Prologの技芸 4.2節の練習問題

(1)

挿入ソート
sort([3,1,2],Ys)
    sort([1,2],Zs1)
        sort([2],Zs2)
            sort([],Zs3)        {Zs3=[]}
                true
            insert(2,[],Zs2)    {Zs2=[2]}
                true
        insert(1,[2],Zs1)       {Zs1=[2|Zs4]}
            1>2
                fail
        insert(1,[2],Zs1)       {Zs1=[1,2|[]]}
            1=<2
                true
    insert(3,[1,2],Ys)          {Ys=[1|Ys1]}
        3>1
            true
        insert(3,[2],Ys1)       {Ys1=[2|Ys2]}
            3>2
                true
            insert(3,[],Ys2)    {Ys2=[3]}
                true

クイックソート
sort([3,1,2],Ys)
    partition([1,2],3,Ls,Bs)        {Ls=[1|Ls1]}
        1 =< 3
            true
        partition([2],3,Ls1,Bs)     {Ls1=[2|Ls2]}
            2 =< 3
                true
            partition([],3,Ls2,Bs)  {Ls2=[], Bs=[]}
                true
    sort([1,2],Ls3)
        partition([2],1,Ls4,Bs1)    {Ls4=[2|Ls5]}
            2 =< 1
                fail
        partition([2],1,Ls4,Bs1)    {Bs1=[2|Bs2]}
            2 > 1
                true
            partition([],1,Ls4,Bs2) {Ls4=[], Bs2=[]}
                true
        sort([],Ls5)                {Ls5=[]}
            true
        sort([2],Bs3)
            partition([],2,Ls6,Bs4) {Ls6=[], Bs4=[]}
                true
            sort([],Ls7)            {Ls7=[]}
                true
            sort([],Bs5)            {Bs5=[]}
                true
            append([],[2],Bs3)      {Bs3=[2]}
                true
        append([],[1,2],Ls3)        {Ls3=[1,2]}
            true
    sort([],Bs6)                    {Bs6=[]}
        true
    append([1,2],[3],Ys)            {Ys=[1,2,3]}
        true

(2)

derivative(3*sin(x)-4*cos(x),x,D)   {D=0}
    constant(3*sin(x)-4*cos(x))
        integer(3*sin(x)-4*cos(x))
            fail
derivative(3*sin(x)-4*cos(x),x,D)   {D=DF-DG}
    derivative(3*sin(x),x,DF)       {DF=0}
        constant(3*sin(x))
            integer(3*sin(x))
                fail
    derivative(3*sin(x),x,DF)       {DF=3*DG1+DF1*sin(x)}
        derivative(3,x,DF1)         {DF1=0}
            constant(3)
                integer(3)
                    true
        derivative(sin(x),x,DG1)    {DG1=0}
            constant(sin(x))
                integer(sin(x))
                    fail
        derivative(sin(x),x,DG1)    {DG1=cos(x)}
            true
    derivative(4*cos(x),x,DG)       {DG=0}
        constant(4*cos(x))
            integer(4*cos(x))
                fail
    derivative(4*cos(x),x,DG)       {DG=4*DG1+DF1*cos(x)}
        derivative(4,x,DF1)         {DF1=0}
            constant(4)
                integer(4)
                    true
        derivative(cos(x),x,DG1)    {DG1=0}
            constant(cos(x))
                integer(cos(x))
                    fail
        derivative(cos(x),x,DG1)    {DG1=-sin(x)}
            true