1 import lib._ |
1 import lib._ |
2 import turing._ |
2 import turing._ |
3 import abacus._ |
3 import abacus._ |
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4 import recs._ |
4 import comp1._ |
5 import comp1._ |
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6 //import comp2._ |
5 |
7 |
6 // Turing machine examples |
8 // Turing machine examples |
7 val TMCopy = TM((WBk, 5), (R, 2), (R, 3), (R, 2), (WOc, 3), |
9 val TMCopy = TM((WBk, 5), (R, 2), (R, 3), (R, 2), (WOc, 3), |
8 (L, 4), (L, 4), (L, 5), (R, 11), (R, 6), |
10 (L, 4), (L, 4), (L, 5), (R, 11), (R, 6), |
9 (R, 7), (WBk, 6), (R, 7), (R, 8), (WOc, 9), |
11 (R, 7), (WBk, 6), (R, 7), (R, 8), (WOc, 9), |
19 // Abacus machine examples |
21 // Abacus machine examples |
20 def Copy(in: Int, out: Int, jump: Int) = |
22 def Copy(in: Int, out: Int, jump: Int) = |
21 Abacus(List(Dec(in, jump), Inc(out), Goto(0))) |
23 Abacus(List(Dec(in, jump), Inc(out), Goto(0))) |
22 |
24 |
23 def Plus(m: Int, n: Int, tmp: Int, jump: Int) = |
25 def Plus(m: Int, n: Int, tmp: Int, jump: Int) = |
24 Abacus(List(Dec(m, 4), Inc(n), Inc(tmp), Goto(0), Dec(tmp, jump), Inc(m), Goto(4))) |
26 Abacus(List(Dec(m, 4), Inc(n), Inc(tmp), Goto(0), Dec(tmp, jump), Inc(m), Goto(4))) |
25 |
27 |
26 def Mult(in1: Int, in2: Int, out: Int, tmp: Int, jump: Int) = |
28 def Mult(in1: Int, in2: Int, out: Int, tmp: Int, jump: Int) = |
27 Abacus(List(Dec(in1, jump))) ++ Plus(in2, out, tmp, -1).shift(1, -1).adjust(-1, 0) |
29 Abacus(List(Dec(in1, jump))) ++ Plus(in2, out, tmp, -1).shift(1, -1).adjust(-1, 0) |
28 |
30 |
29 def Expo(in1: Int, in2: Int, out: Int, tmp1: Int, tmp2: Int, jump: Int) = { |
31 def Expo(in1: Int, in2: Int, out: Int, tmp1: Int, tmp2: Int, jump: Int) = { |
42 println("Compiled Copy 3: " + toTM(Copy(0, 1, Int.MaxValue).p).run(Tape(3,0,0))) |
44 println("Compiled Copy 3: " + toTM(Copy(0, 1, Int.MaxValue).p).run(Tape(3,0,0))) |
43 println("Compiled Plus 3 + 4: " + toTM(Plus(0, 1, 2, Int.MaxValue).p).run(Tape(3,4,0,0))) |
45 println("Compiled Plus 3 + 4: " + toTM(Plus(0, 1, 2, Int.MaxValue).p).run(Tape(3,4,0,0))) |
44 println("Compiled Mult 3 * 5: " + toTM(Mult(0, 1, 2, 3, Int.MaxValue).p).run(Tape(3,5,0,0))) |
46 println("Compiled Mult 3 * 5: " + toTM(Mult(0, 1, 2, 3, Int.MaxValue).p).run(Tape(3,5,0,0))) |
45 println("Compiled Expo 3 ^ 4: " + toTM(Expo(0, 1, 2, 3, 4, 10000).p).run(Tape(3,4,0,0,0))) |
47 println("Compiled Expo 3 ^ 4: " + toTM(Expo(0, 1, 2, 3, 4, 10000).p).run(Tape(3,4,0,0,0))) |
46 |
48 |
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49 // Recursive Function examples |
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50 def arity(f: Rec) = f match { |
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51 case Z => 1 |
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52 case S => 1 |
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53 case Id(n, _) => n |
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54 case Cn(n, _, _) => n |
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55 case Pr(n, _, _) => n + 1 |
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56 case Mn(n, _) => n |
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57 } |
47 |
58 |
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59 val Add = Pr(1, Id(1, 0), Cn(3, S, List(Id(3, 2)))) |
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60 val Mult = Pr(1, Z, Cn(3, Add, List(Id(3, 0), Id(3, 2)))) |
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61 val Pred = Cn(1, Pr(1, Z, Id(3, 1)), List(Id(1, 0), Id(1, 0))) |
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62 val Minus = Pr(1, Id(1, 0), Cn(3, Pred, List(Id(3, 2)))) |
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63 |
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64 def Const(n: Int) : Rec = n match { |
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65 case 0 => Z |
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66 case n => Cn(1, S, List(Const(n - 1))) |
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67 } |
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68 |
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69 val Sign = Cn(1, Minus, List(Const(1), Cn(1, Minus, List(Const(1), Id(1, 0))))) |
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70 val Less = Cn(2, Sign, List(Cn(2, Minus, List(Id(2, 1), Id(2, 0))))) |
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71 val Not = Cn(1, Minus, List(Const(1), Id(1, 0))) |
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72 val Eq = Cn(2, Minus, List(Cn(2, Const(1), List(Id(2, 0))), |
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73 Cn(2, Add, List(Cn(2, Minus, List(Id(2, 0), Id(2, 1))), |
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74 Cn(2, Minus, List(Id(2, 1), Id(2, 0))))))) |
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75 val Conj = Cn(2, Sign, List(Cn(2, Mult, List(Id(2, 0), Id(2, 1))))) |
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76 val Disj = Cn(2, Sign, List(Cn(2, Add, List(Id(2, 0), Id(2, 1))))) |
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77 |
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78 def Nargs(n: Int, m: Int) : List[Rec] = m match { |
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79 case 0 => Nil |
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80 case m => Nargs(n, m - 1) ::: List(Id(n, m - 1)) |
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81 } |
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82 |
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83 def Sigma(f: Rec) = { |
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84 val ar = arity(f) |
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85 Pr(ar - 1, Cn(ar - 1, f, Nargs(ar - 1, ar - 1) ::: |
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86 List(Cn(ar - 1, Const(0), List(Id(ar - 1, 0))))), |
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87 Cn(ar + 1, Add, List(Id(ar + 1, ar), |
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88 Cn(ar + 1, f, Nargs(ar + 1, ar - 1) ::: |
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89 List(Cn(ar + 1, S, List(Id(ar + 1, ar - 1)))))))) |
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90 } |
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91 |
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92 println("Add 3 4: " + Add.eval(List(3, 4))) |
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93 println("Mult 3 4: " + Mult.eval(List(3, 4))) |
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94 println("Pred 9: " + Pred.eval(List(9))) |
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95 println("Pred 0: " + Pred.eval(List(0))) |
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96 println("Minus 6 2: " + Minus.eval(List(6, 2))) |
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97 println("Minus 6 8: " + Minus.eval(List(6, 8))) |
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98 println("Const 8: " + Const(8).eval(List(67))) |
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99 println("Sign 8: " + Sign.eval(List(8))) |
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100 println("Sign 0: " + Sign.eval(List(0))) |
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101 println("Less 4 4: " + Less.eval(List(4, 4))) |
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102 println("Less 4 6: " + Less.eval(List(4, 6))) |
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103 println("Less 6 4: " + Less.eval(List(6, 4))) |
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104 println("Not 0: " + Not.eval(List(0))) |
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105 println("Not 6: " + Not.eval(List(6))) |
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106 println("Eq 4 4: " + Eq.eval(List(4, 4))) |
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107 println("Eq 4 6: " + Eq.eval(List(4, 6))) |
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108 println("Eq 6 4: " + Eq.eval(List(6, 4))) |
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109 println("Conj 0 6: " + Conj.eval(List(0, 6))) |
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110 println("Conj 6 4: " + Conj.eval(List(6, 4))) |
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111 println("Conj 0 0: " + Conj.eval(List(0, 0))) |
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112 println("Disj 0 6: " + Disj.eval(List(0, 6))) |
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113 println("Disj 6 4: " + Disj.eval(List(6, 4))) |
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114 println("Disj 0 0: " + Disj.eval(List(0, 0))) |
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115 //println("Sigma: " + Sigma(S).eval(List(0,1,2))) |
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116 //println("Sigma: " + Sigma(S).eval(List(0,1,2,3,4,5))) |
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117 |
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118 |
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119 val ABCZero = Abacus(List(Goto(1))) |
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120 val ABCSucc = Plus(0, 1, 2, 7) ++ Abacus(List(Inc(1))).shift(Plus(0, 1, 2, 7).p.length, -1) |
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121 def ABCId(n: Int, m: Int) = Plus(m, n, n + 1, 7) |