44 lines
926 B
Text
44 lines
926 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) then a else (- a)
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notation 55 | _ | : abs
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end
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