laziness and function composition (haskell, erlang)

Question

Can someone please explain or give some resources on how function composition works in relation to laziness?

For example how does filter (/='W') . map toUpper $ "justaword" filter (/='W') . map toUpper $ "justaword" work in Haskell compared to it's counterpart in erlang which is not lazy?

Answer 1

Every time another character is demanded (or notification of end), the next character - if any - is mapped to uppercase, that is compared to 'W', delivered if unequal.

filter (/= 'W') . map toUpper $ "justaword"
~> filter (/= 'W') (toUpper 'j' : map toUpper "ustaword")
~> filter (/= 'W') ('J' : map toUpper "ustaword")
~> 'J' : filter (/= 'W') (map toUpper "ustaword")

Now the first character is available, so for queries like null or functions like take 1 , no further work is done. If more characters are demanded by the consumer, they will be produced one by one until the end of the string is reached.

Example:

Prelude Data.Char> take 10 . filter (/= 'W') . map toUpper $ repeat 't'
"TTTTTTTTTT"

repeat produces an infinite list, but as long as only a finite part is consumed, the computation finishes in finite time. However, take 10 . filter (/= 'W') . map toUpper $ repeat 'w' take 10 . filter (/= 'W') . map toUpper $ repeat 'w' take 10 . filter (/= 'W') . map toUpper $ repeat 'w' would not terminate, since none of the produced characters passes the filter to reach the take 10 .