listLib.FOLDL

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

FOLDR_CONV, list_FOLD_CONV