Parallel program design: a foundation
Parallel program design: a foundation
Research topics in functional programming
Co-induction in relational semantics
Theoretical Computer Science
Terminal coalgebras in well-founded set theory
Theoretical Computer Science
Set theory for verification. I: from foundations to functions
Journal of Automated Reasoning
Communication and Concurrency
Reasonong about Classess in Object-Oriented Languages: Logical Models and Tools
ESOP '98 Proceedings of the 7th European Symposium on Programming: Programming Languages and Systems
Inductive Definitions in the system Coq - Rules and Properties
TLCA '93 Proceedings of the International Conference on Typed Lambda Calculi and Applications
A Concrete Final Coalgebra Theorem for ZF Set Theory
TYPES '94 Selected papers from the International Workshop on Types for Proofs and Programs
On the Foundation of Final Semantics: Non-Standard Sets, Metric Spaces, Partial Orders
Proceedings of the REX Workshop on Sematics: Foundations and Applications
A Fixedpoint Approach to Implementing (Co)Inductive Definitions
CADE-12 Proceedings of the 12th International Conference on Automated Deduction
Category Theory and Computer Science
Proof Principles for Datatypes with Iterated Recursion
CTCS '97 Proceedings of the 7th International Conference on Category Theory and Computer Science
Revised Lectures from the International Summer School and Workshop on Algebraic and Coalgebraic Methods in the Mathematics of Program Construction
Algebraic and coalgebraic methods in the mathematics of program construction
On the final sequence of a finitary set functor
Theoretical Computer Science
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A special final coalgebra theorem, in the style of Aczel (1988), is proved within standard Zermelo–Fraenkel set theory. Aczel's Anti-Foundation Axiom is replaced by a variant definition of function that admits non-well-founded constructions. Variant ordered pairs and tuples, of possibly infinite length, are special cases of variant functions. Analogues of Aczel's solution and substitution lemmas are proved in the style of Rutten and Turi (1993). The approach is less general than Aczel's, but the treatment of non-well-founded objects is simple and concrete. The final coalgebra of a functor is its greatest fixedpoint.Compared with previous work (Paulson, 1995a), iterated substitutions and solutions are considered, as well as final coalgebras defined with respect to parameters. The disjoint sum construction is replaced by a smoother treatment of urelements that simplifies many of the derivations.The theory facilitates machine implementation of recursive definitions by letting both inductive and coinductive definitions be represented as fixed points. It has already been applied to the theorem prover Isabelle (Paulson, 1994).