Sumith Kulal
Programming Languages, verification and synthesis.
- Rupanshu, Sumith, Suresh
Mr. X and Ms. Y
advanced language features - lazy evaluation or closures more complex memory layout
harder to predict what memory looks like
potentially leading to space leaks.
Haskell is vulnerable to space leaks and we make this our topic of study.
alive or dead example!
A space leak can occur when the memory contains an expression—where the expression grows regularly but where the evaluated value would not grow. Forcing evaluation usually solves such leaks; this makes evaluation of some variables strict instead of lazy.
f x y = y
f ⊥ b = b
f ⊥ b = ⊥
Lazy Evaluator
Postpone evaluation until it is inevitable.
Lazy evaluation in a nutshell
strictness
based
liveness
based
Space Leaks
built up
unevaluated
expressions
keeping not
needed
references alive
seq :: a -> b -> b
seq ⊥ b = ⊥
seq a b = b
seq2 x y = if (x == 0) then y else y
Declares a function to be strict in an argument.
f !x y = x + y
Bang Patterns
Heap Options
RTS options
foldl vs foldl'
foldl f z [] = z
foldl f z (x:xs) = foldl f (f z x) xs
foldl (+) 0 [1..10]
= foldl (+) 0 (1:[2..10])
= foldl (+) (0 + 1) [2..10]
= foldl (+) ((((((((((0 + 1) + 2) + 3) + 4) + 5) + 6) + 7) + 8) + 9) + 10) []
= ((((((((((0 + 1) + 2) + 3) + 4) + 5) + 6) + 7) + 8) + 9) + 10)
= (45 + 10)
= 55
foldl vs foldl'
foldl' f z [] = z
foldl' f z (x:xs) = let z' = z `f` x
in seq z' $ foldl' f z' xs
foldl' (+) 0 [1..10]
= foldl' (+) 0 (1:[2..10])
= foldl' (+) (0 + 1) [2..10]
= foldl' (+) 1 (2:[3..10])
= foldl' (+) (1 + 2) [3..10]
...
= foldl' (+) (45 + 10) []
= foldl' (+) 55 []
= 55
tick
main = print (f ([1..40000000]})
(0 :: Int, 1 :: Int))
f [] c = c
f (x:xs) c = f xs (tick x c)
tick x (c0, c1) = if (even x)
then (c0, c1 + 1)
else (c0 + 1, c1)
f [1,2,3,4] (0,1)
= f [2,3,4] (tick 1 (0,1))
= f [3,4] (tick 2 (tick 1 (0,1)))
= f [4] (tick 3 (tick 2 (tick 1 (0,1))))
= f [] (tick 4 (tick 3 (tick 2 (tick 1 (0,1)))))
...
= (tick 4 (tick 3 (tick 2 (tick 1 (0,1)))))
= (tick 4 (tick 3 (tick 2 ((0 + 1),1))))
= (tick 4 (tick 3 ((0 + 1),(1 + 1))))
= (tick 4 (((0 + 1) + 1),(1 + 1)))
= (((0 + 1) + 1),((1 + 1) + 1))
= ((1 + 1),(2 + 1))
= (2,3)
tick
main = print (f ([1..40000000]})
(0 :: Int, 1 :: Int))
f [] !c = c
f (x:xs) !c = f xs (tick x c)
tick x (!c0, !c1) = if (even x)
then (c0, c1 + 1)
else (c0 + 1, c1)
f [1,2,3,4] (0,1)
= f [2,3,4] (tick 1 (0,1))
= f [2,3,4] (0+1, 1)
= f [2,3,4] (1, 1)
= f [3,4] (1, 1+1)
= f [3,4] (1, 2)
= f [4] (1+1, 2)
= f [4] (2, 2)
= f [] (2, 2+1)
= f [] (2, 3)
= (2, 3)
foldr
foldr :: (a -> b -> b) -> b -> [a] -> b
foldr f z [] = z
foldr f z (x:xs) = f x (foldr f z xs)
foldr (+) 0 [1..4]
= 1 + (foldr (+) 0 [2..4])
= 1 + (2 + (foldr (+) 0 [3..4]))
= 1 + (2 + (3 + (foldr (+) 0 [4])))
= 1 + (2 + (3 + (0 + 4)))
...
= 10
surprise!
surprise :: String -> String
surprise s = let b = break (== '\n') s
in (fst b) + "\nsurprise\n" + (snd b)
break :: (a -> Bool) -> [a] -> ([a], [a])
break f [] = ([], [])
break f x:xs = | x == xs = ([], xs)
| otherwise = let b = break f xs in (x:(fst b), (snd b))
surprise "P not \nequal to NP"
= (fst b1) + "\nsurprise\n" + (snd b1)
where b1 = break (!= '\n') "P not \nequal to NP"
= 'P' + ((fst b1) + "\nsurprise\n" + (snd b1))
where b1 = ('P':(fst b2), snd b2)
b2 = break (!= '\n') " not \nequal to NP"
= 'P' + ' ' + ((fst b3) + "\nsurprise\n" + (snd b1))
where b1 = ('P':(fst b2), snd b2)
b2 = (' ':(fst b3), snd b3)
b3 = break (!= '\n') "not \nequal to NP"
E (fst b) (snd b)
where b = (E1, E2)
E E1 E2
= 'P' + ' ' + ((fst b3) + "\nsurprise\n" + (snd b3))
where b3 = break (!= '\n') "not \nequal to NP"
garbage
collection
surprise!
break ls = let (xs, ys) = (SYNCHLIST ls)
in (PAR before '\n' ls, PAR after '\n' ls)
Hughes' solution:
*** Exception (reporting due to +RTS -xc):
(THUNK_STATIC), stack trace:
Main.h,
called from Main.g,
called from Main.f,
called from Main.main,
called from Main.CAF
Stack space overflow: current size 33568 bytes.
main = do print (f [1..1000000])
f [] = 0
f x = 1 + g x
g [] = 0
g x = h (tail x)
h [] = 1
h x = foldl (+) 0 x
"Beware of little expenses.
A small leak will sink a great ship."
- Benjamin Franklin
Special thanks to:
By Sumith Kulal
Presented to Prof. Amitabha Sanyal and collaborators.