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Saturating Sorting without Sorts

18 pagesPublished: May 26, 2024


We present a first-order theorem proving framework for establishing the correctness of functional programs implementing sorting algorithms with recursive data structures. We formalize the semantics of recursive programs in many-sorted first-order logic and integrate sortedness/permutation properties within our first-order formalization. Rather than focus- ing on sorting lists of elements of specific first-order theories, such as integer arithmetic, our list formalization relies on a sort parameter abstracting (arithmetic) theories and hence concrete sorts. We formalize the permutation property of lists in first-order logic so that we automatically prove verification conditions of such algorithms purely by superpositon- based first-order reasoning. Doing so, we adjust recent efforts for automating induction in saturation. We advocate a compositional approach for automating proofs by induction re- quired to verify functional programs implementing and preserving sorting and permutation properties over parameterized list structures. Our work turns saturation-based first-order theorem proving into an automated verification engine by (i) guiding automated inductive reasoning with manual proof splits and (ii) fully automating inductive reasoning in satu- ration. We showcase the applicability of our framework over recursive sorting algorithms, including Mergesort and Quicksort.

Keyphrases: automated inductive reasoning, automated reasoning, automated software verification, automated theorem proving, first-order theorem proving, formal methods, recursive programs, sorting algorithms, superposition calculus

In: Nikolaj Bjorner, Marijn Heule and Andrei Voronkov (editors). Proceedings of 25th Conference on Logic for Programming, Artificial Intelligence and Reasoning, vol 100, pages 88--105

BibTeX entry
  author    = {Pamina Georgiou and Marton Hajdu and Laura Kov\textbackslash{}'acs},
  title     = {Saturating Sorting without Sorts},
  booktitle = {Proceedings of 25th Conference on Logic for Programming, Artificial Intelligence and Reasoning},
  editor    = {Nikolaj Bj\{\textbackslash{}o\}rner and Marijn Heule and Andrei Voronkov},
  series    = {EPiC Series in Computing},
  volume    = {100},
  pages     = {88--105},
  year      = {2024},
  publisher = {EasyChair},
  bibsource = {EasyChair,},
  issn      = {2398-7340},
  url       = {},
  doi       = {10.29007/rg9z}}
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