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Research draft

recursion

vr.tr.recursion · XCT.QLT

Let an agent explain recursion, relay definitions, programming techniques, termination and stack concerns, type theory uses and linguistic debates from computer science, mathematics and linguistics sources with positions attributed, describe the named forms, and distinguish recursion from iteration, induction, self-similarity and circular definitions.

Thing Registry Cross-cutting context

Research draft, second pass

A second pass drafted this model: the structure a model of this thing needs, and what is known about it in the world. The line under this one says how the second half was obtained - researched against sources, or recalled without web access, in which case nothing here was read anywhere and every claim is a lead to verify. Unreviewed either way.

written by Claude from model knowledge without web access - no source was read, every claim is a lead to verify

Researched by: Claude

Purpose and description

Let an agent explain recursion, relay definitions, programming techniques, termination and stack concerns, type theory uses and linguistic debates from computer science, mathematics and linguistics sources with positions attributed, describe the named forms, and distinguish recursion from iteration, induction, self-similarity and circular definitions.

The process in which a function, structure or definition refers to itself, used in mathematics to define sequences and sets, in computer science where a function calls itself with base cases to stop, including tail recursion, which compilers can optimise into loops, and anonymous recursion through fixed-point combinators, in type theory in forms such as F-bounded quantification, and in linguistics, where recursivity lets phrases be nested inside phrases, a claim central to generative grammar whose universality is debated, as in discussions of the Piraha language; nesting and self-similarity in fractals are related ideas.

What it is for: Defining and computing things in terms of themselves.

It can be explain recursion across fields; relay programming techniques and pitfalls; describe named forms; distinguish related concepts.

Distinguishing features

Self-reference

Base cases

Call stack use

Cross-disciplinary

What it looks like

Not a physical object; seen in code, formulas, nested structures and fractals.

Physical character

key requirement: base case for termination note

Y combinator: fixed-point combinator for anonymous recursion note - Curry

Piraha recursion debate: from 2005 note - Everett, attributed

How it is recognised

Self-reference with a base case

Anonymous recursion, nesting, F-bounded quantification, tail recursion, linguistic recursivity

Iteration repeats with loops; induction is a proof method; self-similarity is geometric; circular definitions lack a base

Related models

is a kind of - in registry terms

self-similarity

is related to -

mathematical induction

includes -

tail call

is contrasted with -

iteration

In practice

Families and kinds

direct and mutual recursion

tail recursion

structural recursion

anonymous recursion

recursive types and bounded quantification

recursion in syntax

Standards and regulation

No regulation; language standards specify tail call behaviour in some languages such as Scheme

Failure modes and hazards

Infinite recursion without base cases

Stack overflow

Overstating linguistic universality claims

Also called

anonymous recursionnestingF-bounded quantificationtail recursionlinguistic recursivity

Where this came from

wikidata · CC0 1.0

Drafted structure

Bundle to layer to finding to question, as the second pass will find it: 4 bundles · 8 layers · 8 findings · 16 questions.

Understand What recursion is.

Definition.

Definition

Definition.

Definition

Definition.

  1. What is recursion, and how does it differ from iteration, induction, self-similarity and circular definitions? definition
  2. Is the question about programming, mathematics, type theory or linguistics? boundary

Forms

Named forms.

Forms

Forms.

  1. What are anonymous recursion, nesting, F-bounded quantification, tail recursion and linguistic recursivity? definition
  2. Which entry fits the specific form? action
Computing Programming.

Sources.

Base cases

Base cases and termination.

Base cases

Base cases.

  1. How do base cases stop recursion, and what causes stack overflow? provenance
  2. Which references are standard? provenance

Tail calls

Tail call optimisation.

Tail calls

Tail calls.

  1. How do compilers turn tail recursion into loops, and which languages guarantee it? provenance
  2. Which sources are cited? provenance
Theory Mathematics and types.

Science.

Functions

Recursive functions.

Functions

Functions.

  1. How did recursive function theory shape computability? provenance
  2. Which entry fits computable function? action

Types

Recursive types.

Types

Types.

  1. What is F-bounded quantification in object-oriented type systems? provenance
  2. Which entry fits bounded quantification? action
Context Language.

Attribution.

Syntax

Recursion in syntax.

Syntax

Syntax.

  1. Why do generative linguists treat recursion as central to language? provenance
  2. Which entry fits generative grammar? action

Piraha debate

Piraha debate.

Piraha debate

Piraha debate.

  1. What did Everett and his critics argue about recursion in Piraha, with positions attributed? provenance
  2. Is the presentation neutral and attributed? boundary

What the second pass must settle

  • Should linguistic recursion be a separate entry?
  • How should computer science sources be linked?
  • Should F-bounded quantification be moved to type theory entries?