Constructions, inductive types and strong normalization:
Abstract: "This thesis contains an investigation of Conquand's Calculus of Constructions, a basic impredicative Type Theory. We review syntactic properties of the calculus, in particular decidability of equality and type-checking, based on the equality-as-judgement presentation. We present...
Gespeichert in:
1. Verfasser: | |
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Format: | Buch |
Sprache: | English |
Veröffentlicht: |
Edinburgh
Univ. of Edinburgh, Department of Computer Science
1993
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Schlagworte: | |
Zusammenfassung: | Abstract: "This thesis contains an investigation of Conquand's Calculus of Constructions, a basic impredicative Type Theory. We review syntactic properties of the calculus, in particular decidability of equality and type-checking, based on the equality-as-judgement presentation. We present a set-theoretic notion of model, CC-structures, and use this to give a new strong normalization proof based on a modification of the realizability interpretation. An extension of the core calculus by inductive types is investigated and we show, using the example of infinite trees, how the realizability semantics and the strong normalization argument can be extended to non-algebraic inductive types. We emphasize that our interpretation is sound for large eliminations, e.g. allows the definitions of sets by recursion. Finally we apply the extended calculus to a non-trivial problem: the formalization of the strong normalizatin argument for Girard's System F. This formal proof has been developed and checked using the LEGO system, which has been implemented by Randy Pollack. We include the LEGO files in the appendix." |
Beschreibung: | Zugl.: Edinburgh, Univ., Diss., 1993 |
Beschreibung: | 183 S. |
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500 | |a Zugl.: Edinburgh, Univ., Diss., 1993 | ||
520 | 3 | |a Abstract: "This thesis contains an investigation of Conquand's Calculus of Constructions, a basic impredicative Type Theory. We review syntactic properties of the calculus, in particular decidability of equality and type-checking, based on the equality-as-judgement presentation. We present a set-theoretic notion of model, CC-structures, and use this to give a new strong normalization proof based on a modification of the realizability interpretation. An extension of the core calculus by inductive types is investigated and we show, using the example of infinite trees, how the realizability semantics and the strong normalization argument can be extended to non-algebraic inductive types. We emphasize that our interpretation is sound for large eliminations, e.g. allows the definitions of sets by recursion. Finally we apply the extended calculus to a non-trivial problem: the formalization of the strong normalizatin argument for Girard's System F. This formal proof has been developed and checked using the LEGO system, which has been implemented by Randy Pollack. We include the LEGO files in the appendix." | |
650 | 4 | |a Formal languages |x Semantics | |
650 | 4 | |a Lambda calculus | |
650 | 4 | |a Type theory | |
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999 | |a oai:aleph.bib-bvb.de:BVB01-006680047 |
Datensatz im Suchindex
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any_adam_object | |
author | Altenkirch, Thorsten |
author_facet | Altenkirch, Thorsten |
author_role | aut |
author_sort | Altenkirch, Thorsten |
author_variant | t a ta |
building | Verbundindex |
bvnumber | BV010066660 |
classification_tum | DAT 373d |
ctrlnum | (OCoLC)35737535 (DE-599)BVBBV010066660 |
discipline | Informatik |
format | Book |
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genre | (DE-588)4113937-9 Hochschulschrift gnd-content |
genre_facet | Hochschulschrift |
id | DE-604.BV010066660 |
illustrated | Not Illustrated |
indexdate | 2024-07-09T17:45:54Z |
institution | BVB |
language | English |
oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006680047 |
oclc_num | 35737535 |
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owner_facet | DE-91G DE-BY-TUM |
physical | 183 S. |
publishDate | 1993 |
publishDateSearch | 1993 |
publishDateSort | 1993 |
publisher | Univ. of Edinburgh, Department of Computer Science |
record_format | marc |
spelling | Altenkirch, Thorsten Verfasser aut Constructions, inductive types and strong normalization CST 106 93 ECS LFCS 93 279 Edinburgh Univ. of Edinburgh, Department of Computer Science 1993 183 S. txt rdacontent n rdamedia nc rdacarrier Zugl.: Edinburgh, Univ., Diss., 1993 Abstract: "This thesis contains an investigation of Conquand's Calculus of Constructions, a basic impredicative Type Theory. We review syntactic properties of the calculus, in particular decidability of equality and type-checking, based on the equality-as-judgement presentation. We present a set-theoretic notion of model, CC-structures, and use this to give a new strong normalization proof based on a modification of the realizability interpretation. An extension of the core calculus by inductive types is investigated and we show, using the example of infinite trees, how the realizability semantics and the strong normalization argument can be extended to non-algebraic inductive types. We emphasize that our interpretation is sound for large eliminations, e.g. allows the definitions of sets by recursion. Finally we apply the extended calculus to a non-trivial problem: the formalization of the strong normalizatin argument for Girard's System F. This formal proof has been developed and checked using the LEGO system, which has been implemented by Randy Pollack. We include the LEGO files in the appendix." Formal languages Semantics Lambda calculus Type theory (DE-588)4113937-9 Hochschulschrift gnd-content |
spellingShingle | Altenkirch, Thorsten Constructions, inductive types and strong normalization Formal languages Semantics Lambda calculus Type theory |
subject_GND | (DE-588)4113937-9 |
title | Constructions, inductive types and strong normalization |
title_alt | CST 106 93 ECS LFCS 93 279 |
title_auth | Constructions, inductive types and strong normalization |
title_exact_search | Constructions, inductive types and strong normalization |
title_full | Constructions, inductive types and strong normalization |
title_fullStr | Constructions, inductive types and strong normalization |
title_full_unstemmed | Constructions, inductive types and strong normalization |
title_short | Constructions, inductive types and strong normalization |
title_sort | constructions inductive types and strong normalization |
topic | Formal languages Semantics Lambda calculus Type theory |
topic_facet | Formal languages Semantics Lambda calculus Type theory Hochschulschrift |
work_keys_str_mv | AT altenkirchthorsten constructionsinductivetypesandstrongnormalization AT altenkirchthorsten cst10693 AT altenkirchthorsten ecslfcs93279 |