/-
Port of `Showable.agda` (plus the `Showable` instances that lived on
`Lattice/Map.agda` and `Lattice/AboveBelow.agda`).

Lean has `ToString`, but its `String` instance does not quote (the Agda one
does), so to reproduce the Agda output exactly we port the class as-is.
-/
import Spa.Lattice.FiniteMap
import Spa.Lattice.AboveBelow

namespace Spa

/-- Agda: `Showable` (`show` is a Lean keyword, hence `show'`). -/
class Showable (α : Type*) where
  show' : α → String

export Showable (show')

instance : Showable String := ⟨fun s => "\"" ++ s ++ "\""⟩

instance : Showable ℕ := ⟨toString⟩

instance : Showable ℤ := ⟨toString⟩

instance {n : ℕ} : Showable (Fin n) := ⟨fun i => toString i.val⟩

instance {α β : Type*} [Showable α] [Showable β] : Showable (α × β) :=
  ⟨fun p => "(" ++ show' p.1 ++ ", " ++ show' p.2 ++ ")"⟩

instance : Showable PUnit := ⟨fun _ => "()"⟩

/-- Agda: the `Showable` instance of `Lattice/AboveBelow.agda`. -/
instance {α : Type*} [Showable α] : Showable (AboveBelow α) :=
  ⟨fun
    | .bot => "⊥"
    | .top => "⊤"
    | .mk x => show' x⟩

/-- Agda: the `Showable` instance of `Lattice/Map.agda` (inherited by
`FiniteMap`). -/
instance {α β : Type*} {ks : List α} [Showable α] [Showable β] :
    Showable (FiniteMap α β ks) :=
  ⟨fun fm =>
    "{" ++ fm.val.foldr (fun p rest => show' p.1 ++ " ↦ " ++ show' p.2 ++ ", " ++ rest) ""
        ++ "}"⟩

end Spa
