signature SURFACE_SIMPLIFY =
    sig

	structure Complex : SIMPLICIAL_COMPLEX

	(* need a better name for states *)
	type 'a contractibleComplex
	type number

	type contractionRecord = 
	    (* The list of vertices being replace, the (possibly new) vertex
	       they're being replaced by, and a implementation-specific
	       number denoting the error induced by this contraction. *)
	    (Complex.Simplex.Vertex.vertex list * Complex.Simplex.Vertex.vertex * number)

	    (* We have to have some way to peek under the hood, for
	       debugging / regression testing purposes *)
	val writeContractionState : (TextIO.outstream * 'a contractibleComplex) -> unit

	(* Give flag set/test functions (for traverser) & complex, generate initial
	   error metrics and other setup work *)
	val initialize : ('a option -> 'a option) * ('a option -> bool) -> 
	                 'a Complex.complex -> 'a contractibleComplex

	(* contract' provides an efficient way to track changes in the model;
	   this allows logging or updates to a display engine *)
	val contract' : 'a contractibleComplex -> 
	    'a contractibleComplex * 
	    contractionRecord * (Complex.Simplex.simplex Sequence.seq * Complex.Simplex.simplex Sequence.seq)

	val contract : 'a contractibleComplex -> 'a contractibleComplex
	val result : 'a contractibleComplex -> 'a Complex.complex
	val error : 'a contractibleComplex -> number

    end