multi-directional infinte sequence - ML -

i want use datatype sequence defined follows:

 datatype 'a seq = nil | cons of 'a * (unit-> 'a seq);  exception emptyseq;   fun head(cons(x,_)) = x | head nil = raise emptyseq;   fun tail(cons(_,xf)) = xf() | tail nil = raise emptyseq; 

which has option iterate on functions backward , forward:

   datatype direction = | forward;     datatype 'a bseq =   bnil | bcons of 'a * (direction -> 'a bseq); 

and defined well:

fun bhead(bcons(x,_)) = x | bhead bnil = raise emptyseq;  fun bforward(bcons(_,xf)) = xf(forward) | bforward bnil = raise emptyseq;  fun bback(bcons(_,xf)) = xf(back) | bback bnil = raise emptyseq; 

now, i'm trying create function "create_seq" gets int "k" , returns infinte sequence can iterated , forth. example:

 - create_seq 2;  val = bcons (2,fn) : int bseq  - bforward it;  val = bcons (3,fn) : int bseq  - bforward it;  val = bcons (4,fn) : int bseq  - bback it;  val = bcons (3,fn) : int bseq  - bback it;  val = bcons (2,fn) : int bseq  - bback it;  val = bcons (1,fn) : int bseq  - bback it;  val = bcons (0,fn) : int bseq  - bback it;  val = bcons (~1,fn) : int bseq 

this i've been trying , can't figure out why doesn't work:

fun create_seq k = (k,fun check forward = create_seq(k+1)  | check = create_seq(k-1)); 

nor this:

fun create_seq k = (k,fn x => case x of forward => create_seq(k+1)                        | => create_seq(k-1)); 

or this:

fun create_seq k = (k,fn forward => create_seq(k+1)                        | => create_seq(k-1)); 

it seems forgot constructor:

fun intbseq(k:int) = bcons(k,fn forward => intbseq(k+1)| => intbseq(k-1)); 

this should work.