\DOC FOLDL_CONV \TYPE {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 {ADD_CONV} from the library {num_lib}. { - load_library_in_place num_lib; - FOLDL_CONV Num_lib.ADD_CONV (--`FOLDL $+ 0 [0;1;2;3]`--); |- FOLDL $+ 0[0;1;2;3] = 6 } 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. \ENDDOC