mapProgramT

[andrewthad]

In PR #15, I've added a function that makes it possible to map over the instruction type that ProgramT is parameterized over.

[andrewthad]

From what I learned in #14, I thought that it would be possible to also write the functions

mapProgramT :: (forall a. instr1 a -> instr2 a) -> ProgramT instr1 m b -> ProgramT instr2 m b
hoistProgramT :: (forall b. m b -> n b) -> ProgramT instr m a -> ProgramT instr n b

without pattern matching on ProgramT. However, I still cannot find a way to write mapProgramT with pattern matching, so I think that this PR is still relevant.

[HeinrichApfelmus]

The same ideas from #14 can be used to write mapProgramT. Here is one way to do it:

mapProgramT :: Monad m => (forall a. instr1 a -> instr2 a)
    -> ProgramT instr1 m b -> ProgramT instr2 m b
mapProgramT f p = do
    v <- lift $ viewT p
    case v of
        Return a -> return a
        i :>>= k -> singleton (f i) >>= mapProgramT f . k

---

If I were to export the constructors, then this would kind of the defeat the purpose of the library. (Though I'm willing to compromise for the sake of efficiency). Relying on viewT only makes sure that the monad laws and the lifting laws are always satisfied. In contrast, having access to the internal constructors risks breaking these laws.