Theory of recursive functions and effective computability
Theory of recursive functions and effective computability
A connotational theory of program structure
A connotational theory of program structure
The formal semantics of programming languages: an introduction
The formal semantics of programming languages: an introduction
Subrecursive programming systems: complexity & succinctness
Subrecursive programming systems: complexity & succinctness
A Machine-Independent Theory of the Complexity of Recursive Functions
Journal of the ACM (JACM)
Control structures in hypothesis spaces: the influence on learning
Theoretical Computer Science
An Introduction to the General Theory of Algorithms
An Introduction to the General Theory of Algorithms
Experiments with Implementations of Two Theoretical Constructions
Proceedings of the Symposium on Logical Foundations of Computer Science: Logic at Botik '89
Inductive methods for proving properties of programs
Proceedings of ACM conference on Proving assertions about programs
The independence of control structures in abstract programming systems
The independence of control structures in abstract programming systems
Mathematical Theory of Computation
Mathematical Theory of Computation
A Classification of Viruses Through Recursion Theorems
CiE '07 Proceedings of the 3rd conference on Computability in Europe: Computation and Logic in the Real World
Properties Complementary to Program Self-reference
MFCS '07 Proceedings of the 32nd international symposium on Mathematical Foundations of Computer Science 2007
Program Self-reference in Constructive Scott Subdomains
CiE '09 Proceedings of the 5th Conference on Computability in Europe: Mathematical Theory and Computational Practice
Characterizing Programming Systems Allowing Program Self-Reference
Theory of Computing Systems - Special Issue: Computation and Logic in the Real World; Guest Editors: S. Barry Cooper, Elvira Mayordomo and Andrea Sorbi
Independence results for n-ary recursion theorems
FCT'09 Proceedings of the 17th international conference on Fundamentals of computation theory
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In computability theory, program self-reference is formalized by the not-necessarily-constructive form of Kleene's Recursion Theorem (krt). In a programming system in which krt holds, for any preassigned, algorithmic task, there exists a program that, in a sense, creates a copy of itself, and then performs that task using the self-copy. Interpreted in this way, such self-copying programs have usable self-knowledge. Herein, properties complementary to krt are considered. Of particular interest are those properties involving the implementation of control structures. One main result is that no property involving the implementation of denotational control structures is complementary to krt. This is in contrast to a result of Royer, which showed that implementation of if-then-else — a denotational control structure — is complementary to the constructive form of Kleene's Recursion Theorem. Examples of non-denotational control structures whose implementation is complementary to krt are then given. Some such control structures so nearly resemble denotational control structures that they might be called quasi-denotational.