|
| 1 | + |
| 2 | +// FIXME |
| 3 | + |
| 4 | +//object Test { |
| 5 | +// def main(args: Array[String]): Unit = { |
| 6 | +// app(ClassNums) |
| 7 | +// app(IntNums) |
| 8 | +// } |
| 9 | +// |
| 10 | +// def app(peano: Peano): Unit = { |
| 11 | +// import peano._ |
| 12 | +// def divOpt(m: Nat, n: Nat): Option[(Nat, Nat)] = { |
| 13 | +// n match { |
| 14 | +// case Zero => None |
| 15 | +// case s @ Succ(_) => Some(safeDiv(m, s)) |
| 16 | +// } |
| 17 | +// } |
| 18 | +// val two = Succ(Succ(Zero)) |
| 19 | +// val five = Succ(Succ(Succ(two))) |
| 20 | +// println(divOpt(five, two)) |
| 21 | +// println(divOpt(two, five)) |
| 22 | +// println(divOpt(two, Zero)) |
| 23 | +// } |
| 24 | +//} |
| 25 | + |
| 26 | +trait Peano { |
| 27 | + type Nat |
| 28 | + type Zero <: Nat |
| 29 | + type Succ <: Nat |
| 30 | + |
| 31 | + def safeDiv(m: Nat, n: Succ): (Nat, Nat) |
| 32 | + |
| 33 | + implicit def succDeco(succ: Succ): SuccAPI |
| 34 | + trait SuccAPI { |
| 35 | + def pred: Nat |
| 36 | + } |
| 37 | + |
| 38 | + val Zero: Zero |
| 39 | + |
| 40 | + val Succ: SuccExtractor |
| 41 | + trait SuccExtractor { |
| 42 | + def apply(nat: Nat): Succ |
| 43 | + def unapply(nat: Nat): SuccOpt { type UncheckedRefinedArgument <: nat.type } |
| 44 | + } |
| 45 | + trait SuccOpt { |
| 46 | + type UncheckedRefinedArgument <: Succ |
| 47 | + def isEmpty: Boolean |
| 48 | + def get: Nat |
| 49 | + } |
| 50 | +} |
| 51 | + |
| 52 | +object IntNums extends Peano { |
| 53 | + type Nat = Int |
| 54 | + type Zero = Int |
| 55 | + type Succ = Int |
| 56 | + |
| 57 | + def safeDiv(m: Nat, n: Succ): (Nat, Nat) = (m / n, m % n) |
| 58 | + |
| 59 | + val Zero: Zero = 0 |
| 60 | + |
| 61 | + object Succ extends SuccExtractor { |
| 62 | + def apply(nat: Nat): Succ = nat + 1 |
| 63 | + def unapply(nat: Nat) = new SuccOpt { |
| 64 | + type UncheckedRefinedArgument = nat.type |
| 65 | + def isEmpty: Boolean = nat == 0 |
| 66 | + def get: Int = nat - 1 |
| 67 | + } |
| 68 | + } |
| 69 | + |
| 70 | + def succDeco(succ: Succ): SuccAPI = new SuccAPI { |
| 71 | + def pred: Nat = succ - 1 |
| 72 | + } |
| 73 | +} |
| 74 | + |
| 75 | +object ClassNums extends Peano { |
| 76 | + trait NatTrait |
| 77 | + object ZeroObject extends NatTrait { |
| 78 | + override def toString: String = "ZeroObject" |
| 79 | + } |
| 80 | + case class SuccClass(predecessor: NatTrait) extends NatTrait with SuccOpt { |
| 81 | + type UncheckedRefinedArgument = this.type |
| 82 | + def isEmpty: Boolean = false |
| 83 | + def get: NatTrait = this |
| 84 | + } |
| 85 | + |
| 86 | + object SuccNoMatch extends SuccOpt { |
| 87 | + type UncheckedRefinedArgument = Nothing |
| 88 | + def isEmpty: Boolean = true |
| 89 | + def get: NatTrait = throw new NoSuchElementException |
| 90 | + } |
| 91 | + |
| 92 | + type Nat = NatTrait |
| 93 | + type Zero = ZeroObject.type |
| 94 | + type Succ = SuccClass |
| 95 | + |
| 96 | + def safeDiv(m: Nat, n: Succ): (Nat, Nat) = { |
| 97 | + def intValue(x: Nat, acc: Int): Int = x match { |
| 98 | + case nat: SuccClass => intValue(nat.predecessor, acc + 1) |
| 99 | + case _ => acc |
| 100 | + } |
| 101 | + def natValue(x: Int): Nat = |
| 102 | + if (x == 0) ZeroObject |
| 103 | + else new SuccClass(natValue(x - 1)) |
| 104 | + val i = intValue(m, 0) |
| 105 | + val j = intValue(n, 0) |
| 106 | + (natValue(i / j), natValue(i % j)) |
| 107 | + } |
| 108 | + |
| 109 | + val Zero: Zero = ZeroObject |
| 110 | + |
| 111 | + object Succ extends SuccExtractor { |
| 112 | + def apply(nat: Nat): Succ = new SuccClass(nat) |
| 113 | + def unapply(nat: Nat) = nat match { |
| 114 | + case nat: (SuccClass & nat.type) => nat |
| 115 | + case _ => SuccNoMatch |
| 116 | + } |
| 117 | + } |
| 118 | + |
| 119 | + def succDeco(succ: Succ): SuccAPI = new SuccAPI { |
| 120 | + def pred: Nat = succ.predecessor |
| 121 | + } |
| 122 | + |
| 123 | +} |
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