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» Initial Algebra Semantics Is Enough!
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TLCA
2007
Springer
13 years 11 months ago
Initial Algebra Semantics Is Enough!
Initial algebra semantics is a cornerstone of the theory of modern functional programming languages. For each inductive data type, it provides a fold combinator encapsulating struc...
Patricia Johann, Neil Ghani
TLCA
2009
Springer
13 years 11 months ago
Initial Algebra Semantics for Cyclic Sharing Structures
Terms are a concise representation of tree structures. Since they can be naturally defined by an inductive type, they offer data structures in functional programming and mechanis...
Makoto Hamana
CSL
2010
Springer
13 years 6 months ago
Fibrational Induction Rules for Initial Algebras
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 res...
Neil Ghani, Patricia Johann, Clément Fumex
APLAS
2004
ACM
13 years 10 months ago
Build, Augment and Destroy, Universally
Abstract. We give a semantic footing to the fold/build syntax of programming with inductive types, covering shortcut deforestation, based on a universal property. Specifically, we...
Neil Ghani, Tarmo Uustalu, Varmo Vene
POPL
2008
ACM
14 years 5 months ago
Foundations for structured programming with GADTs
GADTs are at the cutting edge of functional programming and become more widely used every day. Nevertheless, the semantic foundations underlying GADTs are not well understood. In ...
Patricia Johann, Neil Ghani