Assertions and Recursions
نویسنده
چکیده
We provide an algebraic description of subtypes and the way they propagate through recursive functions. By abstracting from the concrete domain of functions or relations we obtain a framework which is independent of strict or non-strict, deterministic or non-deterministic semantics. Applications include efficiency increasing simplification of recursions as well as proofs about recursions by noetherian induction, such as termination proofs.
منابع مشابه
A Theory of Design-by-Contract for Distributed Multiparty Interactions
The approach known as Design by Contract (DbC) [23] promotes reliable software development through elaboration of type signatures for sequential programs with logical formulae. This paper presents an assertion method which generalises the notion of DbC to multiparty distributed interactions, enabling the specification and verification of distributed multiparty protocols, based on the π-calculus...
متن کاملA Fast Publicly Verifiable Secret Sharing Scheme using Non-homogeneous Linear Recursions
A non-interactive (t,n)-publicly veriable secret sharing scheme (non-interactive (t,n)-PVSS scheme) is a (t,n)-secret sharing scheme in which anyone, not only the participants of the scheme, can verify the correctness of the produced shares without interacting with the dealer and participants. The (t,n)-PVSS schemes have found a lot of applications in cryptography because they are suitable for<...
متن کاملAnswering N-chain Recursive Queries with Arithmetic
N-chain recursions are important because the majority of single-linear recursions can be compiled to N-chain recursions or so-called bounded recursions [8], which are not recursive at all. It appeared for some time [3, 5] that ALL single linear recursions could be converted to N-chain recursions. Although that is now known [13] to be inaccurate it is still clear that the most popular forms of S...
متن کاملOn Sampling Rates in Stochastic Recursions
We consider the context of “stochastic recursions,” that is, recursions that involve quantities needing to be estimated using a stochastic simulation. Examples include certain stochastic adaptations of fixed-point recursions, line search recursions, and trust-region recursions obtained by replacing function and derivative values appearing within the recursion by their Monte Carlo counterparts. ...
متن کاملA Functional-analytical Approach to the Asymptotics of Recursions
We propose a functional-analytical method to investigate the long-term behavior of recursions (difference equations). It is based on a formulation of given (implicit) recursions as abstract operator equations in sequence spaces. Solving them using appropriate tools from nonlinear analysis yields quantitative convergence results and equips us with a method to verify summable or subexponential de...
متن کامل