The semantics of second-order lambda calculus
Information and Computation
Category theory for computing science
Category theory for computing science
A calculus for overloaded functions with subtyping
Information and Computation
Parallel reductions in &lgr;-calculus
Information and Computation
The Java Language Specification
The Java Language Specification
Computational Adequacy via "Mixed" Inductive Definitions
Proceedings of the 9th International Conference on Mathematical Foundations of Programming Semantics
On Typed Calculi with a Merge Operator
Proceedings of the 14th Conference on Foundations of Software Technology and Theoretical Computer Science
Towards a theory of type structure
Programming Symposium, Proceedings Colloque sur la Programmation
Using category theory to design implicit conversions and generic operators
Semantics-Directed Compiler Generation, Proceedings of a Workshop
A computationally adequate model for overloading via domain-valued functors
Mathematical Structures in Computer Science
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The semantic structure of a polymorphic calculus λm is studied. λm is defined over a hierarchical type structure, and a function in this calculus, called a generic function, can be composed from more than one lambda expression and the ways it behaves on each type are weakly related in that it lax commutes with the coercion functions defined from the subtypes to the supertypes.Since laxness is intermediate between ad hocness (behaviors on each type are not related) and coherency (commuting with the coercion functions), λm has syntactic properties lying between those of calculi with ad hoc generic functions and coherent generic functions studied in Tsuiki (Math. Struct. Comput. Sci. 8 (1998) 321). That is, although λm allows self application and thus is not normalizing, it does not have any unsolvable terms. For this reason, all the semantic domains are connected by mutually recursive equations and, at the same time, they do not have the least elements. We solve them by considering fibrations and expressing the equations as a recursive equation about fibrations. We also show the adequacy theorem for λm following the construction of Pitts and use it to derive some syntactic properties.