scala/ex.scala
author Christian Urban <christian dot urban at kcl dot ac dot uk>
Tue, 26 Feb 2013 23:44:57 +0000
changeset 201 09befdf4fc99
parent 200 8dde2e46c69d
child 205 c7975ab7c52e
permissions -rw-r--r--
syntactic convenience for recursive functions
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import lib._
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import turing._
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import abacus._
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import recs._
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import comp1._
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//import comp2._
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// Turing machine examples
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val TMCopy = TM((WBk, 5), (R, 2), (R, 3), (R, 2), (WOc, 3), 
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                (L, 4), (L, 4), (L, 5), (R, 11), (R, 6), 
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                (R, 7), (WBk, 6), (R, 7), (R, 8), (WOc, 9), 
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                (R, 8), (L, 10), (L, 9), (L, 10), (L, 5), 
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                (L, 0), (R, 12), (WOc, 13), (L, 14), (R, 12), 
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                (R, 12), (L, 15), (WBk, 14), (R, 0), (L, 15))
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println("TMCopy:    " + (TMCopy.run(Tape(3))))
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println("TMfindnth: " + (TMFindnth(3).run(Tape(1,2,3,4,5))))
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println("TMMopup:   " + (TMMopup(3).run(Tape(1,2,3,4,5))))
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// Abacus machine examples
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def Copy(in: Int, out: Int, jump: Int) = 
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  Abacus(Dec(in, jump), Inc(out), Goto(0)) 
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def Plus(m: Int, n: Int, tmp: Int, jump: Int) =
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  Abacus(Dec(m, 4), Inc(n), Inc(tmp), Goto(0), Dec(tmp, jump), Inc(m), Goto(4))
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def Mult(in1: Int, in2: Int, out: Int, tmp: Int, jump: Int) = 
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  Abacus(Dec(in1, jump)) ++ Plus(in2, out, tmp, -1).shift(1, -1).adjust(-1, 0)
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def Expo(in1: Int, in2: Int, out: Int, tmp1: Int, tmp2: Int, jump: Int) = {
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  Abacus(Inc(out), Dec(in1, jump)) ++ 
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  Mult(out, in2, tmp2, tmp1, -1).shift(2, -1).adjust(-1, 10) ++
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  Copy(tmp2, out, -1).shift(10, -1).adjust(-1, 1)
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}
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println("Copy 3:     " + (Copy(0, 1, -1).run(Map(0 -> 3, 1 -> 0))))
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println("Plus 3 + 4: " + (Plus(0, 1, 2, -1).run(Map(0 -> 3, 1 -> 4, 2 -> 0))))
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println("Mult 3 * 5: " + (Mult(0, 1, 2, 3, -1).run(Map(0 -> 3, 1 -> 5, 2 -> 0, 3 -> 0))))
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println("Expo 3 ^ 4: " + (Expo(0, 1, 2, 3, 4, -1).run(Map(0 -> 4, 1 -> 3, 2 -> 0, 3 -> 0, 4 -> 0))))
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// Abacus-to-TM translation examples
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println("Compiled Copy 3:     " + toTM(Copy(0, 1, Int.MaxValue).p).run(Tape(3,0,0)))
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println("Compiled Plus 3 + 4: " + toTM(Plus(0, 1, 2, Int.MaxValue).p).run(Tape(3,4,0,0)))
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println("Compiled Mult 3 * 5: " + toTM(Mult(0, 1, 2, 3, Int.MaxValue).p).run(Tape(3,5,0,0)))
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println("Compiled Expo 3 ^ 4: " + toTM(Expo(0, 1, 2, 3, 4, 10000).p).run(Tape(3,4,0,0,0)))
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// Recursive function examples 
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println("Add 3 4:   " + Add.eval(3, 4))
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println("Mult 3 4:  " + recs.Mult.eval(3, 4))
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println("Twice 4:   " + Twice.eval(4))
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println("FourTm 4:  " + Fourtimes.eval(4))
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println("Pred 9:    " + Pred.eval(9))
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println("Pred 0:    " + Pred.eval(0))
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println("Minus 6 2: " + Minus.eval(6, 2))
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println("Minus 6 8: " + Minus.eval(6, 8))
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println("Const 8:   " + Const(8).eval(67))
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println("Power 2 3: " + Power.eval(2, 3))
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println("Sign 8:    " + Sign.eval(8))
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println("Sign 0:    " + Sign.eval(0))
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println("Less 4 4:  " + Less.eval(4, 4))
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println("Less 4 6:  " + Less.eval(4, 6))
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println("Less 6 4:  " + Less.eval(6, 4))
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println("Not 0:     " + Not.eval(0))
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println("Not 6:     " + Not.eval(6))
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println("Eq 4 4:    " + Eq.eval(4, 4))
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println("Eq 4 6:    " + Eq.eval(4, 6))
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println("Eq 6 4:    " + Eq.eval(6, 4))
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println("Conj 0 6:  " + Conj.eval(0, 6))
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println("Conj 6 4:  " + Conj.eval(6, 4))
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println("Conj 0 0:  " + Conj.eval(0, 0))
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println("Disj 0 6:  " + Disj.eval(0, 6))
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println("Disj 6 4:  " + Disj.eval(6, 4))
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println("Disj 0 0:  " + Disj.eval(0, 0))
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println("Sigma Add 2 3 -> 14:  " + Sigma(Add).eval(2,3))
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println("Accum Add 2 3 -> 120: " + Accum(Add).eval(2,3))
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println("Accum Mult 2 3 -> 0:  " + Accum(recs.Mult).eval(2,3))
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println("Fact 5:  " + Fact.eval(5))
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println("Prime 0..15: " + (0 to 15).map(n => (n, Prime.eval(n))))
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println("NextPrime 3: " + NextPrime.eval(3))
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println("NthPrime 1:  " + NthPrime.eval(1))
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println("Listsum [2, 3, 4 , 5, 6]: " + Listsum(5, 4).eval(2, 3, 4, 5, 6))
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// Ask Jian
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println("Strt:  " + Strt(2).eval(2, 3))
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val ABCZero = Abacus(Goto(1))
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val ABCSucc = Plus(0, 1, 2, 7) ++ Abacus(Inc(1)).shift(Plus(0, 1, 2, 7).p.length, -1)
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def ABCId(n: Int, m: Int) = Plus(m, n, n + 1, 7)