68 lines
No EOL
1.3 KiB
Text
68 lines
No EOL
1.3 KiB
Text
Import Nat.
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Variable Int : Type.
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Alias ℤ : Int.
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Builtin nat_to_int : Nat → Int.
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Coercion nat_to_int.
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Namespace Int.
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Builtin numeral.
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Builtin add : Int → Int → Int.
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Infixl 65 + : add.
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Builtin mul : Int → Int → Int.
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Infixl 70 * : mul.
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Builtin div : Int → Int → Int.
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Infixl 70 div : div.
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Builtin le : Int → Int → Bool.
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Infix 50 <= : le.
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Infix 50 ≤ : le.
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Definition ge (a b : Int) : Bool := b ≤ a.
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Infix 50 >= : ge.
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Infix 50 ≥ : ge.
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Definition lt (a b : Int) : Bool := ¬ (a ≥ b).
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Infix 50 < : lt.
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Definition gt (a b : Int) : Bool := ¬ (a ≤ b).
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Infix 50 > : gt.
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Definition sub (a b : Int) : Int := a + -1 * b.
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Infixl 65 - : sub.
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Definition neg (a : Int) : Int := -1 * a.
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Notation 75 - _ : neg.
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Definition mod (a b : Int) : Int := a - b * (a div b).
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Infixl 70 mod : mod.
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Definition divides (a b : Int) : Bool := (b mod a) = 0.
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Infix 50 | : divides.
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Definition abs (a : Int) : Int := if (0 ≤ a) a (- a).
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Notation 55 | _ | : abs.
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SetOpaque sub true.
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SetOpaque neg true.
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SetOpaque mod true.
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SetOpaque divides true.
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SetOpaque abs true.
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SetOpaque ge true.
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SetOpaque lt true.
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SetOpaque gt true.
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EndNamespace.
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Namespace Nat.
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Definition sub (a b : Nat) : Int := nat_to_int a - nat_to_int b.
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Infixl 65 - : sub.
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Definition neg (a : Nat) : Int := - (nat_to_int a).
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Notation 75 - _ : neg.
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SetOpaque sub true.
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SetOpaque neg true.
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EndNamespace. |