Editing Computability Theory (section)

== <span style="color: #FFFFFF;">Applying</span> ==
'''Modeling 'The Halting Problem' Logic (The Paradox):'''
<syntaxhighlight lang="python">
def hypothetical_halt_checker(program_code):
    """
    Turing proved this function CANNOT EXIST.
    If it did, we could create a paradox.
    """
    pass

def paradox_program(code):
    """
    If the checker says I will HALT, I will run forever.
    If the checker says I will RUN FOREVER, I will halt.
    """
    if hypothetical_halt_checker(code) == "HALTS":
        while True: pass # Run forever
    else:
        return "HALTED"

# This logical 'Loop' proves that the checker can 
# never be 100% correct for all programs.
</syntaxhighlight>

; Computability Milestones
: '''The Entscheidungsproblem''' → The "Decision Problem" that Turing and Church solved, proving math is not fully decidable.
: '''Lambda Calculus''' → Alonzo Church's version of computability, which is the basis for "Functional" programming languages like Haskell and Lisp.
: '''Wang Tiles''' → A set of colored tiles that can "compute" anything; if you can tile a floor with them, you can build a computer.
: '''Game of Life''' → A simple simulation that is "Turing Complete," meaning a simulated "Life" world could theoretically run its own version of Windows.
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