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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 ..."
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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. Copyright c fl1993. All rights reserved. Reproduction of all or part of this work is permitted for educational or research purposes on condition that (1) this copyright notice is included, (2) proper attribution to the author or authors is made and (3) no commercial gain is involved. Technical Reports issued by the Department of Computer Science, Manchester University, are available by anonymous ftp from m1.cs.man.ac.uk (130.88.13.4) in the directory /pub/TR. The files are stored as PostScript, in compressed form, with the report number as filename. Alternatively, reports are available by post from The Computer Library, Department of Computer Science, The University, Oxford R...
Categorical Properties of Logical Frameworks
, 1993
"... In this paper we give a new presentation of ELF which is wellsuited for semantic analysis. We introduce the notions of internal codability, internal definability, internal typed calculi and frame languages. These notions are central to our perspective of logical frameworks. We will argue that a ..."
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In this paper we give a new presentation of ELF which is wellsuited for semantic analysis. We introduce the notions of internal codability, internal definability, internal typed calculi and frame languages. These notions are central to our perspective of logical frameworks. We will argue that a logical framework is a typed calculus which formalizes the relationship between internal typed languages and frame languages. In the second half of the paper, we demonstrate the advantage of our logical framework by showing some categorical properties of it and of encodings in it. By doing so we hope to indicate a sensible model theory of encodings. Copyright c fl1993. All rights reserved. Reproduction of all or part of this work is permitted for educational or research purposes on condition that (1) this copyright notice is included, (2) proper attribution to the author or authors is made and (3) no commercial gain is involved. Technical Reports issued by the Department of Computer Sc...
Encodings In Polymorphism, revisited
, 1992
"... We consider encodings in polymorphism with finite product types. These encodings are given in terms of Ialgebras. They have the property that all canonical terms (ground terms) are normal terms. We transplant the proof of a wellknown result to our setting and show why weak recursion is admissible. ..."
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We consider encodings in polymorphism with finite product types. These encodings are given in terms of Ialgebras. They have the property that all canonical terms (ground terms) are normal terms. We transplant the proof of a wellknown result to our setting and show why weak recursion is admissible. We also show how to carry out the dual encodings using the existential quantifier. Copyright c fl1993. All rights reserved. Reproduction of all or part of this work is permitted for educational or research purposes on condition that (1) this copyright notice is included, (2) proper attribution to the author or authors is made and (3) no commercial gain is involved. Technical Reports issued by the Department of Computer Science, Manchester University, are available by anonymous ftp from m1.cs.man.ac.uk (130.88.13.4) in the directory /pub/TR. The files are stored as PostScript, in compressed form, with the report number as filename. Alternatively, reports are available by post from The Comput...
Inductive, Projective, and Retractive Types
, 1993
"... We give an analysis of classes of recursive types by presenting two extensions of the simplytyped lambda calculus. The first language only allows recursive types with builtin principles of wellfounded induction, while the second allows more general recursive types which permit nonterminating com ..."
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We give an analysis of classes of recursive types by presenting two extensions of the simplytyped lambda calculus. The first language only allows recursive types with builtin principles of wellfounded induction, while the second allows more general recursive types which permit nonterminating computations. We discuss the expressive power of the languages, examine the properties of reductionbased operational semantics for them, and give examples of their use in expressing iteration over large ordinals and in simulating both callbyname and callbyvalue versions of the untyped lambda calculus. The motivations for this work come from category theoretic models. 1 Introduction An examination of the common uses of recursion in defining types reveals that there are two distinct classes of operations being performed. The first class of recursive type contains what are generally known as the "inductive" types, as well as their duals, the "coinductive" or "projective" types. The distingui...
Impredicative Representations of Categorical Datatypes
, 1994
"... this document that certain implications are not based on a well stated formal theory but require a certain amount of handwaving. ..."
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this document that certain implications are not based on a well stated formal theory but require a certain amount of handwaving.
A Verification Environment for I/O Automata Based on . . .
, 1998
"... This thesis deals with the computerassisted verification of embedded systems described as Input/Output automata. We achieve contributions in two fields: the theory of untimed I/O automata and its tool support. For the latter a combination of the theorem prover Isabelle with model checking is used. ..."
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This thesis deals with the computerassisted verification of embedded systems described as Input/Output automata. We achieve contributions in two fields: the theory of untimed I/O automata and its tool support. For the latter a combination of the theorem prover Isabelle with model checking is used. Concerning the theory