GHCi command, tracing steps of instance resolution for Constraint or expression

Another GHCi command (#15610 (closed)), :elab <constraint> traces instance resolution for <constraint>. This is already something people do by hand (ticket:10318#ticket:15613#comment:159914) and would be a great tool for explorers of Haskell

>> :elab Monoid (a -> b -> ([c], Sum Int))
Monoid (a -> b -> ([c], Sum Int))
==> Monoid (b -> ([c], Sum Int))
  ==> Monoid ([c], Sum Int)
    ==> Monoid [c]
    ==> Monoid (Sum Int)
      ==> Num Int

If resolving the type class fails, it can pinpoint what caused it to fail

>> data A
>> :elab Show (A, Int -> Int)
Show (A, Int -> Int)
<~bRZsz NO instance~>

==> Show A
  <NO instance>
==> Show (Int -> Int)
  <NO instance>

A verbose version can explain each step

>> :elab +v Monoid (a -> b -> ([c], Sum Int)
Monoid (a -> b -> ([c], Sum Int)) -- Monoid b => Monoid (a -> b) (‘GHC.Base’)
==> Monoid (b -> ([c], Sum Int))  -- Monoid b => Monoid (a -> b) (‘GHC.Base’)
  ==> Monoid ([c], Sum Int)       -- Monoid b => Monoid (a -> b) (‘GHC.Base’)
    ==> Monoid [c]                --             Monoid [a]      (‘GHC.Base’)
    ==> Monoid (Sum Int)          -- Num    a => Monoid (Sum a)  (‘Data.Monoid’)
      ==> Num Int                 --             Num Int         (‘GHC.Num’)

>> :elab +v Num (Int, Float, Rational)
Num (Int, Float, Rational) --  (Num a, Num b, Num c) => Num (a, b, c)    (‘Data.NumInstances.Tuple’)
==> Num Int                --                           Num Int          (‘GHC.Num’)
==> Num Float              --                           Num Float        (‘GHC.Float’)
==> Num Rational           -- type Rational = Ratio Integer              (‘GHC.Real’)
 =  Num (Ration Integer)   -- Integral a             => Num (Ratio a)    (‘GHC.Real’)
  ==> Integral Integer     --                           Integral Integer (‘GHC.Real’)

---

Not the same idea but similar. Listing instance resolution that takes place in an expression

>> :elab (+) @Int
from: (+) @Int
  Num Int

>> :elab2 comparing (length @[]) <> compare
from: length @[]
  Foldable []

from: comparing (length @[])
  Ord Int

from: comparing (length @[]) <> compare
  Monoid ([a] -> [a] -> Ordering)
  ==> Monoid ([a] -> Ordering)
    ==> Monoid Ordering

>> :elab2 ask 'a'
from: ask 'a'
  MonadReader Char ((->) m)
  ==> MonadReader Char ((->) Char)

not sure about that last one, or how to visualize them but I think it gives the right idea.

Make sure to test it on https://jpaykin.github.io/papers/paykin_dissertation_2018.pdf

lam
  :: (HasLolli exp, KnownNat n,
      Div_ (Remove n ctx') (Remove n ctx') ~ '[],
      Fresh (Remove n ctx') ~ n,
      MergeF (Remove n ctx') '[] ~ Remove n ctx', MergeF ctx' '[] ~ ctx',
      Lookup ctx' n ~ 'Just a, AddF n a (Remove n ctx') ~ ctx',
      Div_ ctx' ctx' ~ '[]) =>
     (Var exp n a -> exp ctx' b) -> exp (Remove n ctx') (a -· b)

and this