lattice-mtl

A Verified Online Monitor for Metric Temporal Logic with Quantitative Semantics (Extended Version)

@InProceedings{ChattopadhyayM20,
  author="Chattopadhyay, Agnishom
      and Mamouras, Konstantinos",
  editor="Deshmukh, Jyotirmoy
      and Ni{\v{c}}kovi{\'{c}}, Dejan",
  title="A Verified Online Monitor for Metric Temporal Logic with Quantitative Semantics",
  booktitle="Runtime Verification",
  year="2020",
  publisher="Springer International Publishing",
  address="Cham",
  pages="383--403",
}

Usage as a library

To use this as a library, see the instructions in extracted/README.md

Extraction

The Extracted Code can be found in extracted/LatticeMtl.ml with some examples of usage in extracted/Examples.ml. To re-run the extraction (and verification) process:

cd src/
make Makefile.coq
make

The current version of the proof was checked using Coq 8.12.1.

Organization of the Proof

The toMonitor : Formula -> Monitor is defined in Monitor/ToMonitor.v. The semantics of the formulae are available in Semantics/InfRobustness.v and the main theorem, toMonitor_correctness can be found in Monitor/ToMonitor.v.

Below is a brief discussion of the organization of the proof:

• Lemmas/: Various useful auxilary functions. Relevant lemmas.
• NonEmptyList/: Type of non-empty lists.
• Algebra/:
  • Algebra/Monoid.v: Definition of Monoids. Extending monoid operations to finite lists.
  • Algebra/Lattice.v: Lattices. Bounded, Distributive Lattices. Order Theoretic Properties of Lattices.
• Syntax/:
  • Syntax/Formula.v: Syntax of Past-time MTL formulas. Some syntactic sugar.
  • Syntax/Normal.v: Definition of and conversion into normal forms. The resulting formulae only contain certain constructs
• Semantics/:
  • Semantics/InfRobustness.v: Semantics of MTL formulas on infinite traces.
  • Semantics/Robustness.v: Semantics on non-empty lists (defined via their extension to infinite traces).
  • Semantics/SimpleProperties.v: Simple properties of some degenerate MTL formulas.
  • Semantics/Incremental.v: Incremental derivations of semantic values. Used to construct the monitors.
  • Semantics/SinceRewrite.v: Translating S_[0,a] to S and Sometime_[0,a].
  • Semantics/Equivalences.v: Other MTL identities.
  • Semantics/NormalizeCorrect.v: Correctness of the normal forms.
• Monitor/
  • Monitor/Mealy.v: Mealy Machines. Denotations. Composition. Unbounded Aggregation.
  • Monitor/Queue.v: Queue. Implementation of Sometime_[n,n]
  • Monitor/AggQueue.v: Sliding window aggregation. Implementation of Sometime_[0,n].
  • Monitor/Monitor.v: Definition of Monitors. implements relation. Combinators for building blocks.
  • Monitor/ToMonitor.v: Translating Formulas to Monitors. Proof of Correctness.
• Extract/: Extraction to OCaml.