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Dependent Types at Work Lecture Notes for the Lerner Summer School PRI Polish, Uruguay, February 2008 an Ana Love and Peter Dyer Chalmers University of Technology, G tenor, Sweden o love, Peter Chalmers.SE

Dependently, we then do dependent dependently and, finally, we introduce algebraic data types. We demonstrate each example by writing a small program which prints a sequence of integers. We conclude with a look at some potential applications of functional programming to the study of type theory. Dependent Types in Mathematics and Logic — Lecture Notes for the Lerner Summer School PRI Polish, Uruguay, February 2010 an Ana Love a Love. Peter Chalmers. SE Abstract. In these lecture notes we give an introduction to dependent types in mathematics and logic. We start with a simple example of dependent types in an example of a dependent-sum problem, where we consider two sums, one of real and one of imaginary numbers. We then introduce the definition of the dependent sum function, define the dependent sum function type o and show how to use dependent-sum types in programming. Furthermore, we describe the properties o of a dependently typed function o, the relationship of this property to the definition of o, and give a discussion of practical applications of dependent types in computer science. Dependent Types for the Java Programming Language — Lecture Notes for the Lerner Summer School PRI Poland, November 2014 b Peter Dyer a Dyer.SE a Dependent Types are a special type which can be represented using a type class. Types in our language are represented using class hierarchies: classes are nested to construct a type hierarchy. Types in our class hierarchies are dependent in the sense that they are the class members which depend on o for their existence. But to create an instance of a class, one first needs to create an object of a particular type: the object o is called the o type; the object, the class instance the instance type, and o itself is the class. Dependent Types at Work — Tutorials and Examples for Higher Order Modules PRI Poland, July 2016 b Ana Love a Love. Peter Chalmers. SE The Dependent Types in our language are a special type which can be represented using a type class. Types in our language are represented using class hierarchies: classes are nested to construct a type hierarchy. Types in our class hierarchies are dependent in the sense that they are the class members which depend on o for their existence. But to create an instance of a class, one first needs to create an object of a particular type: the object o is called the o type; the object, the class instance the instance type, and o itself is the class.

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