Statman's 1-Section Theorem
نویسنده
چکیده
Statman's 1-Section Theorem [17] is an important but little-known result in the model theory of the simplytyped λ-calculus. The λ-Section Theorem states a necessary and sufficient condition on models of the simplytyped λ-calculus for determining whether βη-equational reasoning is complete for proving equations that hold in a model. We review the statement of the theorem, give a detailed proof, and discuss its significance. Comments University of Pennsylvania Department of Computer and Information Science Technical Report No.MSCIS-92-03. This technical report is available at ScholarlyCommons: http://repository.upenn.edu/cis_reports/378 Statmans's 1-Section Theorem MS-CIS-92-03 LOGIC & COMPUTATION 46
منابع مشابه
A Simple Proof of a Theorem of Statman
In this note, we reprove a theorem of Statman that deciding the-equality of two rst-order typable-terms is not elementary recursive Sta79]. The basic idea of our proof, like that of Statman's, is the Henkin quantiier elimination procedure Hen63]. However, our coding is much simpler, and easy to understand.
متن کاملAn alternate proof of Statman's finite completeness theorem
Statman’s finite completeness theorem says that for every pair of non-equivalent terms of simply-typed lamda-calculus there is a model that separates them. A direct method of constructing this model is provided using a simple induction on the Böhm tree of the term.
متن کاملA New Theorem Concerning Scattering of Electromagnetic Waves in Multilayered Metamaterial Spherical Structures
The proposed theorem in this paper is indicative of a kind of duality in the propagation of waves in the dual media of and in the spherical structures. Independent of wave frequency, the number of layers, their thickness, and the type of polarization, this theorem holds true in case of any change in any of these conditions. Theorem: Consider a plane wave incident on a multilayered spheric...
متن کاملStatman's Hierarchy Theorem
In the Simply Typed λ-calculus [Hin97, BDS13] Statman investigates the reducibility relation ≤βη between types: for A,B ∈ T, types freely generated using → and a single ground type 0, define A ≤βη B if there exists a λ-definable injection from the closed terms of type A into those of type B. Unexpectedly, the induced partial order is the (linear) well-ordering (of order type) ω + 4, see [Sta80a...
متن کاملExploiting Strong Convexity from Data with Primal-Dual First-Order Algorithms
In the following appendices, we provide detailed proofs of theorems stated in the main paper. In Section A we first prove a basic inequality which is useful throughout the rest of the convergence analysis. Section B contains general analysis of the batch primal-dual algorithm that are common for proving both Theorem 1 and Theorem 3. Sections C, D, E and F give proofs for Theorem 1, Theorem 3, T...
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:
- Inf. Comput.
دوره 116 شماره
صفحات -
تاریخ انتشار 1995