math - Convergence of Mathematics and Programming Languages -

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It seems that there is a strong movement for the convergence of mathematics and computer programming languages, this is especially evident from its effect.

I feel that many incidents that can be done in mathematics can be mathematically even modeled logically.

I do not think that we want to take advantage of a purely logical language or purely mathematical traction traction for general purpose programming, but I want to list the benefits of every paradigm. I want to know: / P>

  • What are the benefits of modeling programming languages ​​or language features on math?
  • What are the advantages of the principles of modeling of a language? Formal logic?
  • Can a general purpose language either leave argument or math?
  • What are some languages ​​that really show the benefits of any approach?
  • Does the hardware features make one approach more attractive to the other?

    • First of all, I do not see much difference between logic and math; The latter is only systematically implemented for specific constructions in the east.

    In addition to this, I am not convinced that the theoretical beauty of programming languages ​​based in mathematics / logic is really very valuable, efficient, satisfactorious code.

    Specific questions for you

    What are the benefits of modeling about programming languages ​​or mathematics in language? What is the advantage of modeling language on the principles of formal reasoning?

    Evidence of purity becomes very easy - though it is doubtful whether we will ever reach the point where they are practical, real life system.

    Can any general purpose language either leave logic or math?

    "Skip" You can get a language without mathematical operation (though you have to get beautiful espressic; Turing machine is the only one which I can think of, Is not), and you are definitely the one who does not care about anything about formalism (Assembler, C) but I do not think it is possible to have a programming language without argument (although it can be distorted arguments , CF.)

    There are some languages ​​that shows the approach to the benefits of either?

    Well, if you consider Lambda calculus as a logic, then Lisp has shown its proficiency to its language since 1958, whose expressive power is of other languages. Wish (but not to reach).

    Then there is Prolog, only other "serious" language I know that tries to be based in clear formal arguments and - surprisingly surprised - this logic is good on content and something else.

    What hardware features make it more attractive than one?

    Nobody fails to prove the IMO is quite convinced that Compilers + general hardware are more powerful than special hardware. However, one can say that the tolerant forces of today's system are making such languages ​​that completely ignore the hardware constraints where they were not before.


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