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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.
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
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...
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
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.
Strong Categorical Datatypes I
, 1991
"... An endofunctor of a cartesian closed category is often called strong if it is enriched over the exponential. Equivalently this strength can be provided as a natural transformation ` A;X : F (A) \Theta X \Gamma! F (A \Theta X) satisfying some elementary coherence conditions. This latter formulation ..."
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An endofunctor of a cartesian closed category is often called strong if it is enriched over the exponential. Equivalently this strength can be provided as a natural transformation ` A;X : F (A) \Theta X \Gamma! F (A \Theta X) satisfying some elementary coherence conditions. This latter formulation does not require exponentials, relies only on the presence of an Xaction over an Xstrong category, and thereby provides a firstorder viewpoint of strength. The 2category of Xstrong categories is not finitely complete. It particularly lacks many standard constructions including the EilenbergMoore construction. Thankfully, the suggestion  attributed to Plotkin by Moggi  that strength can also be equivalently framed in terms of fibrations using projections to Xobjects as display maps can be fully realized. The equivalence can be portrayed as an embedding of Xstrong categories into the 2category of Xindexed categories or split fibrations over X. This embedding can be u...
Names and HigherOrder Functions
, 1995
"... Many functional programming languages rely on the elimination of `impure' features: assignment to variables, exceptions and even input/output. But some of these are genuinely useful, and it is of real interest to establish how they can be reintroducted in a controlled way. This dissertation loo ..."
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Many functional programming languages rely on the elimination of `impure' features: assignment to variables, exceptions and even input/output. But some of these are genuinely useful, and it is of real interest to establish how they can be reintroducted in a controlled way. This dissertation looks in detail at one example of this: the addition to a functional language of dynamically generated names. Names are created fresh, they can be compared with each other and passed around, but that is all. As a very basic example of state, they capture the graduation between private and public, local and global, by their interaction with higherorder functions.