The category-theoretic solution of recursive program schemes

This is a corrigendum for our paper [MM]. The main results are correct, but we oer some changes to the denitions and proofs concerning interpreted recursive program schemes.

[1]  Michael Barr,et al.  Terminal Coalgebras in Well-Founded Set Theory , 1993, Theor. Comput. Sci..

[2]  Jirí Adámek,et al.  Iterative algebras at work , 2006, Mathematical Structures in Computer Science.

[3]  Stefan Milius Completely iterative algebras and completely iterative monads , 2005, Inf. Comput..

[4]  Jirí Adámek,et al.  On Algebras with Iteration , 2008, J. Log. Comput..

[5]  Stefan Milius On Iteratable Endofunctors , 2002, CTCS.

[6]  Joseph A. Goguen,et al.  Initial Algebra Semantics and Continuous Algebras , 1977, J. ACM.

[7]  Z. Ésik,et al.  Iteration Theories: The Equational Logic of Iterative Processes , 1993 .

[8]  Stefan Milius,et al.  Elgot Algebras † ( Extended Abstract ) , 2006 .

[9]  Christoph Lüth,et al.  Algebras, Coalgebras, Monads and Comonads , 2001, CMCS.

[10]  C. C. Elgot,et al.  On the algebraic structure of rooted trees , 1978 .

[11]  Christoph Lüth,et al.  Solving Algebraic Equations Using Coalgebra , 2003, RAIRO Theor. Informatics Appl..

[12]  Stefan Milius,et al.  The Category Theoretic Solution of Recursive Program Schemes , 2005, CALCO.

[13]  Irène Guessarian,et al.  Algebraic semantics , 1981, Lecture Notes in Computer Science.

[14]  J. Lambek A fixpoint theorem for complete categories , 1968 .

[15]  Maurice Nivat,et al.  The metric space of infinite trees. Algebraic and topological properties , 1980, Fundam. Informaticae.

[16]  Jirí Adámek,et al.  On the Greatest Fixed Point of a Set Functor , 1995, Theor. Comput. Sci..

[17]  Michael F. Barnsley,et al.  Fractals everywhere , 1988 .

[18]  Stefan Milius,et al.  On coalgebra based on classes , 2004, Theor. Comput. Sci..

[19]  Peter Aczel,et al.  Infinite trees and completely iterative theories: a coalgebraic view , 2003, Theor. Comput. Sci..

[20]  B. Courcelle Fundamental properties of infinite trees , 1983 .

[21]  Christoph Lüth,et al.  Dualising Initial Algebras , 2003, Math. Struct. Comput. Sci..

[22]  D. Harrison,et al.  Vicious Circles , 1995 .

[23]  Peter Aczel,et al.  Non-well-founded sets , 1988, CSLI lecture notes series.

[24]  Lawrence S. Moss Uniform Functors on Sets , 2006, Essays Dedicated to Joseph A. Goguen.

[25]  Jirí Adámek,et al.  Free iterative theories: a coalgebraic view , 2003, Mathematical Structures in Computer Science.

[26]  Jirí Adámek On a Description of Terminal Coalgebras and Iterative Theories , 2003, CMCS.

[27]  A. R. D. Mathias,et al.  NON‐WELL‐FOUNDED SETS (CSLI Lecture Notes 14) , 1991 .

[28]  Jirí Adámek,et al.  Banach's Fixed-Point Theorem as a base for data-type equations , 1994, Appl. Categorical Struct..

[29]  Stephen L. Bloom,et al.  All Solutions of a System of Recursion Equations in Infinite Trees and Other Contraction Theories , 1983, J. Comput. Syst. Sci..

[30]  C. C. Elgot Monadic Computation And Iterative Algebraic Theories , 1982 .

[31]  Stefan Milius,et al.  Terminal coalgebras and free iterative theories , 2006, Inf. Comput..

[32]  Stefan Milius,et al.  From Iterative Algebras to Iterative Theories (Extended Abstract) , 2004, CMCS.

[33]  Peter Aczel,et al.  A Coalgebraic View of Infinite Trees and Iteration , 2001, CMCS.

[34]  Ralph Matthes,et al.  Substitution in Non-wellfounded Syntax with Variable Binding , 2003, CMCS.

[35]  James Worrell,et al.  On the final sequence of a finitary set functor , 2005, Theor. Comput. Sci..

[36]  Lawrence S. Moss Parametric corecursion , 2001, Theor. Comput. Sci..

[37]  Pierre America,et al.  Solving Reflexive Domain Equations in a Category of Complete Metric Spaces , 1989, J. Comput. Syst. Sci..

[38]  Jirí Adámek,et al.  On tree coalgebras and coalgebra presentations , 2004, Theor. Comput. Sci..

[39]  S. Lane Categories for the Working Mathematician , 1971 .

[40]  Tom Leinster General self-similarity: an overview , 2004 .

[41]  J. Adámek,et al.  Automata and Algebras in Categories , 1990 .