66 lines
1.5 KiB
Text
66 lines
1.5 KiB
Text
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Import basic.
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Import nat.
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Variable Int : Type.
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Alias ℤ : Int.
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Builtin Int::numeral.
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Builtin Int::add : Int -> Int -> Int.
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Infixl 65 + : Int::add.
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Builtin Int::mul : Int -> Int -> Int.
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Infixl 70 * : Int::mul.
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Builtin Int::div : Int -> Int -> Int.
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Infixl 70 div : Int::div.
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Builtin Int::le : Int -> Int -> Bool.
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Infix 50 <= : Int::le.
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Infix 50 ≤ : Int::le.
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Definition Int::ge (a b : Int) : Bool := b ≤ a.
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Infix 50 >= : Int::ge.
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Infix 50 ≥ : Int::ge.
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Definition Int::lt (a b : Int) : Bool := ¬ (a ≥ b).
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Infix 50 < : Int::lt.
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Definition Int::gt (a b : Int) : Bool := ¬ (a ≤ b).
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Infix 50 > : Int::gt.
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Definition Int::sub (a b : Int) : Int := a + -1 * b.
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Infixl 65 - : Int::sub.
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Definition Int::neg (a : Int) : Int := -1 * a.
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Notation 75 - _ : Int::neg.
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Definition Int::mod (a b : Int) : Int := a - b * (a div b).
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Infixl 70 mod : Int::mod.
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Builtin nat_to_int : Nat -> Int.
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Coercion nat_to_int.
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Definition Int::divides (a b : Int) : Bool := (b mod a) = 0.
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Infix 50 | : Int::divides.
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Definition Int::abs (a : Int) : Int := if (0 ≤ a) a (- a).
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Notation 55 | _ | : Int::abs.
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Definition Nat::sub (a b : Nat) : Int := nat_to_int a - nat_to_int b.
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Infixl 65 - : Nat::sub.
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Definition Nat::neg (a : Nat) : Int := - (nat_to_int a).
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Notation 75 - _ : Nat::neg.
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SetOpaque Int::sub true.
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SetOpaque Int::neg true.
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SetOpaque Int::mod true.
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SetOpaque Int::divides true.
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SetOpaque Int::abs true.
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SetOpaque Int::ge true.
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SetOpaque Int::lt true.
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SetOpaque Int::gt true.
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SetOpaque Nat::sub true.
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SetOpaque Nat::neg true.
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