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Mutual recursion is very common in functional programming, and is often used for programs written in LISP, Scheme, ML, and similar programming languages. For example, Abelson and Sussman describe how a meta-circular evaluator can be used to implement LISP with an eval-apply cycle. [7] In languages such as Prolog, mutual recursion is almost ...
The first Hofstadter sequences were described by Douglas Richard Hofstadter in his book Gödel, Escher, Bach.In order of their presentation in chapter III on figures and background (Figure-Figure sequence) and chapter V on recursive structures and processes (remaining sequences), these sequences are:
The first AI project by Hofstadter stemmed from his teenage fascination with number sequences. When he was 17, he studied the way that triangular and square numbers interleave, and eventually found a recursive relation describing it. In his first course on AI, he set to the students and to himself the task of writing a program that could ...
A strange loop is a hierarchy of levels, each of which is linked to at least one other by some type of relationship. A strange loop hierarchy is "tangled" (Hofstadter refers to this as a "heterarchy"), in that there is no well defined highest or lowest level; moving through the levels, one eventually returns to the starting point, i.e., the original level.
Hofstadter seeks to remedy this problem in I Am a Strange Loop by focusing on and expounding the central message of Gödel, Escher, Bach. He demonstrates how the properties of self-referential systems, demonstrated most famously in Gödel's incompleteness theorems , can be used to describe the unique properties of minds .
Course-of-values recursion defines primitive recursive functions. Some forms of mutual recursion also define primitive recursive functions. The functions that can be programmed in the LOOP programming language are exactly the primitive recursive functions. This gives a different characterization of the power of these functions.
Screenshot of Metacat (Copycat successor) in operation, slightly edited with commentary at bottom. Copycat is a model of analogy making and human cognition based on the concept of the parallel terraced scan, developed in 1988 by Douglas Hofstadter, Melanie Mitchell, and others at the Center for Research on Concepts and Cognition, Indiana University Bloomington. [1]
BlooP and FlooP (Bounded loop and Free loop) are simple programming languages designed by Douglas Hofstadter to illustrate a point in his book Gödel, Escher, Bach. [1] BlooP is a Turing-incomplete programming language whose main control flow structure is a bounded loop (i.e. recursion is not permitted [citation needed]).