holes.lean:4:4-4:7: error: placeholders '_' cannot be used where a function is expected
holes.lean:11:8-11:13: error: don't know how to synthesize placeholder
context:
case hole
x : Nat
y : Nat := g x + g x
⊢ Nat
holes.lean:11:4-11:5: error: don't know how to synthesize placeholder
context:
x : Nat
y : Nat := g x + g x
⊢ Nat
holes.lean:10:15-10:18: error: don't know how to synthesize implicit argument 'β'
  @g Nat (?m x) x
context:
x : Nat
⊢ Type
holes.lean:10:9-10:12: error: don't know how to synthesize implicit argument 'β'
  @g Nat (?m x) x
context:
x : Nat
⊢ Type
holes.lean:13:10-13:11: error: failed to infer binder type
holes.lean:15:16-15:17: error: failed to infer binder type
holes.lean:19:0-19:3: error: don't know how to synthesize implicit argument 'β'
  @f Nat (?m a) a
context:
a : Nat
f : {α : Type} → {β : ?m a} → α → α := fun {α} {β} a => a
⊢ ?m a
holes.lean:18:9-18:10: error: failed to infer binder type
holes.lean:21:25-22:4: error: failed to infer definition type
holes.lean:25:8-25:11: error: failed to infer 'let rec' declaration type