We have pushed on the master branch an experimental extension to Faust: the
`letrec{...}` construction. It is somehow similar to `with{...}`, but for
_difference equations_ instead of regular definitions. It allows to easily
express groups of mutually recursive signals, for example `x(t)` such that:
x(t) = y(t-1)+10;
y(t) = x(t-1)-1;
as:
x letrec { 'x = y+10;
'y = x-1; }
Please remark the special notation `'x=y+10` instead of `x=y'+10`. Here
`'x` represents the _next value_ of `x` defined according of the _current
value_ of `y`. It makes syntactically impossible to write non-sensical
equations like `x=x+1`.
Here is a more involved example. Let say we want to define an envelop
generator with an attack time, a release time and a gate signal. A possible
definition is the following:
ar(a,r,g) = v letrec {
'n = (n+1) * (g<=g');
'v = max(0, v + (n<a)/a - (n>=a)/r) * (g<=g');
};
With the following semantics for `n(t)` and `v(t)`:
n(t) = (n(t-1)+1) * (g(t) <= g(t-1))
v(t) = max(0, v(t-1)+(n(t-1)<a(t))/a(t)-(n(t-1)>=a(t))/r(t) )
* (g(t)<=g(t-1))
Tests and comments are welcome.
Cheers
Yann
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