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Abstract: We present a basis for a category-theoretic account of Mendler-style inductive types. The account is based on suitably defined concepts of Mendler-style algebra and algebra homomorphism; Mendler-style inductive types are identified with initial Mendler-style algebras. We use the identification to obtain a reduction of conventional inductive types to Mendler-style inductive types and a reduction in the presence of certain restricted existential types of Mendler-style inductive types to... (Update)
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BibTeX entry: (Update)
@article{ uv:mensit,
AUTHOR = "Tarmo Uustalu and Varmo Vene",
TITLE = "Mendler-Style Inductive Types, Categorically",
JOURNAL = "Nordic Journal of Computing",
VOLUME = 6,
NUMBER = 3,
SPECIAL = "Selected Papers 10th Nordic Workshop on Programming Theory,
NWPT'98, Turku, Finland, 14--16 Oct 1998",
PAGES = "343--361",
YEAR = 1999,
URL = "citeseer.ist.psu.edu/uustalu99mendlerstyle.html",
URL = "http://www.cs.ioc.ee/~tarmo/papers/nwpt98.ps.gz" }
Citations (may not include all citations):150 The Category-Theoretic Solution of Recursive Domain Equation.. (context) - Smyth, Plotkin - 1982
84 Law and Order in Algorithmics (context) - Fokkinga - 1992
46 Recursive Types Reduced to Inductive Types (context) - Freyd - 1990
37 Formal Parametric Polymorphism - Abadi, Cardelli et al. - 1993
33 Algebraic Specification of Data Types: A Synthetic Approach (context) - Lehmann, Smyth - 1981
31 Inductive Types and Type Constraints in the Second-Order Lam.. (context) - Mendler - 1991
31 Contracting Proofs to Programs (context) - Leivant - 1990
23 Recursive Types and Type Constraints in Second-Order LambdaC.. (context) - Mendler - 1987
21 Categorical Data Types in Parametric Polymorphism (context) - Hasegawa - 1994
12 Fixed-Point Constructions in Order-Enriched Categories (context) - Wand - 1979
8 Natural Deduction for Intuitionistic Least and Greatest Fixe.. (context) - Uustalu - 1998
6 Data Structures and Program Transformation (context) - Malcolm - 1990
1 Extensions of System F by Iteration and Primitive Recursion .. (context) - Matthes - 1998
1 Structural Polymorphism (context) - TYPES - 1993
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