Introduction to Functional Programming using Haskell (2nd Edition)

There is a lot of excellent information in this book.However, it is very dense and the reader should beware that many of the programs in the book don't work. I surmise that they are more intended to show the algorithm rather than the actual Haskell implementation.In Haskell it is particularly important to pay attention to the details, which is why I give this book only three stars.Here is an example of a program in the book that does not work.On page 82 the author Richard Bird provides this sample implementation of the floor function:floor x = searchFrom 0 where searchFrom = decrease . upper . lower lower = until (<=x) decrease upper = until (>x) increase decrease n = n - 1 increase n = n + 1The problem with that implementation is that it does not return an Integer value; rather, it returns a decimal (Double) value. Here's an example: floor (-3.4) -- returns (-4.0)That is wrong. The specification for floor says that it "maps a value of type Float to a value of type Integer." Clearly it is not producing an Integer result.I will now explain how to revise floor so that it returns an Integer value.The heart of the problem is with the until function.Here is how Richard Bird implements it:until :: (a -> Bool) -> (a -> a) -> a -> auntil p f y = if p y then y else until p f (f y)It takes three arguments, p, f, and y. Look at the signature of that function. The type of the third argument, y, dictates the type of the other arguments and the type of the result--whatever type y is, the other arguments must be the same type and the result must be the same type.Function until is first invoked by function lower: lower = until (<=x) decrease 0Here are the three arguments provided to function until:(1) p is the partial function (<=x), where x is the input to the floor function. Suppose x is this value: x = (-3.4)(2) f is the function decrease(3) y is 0Now you may argue, "Hey, the third argument, y, is 0 and that's an Integer, so clearly the result of function until will be an Integer." However, that is not correct. The type of 0 is ambiguous, it could be an Integer or it could be a Double. This ambiguity can be seen by checking its type using WinGHCi::type 00 :: Num a => aThe class Num is high up in Haskell's type hierarchy and it represents any number (Integer, Double, etc.). Thus, we cannot determine the type of function until's result just by examining its third argument. The other arguments will determine whether the 0 is an Integer or a Double. Let's examine the first argument: p is the partial function (<=x), where x = (-3.4)p compares "some value" against (-3.4). Let's check the type of (-3.4) using WinGHCi::type (-3.4)(-3.4) :: Fractional a => aThe datatype Double falls within the class Fractional. So p compares "some value" against a Double. Fundamental rule of Haskell: you cannot compare an Integer against a Double, you can only compare a Double against a Double.Recall that p compares "some value" against (-3.4). What is that "some value"? If we examine the body of function until we see that it is the third argument, y, and we know that y = 0. Ah, now we know how Haskell will treat 0: since the 0 is being compared against a Double value Haskell will treat the 0 as a Double. Okay, now that we know the type of y we can plug it into the type signature for function until:until :: (a -> Bool) -> (a -> a) -> Double -> aAll a's must be of the same type, so the other a's must also be Double:until :: (Double -> Bool) -> (Double -> Double) -> Double -> DoubleTherefore function until will return a Double value. For example: until (<=x) decrease 0 -- returns (0.0)The output of function until is assigned to function lower: lower = until (<=x) decreaseSo the result of function lower is a Double value.The output of lower is then input to upper and the Double datatype propagates through the entire chain of composed functions: decrease . upper . lowerThe result of function floor is therefore a Double value.Okay, so how do we get floor to return an Integer value? The key is to prevent p in function until from casting the type of y to a Double. Recall function lower:lower = until (<=x) decrease 0Notice that p is this partial function: (<=x)We must modify p to express, "Hey, compare x against an Integer value that has been cast to a Double value." That is implemented using a Lambda (anonymous) function: (\a -> (realToFrac a) <= x)Read that as: For whatever value, a, is provided convert it to a Fractional (Double) value and then compare it to x.Wow!So we are telling Haskell that the 0 is not to be treated as a Fractional (Double) value, it is to be treated as a Real (Integer) value.At last, we can implement function floor and it will return the desired Integer result:floor x = searchFrom 0 where searchFrom = decrease . upper . lower lower = until (\a -> (realToFrac a) <= x) decrease upper = until (\a -> (realToFrac a) > x) increase decrease n = n - 1 increase n = n + 1Notice that wherever function until is called (in lower and upper), the first argument, p, is a Lambda (anonymous) function that takes its argument, a, and casts it from a Real (Integer) value to a Fractional (Double) value. Here are a couple examples of using this revised floor function: floor (-3.4) -- returns (-4) floor 3.4 -- returns 3Notice that floor now returns an Integer value, which is what we want.Here is the signature for floor:floor :: (Fractional a, Ord a, Real c) => a -> cRead as: Invoke function floor with a Fractional (Double) value and it will return a Real (Integer) value.On page 83 Richard Bird shows a second version of function floor that uses a binary search:floor x = searchFrom (-1, 1) where searchFrom = fst . middle . cross(lower, upper) lower = until (<= x) double upper = until (> x) double middle = until done improve done (m, n) = (m + 1 == n) improve (m, n) = if p <= x then (p, n) else (m, p) where p = (m + n) div 2That has multiple problems. First, it is syntactically not a well-formed Haskell program because the div operator (on the last line) must have back ticks ( ` ) surrounding it: where p = (m + n) `div` 2Second, the functions lower and upper invoke function until. The first argument to until must be a Lambda function as described above: lower = until (\m -> (realToFrac m) <= x) double upper = until (\n -> (realToFrac n) > x) doubleThird, the function improve compares p (an Integer) against x (a Double), so p must be cast to a Fractional (Double) value: improve (m, n) = if (realToFrac p) <= x then (p, n) else (m, p) where p = (m + n) div 2With those three changes the function works as desired:floor x = searchFrom (-1, 1) where searchFrom = fst . middle . cross(lower, upper) lower = until (\m -> (realToFrac m) <= x) double upper = until (\n -> (realToFrac n) > x) double middle = until done improve done (m, n) = (m + 1 == n) improve (m, n) = if (realToFrac p) <= x then (p, n) else (m, p) where p = (m + n) `div` 2Here are a couple examples of using the revised floor function: floor (-3.4) -- returns (-4) floor 3.4 -- returns 3Notice that floor now returns an Integer value, which is what we want.Here is the signature for floor:floor :: (Fractional a, Ord a, Real c) => a -> cRead as: Invoke function floor with a Fractional (Double) value and it will return a Real (Integer) value.

The bad: Despite the "introduction" level implied in the title, this is a hard book to read. The book is not a "Haskell book" either. The author uses a mathematical notation that easily translates to Haskell but it's not Haskell per se.The good: Having said that, the author gives a very good explanation of some of the concepts that make functional programming different from other paradigms. Some of the explanations given in the book are by far better (and more in-depth) than what's found on the web. That's one of the reason is at times hard to read. For example, the section on curring is very good and raises points that I have not seen in other books/articles.

Book was in great condition when I got it

Bird and Wadler got me started on functional programming. Before that, I'd only seen discussions of C++/STL functors and functions like for, map etcetera.B&W was dense, and magic. It reminded me of the first time I read the K&R C book, you're following along fine, and all of a sudden you're off the deep end!The syntax, sort of ML-like adds to the 'magic' feel of it all. Overall I think it's a good book. But like with K&R, make this your second or third book, to ground you in the fundamentals after you've become somewhat familiar with the syntax and application of a particular fnal language.That said, it covers a wide breadth of topics, and does justice to them as well. But this opinion comes from a newbie at functional programming, so caveat lector!For me, it made me realise that there was a whole 'new' way of programming, vastly bigger than the few functions C++ had in its STL, and that C++ syntax mostly got in the way. However, perhaps because of this book, I never quite grokked Haskell/ML syntax either, though LISP I find easy (easier).

No issues

In recent years functional programming has made it from the nooks of academia into mainstream computing. Well, not quite. The lingo has arrived, and modern scripting languages such as Groovy, Ruby or Python make heavy use of functional constructs. But truly functional languages are as yet at the outskirts of pragmatic or industrial programming. But they are there: Scala is talked of in the Java world, and F# may soon be making more acolytes in the .Net world (and both these languages owe a lot to Haskell).The present book is a well written introduction to functional programming using Haskell. It is aimed at undergraduate students taking university courses in computer science. Thus the book pursues a twofold purpose: It both introduces Haskell as a language and it demonstrates essential programming constructs such as lists and trees and algorithms operating on such structures. Examples tend to be formal, and applications of Haskell to real-world programming challenges are not even mentioned. The very strong side of the book is its measured and precise explanation of the fundamental programming constructs of Haskell (chiefly the rather difficult notion of a monad which is the Haskell way of introducing interaction in a functional setting). Its lack of examples from real-world applications makes the style and content of the book at times rather sterile. It is a useful companion to a lecture on programming (and as such it is highly recommended), but for somebody with a good background in computer science and experience with real-life IT the book may seem off the practical mark at times. For those much better literature is available by now, see for instance  Real World Haskell . The exercises, by the way, tend to rather easy and are mostly aimed at the beginner in programming.I place much hope in functional programming as a paradigm for writing code in the future. But the way into a functional language is rather steep and requires more of a mathematical mind than any of the other major players on the market (Cobol was easy for anybody with a sufficiently neat mind, Object Orientation took a long while to take on, and I guess that functional programming will have an even harder time). But there is no denying that with the growing complexity of the things we want to do in IT our tools will have to match that complexity. So if you are a student today, here is a book to help you get into the ways of the future. Real World Haskell

This book is a classical text for learning functional programming. However it is not the easiest one. For those with a bit of a mathematical mindset this book is highly recommended.