WScT08-Minutes-Certification

• Notation:
  • TCG is Termination Certificate Grammar
  • Rainbow is the translator from TCG, with several backends (one for Color, one for Isabelle)
  • Another format and another translator is CiME from A3PAT
  • what's the file extension (.tc, .tcg, .tcf, .xml?)
    • .xtc (xml termination certificate)
  • introduce version names/numbers for the format and for the translator(s) (in the .xtc, versioning is by using the proper namespace)

• extend TCG format towards common format:
  • make nodes (more) self-contained
  • have system (termination problem) in each node

• DG Approx, SCC analysis
  • give topologically sorted list of SCCs (A3PAT handles graphs and requests this list)
  • have certificate for each missing edge (allow different kinds of certificates)

• want to certify non-termination
  • proposal: new top element: disproof
  • certify loops (is leaf in proof tree)
    • loop has: start term, sequence of steps, final position (and substitution?)
    • step has: position, rule (and substitution?)
  • later: other nodes in non-termination-proof trees?

• extend polynomial and (standard) matrix interpretations to rational domain (new XML node types rational-polynomial-interp and rational-matrix-interp)
  • a rational number is an XML node (enum, denom)
  • need to provide the delta for the ordering

• apply argument filtering on ordering
  • currently, manna-ness has ordering, we want to allow argument-filtering-of-ordering there

• direct checking of TPG trees (no formal verification) might be useful for testing extensions (Christian has a prototype (microTTT) but not exactly for Rainbow)

• re-use in Color some theorems proved in Coccinelle
  • e.g. prover termination by innermost termination (if nonoverlapping)
  • modular termination (?)
  • perhaps have a general transformation (back and forth)

• plan: generate Isabelle proof from TPG tree