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Ebook Free Introduction to Functional Programming using Haskell (2nd Edition)

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Introduction to Functional Programming using Haskell (2nd Edition)

Ebook Free Introduction to Functional Programming using Haskell (2nd Edition)

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From the Back Cover

After the success of the first edition, Introduction to Functional Programming using Haskell has been thoroughly updated and revised to provide a complete grounding in the principles and techniques of programming with functions. The second edition uses the popular language Haskell to express functional programs. There are new chapters on program optimisation, abstract datatypes in a functional setting, and programming in a monadic style. There are complete new case studies, and many new exercises. As in the first edition, there is an emphasis on the fundamental techniques for reasoning about functional programs, and for deriving them systematically from their specifications. The book is self-contained, assuming no prior knowledge of programming and is suitable as an introductory undergraduate text for first- or second-year students.

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Product details

Paperback: 448 pages

Publisher: Prentice Hall; 2 edition (May 9, 1998)

Language: English

ISBN-10: 0134843460

ISBN-13: 978-0134843469

Product Dimensions:

6.5 x 1 x 8.7 inches

Shipping Weight: 1.4 pounds

Average Customer Review:

4.0 out of 5 stars

4 customer reviews

Amazon Best Sellers Rank:

#1,098,816 in Books (See Top 100 in Books)

Book was in great condition when I got it

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.

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.

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).

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Introduction to Functional Programming using Haskell (2nd Edition) PDF