\DOC FOLDR_CONV
\TYPE {FOLDR_CONV : conv -> conv}
\SYNOPSIS
Computes by inference the result of applying a function to the elements
of a
list.
\KEYWORDS
conversion, list.
\DESCRIBE
{FOLDR_CONV} takes a conversion {conv} and a term {tm} in the following
form:
{
FOLDR f e [x0;...xn]
}
It returns the theorem
{
|- FOLDR f e [x0;...xn] = tm'
}
where {tm'} is the result of applying the function {f} iteratively to
the successive elements of the list and the result of the previous
application starting from the tail end of the list. During each
iteration, an expression {f xi ei} is evaluated. The user supplied
conversion {conv} is used to derive a theorem
{
|- f xi ei = e(i+1)
}
which is used in the next iteration.
\FAILURE
{FOLDR_CONV conv tm} fails if {tm} is not of the form described above.
\EXAMPLE
To sum the elements of a list, one can use
{FOLDR_CONV} with {ADD_CONV} from the library {num_lib}.
{
- load_library_in_place num_lib;
- FOLDR_CONV Num_lib.ADD_CONV (--`FOLDR $+ 0 [0;1;2;3]`--);
|- FOLDR $+ 0[0;1;2;3] = 6
}
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
FOLDL_CONV, list_FOLD_CONV.
\ENDDOC