[Haskell-cafe] [Wadler 89] Philip Wadler. "Theorems for free!": Can't get the same results in Haskell

David Feuer david.feuer at gmail.com
Fri Aug 10 03:55:54 CEST 2012

It looks to me like Wadler made a typo. Even great minds like his slip up
like that sometimes. However, I do have some comments below on your code.

On Aug 9, 2012 8:53 PM, "Stayvoid" <stayvoid at gmail.com> wrote:

> I tried to implement it in Haskell:
> (I'm a newbie. I guess it's possible to write a better version.)
> module Param where
> import Prelude

The prelude is imported automatically. You only need to mention it as an
import if you need to *avoid* importing some functions, or want some
functions to be imported only "qualified". This is done if you want to use
a name that clashes with one in the prelude. You'll see things like
import Prelude hiding (foldl',foldl, foldr)
import Prelude qualified as P
in a module implementing a data structure that supports folds.

> odds :: [Int] -> [Int]
> odds [] = []

This is a very awkward approach. There's no reason to have a special case
for the one-element list, and certainly no reason to use ++ to add a single
element to the front of a list. You should do the work in the (x:xs) case

odds [] = []
odds (x:xs)
  | odd x = x : odds xs
  | otherwise = odds xs

In fact, there's a function called "filter" that captures this pattern, so
you can even write:

odds = filter odd

> odds [x] = if odd x
>            then [x]
>            else []
> odds (x:xs) = if odds [x] == []
>               then odds xs
>               else [x] ++ odds xs
> inc :: [Int] -> [Int]
> inc [] = error "Empty list"
> inc [x] = [succ x]
> inc (x:xs) = inc [x] ++ inc xs

Again, this is bizarre. You should be writing:

inc [] = []
inc (x:xs) = succ x : inc xs

Again, there is a function that captures this pattern, so you can shorten
it to

inc = map succ

> Looks fine:
> *Param> odds [1,2,3]
> [1,3]
> *Param> inc [1,2,3]
> [2,3,4]
> But my results differ from the paper's:
> *Param> inc (odds [1,2,3])
> [2,4]
> *Param> odds (inc [1,2,3])
> [3]
> I doubt that there is an error in the paper.

I don't.
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