Extra Considerations

Or, things I find helpful when I remember them.

Foldr and Foldl

• foldr is the constructor replacement function. Uses the incremental pattern. Lemma
• foldl is the for loop. Can be implemented in terms of foldr. Uses the accumulator pattern.

Sections

Note Sections are the partial application of an operator.

map (+1) [1..5]
--    |
--    +--- adding one of the two parameters to the operator leaves it open.
--         This is the same as (\x -> x + 1)
--         Could also be (1+) since (\x -> 1 + x) is the same as (\x -> x + 1)
--         by commutativity.
--λ [2,3,4,5,6]

Caution! Keep in mind the commutativity of the operator! (e.g., (2^) and (^2) are not the same.)

-- A non-commutative example.
(2^) -- left section => (^) 2 => \x -> 2 ^ x
(^2) -- right section) => flip (^) 2 => \x -> x ^ 2

λ> (^2) <$> [3,5]
[9,25]

λ> (2^) <$> [3,5]
[8,32]

Fixity and Precedence

Passing an argument to a function has higher precedence than passing to an operator.

Infix operators have a "fixity" which determines how they favor precedence. <> has right fixity so something like "My name is" <> name <> "." is seen by the compiler as "My name is" <> (name <> ".").