[Haskell-cafe] lengthOP rewrite rules

[Luke Palmer]

This does not answer your question, but you can solve this problem without
rewrite rules by having length return a lazy natural:

   data Nat = Zero | Succ Nat

And defining lazy comparison operators on it.

Of course you cannot replace usages of Prelude.length.  But I am really not
in favor of rules which change semantics, even if they only make things less
strict.  My argument is the following.  I may come to rely on such
nonstrictness as in:

  bad xs = (length xs > 10, length xs > 20)

bad [1..] will return (True,True).  However, if I do an obviously
semantics-preserving refactor:

  bad xs = (l > 10, l > 20)
  where
  l = length xs

My semantics are not preserved: bad [1..] = (_|_, _|_)   (if/unless the
compiler is clever, in which case my semantics depend on the compiler's
cleverness which is even worse)

Luke

2008/12/18 Cetin Sert <cetin.sert at gmail.com>

> Hi *^o^*,
>
> With the following rewrite rules:
>
> lengthOP :: (Num a, Ord a) ⇒ Bool → (a → a → Bool) → [b] → a → Bool
> lengthOP v (⊜) []  n = 0 ⊜ n
> lengthOP v (⊜) xxs n = co xxs 0
>   where
>     co []     c = c ⊜ n
>     co (_:xs) c | n > c     = co xs (c+1)
>                 | otherwise = v
>
> lenEQ = lengthOP False (==)
> lenLT = lengthOP False (<)
> lenLE = lengthOP False (<=)
> lenGT = lengthOP True  (>)
> lenGE = lengthOP True  (>=)
>
> {-# RULES
> -- | length
> "lenEQ_LHS" forall xs n.  (length xs) == n = lenEQ xs n
> "lenLT_LHS" forall xs n.  (length xs) <  n = lenLT xs n
> "lenLE_LHS" forall xs n.  (length xs) <= n = lenLE xs n
> "lenGT_LHS" forall xs n.  (length xs) >  n = lenGT xs n
> "lenGE_LHS" forall xs n.  (length xs) >= n = lenGE xs n
>
> "lenEQ_RHS" forall xs n.  n == (length xs) = lenEQ xs n
> "lenLT_RHS" forall xs n.  n <  (length xs) = lenGE xs n
> "lenLE_RHS" forall xs n.  n <= (length xs) = lenGT xs n
> "lenGT_RHS" forall xs n.  n >  (length xs) = lenLE xs n
> "lenGE_RHS" forall xs n.  n >= (length xs) = lenLT xs n
>
> -- | genericLength
> "glenEQ_LHS" forall xs n.  (genericLength xs) == n = lenEQ xs n
> "glenLT_LHS" forall xs n.  (genericLength xs) <  n = lenLT xs n
> "glenLE_LHS" forall xs n.  (genericLength xs) <= n = lenLE xs n
> "glenGT_LHS" forall xs n.  (genericLength xs) >  n = lenGT xs n
> "glenGE_LHS" forall xs n.  (genericLength xs) >= n = lenGE xs n
>
> "glenEQ_RHS" forall xs n.  n == (genericLength xs) = lenEQ xs n
> "glenLT_RHS" forall xs n.  n <  (genericLength xs) = lenGE xs n
> "glenLE_RHS" forall xs n.  n <= (genericLength xs) = lenGT xs n
> "glenGT_RHS" forall xs n.  n >  (genericLength xs) = lenLE xs n
> "glenGE_RHS" forall xs n.  n >= (genericLength xs) = lenLT xs n
>   #-}
>
> 1) Is there a way to tell where 'length' is mentioned, what is meant is for
> example 'Prelude.length' or any length that works on lists?
> 2) How can I avoid the following error messages?
>
> module Main where
> import Data.List
> main :: IO Int
>   print $ length (repeat 0) > 200
>   print $ 200 < length (repeat 0)
>   print $ genericLength (repeat 0) > 200 -- error
>   print $ 200 < genericLength (repeat 0) -- error
>   return 0
>
> ########:
>     Could not deduce (Ord i) from the context (Eq i, Num i)
>       arising from a use of `lenEQ' at ########
>     Possible fix: add (Ord i) to the context of the RULE "glenEQ_LHS"
>     In the expression: lenEQ xs n
>     When checking the transformation rule "glenEQ_LHS"
>
> ########:
>     Could not deduce (Ord a) from the context (Eq a, Num a)
>       arising from a use of `lenEQ' at ########
>     Possible fix: add (Ord a) to the context of the RULE "glenEQ_RHS"
>     In the expression: lenEQ xs n
>     When checking the transformation rule "glenEQ_RHS"
>
> 3) What speaks for/against broad usage of such rewrite rules involving list
> lengths?
>
> Best Regards,
> Cetin Sert
>
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