63 lines
1.3 KiB
Text
63 lines
1.3 KiB
Text
structure Magma.{u} where
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α : Type u
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mul : α → α → α
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instance : CoeSort Magma.{u} (Type u) where
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coe m := m.α
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def mul {s : Magma} (a b : s) : s :=
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s.mul a b
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infixl:70 (priority := high) "*" => mul
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def Nat.Magma : Magma where
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α := Nat
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mul a b := Nat.mul a b
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def Prod.Magma (m : Magma.{u}) (n : Magma.{v}) : Magma where
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α := m.α × n.α
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mul a b := (a.1 * b.1, a.2 * b.2)
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unif_hint (s : Magma) where
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s =?= Nat.Magma |- s.α =?= Nat
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unif_hint (s : Magma) (m : Magma) (n : Magma) (β : Type u) (δ : Type v) where
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m.α =?= β
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n.α =?= δ
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s =?= Prod.Magma m n
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|-
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s.α =?= β × δ
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def f1 (x : Nat) : Nat :=
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x * x
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#eval f1 10
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def f2 (x y : Nat) : Nat × Nat :=
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(x, y) * (x, y)
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#eval f2 10 20
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def f3 (x y : Nat) : Nat × Nat × Nat :=
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(x, y, y) * (x, y, y)
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#eval f3 7 24
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def magmaOfMul (α : Type u) [Mul α] : Magma where -- Bridge between `Mul α` and `Magma`
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α := α
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mul a b := Mul.mul a b
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unif_hint (s : Magma) (α : Type u) [Mul α] where
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s =?= magmaOfMul α
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|-
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s.α =?= α
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def g (x y : Int) : Int :=
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x * y -- Note that we don't have a hint connecting Magma's carrier and Int
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set_option pp.all true
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#print g -- magmaOfMul is used
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def h (x y : UInt32) : UInt32 :=
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let f z w := z * w * z
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f x y
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