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Well-founded coalgebras, revisited


Theoretical models of recursion schemes have been well studied under the names well-founded coalgebras, recursive coalgebras, corecursive algebras and Elgot algebras. Much of this work focuses on conditions ensuring unique or canonical solutions, e.g. when the coalgebra is well founded.

If the coalgebra is not well founded, then there can be multiple solutions. The standard semantics of recursive programs gives a particular solution, typically the least fixpoint of a certain monotone map on a domain whose least element is the totally undefined function; but this solution may not be the desired one. We have recently proposed programming language constructs to allow the specification of alternative solutions and methods to compute them. We have implemented these new constructs as an extension of OCaml.

In this paper, we prove some theoretical results characterizing well-founded coalgebras, along with several examples for which this extension is useful. We also give several examples that are not well founded but still have a desired solution. In each case, the function would diverge under the standard semantics of recursion, but can be specified and computed with the programming language constructs we have proposed.

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J. Adámek , D. Lücke and S. Milius (2007). Recursive coalgebras of finitary functors. Theoretical Informatics and Applications 41 (4) 447462.

J. Adámek , S. Milius and S. Velebil (2006). Elgot algebras. Logical Methods in Computer Science 2 (5:4) 131.

V. Capretta , T. Uustalu and V. Vene (2009). Corecursive algebras: A study of general structured corecursion. In: M. Vinicius , M. Oliveira and J. Woodcock (eds.) Formal Methods: Foundations and Applications, 12th Brazilian Symp. Formal Methods (SBMF 2009). Lecture Notes in Computer Science 5902, Springer, Berlin, 84100.

D. Harel and D. Kozen (1984). A programming language for the inductive sets, and applications. Information and Control 63 (1–2) 118139.

J.-B. Jeannin , D. Kozen and A. Silva (March 2013). Language constructs for non-well-founded computation. In: M. Felleisen and P. Gardner (eds.) 22nd European Symposium on Programming (ESOP 2013). Lecture Notes in Computer Science 7792, Springer, Rome, Italy, 6180.

J. Lambek (1968). A fixpoint theorem for complete categories. Mathematische Zeitschrift 103 (2) 151161.

S. Mac Lane (1971). Categories for the Working Matematician. Springer.

G. Osius (1974). Categorical set theory: A characterization of the category of sets. Journal of Pure and Applied Algebra 4 79119.

D. Syme (2006). Initializing mutually referential abstract objects: The value recursion challenge. Electronic Notes in Theoretical Computer Science, 148 (2) 325.

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Mathematical Structures in Computer Science
  • ISSN: 0960-1295
  • EISSN: 1469-8072
  • URL: /core/journals/mathematical-structures-in-computer-science
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