
Re: Structured Programming
Posted:
Mar 3, 2014 12:35 AM


R Hansen says: >I see. But that is the layman?s version.
As opposed to the R Hansen version. Exactly. Nevertheless, its just an example of mathematical considerations and influence. It did have considerable influence, if not on you.
Getting back to algol, BNF is essentially just a notation for specifying a context free grammar.
http://en.wikipedia.org/wiki/Backus%E2%80%93Naur_Form   "Meanwhile, string rewriting rules as formal, abstract systems were introduced and studied by mathematicians such as Axel Thue (in 1914), Emil Post (1920s?40s) and Alan Turing (1936). Noam Chomsky, teaching linguistics to students of information theory at MIT, combined linguistics and mathematics, by taking what is essentially Thue's formalism as the basis for the description of the syntax of natural language; he also introduced a clear distinction between generative rules (those of contextfree grammars) and transformation rules (1956).[2][3]
John Backus, a programming language designer at IBM, proposed "metalinguistic formulas"[4][5] to describe the syntax of the new programming language IAL, known today as ALGOL 58 (1959), using the BNF notation."  
See  mathematical to the layman, since mathematicians had been studying formal grammars and languages for some time already. I'm not telling you how to view it.
The block structures in algol are pretty clearly influenced/inspired/intertwined with the choice to use a CFG.
In the development of OOP, you find heavy influence from abstract data types, which are mathematical entities,
In functional programming, ADTs too, and of course functions.
Did you read the Backus Turing lecture? Interesting stuff though its time may still be ahead.
Various type theories are used as the model for corresponding type systems in a wide range of languages, as Kirby likes to point out.
In relational Databases and SQL, one of the big early selling points was the mathematical underpinnings in the theory of relations.
Math has stayed pretty intertwined with PLD, I don't seem them going their separate ways. I think they will become more intertwined in the future, perhaps Backus' ideas will be reinvigorated in some useful new form.
You can scan these for more viewpoints: http://en.wikipedia.org/wiki/Programming_language_theory http://www.cis.upenn.edu/~bcpierce/tapl/main.html
What does it mean to say PLD is separate from math?
Cheers, Joe N

