Positive Inductive-Recursive Definitions
نویسندگان
چکیده
منابع مشابه
Positive Inductive-Recursive Definitions
A new theory of data types which allows for the definition of types as initial algebras of certain functors Fam(C) → Fam(C) is presented. This theory, which we call positive inductive-recursive definitions, is a generalisation of Dybjer and Setzer’s theory of inductive-recursive definitions within which C had to be discrete — our work can therefore be seen as lifting this restriction. This is a...
متن کاملA Finite Axiomatization of Inductive-Recursive Definitions
Induction-recursion is a schema which formalizes the principles for introducing new sets in Martin-Löf’s type theory. It states that we may inductively define a set while simultaneously defining a function from this set into an arbitrary type by structural recursion. This extends the notion of an inductively defined set substantially and allows us to introduce universes and higher order univers...
متن کاملInductive-Inductive Definitions
We present a principle for introducing new types in type theory which generalises strictly positive indexed inductive data types. In this new principle a set A is defined inductively simultaneously with an A-indexed set B, which is also defined inductively. Compared to indexed inductive definitions, the novelty is that the index set A is generated inductively simultaneously with B. In other wor...
متن کاملEvolution of Inductive Definitions
In formal verification, inductive definitions of predicates are widely used when we define recursive notions and algorithms. In actual verification, we often introduce a new inductively defined predicate by modifying an existing inductive definition. In such a case, it is usual that there are some relationships between two predicates, and such relationship theorems make the properties on one pr...
متن کاملElaborating Inductive Definitions
We present an elaboration of inductive definitions down to a universe of datatypes. The universe of datatypes is an internal presentation of strictly positive types within type theory. By elaborating an inductive definition – a syntactic artefact – to its code – its semantics – we obtain an internalised account of inductives inside the type theory itself: we claim that reasoning about inductive...
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: Logical Methods in Computer Science
سال: 2015
ISSN: 1860-5974
DOI: 10.2168/lmcs-11(1:13)2015