11. A method of claim 10 for automatically solving said set of simultaneous parameterized context qualified type equations for parameters other than parameters that specifically represent context qualified types, where said parameters include but are not limited to parameters whose value is determined by application of type differencing transformations, comprising: selecting a chain of context qualified types, where there exists context qualified type difference transformations for each pair of types in said chain, selecting a known instance of a first context qualified type in said chain, selecting a binding list comprising pairs of a variable parameter and a value of said variable parameter, where an initial value of said binding list is a set of variable and values pairs that are determinable before said set of simultaneous parameterized context qualified type equations solution process begins, and where said initial value of said binding list comprises variable and values pairs that are globally applicable to all equations in said set of simultaneous parameterized context qualified type equations, iterating all remaining steps of automatically solving for each pair of context qualified types in said chain plus an instance of a first context qualified type of said pair of context qualified types, and plus said binding list, and where each iteration, after a first iteration of said remaining steps of automatically solving, starts with a new pair of context qualified types shifted one type down said chain plus a new instance computed from an iteration just completed and plus said binding list with accumulated bindings from all previous iterations, selecting a context qualified type difference transformation from a first context qualified type in said pair of context qualified types to a second context qualified type in said pair of context qualified types, where said context qualified type difference transformation comprises a parameterized left hand side pattern that will match an instance of said first context qualified type and a parameterized right hand side that, when instantiated with parameter values from said binding list will become an instance of said second context, qualified type, where said binding list will include any new binding pairs determined by said match, matching said parameterized left hand side pattern against said instance of a first context qualified type of said pair of context qualified types to produce an additional list of binding pairs to be added to said binding list, and substituting each value of a binding pair for each parameter associated with said each value when said each parameter occurs in said parameterized right hand side, thereby producing an instantiated version of said parameterized right hand side, where said instantiated version of said parameterized right hand side is an instance of said second context qualified type.
10. A method of claim 9 for automatically solving said set of simultaneous parameterized context qualified type equations for values of parameters representing context qualified types by incrementally eliminating said parameters representing context qualified types from all right side context qualified type expressions, where a type equation is a triple comprising a left side context qualified type parameter, an equal sign, and an equivalent right side definition that optionally can contain context qualified type parameters, where said equivalent right side definition comprises a composite context qualified type expression or alternatively an expression with no context qualified type elements, where within a correctly formed set of simultaneous parameterized context qualified type equations, at least one context qualified type equation with no type parameters in said equivalent right side definition must exist because context qualified type specialization trees may not be cyclic, which implies a root context qualified type with no super context qualified types, comprising: selecting a context qualified type equation for a left side context qualified type parameter whose said equivalent right side definition has no embedded left side context qualified type parameters and substituting said equivalent right side definition into all other simultaneous context qualified type equations that contain said left side context qualified type parameter, repeating previous step until all left side context qualified type parameters have been eliminated from all right side definitions thereby automatically solving said set of simultaneous parameterized context qualified type equations for values of parameters representing context qualified types, or alternatively, until it is determined that said simultaneous parameterized context qualified type equations are insufficiently constrained where upon an a problem specification error is detected.