\DOC list_FOLD_CONV
\TYPE {list_FOLD_CONV : thm -> conv -> conv}
\SYNOPSIS
Computes by inference the result of applying a function to the elements
of a list.
\KEYWORDS
conversion, list.
\DESCRIBE
Evaluating {list_FOLD_CONV fthm conv tm} returns a theorem
{
|- CONST x0' ... xi' ... xn' = tm'
}
The first argument {fthm} should be a theorem of the form
{
|- !x0 ... xi ... xn. CONST x0 ... xi ... xn = FOLD[LR] f e xi
}
where {FOLD[LR]} means either {FOLDL} or {FOLDR}. The last
argument {tm} is a term of the following form:
{
CONST x0' ... xi' ... xn'
}
where {xi'} is a concrete list. {list_FOLD_CONV} first
instantiates the input theorem using {tm}. It then calls either
{FOLDL_CONV} or {FOLDR_CONV} with the user supplied conversion {conv}
on the right-hand side.
\FAILURE
{list_FOLD_CONV fthm conv tm} fails if {fthm} or {tm} is not of the
form described above, or if they do not agree, or the call to
{FOLDL_CONV} OR {FOLDR_CONV} fails.
\USES
This function is used to implement conversions for logical constants
which can be expressed in terms of the fold operators. For example,
the constant {SUM} can be expressed in terms of {FOLDR} as in the
following theorem:
{
|- !l. SUM l = FOLDR $+ 0 l
}
The conversion for {SUM}, {SUM_CONV} can be implemented as
{
load_library_in_place num_lib;
val SUM_CONV =
list_FOLD_CONV (theorem "list" "SUM_FOLDR") Num_lib.ADD_CONV;
}
Then, evaluating {SUM_CONV (--`SUM [0;1;2;3]`--)} will return
the following theorem:
{
|- SUM [0;1;2;3] = 6
}
\SEEALSO
FOLDL_CONV, FOLDR_CONV.
\ENDDOC