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| 1 | + |
| 2 | +object Test { |
| 3 | + def main(args: Array[String]): Unit = { |
| 4 | + println("CaseNums") |
| 5 | + test(CaseNums) |
| 6 | + println() |
| 7 | + println("IntNums") |
| 8 | + test(IntNums) |
| 9 | + } |
| 10 | + |
| 11 | + def test(numbers: Numbers) = { |
| 12 | + import numbers._ |
| 13 | + |
| 14 | + val zero: Nat = Zero |
| 15 | + val one: Nat = Succ(zero) |
| 16 | + val two: Nat = Succ(one) |
| 17 | + val three: Nat = Succ(two) |
| 18 | + |
| 19 | + zero match { |
| 20 | + case Succ(p) => println("error") |
| 21 | + case Zero => println("ok") // extra argument removed by language extension |
| 22 | + } |
| 23 | + |
| 24 | + one match { |
| 25 | + case Zero => println("error") // extra argument removed by language extension |
| 26 | + case Succ(p) => println("ok") |
| 27 | + } |
| 28 | + |
| 29 | + zero match { |
| 30 | + case s: Succ => println("ok - unchecked error") |
| 31 | + case z: Zero => println("ok - unchecked no error") |
| 32 | + } |
| 33 | + |
| 34 | + def divOpt(a: Nat, b: Nat): Option[(Nat, Nat)] = b match { |
| 35 | + case s @ Succ(p) => |
| 36 | + Some(safeDiv(a, s.asInstanceOf[Succ])) // this case will not be needed |
| 37 | + case _ => None |
| 38 | + } |
| 39 | + println(divOpt(one, zero)) |
| 40 | + println(divOpt(three, two)) |
| 41 | + |
| 42 | + def divOptExpanded(a: Nat, b: Nat): Option[(Nat, Nat)] = { |
| 43 | + val x0 = Succ.unapply(b) |
| 44 | + if (!x0.isEmpty) { |
| 45 | + val s = b.asInstanceOf[x0.Refined] // safe unchecked cast inserted by the language extension |
| 46 | + val p = x0.get |
| 47 | + Some(safeDiv(a, s)) |
| 48 | + } else { |
| 49 | + None |
| 50 | + } |
| 51 | + } |
| 52 | + println(divOptExpanded(one, zero)) |
| 53 | + println(divOptExpanded(three, two)) |
| 54 | + } |
| 55 | +} |
| 56 | + |
| 57 | +trait Numbers { |
| 58 | + |
| 59 | + type Nat |
| 60 | + type Zero <: Nat |
| 61 | + type Succ <: Nat |
| 62 | + |
| 63 | + val Zero: Zero |
| 64 | + |
| 65 | + val Succ: SuccExtractor |
| 66 | + trait SuccExtractor { |
| 67 | + def apply(nat: Nat): Succ |
| 68 | + def unapply(nat: Nat): SuccOpt { type Refined <: nat.type } // check that SuccOpt#Refined <: nat.type. Could be forced by the compiler? |
| 69 | + } |
| 70 | + trait SuccOpt { |
| 71 | + type Refined <: Succ // optionally added by language extension |
| 72 | + def get: Nat |
| 73 | + def isEmpty: Boolean |
| 74 | + } |
| 75 | + |
| 76 | + implicit def SuccDeco(succ: Succ): SuccAPI |
| 77 | + trait SuccAPI { |
| 78 | + def pred: Nat |
| 79 | + } |
| 80 | + |
| 81 | + def safeDiv(a: Nat, b: Succ): (Nat, Nat) |
| 82 | +} |
| 83 | + |
| 84 | +object CaseNums extends Numbers { |
| 85 | + |
| 86 | + trait NatClass |
| 87 | + case object ZeroObj extends NatClass |
| 88 | + case class SuccClass(pred: NatClass) extends NatClass with SuccOpt { |
| 89 | + type Refined = this.type |
| 90 | + def get: NatClass = pred |
| 91 | + def isEmpty: Boolean = false |
| 92 | + } |
| 93 | + |
| 94 | + class EmptySuccOpt extends SuccOpt { |
| 95 | + type Refined = Nothing |
| 96 | + def isEmpty: Boolean = true |
| 97 | + def get: NatClass = throw new Exception("empty") |
| 98 | + } |
| 99 | + |
| 100 | + type Nat = NatClass |
| 101 | + type Zero = ZeroObj.type |
| 102 | + type Succ = SuccClass |
| 103 | + |
| 104 | + val Zero: Zero = ZeroObj |
| 105 | + |
| 106 | + object Succ extends SuccExtractor { |
| 107 | + def apply(nat: Nat): Succ = SuccClass(nat) |
| 108 | + def unapply(nat: Nat) = nat match { |
| 109 | + case succ: SuccClass => succ.asInstanceOf[nat.type & SuccClass] |
| 110 | + case _ => new EmptySuccOpt |
| 111 | + } |
| 112 | + } |
| 113 | + |
| 114 | + def SuccDeco(succ: Succ): SuccAPI = new SuccAPI { |
| 115 | + def pred: Nat = succ.pred |
| 116 | + } |
| 117 | + |
| 118 | + def safeDiv(a: Nat, b: Succ): (Nat, Nat) = { |
| 119 | + def sdiv(div: Nat, rem: Nat): (Nat, Nat) = |
| 120 | + if (lessOrEq(rem, b)) (div, rem) |
| 121 | + else sdiv(Succ(div), minus(rem, b)) |
| 122 | + sdiv(Zero, a) |
| 123 | + } |
| 124 | + |
| 125 | + private def lessOrEq(a: Nat, b: Nat): Boolean = (a, b) match { |
| 126 | + case (Succ(a1), Succ(b1)) => lessOrEq(a1, b1) |
| 127 | + case (Zero, _) => true // extra argument removed by language extension |
| 128 | + case _ => false |
| 129 | + } |
| 130 | + |
| 131 | + // assumes a >= b |
| 132 | + private def minus(a: Nat, b: Nat): Nat = (a, b) match { |
| 133 | + case (Succ(a1), Succ(b1)) => minus(a1, b1) |
| 134 | + case _ => a |
| 135 | + } |
| 136 | + |
| 137 | +} |
| 138 | + |
| 139 | +object IntNums extends Numbers { |
| 140 | + type Nat = Int |
| 141 | + type Zero = Int // 0 |
| 142 | + type Succ = Int // n > 0 |
| 143 | + |
| 144 | + val Zero = 0 |
| 145 | + |
| 146 | + object Succ extends SuccExtractor { |
| 147 | + def apply(nat: Nat): Int = nat + 1 |
| 148 | + def unapply(nat: Nat) = new SuccOpt { |
| 149 | + type Refined = nat.type |
| 150 | + def isEmpty: Boolean = nat <= 0 |
| 151 | + def get: Int = nat - 1 |
| 152 | + } |
| 153 | + } |
| 154 | + |
| 155 | + def SuccDeco(succ: Succ): SuccAPI = new SuccAPI { |
| 156 | + def pred: Int = succ - 1 |
| 157 | + } |
| 158 | + |
| 159 | + def safeDiv(a: Nat, b: Succ): (Nat, Nat) = (a / b, a % b) |
| 160 | +} |
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