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Make invalid laziness unrepresentable

Making invalid laziness unrepresentable, even in nested data structures.

The problem

Lazy and strict data

One circumstance in which thunk leaks occur in Haskell programs is when a lazy field of a data type remains unevaluated for longer than expected. By way of example consider the following data type:

data Foo = Foo Int Bool

During execution of a program what possible states can a value of type Foo be in? There are broadly five:

  1. <thunk>
  2. Foo <evaluated Int> <evaluated Bool>
  3. Foo <evaluated Int> <thunk>
  4. Foo <thunk> <evaluated Bool>
  5. Foo <thunk> <thunk>

The <thunk>s can be arbitrarily large run time data structures! Their unexpected occurrence can cause thunk leaks. What can we do about that? When programming in a strongly typed language we aim to “make invalid states unrepresentable”1 so when we define a data type like Foo we should consider which are its valid states. Haskell is a lazy language so we cannot forbid state 12, but are states like 3, 4 and 5 valid? Perhaps. We should carefully consider our use case; but if not (and it’s more likely not than so) then we should forbid those states statically. How can we do so? We can add strictness annotations thus:

data FooStrict = FooStrict !Int !Bool

(or by enabling StrictData which brutally applies the same transformation to every data type definition, or Strict which is even more brutal). FooStrict has only two possible states:

  1. <thunk>
  2. Foo <evaluated Int> <evaluated Bool>

We have “made invalid laziness unrepresentable”. Much better!

Nested strict data

But the above technique is not particularly general. Consider

data Bar = Bar !(Int, Bool) !(Maybe Double)

Despite the strictness annotations this type has many possible states:

  1. <thunk>
  2. Bar (<thunk>, <thunk>) Nothing
  3. Bar (<evaulated Int>, <thunk>) Nothing
  4. Bar (<thunk>, <evaluated Bool>) Nothing
  5. Bar (<evaluated Int>, <evaluated Bool>) Nothing
  6. Bar (<thunk>, <thunk>) (Just <thunk>)
  7. Bar (<evaluated Int>, <thunk>) (Just <thunk>)
  8. Bar (<thunk>, <evaluated Bool>) (Just <thunk>)
  9. Bar (<evaluated Int>, <evaluated Bool>) (Just <thunk>)
  10. Bar (<thunk>, <thunk>) (Just <evaluated Double>)
  11. Bar (<evaluated Int>, <thunk>) (Just <evaluated Double>)
  12. Bar (<thunk>, <evaluated Bool>) (Just <evaluated Double>)
  13. Bar (<evaluated Int>, <evaluated Bool>) (Just <evaluated Double>)

Plenty of thunks for leaks to hide in! Perhaps for some use cases all the above states are valid but in most cases it is overwhelmingly likely that only the following states are valid:

  1. <thunk> (because we can’t do anything about it anyway)
  2. Bar (<evaluated Int>, <evaluated Bool>) Nothing
  3. Bar (<evaluated Int>, <evaluated Bool>) (Just <evaluated Double>)

No clever application of strictness annotations can restrict us to this set of states! The problem is that there’s no way of “applying strictness inside” the nested data types. How can we make invalid laziness unrepresentable in nested data types?

The solution

Since we cannot “apply strictness inside” the nested data type we need to use separate strict types for those fields of Bar. The usual approach is to write specific strict data definitions, for example

data StrictPair a b = StrictPair !a !b
data StrictMaybe a = StrictNothing | StrictJust !a

but I’m going to show you a more lightweight approach. The library strict-wrapper allows us to rewrite Bar as

data BarStrict = BarStrict !(Strict (Int, Bool))
                           !(Strict (Maybe Double))

Having done so only the valid states are representable:

  1. <thunk>
  2. BarStrict (Strict (<evaluated Int>, <evaluated Bool>))
              (Strict Nothing)
  3. BarStrict (Strict (<evaluated Int>, <evaluated Bool>))
              (Strict (Just <evaluated Double>))

Deeper nesting works too, for example:

data Baz = Baz !(Strict (Int, Strict (Either Bool Int)))
               !(Strict (Maybe Double))

Strict also works well as a wrapper for types whose values will be passed as strict function arguments. For example, the following function has a space leak:

example_leak = foldl' f (0, 0) [1..1000]
    where f :: (Int, Int) -> Int -> (Int, Int)
          f (n, s) i = (n + 1, s + i)

Manually adding strictness avoids the space leak:

example_manual = foldl' f (0, 0) [1..1000]
    where f :: (Int, Int) -> Int -> (Int, Int)
          f (!n, !s) i = (n + 1, s + i)

but using Strict avoids the space leak in a way that is both syntactically convenient and reflected in the type of the accumulator function f, that is to say, invalid laziness in the accumulator argument has been made unrepresentable!

example_Strict = Data.List.foldl' f (Strict (0, 0)) [1..1000]
    where f :: Strict (Int, Int) -> Int -> Strict (Int, Int)
          f (Strict (n, s)) i = Strict (n + 1, s + i)

(Unfortunately we still have to remember to use foldl' rather than foldl. Nothing in the type system can help us there.)


strict-wrapper is implemented using a data family (Strict) which maps basic types to their strict versions.

data instance Strict (a, b)    = StrictPair !a !b
data instance Strict (Maybe a) = StrictNothing | StrictJust !a

To use strict-wrapper all that you need is the data family Strict and the bidirectional pattern synonym, also called Strict. For example, instead of using StrictPair a b as defined above, use Strict (a, b). To create a Strict (a, b) wrap an (a, b) in the Strict constructor; to extract an (a, b), pattern match with Strict.

The alternatives

There are various alternatives to strict-wrapper worth considering although in most cases they are too heavyweight or don’t fulfil the same role.

seq/bang patterns

It is always possible to use seq (or equivalently bang patterns) to ensure that invalid thunk states don’t arise. After all, strictness annotations and strict data types are implemented merely by automatic insertion of seq! However, in pratice it is extremely difficult to maintain the level of discipline required to make sure that the seq calls or bang patterns are inserted in the correct places (and not in the incorrect places). The benefit of programming in a strongly typed functional language is that we can make invalid states unrepresentable. That principle applies as much to invalid data type laziness as to other invalid states.


strict is a library that provides a grab-bag of features related to strictness: strict versions of basic types, strict I/O, and a class to map between strict and lazy types (including ByteString and Text types and monad transformer types).

By contrast, strict-wrapper is a much smaller and more coherent subset of the features of strict: it only provides strict versions of basic types and a class to map between them. In return for being more restrictive the mapping can be made almost zero-cost (see “Efficiency considerations”). Furthermore the Strict data family avoids the need for a whole universe of new strict type names and the Strict pattern/constructor is more ergonomic than toStrict/toLazy mapping functions.


deepseq is an extremely expensive and blunt hammer. It has to walk your entire data structure evaluating any thunks it encounters. Were those thunks actually part of a valid state of your program? In many (perhaps most) cases they were not! In those cases would it not be better to design those thunks out of your data structures and avoid deepseq entirely?


nothunks is a debugging tool that allows inspecting a value at run time to see if it contains any thunks. That is, it can check at run time whether a value is invalid. But if you can make the invalid laziness unrepresentable then why not do so?

Commentary and conclusion

Thunk leaks are a major cause of unpredictable memory usage in Haskell programs; a common cause of thunk leaks is lazy fields in data structures. There are some cases where lazy fields are required, but in the cases that they are not required consider “making invalid laziness unrepresentable” using strictness annotations and a strict data types library like strict or strict-wrapper. This practice might eliminate a substantial proportion of your thunk leaks!

Although strict-wrapper provides a convenient strict version of “small” types like tuples, eithers and maybes, it is not clear what can be done for “large” data structures like lists and maps. Converting the lazy form of a large data structure into the strict form requires walking the whole structure, so one cannot do better than a deepseq. If one wants a spine strict alternative to a list perhaps it is best just to directly use a Seq, Vector or Array, and if one wants a spine and value strict alternative then perhaps Vector.Unboxed or UArray are the right choices.

See also

  1. I believe that Yaron Minsky coined the phrase “make illegal states unrepresentable”, in The Monad.Reader, Issue 7 (April 30, 2007). I mildly prefer talking about “valid” states than “legal” ones.↩︎

  2. barring unlifted data types, which are out of scope for this discussion and this library.↩︎