This does not answer your question, but you can solve this problem without rewrite rules by having length return a lazy natural:<br><br> data Nat = Zero | Succ Nat<br><br>And defining lazy comparison operators on it.<br>
<br>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:<br>
<br> bad xs = (length xs > 10, length xs > 20)<br><br>bad [1..] will return (True,True). However, if I do an obviously semantics-preserving refactor:<br><br> bad xs = (l > 10, l > 20)<br> where<br> l = length xs<br>
<br>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)<br><br>Luke<br><br>2008/12/18 Cetin Sert <span dir="ltr"><<a href="mailto:cetin.sert@gmail.com">cetin.sert@gmail.com</a>></span><br>
<div class="gmail_quote"><blockquote class="gmail_quote" style="border-left: 1px solid rgb(204, 204, 204); margin: 0pt 0pt 0pt 0.8ex; padding-left: 1ex;">Hi *^o^*,<br><br>With the following rewrite rules:<br><br><span style="font-family: courier new,monospace;">lengthOP :: (Num a, Ord a) ⇒ Bool → (a → a → Bool) → [b] → a → Bool</span><br style="font-family: courier new,monospace;">
<span style="font-family: courier new,monospace;">lengthOP v (⊜) [] n = 0 ⊜ n</span><br style="font-family: courier new,monospace;"><span style="font-family: courier new,monospace;">lengthOP v (⊜) xxs n = co xxs 0</span><br style="font-family: courier new,monospace;">
<span style="font-family: courier new,monospace;"> where</span><br style="font-family: courier new,monospace;"><span style="font-family: courier new,monospace;"> co [] c = c ⊜ n</span><br style="font-family: courier new,monospace;">
<span style="font-family: courier new,monospace;"> co (_:xs) c | n > c = co xs (c+1)</span><br style="font-family: courier new,monospace;"><span style="font-family: courier new,monospace;"> | otherwise = v</span><br style="font-family: courier new,monospace;">
<br style="font-family: courier new,monospace;"><span style="font-family: courier new,monospace;">lenEQ = lengthOP False (==)</span><br style="font-family: courier new,monospace;"><span style="font-family: courier new,monospace;">lenLT = lengthOP False (<)</span><br style="font-family: courier new,monospace;">
<span style="font-family: courier new,monospace;">lenLE = lengthOP False (<=)</span><br style="font-family: courier new,monospace;"><span style="font-family: courier new,monospace;">lenGT = lengthOP True (>)</span><br style="font-family: courier new,monospace;">
<span style="font-family: courier new,monospace;">lenGE = lengthOP True (>=)</span><br style="font-family: courier new,monospace;"><br style="font-family: courier new,monospace;"><span style="font-family: courier new,monospace;">{-# RULES</span><br style="font-family: courier new,monospace;">
<span style="font-family: courier new,monospace;">-- | length</span><br style="font-family: courier new,monospace;"><span style="font-family: courier new,monospace;">"lenEQ_LHS" forall xs n. (length xs) == n = lenEQ xs n</span><br style="font-family: courier new,monospace;">
<span style="font-family: courier new,monospace;">"lenLT_LHS" forall xs n. (length xs) < n = lenLT xs n</span><br style="font-family: courier new,monospace;"><span style="font-family: courier new,monospace;">"lenLE_LHS" forall xs n. (length xs) <= n = lenLE xs n</span><br style="font-family: courier new,monospace;">
<span style="font-family: courier new,monospace;">"lenGT_LHS" forall xs n. (length xs) > n = lenGT xs n</span><br style="font-family: courier new,monospace;"><span style="font-family: courier new,monospace;">"lenGE_LHS" forall xs n. (length xs) >= n = lenGE xs n</span><br style="font-family: courier new,monospace;">
<br style="font-family: courier new,monospace;"><span style="font-family: courier new,monospace;">"lenEQ_RHS" forall xs n. n == (length xs) = lenEQ xs n</span><br style="font-family: courier new,monospace;"><span style="font-family: courier new,monospace;">"lenLT_RHS" forall xs n. n < (length xs) = lenGE xs n</span><br style="font-family: courier new,monospace;">
<span style="font-family: courier new,monospace;">"lenLE_RHS" forall xs n. n <= (length xs) = lenGT xs n</span><br style="font-family: courier new,monospace;"><span style="font-family: courier new,monospace;">"lenGT_RHS" forall xs n. n > (length xs) = lenLE xs n</span><br style="font-family: courier new,monospace;">
<span style="font-family: courier new,monospace;">"lenGE_RHS" forall xs n. n >= (length xs) = lenLT xs n</span><br style="font-family: courier new,monospace;"><br style="font-family: courier new,monospace;">
<span style="font-family: courier new,monospace;">-- | genericLength</span><br style="font-family: courier new,monospace;"><span style="font-family: courier new,monospace;">"glenEQ_LHS" forall xs n. (genericLength xs) == n = lenEQ xs n</span><br style="font-family: courier new,monospace;">
<span style="font-family: courier new,monospace;">"glenLT_LHS" forall xs n. (genericLength xs) < n = lenLT xs n</span><br style="font-family: courier new,monospace;"><span style="font-family: courier new,monospace;">"glenLE_LHS" forall xs n. (genericLength xs) <= n = lenLE xs n</span><br style="font-family: courier new,monospace;">
<span style="font-family: courier new,monospace;">"glenGT_LHS" forall xs n. (genericLength xs) > n = lenGT xs n</span><br style="font-family: courier new,monospace;"><span style="font-family: courier new,monospace;">"glenGE_LHS" forall xs n. (genericLength xs) >= n = lenGE xs n</span><br style="font-family: courier new,monospace;">
<br style="font-family: courier new,monospace;"><span style="font-family: courier new,monospace;">"glenEQ_RHS" forall xs n. n == (genericLength xs) = lenEQ xs n</span><br style="font-family: courier new,monospace;">
<span style="font-family: courier new,monospace;">"glenLT_RHS" forall xs n. n < (genericLength xs) = lenGE xs n</span><br style="font-family: courier new,monospace;"><span style="font-family: courier new,monospace;">"glenLE_RHS" forall xs n. n <= (genericLength xs) = lenGT xs n</span><br style="font-family: courier new,monospace;">
<span style="font-family: courier new,monospace;">"glenGT_RHS" forall xs n. n > (genericLength xs) = lenLE xs n</span><br style="font-family: courier new,monospace;"><span style="font-family: courier new,monospace;">"glenGE_RHS" forall xs n. n >= (genericLength xs) = lenLT xs n</span><br style="font-family: courier new,monospace;">
<span style="font-family: courier new,monospace;"> #-}</span><br style="font-family: courier new,monospace;"><br>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?<br>
2) How can I avoid the following error messages?<br><br><span style="font-family: courier new,monospace;">module Main where</span><br style="font-family: courier new,monospace;"><span style="font-family: courier new,monospace;">import Data.List</span><br style="font-family: courier new,monospace;">
<span style="font-family: courier new,monospace;">main :: IO Int</span><br style="font-family: courier new,monospace;"><span style="font-family: courier new,monospace;"> print $ length (repeat 0) > 200</span><br style="font-family: courier new,monospace;">
<span style="font-family: courier new,monospace;"> print $ 200 < length (repeat 0)</span><br style="font-family: courier new,monospace;"><span style="font-family: courier new,monospace;"> print $ genericLength (repeat 0) > 200</span><span style="font-family: courier new,monospace;"> -- error</span><br style="font-family: courier new,monospace;">
<span style="font-family: courier new,monospace;"> print $ 200 < genericLength (repeat 0) -- error</span><br style="font-family: courier new,monospace;"><span style="font-family: courier new,monospace;"> return 0</span><br style="font-family: courier new,monospace;">
<br>########:<br style="font-family: courier new,monospace;"><span style="font-family: courier new,monospace;"> Could not deduce (Ord i) from the context (Eq i, Num i)</span><br style="font-family: courier new,monospace;">
<span style="font-family: courier new,monospace;"> arising from a use of `lenEQ' at </span>########<br style="font-family: courier new,monospace;"><span style="font-family: courier new,monospace;"> Possible fix: add (Ord i) to the context of the RULE "glenEQ_LHS"</span><br style="font-family: courier new,monospace;">
<span style="font-family: courier new,monospace;"> In the expression: lenEQ xs n</span><br style="font-family: courier new,monospace;"><span style="font-family: courier new,monospace;"> When checking the transformation rule "glenEQ_LHS"</span><br style="font-family: courier new,monospace;">
<br style="font-family: courier new,monospace;">########<span style="font-family: courier new,monospace;">:</span><br style="font-family: courier new,monospace;"><span style="font-family: courier new,monospace;"> Could not deduce (Ord a) from the context (Eq a, Num a)</span><br style="font-family: courier new,monospace;">
<span style="font-family: courier new,monospace;"> arising from a use of `lenEQ' at </span>########<br style="font-family: courier new,monospace;"><span style="font-family: courier new,monospace;"> Possible fix: add (Ord a) to the context of the RULE "glenEQ_RHS"</span><br style="font-family: courier new,monospace;">
<span style="font-family: courier new,monospace;"> In the expression: lenEQ xs n</span><br style="font-family: courier new,monospace;"><span style="font-family: courier new,monospace;"> When checking the transformation rule "glenEQ_RHS"</span><br style="font-family: courier new,monospace;">
<br>3) What speaks for/against broad usage of such rewrite rules involving list lengths?<br><br>Best Regards,<br><font color="#888888">Cetin Sert<br>
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<br></blockquote></div><br>