When a transformation should change contained values without changing a data structure's shape, fmap applies the function while preserving that structure. Lists, Maybe values, and other Functors can therefore share the same mapping operation. section 1.3.3 section 6.3.3
The operation generalizes familiar transformations across several containers:
- For a list, fmap is equivalent to map: it can convert integers to strings, double them, or produce nested lists while retaining the list structure. section 6.3.3
- For Maybe values inside a list, nested fmap traverses both layers, transforming Just contents while leaving Nothing unchanged. section 1.3.3
- For SandwichConstructor, fmap transforms continuation results while repacking the original constructors and preserving the script shape. section 6.3.3
Mapping through nested structure
Given maybeNames = [Just "Alice", Just "Bob", Nothing], applying fmap (fmap length) produces [Just 5, Just 3, Nothing]. The outer fmap maps the list; the inner fmap maps each Maybe value. section 1.3.3
Listing 6.3 Functor instance for the free monad
instance Functor SandwichConstructor where #1
fmap f (StartNewSandwich breadType component next) #2
= StartNewSandwich breadType component (f . next)
fmap f (AddComponent component sandwichBody next)
= AddComponent component sandwichBody (f . next)
fmap f (FinishSandwich mbBreadType sandwichBody next)
= FinishSandwich mbBreadType sandwichBody (f . next)
Inspect a custom Functor instance that maps over continuation results without altering SandwichConstructor's constructors. section 6.3.3
