A Normalization Code in Standard Ml Datatype 'a Option = None | Some of 'a 7 Conclusion and Future Work

The following Standard ML code can be used for solving constraint systems. The code assumes that phase 1 described earlier has been performed during constraint generation. The imperative aspects of Standard ML have been used a lot and we believe that this must be done for the complexity analysis to hold. For readability we have used standard list notation for the dependency lists although our complexity analysis requires that the append operation on lists is O(1) in time complexity. The code for a couple of simple subroutines has been omitted for space reasons. The code has been replaced by an ellipsis and a comment describing what the code should do. The functions find and findL are standard, see Tar83, Section 2.1]. val Snode = ref STATIC val DLnode = ref (BTLEQR (ref None)) val Dnode = ref (DYNAMIC DLnode) val worklist = ref (nil : Constraint list) val btvarlist = ref (nil : BType ref list) (* Follow BTLINKs using transition compression: *) fun find n = ... (* Follow BTLLINKs using transition compression: *) fun findL nl = ... fun isD n = (find n = Dnode) fun isDL nl = (findL nl = DLnode) fun isvar (BTVAR _) = true | isvar _ = false fun geteqr (ref (DYNAMIC eqr)) = eqr | geteqr (ref (BTVAR (dps,eqr))) = findL eqr | geteqr _ = crash () fun getmem (ref (BTLEQR mem)) = mem | getmem _ = crash () fun apply f xs = (map f xs; ()) fun mk_eqconstraint c = worklist := EQUAL c :: (!worklist) fun update_dps (k,n) = (k := !k-1; if !k = 0 then mk_eqconstraint (n,Dnode) else ()) fun doC1 (l1,r1) (l2,r2) = (* Combination rule 1 *) case (!(find l1),!(find l2)) of (CONSTR c1,CONSTR c2) => apply mk_eqconstraint (zip (r1::c1) (r2::c2)) | _ => crash () fun doC2 (l,r) = (* Combination rule 2 *) case !(find l) of (CONSTR c) => apply (fn n=>mk_eqconstraint (n,Dnode)) (r::c) | _ => crash () fun unionL n1 n2 = (* Make nodes var-equivalent *) let val (btl1,btl2) = (geteqr bt1,geteqr bt2) in if !btl1 = !btl2 then () else case (!btl1,!btl2) of (BTLEQR (ref None),BTLEQR (ref None)) => if isDL(btl1) then btl2 := BTLLINK btl1 else btl1 := BTLLINK btl2 | (BTLEQR (ref None),BTLEQR (ref (Some c))) => if isDL btl1 then doC3 c; btl2 := BTLLINK btl1 else btl1 := BTLLINK btl2 …