[Haskell-cafe] lengthOP rewrite rules
Cetin Sert
cetin.sert at gmail.com
Thu Dec 18 02:39:39 EST 2008
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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