--- a/scala/ex.scala Tue Feb 26 17:38:37 2013 +0000
+++ b/scala/ex.scala Tue Feb 26 17:39:47 2013 +0000
@@ -20,18 +20,18 @@
// Abacus machine examples
def Copy(in: Int, out: Int, jump: Int) =
- Abacus(List(Dec(in, jump), Inc(out), Goto(0)))
+ Abacus(Dec(in, jump), Inc(out), Goto(0))
def Plus(m: Int, n: Int, tmp: Int, jump: Int) =
- Abacus(List(Dec(m, 4), Inc(n), Inc(tmp), Goto(0), Dec(tmp, jump), Inc(m), Goto(4)))
+ Abacus(Dec(m, 4), Inc(n), Inc(tmp), Goto(0), Dec(tmp, jump), Inc(m), Goto(4))
def Mult(in1: Int, in2: Int, out: Int, tmp: Int, jump: Int) =
- Abacus(List(Dec(in1, jump))) ++ Plus(in2, out, tmp, -1).shift(1, -1).adjust(-1, 0)
+ Abacus(Dec(in1, jump)) ++ Plus(in2, out, tmp, -1).shift(1, -1).adjust(-1, 0)
def Expo(in1: Int, in2: Int, out: Int, tmp1: Int, tmp2: Int, jump: Int) = {
- Abacus(List(Inc(out), Dec(in1, jump))) ++
+ Abacus(Inc(out), Dec(in1, jump)) ++
Mult(out, in2, tmp2, tmp1, -1).shift(2, -1).adjust(-1, 10) ++
- Copy(tmp2, out, -1).shift(10, -1). adjust(-1, 1)
+ Copy(tmp2, out, -1).shift(10, -1).adjust(-1, 1)
}
println("Copy 3: " + (Copy(0, 1, -1).run(Map(0 -> 3, 1 -> 0))))
@@ -46,76 +46,45 @@
println("Compiled Mult 3 * 5: " + toTM(Mult(0, 1, 2, 3, Int.MaxValue).p).run(Tape(3,5,0,0)))
println("Compiled Expo 3 ^ 4: " + toTM(Expo(0, 1, 2, 3, 4, 10000).p).run(Tape(3,4,0,0,0)))
-// Recursive Function examples
-def arity(f: Rec) = f match {
- case Z => 1
- case S => 1
- case Id(n, _) => n
- case Cn(n, _, _) => n
- case Pr(n, _, _) => n + 1
- case Mn(n, _) => n
-}
-
-val Add = Pr(1, Id(1, 0), Cn(3, S, List(Id(3, 2))))
-val Mult = Pr(1, Z, Cn(3, Add, List(Id(3, 0), Id(3, 2))))
-val Pred = Cn(1, Pr(1, Z, Id(3, 1)), List(Id(1, 0), Id(1, 0)))
-val Minus = Pr(1, Id(1, 0), Cn(3, Pred, List(Id(3, 2))))
-
-def Const(n: Int) : Rec = n match {
- case 0 => Z
- case n => Cn(1, S, List(Const(n - 1)))
-}
-
-val Sign = Cn(1, Minus, List(Const(1), Cn(1, Minus, List(Const(1), Id(1, 0)))))
-val Less = Cn(2, Sign, List(Cn(2, Minus, List(Id(2, 1), Id(2, 0)))))
-val Not = Cn(1, Minus, List(Const(1), Id(1, 0)))
-val Eq = Cn(2, Minus, List(Cn(2, Const(1), List(Id(2, 0))),
- Cn(2, Add, List(Cn(2, Minus, List(Id(2, 0), Id(2, 1))),
- Cn(2, Minus, List(Id(2, 1), Id(2, 0)))))))
-val Conj = Cn(2, Sign, List(Cn(2, Mult, List(Id(2, 0), Id(2, 1)))))
-val Disj = Cn(2, Sign, List(Cn(2, Add, List(Id(2, 0), Id(2, 1)))))
-
-def Nargs(n: Int, m: Int) : List[Rec] = m match {
- case 0 => Nil
- case m => Nargs(n, m - 1) ::: List(Id(n, m - 1))
-}
-
-def Sigma(f: Rec) = {
- val ar = arity(f)
- Pr(ar - 1, Cn(ar - 1, f, Nargs(ar - 1, ar - 1) :::
- List(Cn(ar - 1, Const(0), List(Id(ar - 1, 0))))),
- Cn(ar + 1, Add, List(Id(ar + 1, ar),
- Cn(ar + 1, f, Nargs(ar + 1, ar - 1) :::
- List(Cn(ar + 1, S, List(Id(ar + 1, ar - 1))))))))
-}
-
-println("Add 3 4: " + Add.eval(List(3, 4)))
-println("Mult 3 4: " + Mult.eval(List(3, 4)))
-println("Pred 9: " + Pred.eval(List(9)))
-println("Pred 0: " + Pred.eval(List(0)))
-println("Minus 6 2: " + Minus.eval(List(6, 2)))
-println("Minus 6 8: " + Minus.eval(List(6, 8)))
-println("Const 8: " + Const(8).eval(List(67)))
-println("Sign 8: " + Sign.eval(List(8)))
-println("Sign 0: " + Sign.eval(List(0)))
-println("Less 4 4: " + Less.eval(List(4, 4)))
-println("Less 4 6: " + Less.eval(List(4, 6)))
-println("Less 6 4: " + Less.eval(List(6, 4)))
-println("Not 0: " + Not.eval(List(0)))
-println("Not 6: " + Not.eval(List(6)))
-println("Eq 4 4: " + Eq.eval(List(4, 4)))
-println("Eq 4 6: " + Eq.eval(List(4, 6)))
-println("Eq 6 4: " + Eq.eval(List(6, 4)))
-println("Conj 0 6: " + Conj.eval(List(0, 6)))
-println("Conj 6 4: " + Conj.eval(List(6, 4)))
-println("Conj 0 0: " + Conj.eval(List(0, 0)))
-println("Disj 0 6: " + Disj.eval(List(0, 6)))
-println("Disj 6 4: " + Disj.eval(List(6, 4)))
-println("Disj 0 0: " + Disj.eval(List(0, 0)))
-println("Sigma: " + Sigma(Add).eval(List(2,3)))
+// Recursive function examples
+println("Add 3 4: " + Add.eval(3, 4))
+println("Mult 3 4: " + recs.Mult.eval(3, 4))
+println("Twice 4: " + Twice.eval(4))
+println("FourTm 4: " + Fourtimes.eval(4))
+println("Pred 9: " + Pred.eval(9))
+println("Pred 0: " + Pred.eval(0))
+println("Minus 6 2: " + Minus.eval(6, 2))
+println("Minus 6 8: " + Minus.eval(6, 8))
+println("Const 8: " + Const(8).eval(67))
+println("Power 2 3: " + Power.eval(2, 3))
+println("Sign 8: " + Sign.eval(8))
+println("Sign 0: " + Sign.eval(0))
+println("Less 4 4: " + Less.eval(4, 4))
+println("Less 4 6: " + Less.eval(4, 6))
+println("Less 6 4: " + Less.eval(6, 4))
+println("Not 0: " + Not.eval(0))
+println("Not 6: " + Not.eval(6))
+println("Eq 4 4: " + Eq.eval(4, 4))
+println("Eq 4 6: " + Eq.eval(4, 6))
+println("Eq 6 4: " + Eq.eval(6, 4))
+println("Conj 0 6: " + Conj.eval(0, 6))
+println("Conj 6 4: " + Conj.eval(6, 4))
+println("Conj 0 0: " + Conj.eval(0, 0))
+println("Disj 0 6: " + Disj.eval(0, 6))
+println("Disj 6 4: " + Disj.eval(6, 4))
+println("Disj 0 0: " + Disj.eval(0, 0))
+println("Sigma Add 2 3 -> 14: " + Sigma(Add).eval(2,3))
+println("Accum Add 2 3 -> 120: " + Accum(Add).eval(2,3))
+println("Accum Mult 2 3 -> 0: " + Accum(recs.Mult).eval(2,3))
+println("Fact 5: " + Fact.eval(5))
+println("Prime 0..15: " + (0 to 15).map(n => (n, Prime.eval(n))))
+println("NextPrime 3: " + NextPrime.eval(3))
+println("NthPrime 1: " + NthPrime.eval(1))
+println("Listsum [2, 3, 4 , 5, 6]: " + Listsum(5, 4).eval(2, 3, 4, 5, 6))
+// Ask Jian
+println("Strt: " + Strt(2).eval(2, 3))
-
-val ABCZero = Abacus(List(Goto(1)))
-val ABCSucc = Plus(0, 1, 2, 7) ++ Abacus(List(Inc(1))).shift(Plus(0, 1, 2, 7).p.length, -1)
+val ABCZero = Abacus(Goto(1))
+val ABCSucc = Plus(0, 1, 2, 7) ++ Abacus(Inc(1)).shift(Plus(0, 1, 2, 7).p.length, -1)
def ABCId(n: Int, m: Int) = Plus(m, n, n + 1, 7)