{-|
Calculates the relative path to move from one point in the file system to
another.

Constraints:
- it’s only possible to route between two relative paths where the `from` path
  doesn’t have more `../` than the `to`, or between two absolute paths

Examples:
0. route ./meh/moo ../beh/boo ≡ ../../../beh/boo
1. route ../meh/moo ../../beh/boo ≡ ../../../beh/boo
2. route ./meh/moo ./meh/beh/boo ≡ ../beh/boo – **TODO**: Minimize the path when
   relativity is equal and there is a common component prefix.
3. route ./meh/moo ../meh/beh/boo ≡ ../../../meh/beh/boo
4. route /meh/moo/maz /beh/boo ≡ ../../../beh/boo
5. route /meh/moo/maz ../beh/boo ≡ Left RouteFromAbsToRel
6. route ./meh/moo/maz /beh/boo ≡ Left RouteFromRelToAbs
7. route ../../meh/moo/maz ../beh/boo ≡ Left FromTooFarUp
-}
let Typ = ../Typ

let AbsolutePath = ./Type

let RelativePath = ../Relative/Type

let AbsoluteDirectory = ../../Directory/Absolute/Type

let route =
      λ(from : AbsoluteDirectory) →
      λ(type : Typ) →
      λ(to : AbsolutePath type) →
          { parents = List/length Text from.directories
          , directories = to.directories
          , file = to.file
          }
        : RelativePath type

in  route