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Thoughts on the Future of ATP. Wilfred J. Legato NSA. Historical Developments. Automated Theorem Proving (ATP) technology has not advanced significantly since the late 1980’s.

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thoughts on the future of atp

Thoughts on the Future of ATP

Wilfred J. Legato

NSA

historical developments
Historical Developments
  • Automated Theorem Proving (ATP) technology has not advanced significantly since the late 1980’s.
  • There has been remarkable advances in propositional satisfiability (SAT) and equivalence checking (OBDD) algorithms over the past 10 years.
  • SAT and OBDD technology have enabled “push button” approaches to ATP.
measuring progress
Measuring Progress
  • Legato challenge 10 line multiply program- 1990: J Moore, 2 days using Nqthm- 2001: Matt Wilding, 15 hours using Vfaat- 2002: Robert Krug, 17 hours using ACL2 arithmetic3 proof library- 2005: Sandip Ray, 4 hours using J Moore’s inductive assertion method- 2007: Robert Boyer and Warren Hunt, 3 seconds using “g-functions” in ACL2
a clarification
A Clarification
  • The push button solution to the 10 line multiply program only works for small size registers.
  • The previous 4 proofs work for arbitrary size registers, but require human guidance.
  • They also require development of a good modular arithmetic proof library.
some glimmers of hope
Some Glimmers of Hope
  • Bob Boyer and Warren Hunt’s “g-functions” within ACL2 (push button at the bottom)
  • The advent of SMT solvers (push button at the top)
  • Modularization of ACL2 (an environment supporting experimentation with new ATP algorithms)
more glimmers of hope
More Glimmers of Hope
  • Doug Smith’s work with SATware and proposed work on ATPware (a KIDS like treatment of the construction of SAT solvers and automated theorem provers)
  • Movement of the user community towards greater acceptance of ATP technology (success breeds success).
  • Finally, work on the “tool bus” concept emerging from the “Grand Challenge” (the right tool for the right job)
the broader environment
The Broader Environment
  • Theorems evolve from a broader environment- Floyd-Hoare (shallow embedment)

- Interpreters (deep embedment)

- Inductive Assertions (best of both)

- Weakest Preconditions (greater flexibility)

- The Logic as a Programming Language

- Correct by Construction

- Propositional Satisfiability (SMT, Predicate Abstraction, Model Checking)