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Re^4: OT: Mathematics for programming (again)

by Anonymous Monk
on Sep 12, 2008 at 20:09 UTC ( #711002=note: print w/replies, xml ) Need Help??

in reply to Re^3: OT: Mathematics for programming (again)
in thread OT: Mathematics for programming (again)

That's a bit backwards: HOW it gets there is unimportant. That it can accomplish the task eventually is what really matters.

If the Car and the Person were both Touring [sic] complete, and it is known that the Person can Tour France (using feet) then the implication is that the Car can Tour France as well. How it accomplishes that (with wheels) and how long it takes is unimportant. It can simulate the Human's route and make the Tour because it is, by definition, Touring complete.

  • Making a Tour = Loops
  • Touring France = Looping over all elements in a list of cities
  • Using Feet = "for" statement
  • Using Wheels = "JMP" statement

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Re^5: OT: Mathematics for programming (again)
by Jenda (Abbot) on Sep 13, 2008 at 12:00 UTC

    You did not leave von Neumann there. Not "for" and "JMP", but rather "for" and "recursion". And recursion in a language that doesn't have mutable variables. And

    • Making a Tour = implementing an algorithm
    • Touring France = creating the program
    • Using Feet = using loops
    • Using Wheels = using recursion

    The thing is not whether it's possible to implement the same algorithms, but whether reasoning about the individual building blocks of one kind of programming languages will be useful for other kinds.

    With your "for" vs "JMP" you've stayed within the von Neumann architecture, there are languages that are built on , say, lambda calculus. And even though both are turing complete and may be used to implement the same algorithms and eventualy transform the same data to the same result, their building blocks are different.

      Their building blocks may be different, but if your Turing complete language does not include a for loop, you can write code that will simulate a for loop. It may not be efficient, and it may not be core, but you can do it.

      If you can implement a system which analyzes one such language, you can inefficiently port it to other languages by simulating those other languages in your first language.
      This may, however, fall afoul of your "useful" clause in terms of practicality regarding CPU and memory use.

      Equivalent to looping, I buy that. But equivalent_to_X ne X.
      The difference is in terminology and syntax (and efficiency of implementation), but those do not change the essential nature of looping.
      It is more of an: ("X" ne "X/2 + X^0 + 0.5 * X - 1") and (X == (X/2 + X^0 + 0.5 * X - 1))
      Where the LHS is Looping, and the RHS is equivalent to looping in a language without core loop support.

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