A system of rules for transforming programs is described, with the programs in the form of recursion equations An initially very simple, lucid. and hopefully correct program IS transformed into a more efficient one by altering the recursion structure Illustrative examples of program transformations

MLis as tatically typed programming language thatis stwR for the consGHw[URY of boths mall and large programs "Programming in thes mall"is captured by StandardML Core language. "Programming in the large" is captured by Modules language that provides consN1N1N for organisw[ related Core language definitions intos elf-contained modules with desAA11w[ e interfaces While the Core is usA to expres details ofalgorithms and data sawRARNw[U Modules is use toexpres the overalla chitecture of asYG wares ysewA In Standard ML, modular programs mus have asANH1Yw hierarchicalslwN---HA1w the dependency between modules can never be cyclic. In particular, definitions of mutuallyrecursA e Core types and values that aris frequently in practice, can neverswN module boundaries This limitation compromisU modular programming, forcing the programmer to merge conceptually (i.e. architecturally) disural modules We prop os a practical and sndwN extensNY of the Modules language thatcaters for cyclic dependencies between both types andterms defined inswHAUYw modules OurdesEH leverages exissH features of the language,s upports stsU---H compilation of mutually recursw e modules and is eas to implement.

We discuss resource-bounded measures on the class of recursive structures and prove that with respect to such measures a random recursive structure is almost surely isomorphic to the unique countable model of the extension axioms.

In computer science, one is interested mainly in finite objects. Insofar as infinite objects are of interest, they must be computable, i.e., recursive, thus admitting an effective finite representation. This leads to the notion of a recursive graph, or, more generally, a recursive structure, model

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, such as efficient subtyping algorithms. Unlike nominal type systems, implementing a (recursive) structural type system remains a significant challenge. This is because a large gap exists between the formalisation of a recursive structural type system, and its algorithmic realisation. In this paper, we aim to reduce

A long-standing difficulty for connectionist modeling has been how to represent variable-sized recursive data structures, such as trees and lists, in fixed-width patterns. This paper presents a connectionist architecture which automatically develops compact distributed representations

Complex recursive structures, such as fractals, are often described by sets of production rules, also known as L-systems. According to this description, a structure is characterized by a sequence of elements, or letters, from a finite alphabet; a production rule prescribes replacement of each

. Most imperative languages only offer arrays as "first-class" data structures. Other data structures, especially recursive data structures such as trees, have to be manipulated using explicit control of memory, i.e., through pointers to explicitly allocated portions of memory. We believe