Non-trivial Power Types Can't Be Subtypes of Polymorphic Types
نویسنده
چکیده
This paper establishes a new limitative relation between the polymorphic lambda calculus and the kind of higher order type theory which is em bodied in the logic of toposes It is shown that any embedding in a topos of the cartesian closed category of closed types of a model of the poly morphic lambda calculus must place the poly morphic types well away from the powertypes of the topos in the sense that is a subtype of a polymorphic type only in the case that is empty and hence is ter minal As corollaries we obtain strengthenings of Reynolds result on the non existence of set theoretic models of polymorphism
منابع مشابه
Modular Verification of Object-Oriented Programs with Subtypes
Object-oriented programming languages like Smalltalk-80 have a message passing mechanism that allows code to work on instances of many different types. Techniques for the formal specification of such polymorphic functions and abstract types are described, as well as a logic for verifying programs that use message passing but not object mutation or assignment. The reasoning techniques formalize ...
متن کاملStreptococcus pyogenes strains associated with invasive and non-invasive infections present possible links with emm types and superantigens
Objective(s): Streptococcus pyogenes, a notorious human pathogen is responsible to cause a wide range of infections varies from superficial common clinical illness to severe and life threatening infections. To our knowledge this is the first report exploring the emm types and superantigen/exotoxin gene profile of S. pyogenes from Pakistan. Materials a...
متن کاملMolecular Characterization of Iraqi Local Goat Breeds Using Random Amplified Polymorphic DNA Markers
Cashmere is only produced from Maraz (Kurdi) goat breed in Iraqi Kurdistan Region. The objective of this study was to assess the genetic diversity of different Maraz color types, black goat and Shami breeds using random amplified polymorphic DNA (RAPD) markers. Fourteen primers were used and nine out of them were selected based on their number of bands (NB) and polymorphic characteristics. Thes...
متن کاملModular Veriication of Object-oriented Programs with Subtypes Modular Veriication of Object-oriented Programs with Subtypes List of Figures 1.1 the Type Speciication
Object-oriented programming languages like Smalltalk-80 have a message passing mechanism that allows code to work on instances of many diierent types. Techniques for the formal speciication of such polymorphic functions and abstract types are described, as well as a logic for verifying programs that use message passing but not object mutation or assignment. The reasoning techniques formalize in...
متن کامل