Compile-Time Step 2: Determine Method Signature in Java

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15122 Compile-Time Step 2: Determine Method Signature
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type declaration, For example, if T :> List<String> and T :> List<Object>, simply intersecting the sets ST(List<String>) = {List<String>, Collection<String>, Object} and ST(List<Object>) = {List<Object>), Collection<Object>, Object} would yield a set {Object}, and we would have lost track of the fact that T can safely be assumed to be a List In contrast, intersecting EST(List<String>) = {List, Collection, Object} and EST(List<Object>) = {List, Collection, Object} yields {List, Collection, Object}, which we will eventually enable us to infer T = List< > as described below
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The erased candidate set for type parameter Tj , EC, is the intersection of all the sets EST(U) for each U in U1 Uk The minimal erased candidate set for Tj is MEC = { V | V in EC, and for all W V in EC, it is not the case that W <: V}
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For any element G of MEC that is a generic type declaration, de ne the relevant invocations of G, Inv(G) to be: Inv(G) = { V | 1 i k , V in ST(Ui), V = G<>}
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In our running example, the only generic element of MEC is List, and Inv(List) = {List<String>, List<Object>} We now will seek to nd a type argument for List that contains ( 4511) both String and Object This is done by means of the least containing invocation (lci) operation de ned below The rst line de nes lci() on a set, such as Inv(List), as an operation on a list of the elements of the set The next line de nes the operation on such lists, as a pairwise reduction on the elements of the list The third line is the de nition of lci() on pairs of parameterized types, which in turn relies on the notion of least containing type argument (lcta) lcta() is de ned for all six possible cases Then CandidateInvocation(G) de nes the most speci c invocation of the generic G that is contains all the invocations of G that are
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Because we are seeking to infer more precise types, we wish to lter out any candidates that are supertypes of other candidates This is what computing MEC accomplishes In our running example, we had EC = {List, Collection, Object}, and now MEC = {List} The next step will be to recover actual type arguments for the inferred types
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Compile-Time Step 2: Determine Method Signature 15122
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known to be supertypes of Tj This will be our candidate invocation of G in the bound we infer for Tj
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where glb() is as de ned in ( 5110)
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Finally, we de ne a bound for Tj based on on all the elements of the minimal erased candidate set of its supertypes If any of these elements are generic, we use the CandidateInvocation() function to recover the type argument information
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Then, de ne Candidate(W) = CandidateInvocation(W) if W is generic, W otherwise Then the inferred type for Tj is lub(U1 Uk) = Candidate(W1) & & Candidate(Wr) where Wi, 1 i r , are the elements of MEC It is possible that the process above yields an in nite type This is permissible, and Java compilers must recognize such situations and represent them appropriately using cyclic data structures
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and let CandidateInvocation(G) = lci(Inv(G)) where lci, the least containing invocation is de ned lci(S) = lci(e1, , en) where ei in S, 1 i n lci(e1, , en) = lci(lci(e1, e2), e3, , en) lci(G<X1, , Xn>, G<Y1, , Yn>) = G<lcta(X1, Y1),, lcta(Xn, Yn)> where lcta() is the the least containing type argument function de ned (assuming U and V are type expressions) as: lcta(U, V) = U if U = V, extends lub(U, V) otherwise lcta(U, extends V) = extends lub(U, V) lcta(U, super V) = super glb(U, V) lcta( extends U, extends V) = extends lub(U, V) lcta( extends U, super V) = U if U = V, otherwise lcta( super U, super V) = super glb(U, V)
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