to solve the paradoxes of set theory.
: '''The Lambda Calculus (1930s)''' → Alonzo Church's system that added "Types" to functions, creating the foundation for all modern programming.
: '''Haskell (1990)''' → The programming language that became the "Laboratory" for advanced type theory, featuring the most powerful type system in common use.
: '''Homotopy Type Theory (HoTT) (2013)''' → A cutting-edge branch of math that merges type theory with "Geometry" (Topology), suggesting that types are actually "Shapes" in space.
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