Following the recent exchanges, I would like to bring some clarifications
on pattern matching and lists in Faust.
Strictly speaking, there are no lists in Faust. For example the expression
`()` or `NIL` in Lisp, which indicates an empty list, does not exist in
Faust. Similarly, the distinction in Lisp between the number `3` and the
list with only one element `(3)` does not exist in Faust.
However, list operations can be simulated (in part) using the parallel
binary composition operation `,` and pattern matching. The parallel
composition operation is right-associative. This means that the expression
`(1,2,3,4)` is just a simplified form of the fully parenthesized expression
`(1,(2,(3,4)))`. The same is true for `(1,2,(3,4))` which is also a
simplified form of the same fully parenthesized expression `(1,(2,(3,4)))`.
You can think of pattern-matching as always being done on fully
parenthesized expressions. Therefore no Faust function can ever distinguish
`(1,2,3,4)` from `(1,2,(3,4))`, because they represent the same fully
parenthesized expression `(1,(2,(3,4)))`.
This is why `ba.count( ((1,2), (3,4), (5,6)) )` is not 3 but 4, and also
why `ba.count( ( (1,2), ((3,4),5,6) ) )` is not 2 but 4.
# Explanation:
In both cases the fully parenthesized expression is
`((1,2),((3,4),(5,6)))`. The definition of ba.count being:
count( (x,y) ) = 1 + count(y); // rule R1
count( x ) = 1; // rule R2
we have:
ba.count( ((1,2),((3,4),(5,6))) )
-R1-> 1 + ba.count( ((3,4),(5,6)) )
-R1-> 1 + 1 + ba.count( (5,6) )
-R1-> 1 + 1 + 1 + ba.count( 6 )
-R2-> 1 + 1 + 1 + 1
Please note that pattern matching is not limited to parallel composition,
the other composition operators (<: : :> ~) can be used too.
Yann
*Yann Orlarey*
Directeur scientifique/Scientific director
orla...@grame.fr <x...@grame.fr> T : +33 (0) 4 72 07 37 00
GRAME - Centre national de création musicale
11 cours de Verdun Gensoul | 69002 Lyon
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