λCalculi with Explicit Substitutions Preserving Strong Normalization
This paper studies preservation of beta -strong normalization by two different confluent lambda -calculi with explicit substitutions defined in [19]; the particularity of these calculi, called lambda sub(d) and lambda sub(dn) respectively, is that both have a (weak) composition operator for substitu...
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| Published in: | Applicable algebra in engineering, communication and computing Vol. 9; no. 4; pp. 333 - 371 |
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| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
1999
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| Online Access: | Get full text |
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| Summary: | This paper studies preservation of beta -strong normalization by two different confluent lambda -calculi with explicit substitutions defined in [19]; the particularity of these calculi, called lambda sub(d) and lambda sub(dn) respectively, is that both have a (weak) composition operator for substitutions. We apply an abstract simulation technique to reduce preservation of beta -strong normalization of lambda sub(d) and lambda sub(dn) to that of another calculus, called lambda sub(f), having no composition operator. Then, preservation of beta -strong normalization of lambda sub(f) is shown using the same technique as in [2]. As a consequence, lambda sub(d) and lambda sub(dn) become the first lambda -calculi with explicit substitutions having (weak) composition and preserving beta -strong normalization. As an aside, we also show how to apply our technique to reduce preservation of beta -strong normalization of the calculus lambda sub(v) in [20] to that of lambda sub(f). |
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| Bibliography: | ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23 |
| ISSN: | 0938-1279 1432-0622 |
| DOI: | 10.1007/s002000050110 |