We ask the attention for a de nition schema from higher order subrecursion the ory called bar recursion Bar recursion originates with Spector where bar recursion of all nite types is shown to characterize the class of provably total re cursive functions of analysis This class has also been characterized by Girard as those functions which are de nable in the second order typed lambda calculus or...

We question the need for recursion in human cognitive processing by arguing that a generally simpler and less resource demanding process – iteration – is sufficient to account for human natural language and arithmetic performance. We claim that the only motivation for recursion, the infinity in natural language and arithmetic competence, is equally approachable by iteration and recursion. Secon...

Recursion can complicate program analysis significantly. Some program analyzers simply ignore recursion or even refuse to check recursive programs. In this paper, we propose an algorithm that uses a recursion-free program analyzer as a black box to check recursive programs. With extended program constructs for assumptions, assertions, and nondeterministic values, our algorithm computes function...

Using the methods of the theory of formal symmetries, we obtain new easily verifiable sufficient conditions for a recursion operator to produce a hierarchy of local generalized symmetries. An important advantage of our approach is that under certain mild assumptions it allows to bypass the cumbersome check of hereditariness of the recursion operator in question, what is particularly useful for ...

In this paper we explain how recursion operators can be used to structure and reason about program semantics within a functional language. In particular, we show how the recursion operator fold can be used to structure denotational semantics, how the dual recursion operator unfold can be used to structure operational semantics, and how algebraic properties of these operators can be used to reas...

The focus of this paper is the technique of recur8\on analysis. Recursion analysis is used by the Boyer-Moore Theorem Prover to choose an appropriate induct ion schema and variable to prove theorems by mathematical induct ion. A rat ional reconstruction of recursion analysis is out l ined, using the technique of proof plans. This rat ional reconstruction suggests an extension of recursion analy...