47 lines
1.1 KiB
Text
47 lines
1.1 KiB
Text
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Import basic.
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Import nat.
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Import int.
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Variable Real : Type.
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Alias ℝ : Real.
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Builtin Real::numeral.
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Builtin Real::add : Real → Real → Real.
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Infixl 65 + : Real::add.
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Builtin Real::mul : Real → Real → Real.
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Infixl 70 * : Real::mul.
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Builtin Real::div : Real → Real → Real.
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Infixl 70 / : Real::div.
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Builtin Real::le : Real → Real → Bool.
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Infix 50 <= : Real::le.
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Infix 50 ≤ : Real::le.
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Definition Real::ge (a b : Real) : Bool := b ≤ a.
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Infix 50 >= : Real::ge.
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Infix 50 ≥ : Real::ge.
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Definition Real::lt (a b : Real) : Bool := ¬ (a ≥ b).
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Infix 50 < : Real::lt.
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Definition Real::gt (a b : Real) : Bool := ¬ (a ≤ b).
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Infix 50 > : Real::gt.
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Definition Real::sub (a b : Real) : Real := a + -1.0 * b.
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Infixl 65 - : Real::sub.
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Definition Real::neg (a : Real) : Real := -1.0 * a.
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Notation 75 - _ : Real::neg.
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Definition Real::abs (a : Real) : Real := if (0.0 ≤ a) a (- a).
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Notation 55 | _ | : Real::abs.
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Builtin int_to_real : Int → Real.
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Coercion int_to_real.
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Definition nat_to_real (a : Nat) : Real := int_to_real (nat_to_int a).
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Coercion nat_to_real.
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