and 
belong to this class). From our point of view, the following informal
remarks could help to characterize this class.
In spite of all these successive refinements and generalizations, one class of
programs remains undeforested (e.g., and belong to this class). From our point of view, the following informal
remarks could help to characterize this class.
Functional methods always use functors to drive transformations and computations, while symbolic composition and attribute grammars do not. The example of rev is meaningful:
Let 
be the functor that drives the recursion of this
function. does not follow the construction of the resulting list of
reverse. But following the recursive calls of rev, it hides the
construction of the result. More precisely, the constructor 
is hidden in the second parameter of the 
call. Because of this, no
further deforestation can reach it.
In attribute grammars, symbolic composition catches each constructor of the
result, directly from the specification. It does not need to do this using any
particular abstract intermediate notion, such as functors. The reason is that
all the result constructions, even if they do not follow the functor of the
recursion, remain visible in an attribute grammar specification. We believe
this is why symbolic composition is able to perform more deforestation. See for
example the section 3.2 where the previous is
deforested. To deforest such programs, functional approaches should use a
functor that describes completely the result construction scheme, particularly
taking into account accumulative parameters in which constructions or
transmissions of -- parts of -- the result occur.
To conclude, one of the important contribution of this paper is to show that symbolic composition is actually a general deforestation method. Thanks to FP-to-AG, symbolic composition is no longer restricted to attribute grammars.