69 lines
No EOL
1.3 KiB
Text
69 lines
No EOL
1.3 KiB
Text
import Nat
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import if_then_else
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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) then a else (- a)
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notation 55 | _ | : abs
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set_opaque sub true
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set_opaque neg true
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set_opaque mod true
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set_opaque divides true
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set_opaque abs true
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set_opaque ge true
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set_opaque lt true
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set_opaque gt true
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end
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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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set_opaque sub true
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set_opaque neg true
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end |