interpretor/faust-0.9.47mr3/examples/rewriting/fold.dsp

   1
   2 // How to emulate Faust's seq, par, sum.
   3 // x(k) is assumed to yield the kth signal.
   4
   5 xseq(1,x)       = x(0);
   6 xseq(n,x)       = xseq(n-1,x) : x(n-1);
   7
   8 xpar(1,x)       = x(0);
   9 xpar(n,x)       = xpar(n-1,x) , x(n-1);
  10
  11 xsum(1,x)       = x(0);
  12 xsum(n,x)       = xsum(n-1,x) + x(n-1);
  13
  14 // These are all very similar. Abstracting
  15 // on the binary "accumulator" function, we
  16 // get the familiar fold(-left) function:
  17
  18 fold(1,f,x)     = x(0);
  19 fold(n,f,x)     = f(fold(n-1,f,x),x(n-1));
  20
  21 // Now seq, par, sum can be defined as:
  22
  23 fseq(n)         = fold(n,\(x,y).(x:y));
  24 fpar(n)         = fold(n,\(x,y).(x,y));
  25 fsum(n)         = fold(n,+);
  26 fprod(n)        = fold(n,*);
  27
  28 // Often it is more convenient to specify
  29 // parameters as a Faust tuple. We can match
  30 // against the (xs,x) pattern to decompose
  31 // these.
  32
  33 vfold(f,(xs,x)) = f(vfold(f,xs),x);
  34 vfold(f,x)      = x;
  35
  36 // Tuple version of seq, par, sum:
  37
  38 vseq            = vfold(\(x,y).(x:y));
  39 vpar            = vfold(\(x,y).(x,y));
  40 vsum            = vfold(+);
  41 vprod           = vfold(*);
  42
  43 // Examples:
  44
  45 import("music.lib");
  46 f0              = 440;
  47 a(0)            = 1;
  48 a(1)            = 0.5;
  49 a(2)            = 0.3;
  50 h(i)            = a(i)*osc((i+1)*f0);
  51
  52 // sums
  53 //process               = xsum(3,h);
  54 //process       = fsum(3,h);
  55 //process       = vsum((h(0),h(1),h(2)));
  56
  57 reverse (x:y)   = reverse(y):reverse(x);
  58 reverse(x)      = x;
  59
  60 // sequences from tuples (parallel -> serial)
  61 process = reverse(vseq((sin,cos,tan)));