Monotonicity Inference for Higher-Order Formulas

Formulas are often monotonic in the sense that satisfiability for a given domain of discourse entails satisfiability for all larger domains. Monotonicity is undecidable in general, but we devised three calculi that infer it in many cases for higher-order logic. The third calculus has been implemented in Isabelle’s model finder Nitpick, where it is used both to prune the search space and to soundly interpret infinite types with finite sets, leading to dramatic speed and precision improvements.

[1]  John C. Mitchell,et al.  Foundations for programming languages , 1996, Foundation of computing series.

[2]  Jasmin Christian Blanchette,et al.  Monotonicity Inference for Higher-Order Formulas , 2010, IJCAR.

[3]  Daniel Jackson,et al.  Software Abstractions - Logic, Language, and Analysis , 2006 .

[4]  Michael Norrish,et al.  A Brief Overview of HOL4 , 2008, TPHOLs.

[5]  Lee Momtahan.  Towards a Small Model Theorem for Data Independent Systems in Alloy , 2005, Electron. Notes Theor. Comput. Sci..

[6]  Viktor Kuncak,et al.  Relational analysis of algebraic datatypes , 2005, ESEC/FSE-13.

[7]  Peter B. Andrews.  An introduction to mathematical logic and type theory - to truth through proof , 1986, Computer science and applied mathematics.

[8]  Emina Torlak,et al.  Kodkod: A Relational Model Finder , 2007, TACAS.

[9]  Tobias Nipkow.  Verifying a Hotel Key Card System , 2006, ICTAC.

[10]  Greg Nelson,et al.  Simplification by Cooperating Decision Procedures , 1979, TOPL.

[11]  Naoki Kobayashi,et al.  Substructural Type Systems for Program Analysis , 2008, FLOPS.

[12]  Calogero G. Zarba,et al.  Combining Decision Procedures for Sorted Theories , 2004, JELIA.

[13]  Tjark Weber,et al.  SAT-based finite model generation for higher-order logic , 2008 .

[14]  Amir Pnueli,et al.  The Small Model Property: How Small Can It Be? , 2002, Inf. Comput..

[15]  Manu Sridharan,et al.  A micromodularity mechanism , 2001, ESEC/FSE-9.

[16]  Tobias Nipkow,et al.  A Proof Assistant for Higher-Order Logic , 2002 .

[17]  Koen Claessen,et al.  Sort It Out with Monotonicity - Translating between Many-Sorted and Unsorted First-Order Logic , 2011, CADE.

[18]  Tobias Nipkow,et al.  Nitpick: A Counterexample Generator for Higher-Order Logic Based on a Relational Model Finder , 2010, ITP.

[19]  N. S. Barnett,et al.  Private communication , 1969 .

[20]  John Harrison,et al.  HOL Light: A Tutorial Introduction , 1996, FMCAD.

[21]  K. Claessen,et al.  New Techniques that Improve MACE-style Finite Model Finding , 2007 .

[22]  Stefan Berghofer,et al.  Inductive Datatypes in HOL - Lessons Learned in Formal-Logic Engineering , 1999, TPHOLs.

[23]  Hantao Zhang,et al.  SEM: a System for Enumerating Models , 1995, IJCAI.

[24]  M. Gordon,et al.  Introduction to HOL: a theorem proving environment for higher order logic , 1993 .

[25]  W. McCune.  A Davis-Putnam program and its application to finite-order model search: Quasigroup existence problems , 1994 .