Recursion in programs, thought, and language

Abstract

This article presents a theory of recursion in thinking and language. In the logic of computability, a function maps one or more sets to another, and it can have a recursive definition that is semi-circular, i.e., referring in part to the function itself. Any function that is computableand many are notcan be computed in an infinite number of distinct programs. Some of these programs are semi-circular too, but they needn't be, because repeated loops of instructions can compute any recursive function. Our theory aims to explain how naive individuals devise informal programs in natural language, and is itself implemented in a computer program that creates programs. Participants in our experiments spontaneously simulate loops of instructions in kinematic mental models. They rely on such loops to compute recursive functions for rearranging the order of cars in trains on a track with a siding. Kolmogorov complexity predicts the relative difficulty of abducing such programsfor easy rearrangements, such as reversing the order of the cars, to difficult ones, such as splitting a train in two and interleaving the two resulting halves (equivalent to a faro shuffle). This rearrangement uses both the siding and part of the track as working memories, shuffling cars between them, and so it relies on the power of a linear-bounded computer. Linguistic evidence implies that this power is more than necessary to compose the meanings of sentences in natural language from those of their grammatical constituents. KeywordsComputational power . Recursion . Informal programs . Grammar . Mental models . Working memory "General rules for programming have been discovered. Most of them have been used in Kansas City freight yards for some time" -Lehmer (1949, p.142) * P. N. Johnson-Laird

The Significances of Recursion in Early Language Learning: The Study of Psycholinguistics

“…They can engage in routine social conversation in a limited number of professions, participate in formal and informal conversations with correct grammar and vocabulary about practical, social, and professional issues, and use the target language fluently and accurately at all levels of professional context (Amiruddin & Jannah, 2022). To provide an overview, the concept of recursion was developed to address the problem of stimulus poverty (Johnson-Laird et al, 2022) and(Poletiek et al, 2018). The Problem of stimulus poverty is that the students can produce phrases that they have never heard before and hence do not originate from their external input (Johnson-Laird et al, 2022) and (Shen et al, 2002).…”

“…To provide an overview, the concept of recursion was developed to address the problem of stimulus poverty (Johnson-Laird et al, 2022) and(Poletiek et al, 2018). The Problem of stimulus poverty is that the students can produce phrases that they have never heard before and hence do not originate from their external input (Johnson-Laird et al, 2022) and (Shen et al, 2002). Given that language knowledge is supposed to be tacit and partially innate/internal, it refers as 'I(internal/innate)-language'.…”

“…The power to produce an unlimited number of sentences and meaningful utterances is the core of language. Because of recursion, there is no limit to the amount of things we may say, even inside a single phrase (Johnson-Laird et al, 2022).…”

“…Recursion is commonly characterized as embedding one sentence within another; however this definition is not universally accepted. When the term refers to language, the initial usage of recursion in mathematics, formal logic, and computer science presents a definitional challenge (Johnson-Laird et al, 2022). In these disciplines, recursion refers to any instruction that invokes another instruction of the same kind and has a terminating condition.…”

Evaluation, computation and coding of iterative function using recursive approach

“…Johnson-Naird et al (2021) explained how naïve individuals devise informal programs in natural language and is itself implemented in a computer program that creates programs using recursion. Jinping (2013) focused on the analytical program writing technique of the recursive algorithm, as well as the optimization of recursive program. Zhu and Sun (2023) analyzed the concept and function of C language recursion, process description of recursion algorithm, and finally gives the implementation strategy of C language recursion algorithm.…”