48 lines
1.4 KiB
Lean4
48 lines
1.4 KiB
Lean4
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/-
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Port of `Showable.agda` (plus the `Showable` instances that lived on
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`Lattice/Map.agda` and `Lattice/AboveBelow.agda`).
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Lean has `ToString`, but its `String` instance does not quote (the Agda one
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does), so to reproduce the Agda output exactly we port the class as-is.
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-/
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import Spa.Lattice.FiniteMap
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import Spa.Lattice.AboveBelow
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namespace Spa
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/-- Agda: `Showable` (`show` is a Lean keyword, hence `show'`). -/
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class Showable (α : Type*) where
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show' : α → String
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export Showable (show')
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instance : Showable String := ⟨fun s => "\"" ++ s ++ "\""⟩
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instance : Showable ℕ := ⟨toString⟩
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instance : Showable ℤ := ⟨toString⟩
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instance {n : ℕ} : Showable (Fin n) := ⟨fun i => toString i.val⟩
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instance {α β : Type*} [Showable α] [Showable β] : Showable (α × β) :=
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⟨fun p => "(" ++ show' p.1 ++ ", " ++ show' p.2 ++ ")"⟩
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instance : Showable PUnit := ⟨fun _ => "()"⟩
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/-- Agda: the `Showable` instance of `Lattice/AboveBelow.agda`. -/
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instance {α : Type*} [Showable α] : Showable (AboveBelow α) :=
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⟨fun
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| .bot => "⊥"
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| .top => "⊤"
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| .mk x => show' x⟩
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/-- Agda: the `Showable` instance of `Lattice/Map.agda` (inherited by
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`FiniteMap`). -/
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instance {α β : Type*} {ks : List α} [Showable α] [Showable β] :
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Showable (FiniteMap α β ks) :=
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⟨fun fm =>
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"{" ++ fm.val.foldr (fun p rest => show' p.1 ++ " ↦ " ++ show' p.2 ++ ", " ++ rest) ""
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++ "}"⟩
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end Spa
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