منابع مشابه
A Universe of Strictly Positive Families
In order to represent, compute and reason with advanced data types one must go beyond the traditional treatment of data types as being inductive types and, instead, consider them as inductive families. Strictly positive types (SPTs) form a grammar for defining inductive types and, consequently, a fundamental question in the theory of inductive families is what constitutes a corresponding gramma...
متن کاملConstructing Strictly Positive Families
In order to represent, compute and reason with advanced data types one must go beyond the traditional treatment of data types as being inductive types and, instead, consider them as inductive families. Strictly positive types (SPTs) form a grammar for defining inductive types and, consequently, a fundamental question in the the theory of inductive families is what constitutes a corresponding gr...
متن کاملGeneric Programming for Dependent Types Constructing Strictly Positive Families
We begin by revisiting the idea of using a universe of types to write generic programs in a dependently typed setting by constructing a universe for Strictly Positive Types (SPTs). Here we extend this construction to cover dependent types, i.e. Strictly Positive Families (SPFs), thereby fixing a gap left open in previous work. Using the approach presented here we are able to represent all of Ep...
متن کاملConstructing Strictly Positive Types
We introduce container functors as a representation of data types providing a new conceptual analysis of data structures and polymorphic functions. Our development exploits Type Theory as a convenient way to define constructions within locally cartesian closed categories. We show that container morphisms can be full and faithfully interpreted as polymorphic functions (i.e. natural transformatio...
متن کاملStrictly Hermitian Positive Definite Functions
Let H be any complex inner product space with inner product < ·, · >. We say that f : | C → | C is Hermitian positive definite on H if the matrix ( f(< z,z >) )n r,s=1 (∗) is Hermitian positive definite for all choice of z, . . . ,z in H, all n. It is strictly Hermitian positive definite if the matrix (∗) is also non-singular for any choice of distinct z, . . . ,z in H. In this article we prove...
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ژورنال
عنوان ژورنال: International Journal of Foundations of Computer Science
سال: 2009
ISSN: 0129-0541,1793-6373
DOI: 10.1142/s0129054109006462