`MAP_CONV : conv -> conv`
STRUCTURE
SYNOPSIS
Compute the result of mapping a function down a list.
DESCRIPTION
The function MAP_CONV is a parameterized conversion for computing the result of mapping a function f:ty1->ty2 down a list “[t1;...;tn]” of elements of type ty1. The first argument to MAP_CONV is expected to be a conversion that computes the result of applying the function f to an element of this list. When applied to a term “f ti”, this conversion should return a theorem of the form |- (f ti) = ri, where ri is the result of applying the function f to the element ti.

Given an appropriate conv, the conversion MAP_CONV conv takes a term of the form “MAP f [t1;...;tn]” to the theorem

```   |- MAP f [t1;...;tn] = [r1;...;rn]
```
where conv “f ti” returns |- (f ti) = ri for i from 1 to n.
EXAMPLE
The following is a very simple example in which no computation is done for applications of the function being mapped down a list:
```   - MAP_CONV ALL_CONV “MAP SUC [1;2;1;4]”;
|- MAP SUC[1;2;1;4] = [SUC 1;SUC 2;SUC 1;SUC 4]
```
The result just contains applications of SUC, since the supplied conversion ALL_CONV does no evaulation.

We now construct a conversion that maps SUC n for any numeral n to the numeral standing for the successor of n:

```   - fun SUC_CONV tm =
let val n = string_to_int(#Name(dest_const(rand tm)))
val sucn = mk_const{{Name =int_to_string(n+1), Ty=(==`:num`==)}}
in
SYM (num_CONV sucn)
end;
SUC_CONV = - : conv
```
The result is a conversion that inverts num_CONV:
```   - num_CONV “4”;
|- 4 = SUC 3

- SUC_CONV “SUC 3”;
|- SUC 3 = 4
```
The conversion SUC_CONV can then be used to compute the result of mapping the successor function down a list of numerals:
```   - MAP_CONV SUC_CONV “MAP SUC [1;2;1;4]”;
|- MAP SUC[1;2;1;4] = [2;3;2;5]
```
FAILURE
MAP_CONV conv fails if applied to a term not of the form “MAP f [t1;...;tn]”. An application of MAP_CONV conv to a term “MAP f [t1;...;tn]” fails unless for all ti in the list [t1;...;tn], evaluating conv “f ti” returns |- (f ti) = ri for some ri.