Non-Strictness

• Truly lazy language memoizes results of all functions it ever evaluates which will consume large amounts of memory for practical programs.

• Non-strictness means language should be able to evaluate expressions with bottoms in them as long as they (bottoms) are never evaluated.

• Implementations of Haskell are technically required to be non-strict rather than lazy, but for practical purposes lets call it lazy.

• Most expressions are only reduced/evaluated when necessary. Never needed - never evauluated. Unevaluated expressions are called thunks. The garbage collector (GC) sweeps the thunks away if never evaluated.

• So GHC is totally non-strict (as required by the specification of the language) and somewhat lazy (not truly lazy because of the garbage collection).

• evaluation = thunk -> value

• Thunk is placeholder in the underlying graph of the program.

• If thunk is evaluated, it can often be shared between expressions - this is laziness.

• The idea is that evaluation is driven by demand, not by construction. This also means we can never guarantee is something will ever be evaluated.

Outside in evaluation

• Strict languages evaluate inside-out, non-strict like Haskell do the opposite - they evaluate outside-in. Evaluation proceeds from outermost parts of expressions and works inward based on what values are forced.

Example:

foldr' k z xs = go xs
  where
    go []     = z
    go (y:ys) = y `k` go ys

c = foldr' const 'z' ['a'..'e'] -- returns 'a'

const returns first argument without evaluating second, hence our list tail never gets evaluated - so this foldr' will work even on list with undefined in it - as long as it is not the first element.

const was in outermost position so it was evaluated first.

• Outside in evaluation is the reason why length of list never evaluates the elements of the list.

Making Haskell Strict

• There are mechanisms to force evaluation

seq :: a -> b -> b

• seq magically forces evaluation of first argument if and when the second argument has to be evaluated.
• It creates a graph of evaluations - forcing one exp will force another. eg.

  a `seq` b `seq` c `seq d
  means c will be evaluated before d, but before that b but before that a must be evaluated. So d -> c -> b -> a.
• seq forces evaluation to weak head normal form (WHNF) - which means it stops at the first data constructor or lambda.

eg.

let x = (,) undefined undefined
x `seq` 1 -- works
let y = \_ -> undefined
y `seq` 2 -- works as well
let z = undefined
z `seq` 3 -- does not work - undefined itself is bottom

• x and y in above example work because bottom is enclosed inside data constructor or function and haskell does not need to evaluate inside unless it is forced to (which seek does not) - this is WHNF.
• case also forces data constructor evaluation but not inner values (depends on nesting in the pattern).

Call by *

• Call by value: args evaluated before entering function, exps evaluated before bindings - strict convention.

• Call by name: exps not necessarily evaluated - outside-in evaluation.

• Call by need: same as call by name, but evaluated only once.

• GHC oscillates between by-need and by-name based on optimizations. It can do this because of pure code.

• Sidenote: :sprint allows to see thunks in ghci. _ is shown for unevaluated values.

Sharing evaluations

• When a computation is named, results of evaluating that computation can be shared between all references to that name without re-evaluating.

• Imp to note sharing based on names not values. So let x = 1 and let y = 1 won't be shared. But in let x = 1 and then x + x value is shared.

• Inlining expressions where they get used prevents sharing - thunks evaluated separately.

• Sharing doesn't work in presence of constraints like typeclasses - since they are functions in Core (GHC's intermediate language) which are waiting to be converted to concrete types - and unapplied functions are not shareable values.

  ie. in Core, Num a => a is really function Num a -> a.

  But it works if you give a concrete type.

• In short, polymorphic values maybe evaluated once but still not shared because, underneath, they continue to be functions awaiting application.

Preventing sharing

• We might want to prevent sharing if a large amount of data is there in order to compute a small value. We can discard the large data while preserving the small result.

• Trick to prevent sharing is turning values into unit functions:

import Debug.Trace
let f x = (x ()) + (x ())
f (\_ -> trace "hi" 2)

-- hi
-- hi
-- 4

• Functions are not shared when there are named arguments but are when they are pointfree. :/

Forcing sharing

• Name the result using let binding. Names are what make values shareable.

Lazy patterns

Add tilde ~ before a pattern to make it lazy.

strictPattern :: (a, b) -> String
strictPattern (a, b) = const "hello" a

lazyPattern :: (a, b) -> String
lazyPattern ~(a, b) = const "hello" a

strictPattern undefined -- error

lazyPattern undefined -- no error
-- "hello" returned

• strictPattern undefined above^ worked because we never needed a so pattern was never evaluated.

• Caveat is that lazy pattern cannot be used to discriminate cases of a sum.

Bang patterns

• Evaluate argument to function whether we use it or not

f :: Int -> Int
f !x = 1

• Forcing something (with either seq or !) is expressed in Core as case expressions.

• We can specify bang pattern in data declarations.

type Name = String
type Age = Int
data Person = Person !Name Age

age (Person _ a) = a

age (Person undefined 20) -- fails even if first argument is not used

• Idea here is sometimes its cheaper to just compute something than to construct thunk and then evaluate later.

Strict/StrictData pragmas

• Avoid putting seq and ! yourself. Makes everything strict in that module.

• Can use ~ to bring back laziness.