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A Predicative TypeTheoretic Interpretation of Objects
, 1997
"... Predicative type theories are powerful tools for giving foundational interpretations of programming languages. Due to their explicit inductive construction, predicative type theories have multiple mathematical models that provide precise definitions of programming language features. However, not all ..."
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Predicative type theories are powerful tools for giving foundational interpretations of programming languages. Due to their explicit inductive construction, predicative type theories have multiple mathematical models that provide precise definitions of programming language features. However, not all features have predicative interpretations, and current interpretations of objects rely on impredicative type theories, such as Girard's System F, because of the difficulty in specifying a type for objects in the presence of selfapplication. In this paper we show that objects have a predicative interpretation. We show that predicativity is associated with method monotonicity, and that binary methods prevent the inductive type construction. Our interpretation differs from impredicative accounts by replacing the use of recursive types for objects with conditions for method polymorphism over the self type. We further give a propositional meaning to objects in the type theory, providing a calc...
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