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The Coq Proof Assistant

Library AAC_tactics.AAC

  • Theory file for the aac_rewrite tactic
  • Environments for the reification process: we use positive maps to index elements
  • Classes for properties of operators
  • Utilities for the evaluation function
  • Utilities for positive numbers
  • Dependent types utilities
  • Utilities about (non-empty) lists and multisets
  • Packaging structures
    • free symbols
    • binary operations
  • Reification, normalisation, and decision
    • Almost normalised syntax
    • Evaluation from syntax to the abstract domain
    • Normalisation
    • Correctness
  • Lemmas for performing transitivity steps

Library AAC_tactics.Instances

Library AAC_tactics.Tutorial

  • Tutorial for using the aac_tactics library.
    • Introductory example
    • Usage
      • Selecting what and where to rewrite
      • Distinction between aac_rewrite and aacu_rewrite:
      • Declaring instances
      • Working with inequations
      • Normalising goals
    • Examples from the web page
      • Reverse triangle inequality
      • Pythagorean triples

Library AAC_tactics.Caveats

  • Currently known caveats and limitations of the aac_tactics library.
    • Limitations
      • 1. Dependent parameters
      • 2. Exogeneous morphisms
      • 3. Treatment of variance with inequations.
    • Caveats
      • 1. Special treatment for units.
      • 2. Existential variables.
      • 3. Distinction between aac_rewrite and aacu_rewrite
      • 4. Rewriting units
      • 5. Rewriting too much things.
      • 6. Rewriting nullifiable patterns.
        • If the pattern is a unit or can be instanciated to be equal
      • Another example of the former case is the following, where the hypothesis can be instanciated to be equal to 1
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