Towards a proof theory of rewriting: the simply-typed 2-lambda calculus
Abstract: "This paper describes the simply-typed 2-[lambda]- calculus, a language with three levels: types, terms and rewrites. The types and terms are those of the simply-typed [lambda]-calculus, and the rewrites are expressions denoting sequences of [beta]-reductions and [eta]- expansions. An...
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge
1994
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| Series: | Computer Laboratory <Cambridge>: Technical report
336 |
| Subjects: | |
| Summary: | Abstract: "This paper describes the simply-typed 2-[lambda]- calculus, a language with three levels: types, terms and rewrites. The types and terms are those of the simply-typed [lambda]-calculus, and the rewrites are expressions denoting sequences of [beta]-reductions and [eta]- expansions. An equational theory is imposed on the rewrites, based on 2- categorical justifications, and the word problem for this theory is solved by finding a canonical expression in each equivalence class. The canonical form of rewrites allows us to prove several properties of the calculus, including a strong form of confluence and a classification of the long-[beta]-[eta]-normal forms in terms of their rewrites. Finally we use these properties as the basic definitions of a theory of categorical rewriting, and find that the expected relationships between confluence, strong normalisation and normal forms hold." |
| Physical Description: | 28 S. |
Staff View
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| id | DE-604.BV010413423 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:52:05Z |
| institution | BVB |
| language | English |
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| physical | 28 S. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
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| series | Computer Laboratory <Cambridge>: Technical report |
| series2 | Computer Laboratory <Cambridge>: Technical report |
| spelling | Hilken, Barnaby P. Verfasser aut Towards a proof theory of rewriting the simply-typed 2-lambda calculus Cambridge 1994 28 S. txt rdacontent n rdamedia nc rdacarrier Computer Laboratory <Cambridge>: Technical report 336 Abstract: "This paper describes the simply-typed 2-[lambda]- calculus, a language with three levels: types, terms and rewrites. The types and terms are those of the simply-typed [lambda]-calculus, and the rewrites are expressions denoting sequences of [beta]-reductions and [eta]- expansions. An equational theory is imposed on the rewrites, based on 2- categorical justifications, and the word problem for this theory is solved by finding a canonical expression in each equivalence class. The canonical form of rewrites allows us to prove several properties of the calculus, including a strong form of confluence and a classification of the long-[beta]-[eta]-normal forms in terms of their rewrites. Finally we use these properties as the basic definitions of a theory of categorical rewriting, and find that the expected relationships between confluence, strong normalisation and normal forms hold." Applied statistics, operational research sigle Computer software sigle Proof theory Computer Laboratory <Cambridge>: Technical report 336 (DE-604)BV004055605 336 |
| spellingShingle | Hilken, Barnaby P. Towards a proof theory of rewriting the simply-typed 2-lambda calculus Computer Laboratory <Cambridge>: Technical report Applied statistics, operational research sigle Computer software sigle Proof theory |
| title | Towards a proof theory of rewriting the simply-typed 2-lambda calculus |
| title_auth | Towards a proof theory of rewriting the simply-typed 2-lambda calculus |
| title_exact_search | Towards a proof theory of rewriting the simply-typed 2-lambda calculus |
| title_full | Towards a proof theory of rewriting the simply-typed 2-lambda calculus |
| title_fullStr | Towards a proof theory of rewriting the simply-typed 2-lambda calculus |
| title_full_unstemmed | Towards a proof theory of rewriting the simply-typed 2-lambda calculus |
| title_short | Towards a proof theory of rewriting |
| title_sort | towards a proof theory of rewriting the simply typed 2 lambda calculus |
| title_sub | the simply-typed 2-lambda calculus |
| topic | Applied statistics, operational research sigle Computer software sigle Proof theory |
| topic_facet | Applied statistics, operational research Computer software Proof theory |
| volume_link | (DE-604)BV004055605 |
| work_keys_str_mv | AT hilkenbarnabyp towardsaprooftheoryofrewritingthesimplytyped2lambdacalculus |