12. A method of claim 11 for automatically introducing and instantiating existential parameters with values for said existential parameters as a side effect of solving a set of simultaneous parameterized context qualified type equations and applying context qualified type difference transformations to solve for instances of said context qualified types, where an existential parameter is a parameter that is required to have a value in order to automatically solve said set of simultaneous parameterized context qualified type equations for parameters other than parameters that specifically represent context qualified types, comprising: expressing said set of simultaneous parameterized context qualified type equations, introducing existential parameters implied by said set of simultaneous parameterized context qualified type equations, introducing existential parameters implied by said set of type differencing transformations associated with said set of simultaneous parameterized context qualified type equations, and determining said values of or stand-ins for said values of said existential parameters, by matching contexts of said existential parameters against type expressions and instance expressions.
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.