Efficient Extensional Binary Tries

Andrew W. Appel, Xavier Leroy

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


Lookup tables (finite maps) are a ubiquitous data structure. In pure functional languages they are best represented using trees instead of hash tables. In pure functional languages within constructive logic, without a primitive integer type, they are well represented using binary tries instead of search trees. In this work, we introduce canonical binary tries, an improved binary-trie data structure that enjoys a natural extensionality property, quite useful in proofs, and supports sparseness more efficiently. We provide full proofs of correctness in Coq. We provide microbenchmark measurements of canonical binary tries versus several other data structures for finite maps, in a variety of application contexts; as well as measurement of canonical versus original tries in two big, real systems. The application context of data structures contained in theorem statements imposes unusual requirements for which canonical tries are particularly well suited.

Original languageEnglish (US)
Article number8
JournalJournal of Automated Reasoning
Issue number1
StatePublished - Mar 2023
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Software
  • Computational Theory and Mathematics
  • Artificial Intelligence


  • CompCert
  • Coq
  • Program proof
  • VST
  • Verified data structures


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