The Reasoned Schemer
by William E. Byrd, Daniel P. Friedman, Oleg Kiselyov
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Book Summary Information
Author: Daniel P. Friedman, Oleg Kiselyov, William E. ByrdEdition: Paperback
Audio: English (Unknown); English (Original Language); English (Published)
Published: 2005-10-14
ISBN: 0262562146
Number of pages: 176
Publisher: The MIT Press
Book Reviews of The Reasoned Schemer
Book Review: Better go to the Source
Summary: 3 Stars
I guess this book is OK, but it could really be written in all of about 5 to 10 pages of text with half a page of implementation code - in Haskell.
Main idea: use (potentially) infinite lists to represent (potentially) infinite streams of solutions to a problem. Have "goals" as procedures that work on (partial) solutions, producing new lists (empty/singleton/plural) of (more complete) solutions for each solution processed. Have a mechanism of combining these solutions streams. Now AND is just a sequential combinator and goal applicator; OR is a sequential combinator for parallel application; OR/i (for interleaving) combines its result streams in an interleaving fashion.
It suffices to have these combinators binary, because any type of COND is anyhow broken down to these binary combinations, as in a typical COND rewrite with IFs - and that's what the book itself does too, in a somewhat complex Scheme macro syntax. Expressed in Haskell, the intent is clear and the meaning is immediately obvious:
Sequential stream combination ("mplus" of the book):
(1) [] ++: ys = ys
(2) (x:xs) ++: ys = x:(xs ++: ys)
Alternating stream combination ("mplus/i"):
(3) [] ++/ ys = ys
(4) (x:xs) ++/ ys = x:(ys ++/ xs)
Sequential feed ("bind"):
(5) [] >>: g = []
(6) (x:xs) >>: g = g x ++: (xs >>: g)
Alternating feed ("bind/i"):
(7) [] >>/ g = []
(8) (x:xs) >>/ g = g x ++/ (xs >>/ g)
"OR" goal combination ("cond/e"):
(9) (f ||: g) x = f x ++: g x
"Alternating OR" goal combination ("cond/i"):
(10) (f ||/ g) x = f x ++/ g x
"AND" goal combination ("all"):
(11) (f &&: g) x = f x >>: g
"Alternating AND" goal combination ("all/i" of the book):
(12) (f &&/ g) x = f x >>/ g
That's about all there is to it. If you're unfamiliar with Haskell, it's a type-inferencing, auto-currying LISP with unparenthesised syntax where "f x" stands for functional application, "[]" stands for empty list, "x:xs" for cons cell (x . xs), and parentheses are used for grouping of expressions. It is non-strict, so lazy lists are used throughout, and _everything_ is a delayed lambda, calculated on "as-needed" basis. Having finally produced a stream of solutions, we rely on Haskell to only calculate as much of it as is actually requested by a user (usually one by one, as in Prolog), thus in effect performing depth-first search of a problem space.
It should be clear now that the actual nature of our solutions should be regarded quite apart from the mechanism of producing, combining and managing these infinite streams. Unification can then be viewed as just another "knowledge-enhancing" goal capable of rejecting the solution it's supplied with, by producing an empty list, or updating it, by producing a new list containing an updated solution(s). These solutions can be of any type, whether built-in or user-defined native Haskell type, and not just general symbolic structure capable of representing a kind of symbolic terms Prolog has, which is what's done in the book - where everything is represented through this symbolic structure, even numbers.
Implementing arithmetical relations on top of that is a standard exercise in hopeless inefficiency. The book wants to add logic programming capabilities to the existing Scheme system. Surely we don't have to reinvent numbers for this, and in such an incredibly inefficient way at that!
Instead of reusing blind structural unification of Prolog, the authors could discuss how it can be seen as creating equality constraints, then proceed to implement _them_ thus having truly added the relational capabilities ON TOP of the existing Scheme system, with its numeric functions working for us directly, hopefully.
If this book had THAT, THEN it would have been a great book.
Alas, no. The authors decided instead to stay at a fairly rudimental level, and be very verbose and inexplicit at the same time. And here I come to a point about their whole methodology in this as in their other books of this series, of presenting their material by examples only, making it unnecessarily obscure for a reader. It seems to me they've gone to the other extreme here from the pseudo-scientific type of dry presentation full of abstruse terminology. The golden path, as always, may lie somewhere in the middle - first presenting the material through examples and just playing with it (like they do here), but then proceeding to more precise formulation and discussion of the issues.
This book is long on promise, but short on clarity and depth.
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