Mapping

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OCaml programs

Mapping

Consider the following codes (** Computes the list of twice each element in a list of integers *) (* *) let rec map_twice = function li -> if is_empty_list (li) then empty_list () else cons_list (2 * head (li), map_twice (tail (li))) (** Computes he list of the lengths of the elements in a list of lists *) (* *) let rec map_length = function llx -> if is_empty_list (llx) then empty_list () (* ----- llx : type error ----- *) else cons_list (List.length (head (llx)), map_length (tail (llx)))

Look at the definitions of  map_twice  and  map_length . Clearly their structures are similar. Transform what is identical in them into a functional value (named  map_to_all ) that can be applied to obtain the value of  map_twice  or that of  map_length : let map_to_all = function f -> (let rec g = function lx -> if is_empty_list (lx) then empty_list () else cons_list (f (head (lx)), g (tail (lx))) in g)

The type of  map_to_all  is ('a -> 'b) -> ('a list -> 'b list)

An example of application of the higher-order function  map_to_all : (** Computes the list of three times each element in a list of integers *) (* *) map_to_all (function x -> 3 * x) Now an example of application of the result of this application of the higher-order function  map_to_all : (** Computes the list of three times each element in a list of integers *) (* *) (map_to_all (function x -> 3 * x)) ([1 ; 2 ; 3])

Note that  map_to_all  and  List.map  (the function  map  provided by the Objective Caml module  List ) have the same value.

Finally note that the value of  map_to_all  can also be recursively defined: let rec map_to_all_1 = function f -> (function lx -> if is_empty_list (lx) then empty_list () else cons_list (f (head (lx)), (map_to_all_1 (f)) (tail (lx))))

Mapping

Documentation and user's manual

Table of contents

OCaml programs