Inductive Data Types Based on Fibrations Theory in Programming
نویسندگان
چکیده
منابع مشابه
Inductive Data Types Based on Fibrations Theory in Programming
Traditional methods including algebra and category theory have some deficiencies in analyzing semantics properties and describing inductive rules of inductive data types, we present a method based on Fibrations theory aiming at those questions above. We systematically analyze some basic logical structures of inductive data types about a fibration such as re-indexing functor, truth functor and c...
متن کاملHigher Inductive Types in Programming
We propose general rules for higher inductive types with non-dependent and dependent elimination rules. These can be used to give a formal treatment of data types with laws as has been discussed by David Turner in his earliest papers on Miranda [Turner(1985)]. The non-dependent elimination scheme is particularly useful for defining functions by recursion and pattern matching, while the dependen...
متن کاملProgramming Inductive Proofs - A New Approach Based on Contextual Types
In this paper, we present an overview to programming with proofs in the reasoning framework, Beluga. Beluga supports the specification of formal systems given by axioms and inference rules within the logical framework LF. It also supports implementing proofs about formal systems as dependently typed recursive functions. What distinguishes Beluga from other frameworks is that it not only represe...
متن کاملInductive Data Types: Well-ordering Types Revisited
We consider Martin-Löf’s well-ordering type constructor in the context of an impredicative type theory. We show that the well-ordering types can represent various inductive types faithfully in the presence of the filling-up equality rules or η-rules. We also discuss various properties of the filling-up rules. ! " ! # $ % &" '( ) '* + '' + ,. '' " ''/0 % &..'1 " '2 34",5 6 ,5/0 7 % ! 0 " ! # &" ...
متن کاملInductive Logic Programming : Theory And
> Inductive Logic Programming (ILP) is a new discipline which investigates the inductive construction of rst-order clausal theories from examples and background knowledge. We survey the most important theories and methods of this new eld. Firstly, various problem speciications of ILP are formalised in semantic settings for ILP, yielding a \model-theory" for ILP. Secondly, a generic ILP algorith...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Computing and Information Technology
سال: 2016
ISSN: 1846-3908
DOI: 10.20532/cit.2016.1002716