{-# OPTIONS -cpp #-}
-----------------------------------------------------------------------------
-- |
-- Module : StackSet
-- Copyright : (c) Don Stewart 2007
-- License : BSD3-style (see LICENSE)
--
-- Maintainer : dons@cse.unsw.edu.au
-- Stability : stable
-- Portability : portable, needs GHC 6.6
--
-----------------------------------------------------------------------------
--
-- The 'StackSet' data type encodes a set of stacks. A given stack in the
-- set is always current.
--
module StackSet (
StackSet, -- abstract
-- * Introduction
empty, -- :: Int -> StackSet a
fromList, -- :: [[a]] -> StackSet a
-- * Inspection
member, -- :: Ord a => a -> StackSet a -> Bool
peek, -- :: StackSet a -> Maybe a
stack, -- :: StackSet a -> [a]
cursor, -- :: StackSet a -> Int
index, -- :: StackSet a -> Int -> Maybe [a]
-- * Modification to the current stack
push, -- :: Ord a => a -> StackSet a -> StackSet a
pop, -- :: Ord a => StackSet a -> StackSet a
rotate, -- :: Ordering -> StackSet a -> StackSet a
shift, -- :: Ord a => Int -> StackSet a -> StackSet a
-- * Modification to arbitrary stacks
delete, -- :: Ord a => a -> StackSet a -> StackSet a
-- * Changing which stack is 'current'
view, -- :: Int -> StackSet a -> StackSet a
) where
import Data.Maybe
import qualified Data.Foldable as F
import qualified Data.List as L
import qualified Data.Map as M
import qualified Data.Sequence as S
-- All for testing:
#if TESTING
import Control.Exception (assert)
import Control.Monad
import Test.QuickCheck
import System.IO
import System.Random
import Text.Printf
import Data.List (sort,group,sort,intersperse)
#endif
------------------------------------------------------------------------
-- | The StackSet data structure. A table of stacks, with a cursor
data StackSet a =
StackSet
{ cursor :: {-# UNPACK #-} !Int -- ^ the currently visible stack
, size :: {-# UNPACK #-} !Int -- ^ size of the stack list
, stacks :: {-# UNPACK #-} !(S.Seq [a]) -- ^ the separate stacks
, cache :: {-# UNPACK #-} !(M.Map a Int) -- ^ a cache of windows back to their stacks
} deriving Eq
instance Show a => Show (StackSet a) where show = show . toList
-- Ord a constraint on 'a' as we use it as a key.
--
-- The cache is used to check on insertion that we don't already have
-- this window managed on another stack
--
-- Currently stacks are of a fixed size. There's no firm reason to
-- do this (new empty stacks could be created on the fly).
------------------------------------------------------------------------
-- | Create a new empty stacks of size 'n', indexed from 0. The
-- 0-indexed stack will be current.
empty :: Int -> StackSet a
empty n = StackSet { cursor = 0
, size = n -- constant
, stacks = S.fromList (replicate n [])
, cache = M.empty
}
-- | True if x is somewhere in the StackSet
member :: Ord a => a -> StackSet a -> Bool
member a w = M.member a (cache w)
------------------------------------------------------------------------
-- | fromList. Build a new StackSet from a list of list of elements
-- If there are duplicates in the list, the last occurence wins.
fromList :: Ord a => (Int,[[a]]) -> StackSet a
fromList (_,[])
= error "Cannot build a StackSet from an empty list"
fromList (n,xs)
| n < 0 || n >= length xs
= error $ "Cursor index is out of range: " ++ show (n, length xs)
fromList (o,xs) = view o $
foldr (\(i,ys) s ->
foldr (\a t -> insert a i t) s ys)
(empty (length xs)) (zip [0..] xs)
-- | toList. Flatten a stackset to a list of lists
toList :: StackSet a -> (Int,[[a]])
toList x = (cursor x, F.toList (stacks x))
------------------------------------------------------------------------
-- | Push. Insert an element onto the top of the current stack.
-- If the element is already in the current stack, it is moved to the top.
-- If the element is managed on another stack, it is removed from that
-- stack first.
push :: Ord a => a -> StackSet a -> StackSet a
push k w = insert k (cursor w) w
-- | Pop. Pop the element off the top of the stack and discard it.
-- A new StackSet is returned. If the current stack is empty, the
-- original StackSet is returned unchanged.
pop :: Ord a => StackSet a -> StackSet a
pop w = case peek w of
Nothing -> w
Just t -> delete t w
-- | Extract the element on the top of the current stack. If no such
-- element exists, Nothing is returned.
peek :: StackSet a -> Maybe a
peek = listToMaybe . stack
-- | Index. Extract stack at index 'n'. If the index is invalid,
-- Nothing is returned.
index :: StackSet a -> Int -> Maybe [a]
index w n | n < 0 || n >= size w = Nothing
| otherwise = Just (stacks w `S.index` n)
-- | Return the current stack
stack :: StackSet a -> [a]
stack w = case index w (cursor w) of
Just s -> s
Nothing -> error $ "current: no 'current' stack in StackSet: " ++ show (cursor w) -- can't happen
-- | rotate. cycle the current window list up or down.
--
-- rotate EQ --> [5,6,7,8,1,2,3,4]
-- rotate GT --> [6,7,8,1,2,3,4,5]
-- rotate LT --> [4,5,6,7,8,1,2,3]
--
-- where xs = [5..8] ++ [1..4]
--
rotate :: Ordering -> StackSet a -> StackSet a
rotate o = unsafeModify rot -- safe, since 'rot' is guaranteed to only permute the list
where
rot s = take l . drop offset . cycle $ s
where
n = fromEnum o - 1
l = length s
offset = if n < 0 then l + n else n
-- ---------------------------------------------------------------------
-- | view. Set the stack specified by the Int argument as being the
-- current StackSet. If the index is out of range, the original
-- StackSet is returned. StackSet are indexed from 0.
view :: Int -> StackSet a -> StackSet a
view n w | n >= 0 && n < size w = w { cursor = n }
| otherwise = w
-- | shift. move the client on top of the current stack to the top of stack 'n'.
-- The new StackSet is returned.
--
-- If the stack to move to is not valid, the original StackSet is returned.
-- If there are no elements in the current stack, nothing changes.
--
shift :: Ord a => Int -> StackSet a -> StackSet a
shift n w | n < 0 || n >= size w = w
| otherwise = case peek w of
Nothing -> w -- nothing to do
Just k -> insert k n (pop w)
------------------------------------------------------------------------
-- | Insert an element onto the top of stack 'n'.
-- If the index is wrong, the original StackSet is returned unchanged.
-- If the element is already in the stack 'n', it is moved to the top.
-- If the element exists on another stack, it is removed from that stack.
--
insert :: Ord a => a -> Int -> StackSet a -> StackSet a
insert k n old
| n < 0 || n >= size old = old
| otherwise = new { cache = M.insert k n (cache new)
, stacks = S.adjust (L.nub . (k:)) n (stacks new) }
where new = delete k old
-- | Delete an element entirely from from the StackSet.
-- This can be used to ensure that a given element is not managed elsewhere.
-- If the element doesn't exist, the original StackSet is returned unmodified.
delete :: Ord a => a -> StackSet a -> StackSet a
delete k w = case M.lookup k (cache w) of
Nothing -> w -- we don't know about this window
Just i -> w { cache = M.delete k (cache w)
, stacks = S.adjust (L.delete k) i (stacks w) }
-- ---------------------------------------------------------------------
-- Internal functions
-- | modify the current stack with a pure function. This function is
-- unsafe: the argument function must only permute the current stack,
-- and must not add or remove elements, or duplicate elements.
--
unsafeModify :: ([a] -> [a]) -> StackSet a -> StackSet a
unsafeModify f w = w { stacks = S.adjust f (cursor w) (stacks w) }
#if TESTING
-- ---------------------------------------------------------------------
-- QuickCheck properties
-- | Height of stack 'n'
height :: Int -> StackSet a -> Int
height i w = length (S.index (stacks w) i)
-- build (non-empty) StackSets with between 1 and 100 stacks
instance (Ord a, Arbitrary a) => Arbitrary (StackSet a) where
arbitrary = do
sz <- choose (1,20)
n <- choose (0,sz-1)
ls <- vector sz
return $ fromList (n,ls)
coarbitrary = error "no coarbitrary for StackSet"
prop_id x = fromList (toList x) == x
where _ = x :: StackSet Int
prop_uniq_pushpop i x = not (member i x) ==>
(pop . push i) x == x
where _ = x :: StackSet Int
prop_pushpop i x =
(pop . push i) x == delete i x
where _ = x :: StackSet Int
-- popping an empty stack leaves an empty stack
prop_popempty x = height (cursor x) x == 0 ==> pop x == x
where _ = x :: StackSet Int
prop_popone x =
let l = height (cursor x) x
in l > 0 ==> height (cursor x) (pop x) == l-1
where _ = x :: StackSet Int
-- check the cache of the size works
prop_size_length x =
size x == S.length (stacks x)
where _ = x :: StackSet Int
prop_delete_uniq i x = not (member i x) ==>
delete i x == x
where _ = x :: StackSet Int
prop_delete2 i x =
delete i x == delete i (delete i x)
where _ = x :: StackSet Int
prop_uniq_insertdelete i n x = not (member i x) ==>
delete i (insert i n x) == x
where _ = x :: StackSet Int
prop_insertdelete i n x =
delete i (insert i n x) == delete i x
where _ = x :: StackSet Int
prop_rotaterotate x = rotate LT (rotate GT x) == x
where _ = x :: StackSet Int
prop_viewview r x =
let n = cursor x
sz = size x
i = r `mod` sz
in
view n (view i x) == x
where _ = x :: StackSet Int
prop_shiftshift r x =
let n = cursor x
in
shift n (shift r x) == x
where _ = x :: StackSet Int
------------------------------------------------------------------------
testall :: IO ()
testall = mapM_ (\(s,a) -> printf "%-25s: " s >> a n) tests
where
n = 100
tests =
[("fromList.toList ", mytest prop_id)
,("pop/push ", mytest prop_uniq_pushpop)
,("pop/push/delete ", mytest prop_pushpop)
,("pop/empty ", mytest prop_popempty)
,("size/length ", mytest prop_size_length)
,("delete/not.member", mytest prop_delete_uniq)
,("delete idempotent", mytest prop_delete2)
,("delete/insert new", mytest prop_uniq_insertdelete)
,("delete/insert ", mytest prop_insertdelete)
,("rotate/rotate ", mytest prop_rotaterotate)
,("pop one ", mytest prop_popone)
,("view/view ", mytest prop_viewview)
]
debug = False
mytest :: Testable a => a -> Int -> IO ()
mytest a n = mycheck defaultConfig
{ configMaxTest=n
, configEvery= \n args -> if debug then show n ++ ":\n" ++ unlines args else [] } a
mycheck :: Testable a => Config -> a -> IO ()
mycheck config a = do
rnd <- newStdGen
mytests config (evaluate a) rnd 0 0 []
mytests :: Config -> Gen Result -> StdGen -> Int -> Int -> [[String]] -> IO ()
mytests config gen rnd0 ntest nfail stamps
| ntest == configMaxTest config = do done "OK," ntest stamps
| nfail == configMaxFail config = do done "Arguments exhausted after" ntest stamps
| otherwise =
do putStr (configEvery config ntest (arguments result)) >> hFlush stdout
case ok result of
Nothing ->
mytests config gen rnd1 ntest (nfail+1) stamps
Just True ->
mytests config gen rnd1 (ntest+1) nfail (stamp result:stamps)
Just False ->
putStr ( "Falsifiable after "
++ show ntest
++ " tests:\n"
++ unlines (arguments result)
) >> hFlush stdout
where
result = generate (configSize config ntest) rnd2 gen
(rnd1,rnd2) = split rnd0
done :: String -> Int -> [[String]] -> IO ()
done mesg ntest stamps = putStr ( mesg ++ " " ++ show ntest ++ " tests" ++ table )
where
table = display
. map entry
. reverse
. sort
. map pairLength
. group
. sort
. filter (not . null)
$ stamps
display [] = ".\n"
display [x] = " (" ++ x ++ ").\n"
display xs = ".\n" ++ unlines (map (++ ".") xs)
pairLength xss@(xs:_) = (length xss, xs)
entry (n, xs) = percentage n ntest
++ " "
++ concat (intersperse ", " xs)
percentage n m = show ((100 * n) `div` m) ++ "%"
------------------------------------------------------------------------
#endif
