44 lines
957 B
Text
44 lines
957 B
Text
Import Int.
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Variable Real : Type.
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Alias ℝ : Real.
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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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Namespace Real.
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Builtin numeral.
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Builtin add : Real → Real → Real.
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Infixl 65 + : add.
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Builtin mul : Real → Real → Real.
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Infixl 70 * : mul.
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Builtin div : Real → Real → Real.
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Infixl 70 / : div.
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Builtin le : Real → Real → Bool.
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Infix 50 <= : le.
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Infix 50 ≤ : le.
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Definition ge (a b : Real) : 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 : Real) : Bool := ¬ (a ≥ b).
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Infix 50 < : lt.
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Definition gt (a b : Real) : Bool := ¬ (a ≤ b).
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Infix 50 > : gt.
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Definition sub (a b : Real) : Real := a + -1.0 * b.
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Infixl 65 - : sub.
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Definition neg (a : Real) : Real := -1.0 * a.
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Notation 75 - _ : neg.
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Definition abs (a : Real) : Real := if (0.0 ≤ a) a (- a).
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Notation 55 | _ | : abs.
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EndNamespace.
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