seq
While its name might suggest otherwise, the seq
function's purpose is to introduce strictness to a Haskell program. As indicated by its type signature:
seq :: a -> b -> b
it takes two arguments of any type, and returns the second. However, it also has the important property that it is always strict in its first argument. In essence, seq
is defined by the following two equations:
⊥ `seq` b = ⊥
a `seq` b | a ≠ ⊥ = b
(See Bottom for an explanation of the ⊥
symbol.)
History
The need to specify an order of evaluation in otherwise-nonstrict programming languages has appeared before:
We can use
VAL
to define a "sequential evaluation" operator which evaluates its first argument and then returns its second:a ; b = (λx. b) val aand we can define other functions which control evaluation order [...]
- The Design and Implementation of Programming Languages (page 88 of 159).
`seq' applied to two values, returns the second but checks that the first value is not completely undefined. Sometimes needed, e.g. to ensure correct synchronisation in interactive programs.
> seq :: *->**->** ||defined internally
and in Haskell since at least 1996:
The
seq
combinator implements sequential composition. When the expressione1 ‘seq‘ e2
is evaluated,e1
is evaluated to weak head normal form first, and then the value ofe2
is returned. In the following parallelnfib
function,seq
is used to force the evaluation ofn2
before the addition takes place. This is because Haskell does not specify which operand is evaluated first, and ifn1
was evaluated beforen2
, there would be no parallelism. nfib :: Int -> Int nfib n | n <= 1 = 1 | otherwise = n1 ‘par‘ (n2 ‘seq‘ n1 + n2 + 1) where n1 = nfib (n-1) n2 = nfib (n-2)
...the same year seq
was introduced in Haskell 1.3 as a method of the (now-abandoned) Eval
type class:
class Eval a where
strict :: (a -> b) -> a -> b
seq :: a -> b -> b
strict f x = x ‘seq‘ f x
However, despite that need by the time Haskell 98 was released seq
had been reduced to a primitive strictness definition. But in 2009, all doubts about the need for a primitive sequencing definition were vanquished:
2.1 The need for
pseq
The
pseq
combinator is used for sequencing; informally, it evaluates its first argument to weak-head normal form, and then evaluates its second argument, returning the value of its second argument. Consider this definition ofparMap
: parMap f [] = [] parMap f (x:xs) = y ‘par‘ (ys ‘pseq‘ y:ys) where y = f x ys = parMap f xsThe intention here is to spark the evaluation of
f x
, and then evaluateparMap f xs
, before returning the new listy:ys
. The programmer is hoping to express an ordering of the evaluation: first sparky
, then evaluateys
.
- Runtime Support for Multicore Haskell (page 2 of 12).
Alas, this confirmation failed to influence Haskell 2010 - to this day, seq
remains just a primitive strictness definition. So for enhanced confusion the only Haskell implementation still in widespread use now provides both seq
and pseq
.
Demystifying seq
A common misconception regarding seq
is that seq x
"evaluates" x
. Well, sort of. seq
doesn't evaluate anything just by virtue of existing in the source file, all it does is introduce an artificial data dependency of one value on another: when the result of seq
is evaluated, the first argument must also (sort of; see below) be evaluated. As an example, suppose x :: Integer
, then seq x b
behaves essentially like if x == 0 then b else b
– unconditionally equal to b, but forcing x
along the way. In particular, the expression x `seq` x
is completely redundant, and always has exactly the same effect as just writing x
.
Strictly speaking, the two equations of seq
are all it must satisfy, and if the compiler can statically prove that the first argument is not ⊥, or that its second argument is, it doesn't have to evaluate anything to meet its obligations. In practice, this almost never happens, and would probably be considered highly counterintuitive behaviour on the part of GHC (or whatever else you use to run your code). So for example, in seq a b
it is perfectly legitimate for seq
to:
- 1. evaluate
b
- its second argument,
- 2. before evaluating
a
- its first argument,
- 3. then returning
b
.
In this larger example:
let x = ... in
let y = sum [0..47] in
x `seq` 3 + y + y^2
seq
immediately evaluating its second argument (3 + y + y^2
) avoids having to allocate space to store y
:
let x = ... in
case sum [0..47] of
y -> x `seq` 3 + y + y^2
However, sometimes this ambiguity is undesirable, hence the need for pseq
.
Common uses of seq
seq
is typically used in the semantic interpretation of other strictness techniques, like strictness annotations in data types, or GHC's BangPatterns extension. For example, the meaning of this:
f !x !y = z
is this:
f x y | x `seq` y `seq` False = undefined
| otherwise = z
although that literal translation may not actually take place.
seq
is frequently used with accumulating parameters to ensure that they don't become huge thunks, which will be forced at the end anyway. For example, strict foldl
:
foldl' :: (a -> b -> a) -> a -> [b] -> a
foldl' _ z [] = z
foldl' f z (x:xs) = let z' = f z x in z' `seq` foldl' f z' xs
It's also used to define strict application:
($!) :: (a -> b) -> a -> b
f $! x = x `seq` f x
which is useful for some of the same reasons.
Controversy?
The presence of seq
in Haskell does have some disadvantages:
1. It is the only reason why Haskell programs are able to distinguish between the following two values: undefined :: a -> b const undefined :: a -> b
This violates the principle of extensionality of functions, or eta-conversion from the lambda calculus, because
f
and\x -> f x
are distinct functions, even though they return the same output for every input.2. It can invalidate optimisation techniques which would normally be safe, causing the following two expressions to differ: foldr ⊥ 0 (build seq) = foldr ⊥ 0 (seq (:) []) = foldr ⊥ 0 [] = 0 seq ⊥ 0 = ⊥
This weakens the ability to use parametricity, which implies
foldr k z (build g) == g k z
for suitable values ofg
,k
andz
.3. It can invalidate laws which would otherwise hold, also causing expressions to have differing results: seq (⊥ >>= return :: State s a) True = True seq (⊥ :: State s a) True = ⊥
This violates the first monad law, that
m >>= return == m
.
But seq
(sequential or otherwise) isn't alone in causing such difficulties:
1. When combined with call-by-need semantics, the use of weak-head normal form is also detrimental to extensionality. 2. When combined with GADTs, the associated map functions which uphold the functor laws is also problematic for parametricity. 3. The ability to define the fixed-point combinator in Haskell using recursion: yet :: (a -> a) -> a yet f = f (yet f)
4. Strictness must be considered when deriving laws for various recursive algorithms (see chapter 6). 5. Similar to seq
and⊥
, the use of division and zero present their own challenges!
Therefore all such claims against seq
(or calls for its outright removal) should be examined in this context.
See also
- Parallelism in 6.6 and seq vs. pseq, Haskell mail archives.
- Questioning seq, Haskell mail archives.
- seq [bedlam], the GHC wiki.