Module type SetMap.Projection

module type Projection = sig .. end

type elt_a

type elt_b

type 'a map_a

type 'a map_b

type set_a

type set_b

val proj_map : (elt_a -> elt_b) ->
       'b ->
       ('b -> 'a -> 'b) -> 'a map_a -> 'b map_b

proj_map f init merge map is a map mapping each element b to the result of the itteration of the function merge over the image in map of the element a in f such that f(a)=b, starting with the element init.

val proj_map_monadic : 'parameters ->
       'method_handler ->
       (elt_a -> elt_b) ->
       'b ->
       ('parameters -> 'method_handler -> 'b -> 'a -> 'method_handler * 'b) ->
       'a map_a -> 'method_handler * 'b map_b

val proj_set : (elt_a -> elt_b) ->
       set_a -> set_b

proj_set f set is the set {f(a) | a\in S}

val proj_set_monadic : 'parameters ->
       'method_handler ->
       ('parameters ->
        'method_handler ->
        elt_a -> 'method_handler * elt_b) ->
       set_a -> 'method_handler * set_b

val partition_set : (elt_a -> elt_b) ->
       set_a -> set_a map_b

partition_set f set is the map mapping any element b with an antecedent for f in the set set, into the set of its antecedents, ie to the set {a\in set | f(a)=b}.

val partition_set_monadic : 'parameters ->
       'method_handler ->
       ('parameters ->
        'method_handler ->
        elt_a -> 'method_handler * elt_b) ->
       set_a ->
       'method_handler * set_a map_b