SCANR_CONV : conv -> conv
STRUCTURE
listLib
SYNOPSIS
Computes by inference the result of applying a function to the elements of a list.
DESCRIPTION
SCANR_CONV takes a conversion conv and a term tm in the following form: 
   SCANR f e0 [xn;...;x1]
It returns the theorem 
   |- SCANR f e0 [xn;...;x1] = [en; ...;e1;e0]
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 right-hand side (the tail) 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
SCANR_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 SCANR_CONV with ADD_CONV from the library num_lib. 
   - load_library_in_place num_lib;
   - SCANR_CONV Num_lib.ADD_CONV “SCANR $+ 0 [1;2;3]”;
   |- SCANR $+ 0[1;2;3] = [6;5;3;0]
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
SCANL_CONV, FOLDL_CONV, FOLDR_CONV, list_FOLD_CONV
HOL  Kananaskis-13