%
% (c) The GRASP/AQUA Project, Glasgow University, 1992-1998
%
\section[Util]{Highly random utility functions}
\begin{code}
-- IF_NOT_GHC is meant to make this module useful outside the context of GHC
#define IF_NOT_GHC(a)
module Util (
#if NOT_USED
-- The Eager monad
Eager, thenEager, returnEager, mapEager, appEager, runEager,
#endif
-- general list processing
zipEqual, zipWithEqual, zipWith3Equal, zipWith4Equal,
zipLazy, stretchZipWith,
mapAndUnzip, mapAndUnzip3,
nOfThem, lengthExceeds, isSingleton, only,
snocView,
isIn, isn'tIn,
-- for-loop
nTimes,
-- maybe-ish
unJust,
-- sorting
IF_NOT_GHC(quicksort COMMA stableSortLt COMMA mergesort COMMA)
sortLt,
IF_NOT_GHC(mergeSort COMMA) naturalMergeSortLe, -- from Carsten
IF_NOT_GHC(naturalMergeSort COMMA mergeSortLe COMMA)
-- transitive closures
transitiveClosure,
-- accumulating
mapAccumL, mapAccumR, mapAccumB,
foldl2, count,
-- comparisons
eqListBy, thenCmp, cmpList, prefixMatch, suffixMatch,
-- strictness
foldl', seqList,
-- pairs
IF_NOT_GHC(cfst COMMA applyToPair COMMA applyToFst COMMA)
IF_NOT_GHC(applyToSnd COMMA foldPair COMMA)
unzipWith
, global
#if __GLASGOW_HASKELL__ <= 408
, catchJust
, ioErrors
, throwTo
#endif
) where
#include "../includes/config.h"
#include "HsVersions.h"
import List ( zipWith4 )
import Maybe ( Maybe(..) )
import Panic ( panic )
import IOExts ( IORef, newIORef, unsafePerformIO )
import FastTypes
#if __GLASGOW_HASKELL__ <= 408
import Exception ( catchIO, justIoErrors, raiseInThread )
#endif
infixr 9 `thenCmp`
\end{code}
%************************************************************************
%* *
\subsection{The Eager monad}
%* *
%************************************************************************
The @Eager@ monad is just an encoding of continuation-passing style,
used to allow you to express "do this and then that", mainly to avoid
space leaks. It's done with a type synonym to save bureaucracy.
\begin{code}
#if NOT_USED
type Eager ans a = (a -> ans) -> ans
runEager :: Eager a a -> a
runEager m = m (\x -> x)
appEager :: Eager ans a -> (a -> ans) -> ans
appEager m cont = m cont
thenEager :: Eager ans a -> (a -> Eager ans b) -> Eager ans b
thenEager m k cont = m (\r -> k r cont)
returnEager :: a -> Eager ans a
returnEager v cont = cont v
mapEager :: (a -> Eager ans b) -> [a] -> Eager ans [b]
mapEager f [] = returnEager []
mapEager f (x:xs) = f x `thenEager` \ y ->
mapEager f xs `thenEager` \ ys ->
returnEager (y:ys)
#endif
\end{code}
%************************************************************************
%* *
\subsection{A for loop}
%* *
%************************************************************************
\begin{code}
-- Compose a function with itself n times. (nth rather than twice)
nTimes :: Int -> (a -> a) -> (a -> a)
nTimes 0 _ = id
nTimes 1 f = f
nTimes n f = f . nTimes (n-1) f
\end{code}
%************************************************************************
%* *
\subsection{Maybe-ery}
%* *
%************************************************************************
\begin{code}
unJust :: String -> Maybe a -> a
unJust who (Just x) = x
unJust who Nothing = panic ("unJust of Nothing, called by " ++ who)
\end{code}
%************************************************************************
%* *
\subsection[Utils-lists]{General list processing}
%* *
%************************************************************************
A paranoid @zip@ (and some @zipWith@ friends) that checks the lists
are of equal length. Alastair Reid thinks this should only happen if
DEBUGging on; hey, why not?
\begin{code}
zipEqual :: String -> [a] -> [b] -> [(a,b)]
zipWithEqual :: String -> (a->b->c) -> [a]->[b]->[c]
zipWith3Equal :: String -> (a->b->c->d) -> [a]->[b]->[c]->[d]
zipWith4Equal :: String -> (a->b->c->d->e) -> [a]->[b]->[c]->[d]->[e]
#ifndef DEBUG
zipEqual _ = zip
zipWithEqual _ = zipWith
zipWith3Equal _ = zipWith3
zipWith4Equal _ = zipWith4
#else
zipEqual msg [] [] = []
zipEqual msg (a:as) (b:bs) = (a,b) : zipEqual msg as bs
zipEqual msg as bs = panic ("zipEqual: unequal lists:"++msg)
zipWithEqual msg z (a:as) (b:bs)= z a b : zipWithEqual msg z as bs
zipWithEqual msg _ [] [] = []
zipWithEqual msg _ _ _ = panic ("zipWithEqual: unequal lists:"++msg)
zipWith3Equal msg z (a:as) (b:bs) (c:cs)
= z a b c : zipWith3Equal msg z as bs cs
zipWith3Equal msg _ [] [] [] = []
zipWith3Equal msg _ _ _ _ = panic ("zipWith3Equal: unequal lists:"++msg)
zipWith4Equal msg z (a:as) (b:bs) (c:cs) (d:ds)
= z a b c d : zipWith4Equal msg z as bs cs ds
zipWith4Equal msg _ [] [] [] [] = []
zipWith4Equal msg _ _ _ _ _ = panic ("zipWith4Equal: unequal lists:"++msg)
#endif
\end{code}
\begin{code}
-- zipLazy is lazy in the second list (observe the ~)
zipLazy :: [a] -> [b] -> [(a,b)]
zipLazy [] ys = []
zipLazy (x:xs) ~(y:ys) = (x,y) : zipLazy xs ys
\end{code}
\begin{code}
stretchZipWith :: (a -> Bool) -> b -> (a->b->c) -> [a] -> [b] -> [c]
-- (stretchZipWith p z f xs ys) stretches ys by inserting z in
-- the places where p returns *True*
stretchZipWith p z f [] ys = []
stretchZipWith p z f (x:xs) ys
| p x = f x z : stretchZipWith p z f xs ys
| otherwise = case ys of
[] -> []
(y:ys) -> f x y : stretchZipWith p z f xs ys
\end{code}
\begin{code}
mapAndUnzip :: (a -> (b, c)) -> [a] -> ([b], [c])
mapAndUnzip f [] = ([],[])
mapAndUnzip f (x:xs)
= let
(r1, r2) = f x
(rs1, rs2) = mapAndUnzip f xs
in
(r1:rs1, r2:rs2)
mapAndUnzip3 :: (a -> (b, c, d)) -> [a] -> ([b], [c], [d])
mapAndUnzip3 f [] = ([],[],[])
mapAndUnzip3 f (x:xs)
= let
(r1, r2, r3) = f x
(rs1, rs2, rs3) = mapAndUnzip3 f xs
in
(r1:rs1, r2:rs2, r3:rs3)
\end{code}
\begin{code}
nOfThem :: Int -> a -> [a]
nOfThem n thing = replicate n thing
lengthExceeds :: [a] -> Int -> Bool
-- (lengthExceeds xs n) is True if length xs > n
(x:xs) `lengthExceeds` n = n < 1 || xs `lengthExceeds` (n - 1)
[] `lengthExceeds` n = n < 0
isSingleton :: [a] -> Bool
isSingleton [x] = True
isSingleton _ = False
only :: [a] -> a
#ifdef DEBUG
only [a] = a
#else
only (a:_) = a
#endif
\end{code}
\begin{code}
snocView :: [a] -> ([a], a) -- Split off the last element
snocView xs = go xs []
where
go [x] acc = (reverse acc, x)
go (x:xs) acc = go xs (x:acc)
\end{code}
Debugging/specialising versions of \tr{elem} and \tr{notElem}
\begin{code}
isIn, isn'tIn :: (Eq a) => String -> a -> [a] -> Bool
# ifndef DEBUG
isIn msg x ys = elem__ x ys
isn'tIn msg x ys = notElem__ x ys
--these are here to be SPECIALIZEd (automagically)
elem__ _ [] = False
elem__ x (y:ys) = x==y || elem__ x ys
notElem__ x [] = True
notElem__ x (y:ys) = x /= y && notElem__ x ys
# else {- DEBUG -}
isIn msg x ys
= elem (_ILIT 0) x ys
where
elem i _ [] = False
elem i x (y:ys)
| i ># _ILIT 100 = panic ("Over-long elem in: " ++ msg)
| otherwise = x == y || elem (i +# _ILIT(1)) x ys
isn'tIn msg x ys
= notElem (_ILIT 0) x ys
where
notElem i x [] = True
notElem i x (y:ys)
| i ># _ILIT 100 = panic ("Over-long notElem in: " ++ msg)
| otherwise = x /= y && notElem (i +# _ILIT(1)) x ys
# endif {- DEBUG -}
\end{code}
%************************************************************************
%* *
\subsection[Utils-sorting]{Sorting}
%* *
%************************************************************************
%************************************************************************
%* *
\subsubsection[Utils-quicksorting]{Quicksorts}
%* *
%************************************************************************
\begin{code}
#if NOT_USED
-- tail-recursive, etc., "quicker sort" [as per Meira thesis]
quicksort :: (a -> a -> Bool) -- Less-than predicate
-> [a] -- Input list
-> [a] -- Result list in increasing order
quicksort lt [] = []
quicksort lt [x] = [x]
quicksort lt (x:xs) = split x [] [] xs
where
split x lo hi [] = quicksort lt lo ++ (x : quicksort lt hi)
split x lo hi (y:ys) | y `lt` x = split x (y:lo) hi ys
| True = split x lo (y:hi) ys
#endif
\end{code}
Quicksort variant from Lennart's Haskell-library contribution. This
is a {\em stable} sort.
\begin{code}
stableSortLt = sortLt -- synonym; when we want to highlight stable-ness
sortLt :: (a -> a -> Bool) -- Less-than predicate
-> [a] -- Input list
-> [a] -- Result list
sortLt lt l = qsort lt l []
-- qsort is stable and does not concatenate.
qsort :: (a -> a -> Bool) -- Less-than predicate
-> [a] -- xs, Input list
-> [a] -- r, Concatenate this list to the sorted input list
-> [a] -- Result = sort xs ++ r
qsort lt [] r = r
qsort lt [x] r = x:r
qsort lt (x:xs) r = qpart lt x xs [] [] r
-- qpart partitions and sorts the sublists
-- rlt contains things less than x,
-- rge contains the ones greater than or equal to x.
-- Both have equal elements reversed with respect to the original list.
qpart lt x [] rlt rge r =
-- rlt and rge are in reverse order and must be sorted with an
-- anti-stable sorting
rqsort lt rlt (x : rqsort lt rge r)
qpart lt x (y:ys) rlt rge r =
if lt y x then
-- y < x
qpart lt x ys (y:rlt) rge r
else
-- y >= x
qpart lt x ys rlt (y:rge) r
-- rqsort is as qsort but anti-stable, i.e. reverses equal elements
rqsort lt [] r = r
rqsort lt [x] r = x:r
rqsort lt (x:xs) r = rqpart lt x xs [] [] r
rqpart lt x [] rle rgt r =
qsort lt rle (x : qsort lt rgt r)
rqpart lt x (y:ys) rle rgt r =
if lt x y then
-- y > x
rqpart lt x ys rle (y:rgt) r
else
-- y <= x
rqpart lt x ys (y:rle) rgt r
\end{code}
%************************************************************************
%* *
\subsubsection[Utils-dull-mergesort]{A rather dull mergesort}
%* *
%************************************************************************
\begin{code}
#if NOT_USED
mergesort :: (a -> a -> Ordering) -> [a] -> [a]
mergesort cmp xs = merge_lists (split_into_runs [] xs)
where
a `le` b = case cmp a b of { LT -> True; EQ -> True; GT -> False }
a `ge` b = case cmp a b of { LT -> False; EQ -> True; GT -> True }
split_into_runs [] [] = []
split_into_runs run [] = [run]
split_into_runs [] (x:xs) = split_into_runs [x] xs
split_into_runs [r] (x:xs) | x `ge` r = split_into_runs [r,x] xs
split_into_runs rl@(r:rs) (x:xs) | x `le` r = split_into_runs (x:rl) xs
| True = rl : (split_into_runs [x] xs)
merge_lists [] = []
merge_lists (x:xs) = merge x (merge_lists xs)
merge [] ys = ys
merge xs [] = xs
merge xl@(x:xs) yl@(y:ys)
= case cmp x y of
EQ -> x : y : (merge xs ys)
LT -> x : (merge xs yl)
GT -> y : (merge xl ys)
#endif
\end{code}
%************************************************************************
%* *
\subsubsection[Utils-Carsten-mergesort]{A mergesort from Carsten}
%* *
%************************************************************************
\begin{display}
Date: Mon, 3 May 93 20:45:23 +0200
From: Carsten Kehler Holst
To: partain@dcs.gla.ac.uk
Subject: natural merge sort beats quick sort [ and it is prettier ]
Here is a piece of Haskell code that I'm rather fond of. See it as an
attempt to get rid of the ridiculous quick-sort routine. group is
quite useful by itself I think it was John's idea originally though I
believe the lazy version is due to me [surprisingly complicated].
gamma [used to be called] is called gamma because I got inspired by
the Gamma calculus. It is not very close to the calculus but does
behave less sequentially than both foldr and foldl. One could imagine
a version of gamma that took a unit element as well thereby avoiding
the problem with empty lists.
I've tried this code against
1) insertion sort - as provided by haskell
2) the normal implementation of quick sort
3) a deforested version of quick sort due to Jan Sparud
4) a super-optimized-quick-sort of Lennart's
If the list is partially sorted both merge sort and in particular
natural merge sort wins. If the list is random [ average length of
rising subsequences = approx 2 ] mergesort still wins and natural
merge sort is marginally beaten by Lennart's soqs. The space
consumption of merge sort is a bit worse than Lennart's quick sort
approx a factor of 2. And a lot worse if Sparud's bug-fix [see his
fpca article ] isn't used because of group.
have fun
Carsten
\end{display}
\begin{code}
group :: (a -> a -> Bool) -> [a] -> [[a]]
{-
Date: Mon, 12 Feb 1996 15:09:41 +0000
From: Andy Gill
Here is a `better' definition of group.
-}
group p [] = []
group p (x:xs) = group' xs x x (x :)
where
group' [] _ _ s = [s []]
group' (x:xs) x_min x_max s
| not (x `p` x_max) = group' xs x_min x (s . (x :))
| x `p` x_min = group' xs x x_max ((x :) . s)
| otherwise = s [] : group' xs x x (x :)
-- This one works forwards *and* backwards, as well as also being
-- faster that the one in Util.lhs.
{- ORIG:
group p [] = [[]]
group p (x:xs) =
let ((h1:t1):tt1) = group p xs
(t,tt) = if null xs then ([],[]) else
if x `p` h1 then (h1:t1,tt1) else
([], (h1:t1):tt1)
in ((x:t):tt)
-}
generalMerge :: (a -> a -> Bool) -> [a] -> [a] -> [a]
generalMerge p xs [] = xs
generalMerge p [] ys = ys
generalMerge p (x:xs) (y:ys) | x `p` y = x : generalMerge p xs (y:ys)
| otherwise = y : generalMerge p (x:xs) ys
-- gamma is now called balancedFold
balancedFold :: (a -> a -> a) -> [a] -> a
balancedFold f [] = error "can't reduce an empty list using balancedFold"
balancedFold f [x] = x
balancedFold f l = balancedFold f (balancedFold' f l)
balancedFold' :: (a -> a -> a) -> [a] -> [a]
balancedFold' f (x:y:xs) = f x y : balancedFold' f xs
balancedFold' f xs = xs
generalMergeSort p [] = []
generalMergeSort p xs = (balancedFold (generalMerge p) . map (: [])) xs
generalNaturalMergeSort p [] = []
generalNaturalMergeSort p xs = (balancedFold (generalMerge p) . group p) xs
mergeSort, naturalMergeSort :: Ord a => [a] -> [a]
mergeSort = generalMergeSort (<=)
naturalMergeSort = generalNaturalMergeSort (<=)
mergeSortLe le = generalMergeSort le
naturalMergeSortLe le = generalNaturalMergeSort le
\end{code}
%************************************************************************
%* *
\subsection[Utils-transitive-closure]{Transitive closure}
%* *
%************************************************************************
This algorithm for transitive closure is straightforward, albeit quadratic.
\begin{code}
transitiveClosure :: (a -> [a]) -- Successor function
-> (a -> a -> Bool) -- Equality predicate
-> [a]
-> [a] -- The transitive closure
transitiveClosure succ eq xs
= go [] xs
where
go done [] = done
go done (x:xs) | x `is_in` done = go done xs
| otherwise = go (x:done) (succ x ++ xs)
x `is_in` [] = False
x `is_in` (y:ys) | eq x y = True
| otherwise = x `is_in` ys
\end{code}
%************************************************************************
%* *
\subsection[Utils-accum]{Accumulating}
%* *
%************************************************************************
@mapAccumL@ behaves like a combination
of @map@ and @foldl@;
it applies a function to each element of a list, passing an accumulating
parameter from left to right, and returning a final value of this
accumulator together with the new list.
\begin{code}
mapAccumL :: (acc -> x -> (acc, y)) -- Function of elt of input list
-- and accumulator, returning new
-- accumulator and elt of result list
-> acc -- Initial accumulator
-> [x] -- Input list
-> (acc, [y]) -- Final accumulator and result list
mapAccumL f b [] = (b, [])
mapAccumL f b (x:xs) = (b'', x':xs') where
(b', x') = f b x
(b'', xs') = mapAccumL f b' xs
\end{code}
@mapAccumR@ does the same, but working from right to left instead. Its type is
the same as @mapAccumL@, though.
\begin{code}
mapAccumR :: (acc -> x -> (acc, y)) -- Function of elt of input list
-- and accumulator, returning new
-- accumulator and elt of result list
-> acc -- Initial accumulator
-> [x] -- Input list
-> (acc, [y]) -- Final accumulator and result list
mapAccumR f b [] = (b, [])
mapAccumR f b (x:xs) = (b'', x':xs') where
(b'', x') = f b' x
(b', xs') = mapAccumR f b xs
\end{code}
Here is the bi-directional version, that works from both left and right.
\begin{code}
mapAccumB :: (accl -> accr -> x -> (accl, accr,y))
-- Function of elt of input list
-- and accumulator, returning new
-- accumulator and elt of result list
-> accl -- Initial accumulator from left
-> accr -- Initial accumulator from right
-> [x] -- Input list
-> (accl, accr, [y]) -- Final accumulators and result list
mapAccumB f a b [] = (a,b,[])
mapAccumB f a b (x:xs) = (a'',b'',y:ys)
where
(a',b'',y) = f a b' x
(a'',b',ys) = mapAccumB f a' b xs
\end{code}
A strict version of foldl.
\begin{code}
foldl' :: (a -> b -> a) -> a -> [b] -> a
foldl' f z xs = lgo z xs
where
lgo z [] = z
lgo z (x:xs) = (lgo $! (f z x)) xs
\end{code}
A combination of foldl with zip. It works with equal length lists.
\begin{code}
foldl2 :: (acc -> a -> b -> acc) -> acc -> [a] -> [b] -> acc
foldl2 k z [] [] = z
foldl2 k z (a:as) (b:bs) = foldl2 k (k z a b) as bs
\end{code}
Count the number of times a predicate is true
\begin{code}
count :: (a -> Bool) -> [a] -> Int
count p [] = 0
count p (x:xs) | p x = 1 + count p xs
| otherwise = count p xs
\end{code}
%************************************************************************
%* *
\subsection[Utils-comparison]{Comparisons}
%* *
%************************************************************************
\begin{code}
eqListBy :: (a->a->Bool) -> [a] -> [a] -> Bool
eqListBy eq [] [] = True
eqListBy eq (x:xs) (y:ys) = eq x y && eqListBy eq xs ys
eqListBy eq xs ys = False
thenCmp :: Ordering -> Ordering -> Ordering
{-# INLINE thenCmp #-}
thenCmp EQ any = any
thenCmp other any = other
cmpList :: (a -> a -> Ordering) -> [a] -> [a] -> Ordering
-- `cmpList' uses a user-specified comparer
cmpList cmp [] [] = EQ
cmpList cmp [] _ = LT
cmpList cmp _ [] = GT
cmpList cmp (a:as) (b:bs)
= case cmp a b of { EQ -> cmpList cmp as bs; xxx -> xxx }
\end{code}
\begin{code}
prefixMatch :: Eq a => [a] -> [a] -> Bool
prefixMatch [] _str = True
prefixMatch _pat [] = False
prefixMatch (p:ps) (s:ss) | p == s = prefixMatch ps ss
| otherwise = False
suffixMatch :: Eq a => [a] -> [a] -> Bool
suffixMatch pat str = prefixMatch (reverse pat) (reverse str)
\end{code}
%************************************************************************
%* *
\subsection[Utils-pairs]{Pairs}
%* *
%************************************************************************
The following are curried versions of @fst@ and @snd@.
\begin{code}
cfst :: a -> b -> a -- stranal-sem only (Note)
cfst x y = x
\end{code}
The following provide us higher order functions that, when applied
to a function, operate on pairs.
\begin{code}
applyToPair :: ((a -> c),(b -> d)) -> (a,b) -> (c,d)
applyToPair (f,g) (x,y) = (f x, g y)
applyToFst :: (a -> c) -> (a,b)-> (c,b)
applyToFst f (x,y) = (f x,y)
applyToSnd :: (b -> d) -> (a,b) -> (a,d)
applyToSnd f (x,y) = (x,f y)
foldPair :: (a->a->a,b->b->b) -> (a,b) -> [(a,b)] -> (a,b)
foldPair fg ab [] = ab
foldPair fg@(f,g) ab ((a,b):abs) = (f a u,g b v)
where (u,v) = foldPair fg ab abs
\end{code}
\begin{code}
unzipWith :: (a -> b -> c) -> [(a, b)] -> [c]
unzipWith f pairs = map ( \ (a, b) -> f a b ) pairs
\end{code}
\begin{code}
seqList :: [a] -> b -> b
seqList [] b = b
seqList (x:xs) b = x `seq` seqList xs b
\end{code}
Global variables:
\begin{code}
global :: a -> IORef a
global a = unsafePerformIO (newIORef a)
\end{code}
Compatibility stuff:
\begin{code}
#if __GLASGOW_HASKELL__ <= 408
catchJust = catchIO
ioErrors = justIoErrors
throwTo = raiseInThread
#endif
\end{code}