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Understanding Inductive Types in Constructions
, 1993
"... In this paper we extend the Calculus of Constructions with generalized inductive types. The extension is justified by showing that the usual set theoretical model can be effectivized. It is also pointed out that the model given in a published paper for a collection of inductive types in a different ..."
Abstract

Cited by 2 (1 self)
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In this paper we extend the Calculus of Constructions with generalized inductive types. The extension is justified by showing that the usual set theoretical model can be effectivized. It is also pointed out that the model given in a published paper for a collection of inductive types in a different style is wrong.
SPECIFYING AND REASONING IN THE CALCULUS OF OBJECTS
, 2005
"... Since type theory merges constructive logic with functional programming language it appears a very promising system for formal program construction. The present thesis deals with this idea in the environment of a type theoretic system equipped with the type constructor representing a simple form of ..."
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Since type theory merges constructive logic with functional programming language it appears a very promising system for formal program construction. The present thesis deals with this idea in the environment of a type theoretic system equipped with the type constructor representing a simple form of objects. The presented interpretation of an object type requires rather nontrivial extension of the underlaying calculus of the type theory. The notion of box, which is the content containment structure with a marker variable, is added to the syntax of the calculus that allows to delimit internal states of objects in the definitions of methods. The acquired overall simple notation is a justification of the need for this extraordinary extension. The objectives of this thesis are mainly to give the formal representation of simple object model and to show its significant metatheoretical properties. We also show the capabilities of the system for specifying and reasoning about programs by defining the basic concepts of program specifications and several stewise refinement operations and techniques for reasoning about the correctness of programs. To do this the Core Calculus of Objects (CCO) is introduced. CCO is derived from