[Haskell-cafe] What Does Graham Hutton Mean by Effect

[Steven Leiva]

Hi Everyone,
I am reading the 2nd edition of Graham Hutton's Programming in Haskell. I'm not
reading the entire book, just the parts of Haskell that I am still iffy on.
Anyway, in Chapter 12, Section 3, Hutton introduces monads.
He start off with the following code:  
first                   module Expr wheredata Expr = Val Int | Div Expr Expreval :: Expr -> Inteval (Val n) = neval (Div el er) = eval el `div` eval er
                

Not using Mixmax yet?  

And then he points out that the second clause of eval will raise an error if 
eval er evaluates to 0.
One solution is that, instead of using the div function, we use a safeDiv:: Int
-> Int -> Maybe Int function, which evaluate to Nothing if the divisor is 0.
This means that expr's type changes from eval :: Eval -> Int to eval :: Eval ->
Maybe Int, and this means that implementing eval becomes very verbose:

second                   module Expr wheredata Expr = Val Int | Div Expr Expreval :: Expr -> Maybe Inteval (Val n) = Just neval (Div el er) = case eval el of                    Nothing -> Nothing                    Just y -> case eval er of                                Nothing -> Nothing                                Just x -> y `safeDiv` xsafeDiv :: Int -> Int -> Maybe IntsafeDiv x y    | y == 0 = Nothing    | otherwise = Just (x `div` y)
                

Not using Mixmax yet?  

In order to make eval more concise, we can try the applicative style, where the
second clause of the eval function becomes pure safeDiv <*> eval el <*> eval er.
Of course, that doesn't work because pure safeDiv has the type Int -> Int ->
Maybe Int, and what we need is a function of type Int -> Int -> Int.
Anyways, this is all setup / context to what Hutton says next:
The conclusion is that the function eval does not fit the pattern of effectful
programming that is capture by applicative functors. The applicative style
restricts us to applying pure functions to effectful arguments: eval does not
fit this pattern because the function safeDiv that is used to process the
resulting values is not a pure function, but may itself fail.
I am confused by Hutton's use of the word effectful and by his description of
safeDiv as "not a pure function". I tried skimming the other sections of the
book to see if he provided a definition of this somewhere, but if he did, I
couldn't find it. So my question is, in what way does Hutton mean for the reader
to understand the words effect / effectful, and why does he describe the
function safeDiv as not a pure function?
Thank you!
Steven Leiva
305.528.6038
leiva.steven at gmail.com
http://www.linkedin.com/in/stevenleiva
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