1 research outputs found
Formula Transformers and Combinatorial Test Generators for Propositional Intuitionistic Theorem Provers
We develop combinatorial test generation algorithms for progressively more
powerful theorem provers, covering formula languages ranging from the
implicational fragment of intuitionistic logic to full intuitionistic
propositional logic. Our algorithms support exhaustive and random generators
for formulas of these logics.
To provide known-to-be-provable formulas, via the Curry-Howard
formulas-as-types correspondence, we use generators for typable lambda terms
and combinator expressions. Besides generators for several classes of formulas,
we design algorithms that restrict formula generation to canonical
representatives among equiprovable formulas and introduce program
transformations that reduce formulas to equivalent formulas of a simpler
structure. The same transformations, when applied in reverse, create harder
formulas that can catch soundness or incompleteness bugs.
To test the effectiveness of the testing framework itself, we describe use
cases for deriving lightweight theorem provers for several of these logics and
for finding bugs in known theorem provers. Our Prolog implementation available
at: https://github.com/ptarau/TypesAndProofs and a subset of formula generators
and theorem provers, implemented in Python is available at:
https://github.com/ptarau/PythonProvers.
Keywords: term and formula generation algorithms, Prolog-based theorem
provers, formulas-as-types, type inference and type inhabitation, combinatorial
testing, finding bugs in theorem provers.Comment: 32 page