Abstract
| Original language | English |
|---|---|
| Title of host publication | Computer Science Logic |
| Subtitle of host publication | 24th International Workshop, CSL 2010, 19th Annual Conference of the EACSL, Brno, Czech Republic, August 23-27, 2010. Proceedings |
| Editors | Anuj Dawar , Helmut Veith |
| Publisher | Springer |
| Pages | 336-350 |
| Number of pages | 15 |
| Volume | 6247 |
| ISBN (Print) | 978-3-642-15204-7 |
| DOIs | |
| Publication status | Published - 2010 |
Publication series
| Name | Lecture Notes In Computer Science |
|---|---|
| Publisher | Springer |
| Volume | 6247 |
| ISSN (Print) | 0302-9743 |
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Keywords
- fibrational Induction Rules
- initial algebras
- computer science
Cite this
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Fibrational induction rules for initial algebras. / Ghani, Neil; Johann, Patricia; Fumex, Clement.
Computer Science Logic: 24th International Workshop, CSL 2010, 19th Annual Conference of the EACSL, Brno, Czech Republic, August 23-27, 2010. Proceedings. ed. / Anuj Dawar ; Helmut Veith. Vol. 6247 Springer, 2010. p. 336-350 (Lecture Notes In Computer Science; Vol. 6247).Research output: Chapter in Book/Report/Conference proceeding › Conference contribution book
TY - GEN
T1 - Fibrational induction rules for initial algebras
AU - Ghani, Neil
AU - Johann, Patricia
AU - Fumex, Clement
PY - 2010
Y1 - 2010
N2 - This paper provides an induction rule that can be used to prove properties of data structures whose types are inductive, i.e., are carriers of initial algebras of functors. Our results are semantic in nature and are inspired by Hermida and Jacobs’ elegant algebraic formulation of induction for polynomial data types. Our contribution is to derive, under slightly different assumptions, an induction rule that is generic over all inductive types, polynomial or not. Our induction rule is generic over the kinds of properties to be proved as well: like Hermida and Jacobs, we work in a general fibrational setting and so can accommodate very general notions of properties on inductive types rather than just those of particular syntactic forms. We establish the correctness of our generic induction rule by reducing induction to iteration. We show how our rule can be instantiated to give induction rules for the data types of rose trees, finite hereditary sets, and hyperfunctions. The former lies outside the scope of Hermida and Jacobs’ work because it is not polynomial; as far as we are aware, no induction rules have been known to exist for the latter two in a general fibrational framework. Our instantiation for hyperfunctions underscores the value of working in the general fibrational setting since this data type cannot be interpreted as a set.
AB - This paper provides an induction rule that can be used to prove properties of data structures whose types are inductive, i.e., are carriers of initial algebras of functors. Our results are semantic in nature and are inspired by Hermida and Jacobs’ elegant algebraic formulation of induction for polynomial data types. Our contribution is to derive, under slightly different assumptions, an induction rule that is generic over all inductive types, polynomial or not. Our induction rule is generic over the kinds of properties to be proved as well: like Hermida and Jacobs, we work in a general fibrational setting and so can accommodate very general notions of properties on inductive types rather than just those of particular syntactic forms. We establish the correctness of our generic induction rule by reducing induction to iteration. We show how our rule can be instantiated to give induction rules for the data types of rose trees, finite hereditary sets, and hyperfunctions. The former lies outside the scope of Hermida and Jacobs’ work because it is not polynomial; as far as we are aware, no induction rules have been known to exist for the latter two in a general fibrational framework. Our instantiation for hyperfunctions underscores the value of working in the general fibrational setting since this data type cannot be interpreted as a set.
KW - fibrational Induction Rules
KW - initial algebras
KW - computer science
UR - http://mfcsl2010.fi.muni.cz/csl
U2 - 10.1007/978-3-642-15205-4_27
DO - 10.1007/978-3-642-15205-4_27
M3 - Conference contribution book
SN - 978-3-642-15204-7
VL - 6247
T3 - Lecture Notes In Computer Science
SP - 336
EP - 350
BT - Computer Science Logic
A2 - Dawar , Anuj
A2 - Veith, Helmut
PB - Springer
ER -