## Categorical Properties of Logical Frameworks (1993)

Citations: | 1 - 1 self |

### BibTeX

@MISC{Fu93categoricalproperties,

author = {Yuxi Fu and Yuxi Fu},

title = {Categorical Properties of Logical Frameworks},

year = {1993}

}

### OpenURL

### Abstract

In this paper we give a new presentation of ELF which is well-suited 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...

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Citation Context ...t from The Computer Library, Department of Computer Science, The University, Oxford Road, Manchester M13 9PL, U.K. 1 Introduction The notion of logical frameworks first appeared in Martin-Lof's work (=-=[NPS90]-=-). It was meant to be a simple language with which his set theory can be precisely defined. The idea is picked up and extended in [HHP87, HHP92]. According to the authors, logical frameworks are langu... |

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Citation Context ...ne before they are used and it is done once for all. The run-time objects are the terms constructed in terms of the formulated language. Another advantage in insisting on such a dichotomy is shown in =-=[Luo92]-=-. There the author takes the view that, as far as programmes are concerned, the natural notion for computational equality is the intensional one. But when reasoning about programs, say in a correctnes... |

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Citation Context ...ical systems we can ever have. Other type theories have too sophisticated type constructors to be decidable. One example is the NuPRL system ([ea86]). The logical theory of constructions described in =-=[MA88]-=- has altogether a different flavour. Most of the languages we just mentioned do not purport to be logical frameworks. Analogous to the compile/run-time dichotomy in functional programming languages vi... |

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Some Semantic Issues In Type Theory
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Citation Context ...ity. The nice thing about our approach is that it brings out the internal categorical aspects of this phenomenon. 12 Acknowledgement The material in this paper is taken from the author's Ph.D thesis (=-=[Fu92]-=-). My supervisor David Rydeheard has been very helpful all the way over the last two years. The examiners Peter Aczel and Martin Hyland have raised some interesting points and made quite a few comment... |