----------------------------------------------------------------------
SCANL_CONV                                                   (listLib)
----------------------------------------------------------------------
SCANL_CONV : conv -> conv

SYNOPSIS
Computes by inference the result of applying a function to the elements of a list.

KEYWORDS
conversion, list.

DESCRIBE
{SCANL_CONV} takes a conversion {conv} and a term {tm} in the following form:

   SCANL f e0 [x1;...xn]

It returns the theorem

   |- SCANL f e0 [x1;...xn] = [e0; e1; ...;en]

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 left-hand side (the
head) 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
{SCANL_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
{SCANL_CONV} with {ADD_CONV} from the library {num_lib}.

   - load_library_in_place num_lib;
   - SCANL_CONV Num_lib.ADD_CONV “SCANL $+ 0 [1;2;3]”;
   |- SCANL $+ 0[1;2;3] = [0;1;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
listLib.SCANR_CONV, listLib.FOLDL_CONV, listLib.FOLDR_CONV,
listLib.list_FOLD_CONV.

----------------------------------------------------------------------