What's the difference between partial evaluation and function inlining in a functional language?

Question

I know that:

1. Function inlining is to replace a function call with the function definition.
2. Partial evaluation is to evaluate the known (static) parts of a

Answer 1

Consider the following code:

map f xs = case xs of [] -> []; (x:xs') -> f x : map f xs'
f x y = if x % 2 == 0 then y + x / 2 else y + x

main = map (f 3) [1..100]

After partial evaluating f 3:

f3 y = if 3 % 2 == 0 then y + 3 / 2 else y + 3
main = map f3 [1..100]

And then after constant folding 3 % 2 == 0:

f3 y = y + 3
main = map f3 [1..100]

Now let's consider inlining f:

NOTICE: f in f 3 will not be inlined since it is not a fully application, but we can adjust f's definition to make it happen, for more detail, see the ghc doc here

f x = \y -> if x % 2 == 0 then y + x / 2 else y + x

main = map (\y -> if 3 % 2 == 0 then y + 3 / 2 else y + 3) [1..100]

And then after constant folding 3 % 2 == 0:

main = map (\y -> y + 3) [1..100]

The above example shows that, both inlining and partial evaluation can provide extra optimization opportunities, but they are still very different:

1. when the special version (f 3 in the above example) appears many times, inlining will produce very many duplicated codes.
2. partial evaluation still works when the first argument is not a static constant, but inlining will not.

For the second point, consider the following example:

main = [f x y | x <- [1..10], y <- [1..100]]

In this case, partial evaluation can generate 10 specialized version for f x dynamically, but inlining can do nothing.