Solution to the Range Problem for Combinatory Logic
نویسندگان
چکیده
The λ-theory H is obtained from β-conversion by identifying all closed unsolvable terms (or, equivalently, terms without head normal form). The range problem for the theory H asks whether a closed term has always (up to equality in H) either an infinite range or a singleton range (that is, it is a constant function). Here we give a partial solution to this problem, giving a positive answer for the theory H restricted to Combinatory Logic. The method of proof applies also to the Lazy λ-Calculus.
منابع مشابه
Higher-Order Uni cation via Combinators
We present an algorithm for uniication in the simply typed lambda calculus which enumerates complete sets of uniiers using a nitely branching search space. In fact, the types of terms may contain type-variables, so that a solution may involve type-substitution as well as term-substitution. the problem is rst translated into the problem of uniication with respect to extensional equality in combi...
متن کاملAnalysing Price, Quality and Lead Time Decisions with the Hybrid Solution Method of Fuzzy Logic and Genetic Algorithm
In this paper, the problem of determining the quality level, lead time for order delivery and price of a product produced by a manufacturer is considered. In this problem the demand for the product is influenced by all three decision variables: price, lead time and quality level. To formulate the demand function, a fuzzy rule base that estimates the demand value based on the three decision vari...
متن کاملType-2 Fuzzy Logic Approach To Increase The Accuracy Of Software Development Effort Estimation
predicting the effort of a successful project has been a major problem for software engineers the significance of which has led to extensive investigation in this area. One of the main objectives of software engineering society is the development of useful models to predict the costs of software product development. The absence of these activities before starting the project will lead to variou...
متن کاملBounded Combinatory Logic
In combinatory logic one usually assumes a fixed set of basic combinators (axiom schemes), usually K and S. In this setting the set of provable formulas (inhabited types) is Pspacecomplete in simple types and undecidable in intersection types. When arbitrary sets of axiom schemes are considered, the inhabitation problem is undecidable even in simple types (this is known as Linial-Post theorem)....
متن کاملA solution to Curry and Hindley's problem on combinatory strong reduction
It has often been remarked that the metatheory of strong reduction , the combinatory analogue of βη-reduction βη in λ -calculus, is rather complicated. In particular, although the confluence of is an easy consequence of βη being confluent, no direct proof of this fact is known. Curry and Hindley’s problem, dating back to 1958, asks for a self-contained proof of the confluence of , one which mak...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Fundam. Inform.
دوره 111 شماره
صفحات -
تاریخ انتشار 2011