\DOC MAP2_CONV
\TYPE {MAP2_CONV : conv -> conv}
\SYNOPSIS
Compute the result of mapping a binary function down two lists.
\KEYWORDS
conversion, list.
\DESCRIBE
The function {MAP2_CONV} is a conversion for computing the result
of mapping a binary function {f:ty1->ty2->ty3} down two lists
{--`[l11;...;l1n]`--} whose elements are of type {ty1} and
{--`[l21;...;l2n]`--} whose elements are of type {ty2}. The lengths of
the two lists must be identical. The first
argument to {MAP2_CONV} is expected to be a conversion
that computes the result of applying the function {f} to a pair of
corresponding elements of these lists. When applied to a term
{--`f l1i l2i`--}, this conversion should return a theorem of the form
{|- (f l1i l2i) = ri}, where {ri} is the result of applying the function
{f} to the elements {l1i} and {l2i}.
Given an appropriate {conv}, the conversion {MAP2_CONV conv} takes a
term of the form {--`MAP2 f [l11;...;dl2tn] [l21;...;l2n]`--} and returns
the theorem
{
|- MAP2 f [l11;...;l1n] [l21;...;l2n] = [r1;...;rn]
}
where {conv (--`f l1i l2i`--)} returns {|- (f l1i l2i) = ri} for
{i} from {1} to {n}.
\EXAMPLE
The following is a very simple example in which the corresponding
elements from the two lists are summed to form the resulting list:
{
- load_library_in_place num_lib;
- MAP2_CONV Num_lib.ADD_CONV (--`MAP2 $+ [1;2;3] [1;2;3]`--);
|- MAP2 $+ [1;2;3] [1;2;3] = [2;4;6]
}
\FAILURE
{MAP2_CONV conv} fails if applied to a term not of the form
described above. An application of {MAP2_CONV conv} to a term
{--`MAP2 f [l11;...;l1n] [l21;...;l2n]`--} fails unless for all {i} where
{1<=i<=n}
evaluating {conv (--`f l1i l2i`--)} returns {|- (f l1i l2i) = ri} for
some {ri}.
\SEEALSO
MAP_CONV
\ENDDOC