Representing Contractive Functions on Streams (Extended Version)
نویسندگان
چکیده
Streams, or infinite lists, have many applications in functional programming, and are naturally defined using recursive equations. But how do we ensure that such equations make sense, i.e. that they actually produce well-defined streams? In this article we present a new approach to this problem, based upon the topological notion of contractive functions on streams. In particular, we give a sound and complete representation theorem for contractive functions on streams, illustrate the use of this theorem as a practical means to produce well-defined streams, and show how the efficiency of the resulting definitions can be improved using another representation of contractive functions.
منابع مشابه
Representing Contractive Functions on Streams
Streams, or infinite lists, have many applications in functional programming, and are naturally defined using recursive equations. But how do we ensure that such equations make sense, i.e. that they actually produce well-defined streams? In this article we present a new approach to this problem, based upon the topological notion of contractive functions on streams. In particular, we give a soun...
متن کاملCoinductive Properties of Lipschitz Functions on Streams
A simple hierarchical structure is imposed on the set of Lipschitz functions on streams (i.e. sequences over a fixed alphabet set) under the standard metric. We prove that sets of non-expanding and contractive functions are closed under a certain coiterative construction. The closure property is used to construct new final stream coalgebras over finite alphabets. For an example, we show that th...
متن کامل$C$-class Functions and Common Fixed Point Theorems Satisfying $varphi $-weakly Contractive Conditions
In this paper, we discuss and extend some recent common fixed point results established by using $varphi-$weakly contractive mappings. A very important step in the development of the fixed point theory was given by A.H. Ansari by the introduction of a $C-$class function. Using $C-$class functions, we generalize some known fixed point results. This type of functions is a very important class of ...
متن کاملOn the existence of fixed points for contraction mappings depending on two functions
In this paper we study the existence of fixed points for mappings defined on complete metric spaces, satisfying a general contractive inequality depending on two additional mappings.
متن کاملStable Iteration Procedures in Metric Spaces which Generalize a Picard-Type Iteration
This paper investigates the stability of iteration procedures defined by continuous functions acting on self-maps in continuous metric spaces. Some of the obtained results extend the contraction principle to the use of altering-distance functions and extended altering-distance functions, the last ones being piecewise continuous. The conditions for themaps to be contractive for the achievement o...
متن کامل