`FOLDL_CONV : conv -> conv`
STRUCTURE
SYNOPSIS
Computes by inference the result of applying a function to the elements of a list.
DESCRIPTION
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