\DOC SCANR_CONV
\TYPE {SCANR_CONV : conv -> conv}
\SYNOPSIS
Computes by inference the result of applying a function to the elements
of a
list.
\KEYWORDS
conversion, list.
\DESCRIBE
{SCANR_CONV} takes a conversion {conv} and a term {tm} in the following
form:
{
SCANR f e0 [xn;...;x1]
}
It returns the theorem
{
|- SCANR f e0 [xn;...;x1] = [en; ...;e1;e0]
}
where {ei} is the result of applying the function {f} to
the result of the previous iteration and the current element, i.e.,
{ei = f e(i-1) xi}. The iteration starts from the right-hand side (the
tail) of the list.
The user supplied conversion {conv} is used to derive a theorem
{
|- f e(i-1) xi = ei
}
which is used in the next iteration.
\FAILURE
{SCANR_CONV conv tm} fails if {tm} is not of the form described above,
or failure occurs when evaluating {conv (--`f e(i-1) xi`--)}.
\EXAMPLE
To sum the elements of a list and save the result at each step, one can
use
{SCANR_CONV} with {ADD_CONV} from the library {num_lib}.
{
- load_library_in_place num_lib;
- SCANR_CONV Num_lib.ADD_CONV (--`SCANR $+ 0 [1;2;3]`--);
|- SCANR $+ 0[1;2;3] = [6;5;3;0]
}
In general, if the function {f} is an explicit lambda abstraction
{(\x x'. t[x,x'])}, the conversion should be in the form
{
((RATOR_CONV BETA_CONV) THENC BETA_CONV THENC conv'))
}
where {conv'} applied to {t[x,x']} returns the theorem
{
|-t[x,x'] = e''.
}
\SEEALSO
SCANL_CONV, FOLDL_CONV, FOLDR_CONV, list_FOLD_CONV.
\ENDDOC