Klicka på en bild för att gå till Google Book Search.
Laddar... Combinators: A Centennial Viewav Stephen Wolfram
Ingen/inga Laddar...
Gå med i LibraryThing för att få reda på om du skulle tycka om den här boken. Det finns inga diskussioner på LibraryThing om den här boken. inga recensioner | lägg till en recension
Combinators have inspired ideas about computation ever since they were first invented in 1920, and in this innovative book, Stephen Wolfram provides a modern view of combinators and their significance. Informed by his work on the computational universe of possible programs and on computational language design, Wolfram explains new and existing ideas about combinators with unique clarity and stunning visualizations, as well as provides insights on their historical connections and the curious story of Moses schönfinkel, inventor of combinators. Though invented well before Turing machines, combinators have often been viewed as an inaccessibly abstract approach to computation. This book brings them to life as never before in a thought-provoking exposition of interest across mathematics and computer science, as well as to those concerned with the foundations of formal and computational thinking, and with the history of ideas. Book jacket. Inga biblioteksbeskrivningar kunde hittas. |
Pågående diskussionerIngen/inga
Google Books — Laddar... GenrerKlassifikation enligt LCBetygMedelbetyg:
Är det här du? |
So for example try onomasti komodein. You can look it up on wiki, but doing so gives you very little real understanding of what it is and how it fits into the Athenian political system, or its cultural or literary context. Similarly I can look up 'fractals' and read the wiki entry, but I won’t really understand what 'fractals' means like someone with proper mathematical knowledge will. Such were the small beginnings of my terrible addiction. Then I started dreaming of understanding Fourier transforms and Taylor series even though I was still not sure why similar triangles weren’t also congruent triangles (or maybe they are; the internet is huge but sometimes conflicting). It's fairly unlikely that I'll win any prizes (although I still do the Euro Millions every month or two), but if I live long enough then one day I hope that I'll understand that bit of quantum physics and Schönfinkel’s S-and-Ks where something could come out of nothing…
Functional Programming and Haskell in particular, curried functions, higher-order functions, and λ-expressions, Schönfinkeled functions, anyone? Wolfram dedicates a few pages to some to these concepts but does not dwell much on them. I’d say that Schönfinkel's contribution is the most important one to λ-Calculus and functional programming in particular. Without Schönfinkel we’d still be in the Stone Age computer-science-wise. And what is a curried function you may wonder? I’m not very fond of the way Wolfram explains what a curried function is. In my book it’s a normal function with optional parameters that default to 0, nil, NULL, etc. or simply a normal function that passes to sub actions based on conditionals (if you think of an ATM a curried function would be a wrapper function that collects the input then passes onto the main action when all input is ready). Simple right?
The proofs of Alonso Church and Alan Turing came from earlier concepts like the concepts of Cantor's recursiveness, of the combinatorial logic of Schönfinkel and of the λ-Calculus with Haskell Curry. The methods introduced by Gödel and used by Kleene and Rosser show that Church's system was inconsistent, and it also prevailed in the negative solution of Church's decision problem. Church first demonstrated that a given expression of λ-Calculus with normal form is non-recursive. In the same paper, Church stated what is now known as the Church's Thesis, for example, that general recursive functions (and therefore λ-definable ones) are also exactly those that are effectively “computable”. The theorem and thesis combine to produce the result, that having a normal form is not a property effectively decidable. Kleene himself also emphasises the importance of Gödel in the work he and Rosser did in their contributions to recursion theory in the early 1930s. I remember writing a paper on this back in the day in college.
Only Wolfram to write a book about something that almost no one, outside of the Computer Science field, knows anything about in this day and of fast food thought. You got to love it!
NB: The nice people at Wolfram were kind enough to send me this book for me to have a go at it which I did. Most of it was read on a Cruise to Italy as well but I've just finished it today. Between Louise Glück's Averno and Wolfram's "Combinators", what a marvellous contrast! ( )