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FOLDL_CONV                                                   (listLib)
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FOLDL_CONV : conv -> conv

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

KEYWORDS
conversion, list.

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

   FOLDL f e [x0;...xn]

It returns the theorem

   |- FOLDL 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 ei xi} is evaluated. The user supplied
conversion {conv} is used to derive a theorem

   |- f ei xi = e(i+1)

which is used in the next iteration.

FAILURE
{FOLDL_CONV conv tm} fails if {tm} is not of the form described above.

EXAMPLE
To sum the elements of a list,  one can use
{FOLDL_CONV} with {REDUCE_CONV} from the library {numLib}.

   - FOLDL_CONV numLib.REDUCE_CONV ``FOLDL $+ 0 [0;1;2;3]``;
   val it = |- FOLDL $+ 0 [0;1;2;3] = 6 : thm

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.FOLDR_CONV, listLib.list_FOLD_CONV.

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