Module Rtree

type 'a t

Type of regular tree with nodes labelled by values of type 'a The implementation uses de Bruijn indices, so binding capture is avoided by the lift operator (see example below)

Building trees

val mk_node : 'a -> 'a t array -> 'a t

build a node given a label and the vector of sons

val mk_rec_calls : int -> 'a t array

Build mutually recursive trees: X_1 = f_1(X_1,..,X_n) ... X_n = f_n(X_1,..,X_n) is obtained by the following pseudo-code let vx = mk_rec_calls n in let |x_1;..;x_n| = mk_rec|f_1(vx.(0),..,vx.(n-1);..;f_n(vx.(0),..,vx.(n-1))|

First example: build rec X = a(X,Y) and Y = b(X,Y,Y) let |vx;vy| = mk_rec_calls 2 in let |x;y| = mk_rec |mk_node a [|vx;vy|]; mk_node b [|vx;vy;vy|]|

Another example: nested recursive trees rec Y = b(rec X = a(X,Y),Y,Y) let |vy| = mk_rec_calls 1 in let |vx| = mk_rec_calls 1 in let |x| = mk_rec|mk_node a vx;lift 1 vy| let |y| = mk_rec|mk_node b x;vy;vy| (note the lift to avoid

val mk_rec : 'a t array -> 'a t array
val lift : int -> 'a t -> 'a t

lift k t increases of k the free parameters of t. Needed to avoid captures when a tree appears under mk_rec

val is_node : 'a t -> bool
val dest_node : 'a t -> 'a * 'a t array

Destructors (recursive calls are expanded)

val dest_param : 'a t -> int * int

dest_param is not needed for closed trees (i.e. with no free variable)

val is_infinite : ('a -> 'a -> bool) -> 'a t -> bool

Tells if a tree has an infinite branch. The first arg is a comparison used to detect already seen elements, hence loops

val equiv : ('a -> 'a -> bool) -> ('a -> 'a -> bool) -> 'a t -> 'a t -> bool

Rtree.equiv eq eqlab t1 t2 compares t1 t2 (top-down). If t1 and t2 are both nodes, eqlab is called on their labels, in case of success deeper nodes are examined. In case of loop (detected via structural equality parametrized by eq), then the comparison is successful.

val equal : ('a -> 'a -> bool) -> 'a t -> 'a t -> bool

Rtree.equal eq t1 t2 compares t1 and t2, first via physical equality, then by structural equality (using eq on elements), then by logical equivalence Rtree.equiv eq eq

val inter : ('a -> 'a -> bool) -> ('a -> 'a -> 'a option) -> 'a -> 'a t -> 'a t -> 'a t
val incl : ('a -> 'a -> bool) -> ('a -> 'a -> 'a option) -> 'a -> 'a t -> 'a t -> bool

Iterators

val map : ('a -> 'b) -> 'a t -> 'b t

See also Smart.map

val pp_tree : ('a -> Pp.t) -> 'a t -> Pp.t

A rather simple minded pretty-printer

module Smart : sig ... end