Confluence of the coinductive [lambda]-calculus
نویسنده
چکیده
The coinductive λ-calculus Λ arises by a coinductive interpretation of the grammar of the standard λ-calculus Λ and contains non-wellfounded λ-terms. An appropriate notion of reduction is analyzed and proven to be confluent by means of a detailed analysis of the usual Tait/MartinLöf style development argument. This yields bounds for the lengths of those joining reduction sequences that are guaranteed to exist by confluence. These bounds also apply to the wellfounded λ-calculus, thus adding quantitative information to the classic result.
منابع مشابه
A Coinductive Confluence Proof for Infinitary Lambda-Calculus
We present a new coinductive proof of confluence of Böhm reduction in infinitary lambda-calculus. The proof is simpler than previous proofs of this result. The technique of the proof is new, i.e., it is not merely a coinductive reformulation of any earlier proofs.
متن کاملCoinductive Techniques in Infinitary Lambda-Calculus
The main aim of this paper is to promote a certain informal but rigorous style of doing coinductive proofs, similar to inductive proofs as commonly done by mathematicians. For this purpose we develop a theory which may serve as a reasonably direct justification for coinductive proofs written in this informal style, i.e., converting an informal coinductive proof into a non-coinductive argument m...
متن کاملStandardization for the Coinductive Lambda-Calculus
In the calculus Λ of possibly non-wellfounded λ-terms, standardization is proved for a parallel notion of reduction. For this system confluence has recently been established by means of a bounding argument for the number of reductions provoked by the joining function which witnesses the confluence statement. Similarly, bounds have to be introduced in order to turn the proof of standardization f...
متن کاملMonad Translating Inductive and Coinductive Types
We show that the call-by-name monad translation of simply typed lambda calculus extended with sum and product types extends to special and general inductive and coinductive types so that its crucial property of preserving typings and βand commuting reductions is maintained. Specific similar-purpose translations such as CPS translations follow from the general monad translations by specializatio...
متن کاملCall-by-Value and Call-by-Name Dual Calculi with Inductive and Coinductive Types
This paper extends the dual calculus with inductive types and coinductive types. The paper first introduces a non-deterministic dual calculus with inductive and coinductive types. Besides the same duality of the original dual calculus, it has the duality of inductive and coinductive types, that is, the duality of terms and coterms for inductive and coinductive types, and the duality of their re...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Theor. Comput. Sci.
دوره 311 شماره
صفحات -
تاریخ انتشار 2004