Monotonic versus antimonotonic exponentiation
We investigate the relationship between the monotonic (→) and the antimonotonic exponentiation (➾) in a type system with subtyping. We present a model in which we can develop both exponentiations at the same time. In this model the monotonic and the antimonotonic exponentiation enjoy a duality, namely α➾β=∁(α→∁β) where ∁ is the type constructor complement. We give a sound and complete system of axioms for the type system with the type constructors →, ➾, ∪, ∩, ∁, ⊥, T.
Unable to display preview. Download preview PDF.
- 1.Engeler, E.: Algebras and combinators. Algebra Universalis 13 (1981) 389–392Google Scholar
- 2.Otth, D.: Konsistente Operatoren. ETHZ Report(1990)Google Scholar
- 3.Otth, D.: Types and Consistency in Combinatory Algebras. Dissertation 9800, ETHZ (1992).Google Scholar
- 4.Plotkin, G.: A powerdomain construction. SIAM J. Comput. 5 (1976) 452–487Google Scholar
- 5.Schellinx, H.: Isomorphisms and nonisomorphisms of graph models. J. of Symbolic Logic, 56 (1991) 227–249Google Scholar
- 6.Scott, D.: Data types as lattices. SIAM J. Comput. 5 (1976) 522–587Google Scholar