Sorting and Searching by Distribution: From Generic Discrimination to Generic Tries
A discriminator partitions values associated with keys into groups listed in ascending order. Discriminators can be defined generically by structural recursion on representations of ordering relations. Employing type-indexed families we demonstrate how tries with an optimal-time lookup function can...
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Format: | Conference item |
Published: |
Springer International Publishing
2013
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Summary: | A discriminator partitions values associated with keys into groups listed in ascending order. Discriminators can be defined generically by structural recursion on representations of ordering relations. Employing type-indexed families we demonstrate how tries with an optimal-time lookup function can be constructed generically in worst-case linear time. We provide generic implementations of comparison, sorting, discrimination and trie building functions and give equational proofs of correctness that highlight core relations between these algorithms. |
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