X-Git-Url: https://scm.cri.ensmp.fr/git/Faustine.git/blobdiff_plain/1059e1cc0c2ecfa237406949aa26155b6a5b9154..66f23d4fabf89ad09adbd4dfc15ac6b5b2b7da83:/interpreter/preprocessor/faust-0.9.47mr3/examples/rewriting/fold.dsp

diff --git a/interpreter/preprocessor/faust-0.9.47mr3/examples/rewriting/fold.dsp b/interpreter/preprocessor/faust-0.9.47mr3/examples/rewriting/fold.dsp
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+
+// How to emulate Faust's seq, par, sum.
+// x(k) is assumed to yield the kth signal.
+
+xseq(1,x)	= x(0);
+xseq(n,x)	= xseq(n-1,x) : x(n-1);
+
+xpar(1,x)	= x(0);
+xpar(n,x)	= xpar(n-1,x) , x(n-1);
+
+xsum(1,x)	= x(0);
+xsum(n,x)	= xsum(n-1,x) + x(n-1);
+
+// These are all very similar. Abstracting
+// on the binary "accumulator" function, we
+// get the familiar fold(-left) function:
+
+fold(1,f,x)	= x(0);
+fold(n,f,x)	= f(fold(n-1,f,x),x(n-1));
+
+// Now seq, par, sum can be defined as:
+
+fseq(n)		= fold(n,\(x,y).(x:y));
+fpar(n)		= fold(n,\(x,y).(x,y));
+fsum(n)		= fold(n,+);
+fprod(n)	= fold(n,*);
+
+// Often it is more convenient to specify
+// parameters as a Faust tuple. We can match
+// against the (xs,x) pattern to decompose
+// these.
+
+vfold(f,(xs,x))	= f(vfold(f,xs),x);
+vfold(f,x)	= x;
+
+// Tuple version of seq, par, sum:
+
+vseq		= vfold(\(x,y).(x:y));
+vpar		= vfold(\(x,y).(x,y));
+vsum		= vfold(+);
+vprod		= vfold(*);
+
+// Examples:
+
+import("music.lib");
+f0		= 440;
+a(0)		= 1;
+a(1)		= 0.5;
+a(2)		= 0.3;
+h(i)		= a(i)*osc((i+1)*f0);
+
+// sums
+//process		= xsum(3,h);
+//process	= fsum(3,h);
+//process	= vsum((h(0),h(1),h(2)));
+
+reverse (x:y)	= reverse(y):reverse(x);
+reverse(x)	= x;
+
+// sequences from tuples (parallel -> serial)
+process	= reverse(vseq((sin,cos,tan)));