Two set-based implementations of quotients in type theory
نویسنده
چکیده
We present and compare two different implementations of quotient types in Intensional Type Theory. We first introduce quotients as particular inductive-like types following Martin Hofmann’s extension of Calculus of Constructions with quotient types [6]. Then we give an impredicative encoding of quotients. This implementation is reminiscent of Church numerals and more generally of encodings of inductive types in Calculus of Constructions.
منابع مشابه
Quotient types in type theory
Martin-Löf’s intuitionistic type theory (Type Theory) is a formal system that serves not only as a foundation of constructive mathematics but also as a dependently typed programming language. Dependent types are types that depend on values of other types. Type Theory is based on the Curry-Howard isomorphism which relates computer programs with mathematical proofs so that we can do computer-aide...
متن کاملModelling and Experimental Testing of Asymmetric Information Problems in Lease and Hire Contracts (Based on Contract Theory)
This article aims to study lease and hiring contract in the Iranian-Islamic setting and analyze the asymmetric information problem in these contracts. For doing this, we study the characteristics of lease and hiring contracts in Iran (real world experimental characteristics that recognized in other studies), using library method, then we mathematically model different aspects of asymmetric info...
متن کاملSampling of Multiple Variables Based on Partially Ordered Set Theory
We introduce a new method for ranked set sampling with multiple criteria. The method relaxes the restriction of selecting just one individual variable from each ranked set. Under the new method for ranking, units are ranked in sets based on linear extensions in partially order set theory with considering all variables simultaneously. Results willbe evaluated by a relatively extensive simulation...
متن کاملAn integrated multi-criteria decision-making methodology based on type-2 fuzzy sets for selection among energy alternatives in Turkey
Energy is a critical factor to obtain a sustainable development for countries and governments. Selection of the most appropriate energy alternative is a completely critical and a complex decision making problem. In this paper, an integrated multi-criteria decision-making (MCDM) methodology based on type-2 fuzzy sets is proposed for selection among energy alternatives. Then a roadmap has been cr...
متن کاملEffectiveness of training on preventative nutritional behaviors for type-2 diabetes among the female adolescents: Examination of theory of planned behavior
Background: Since type-2 diabetes is the most common chronic disease among Iranian female adolescents, we applied theory of planned behavior to examine the effect of training to intention to preventative nutritional behaviors for type-2 diabetes among female adolescents. Methods: In this experimental study 200 (11-14 year old) girls from 8 schools of Tehran city (100 in each intervent...
متن کامل