35 research outputs found
Matrix Interpretations on Polyhedral Domains
We refine matrix interpretations for proving termination and complexity bounds of term rewrite systems we restricting them to domains that satisfy a system of linear inequalities. Admissibility of such a restriction is shown by certificates whose validity can be expressed as a constraint program. This refinement is orthogonal to other features of matrix interpretations (complexity bounds, dependency pairs), but can be used to improve complexity bounds, and we discuss its relation with the usable rules criterion. We present an implementation and experiments
Confluence of nearly orthogonal infinitary term rewriting systems
We give a relatively simple coinductive proof of confluence, modulo
equivalence of root-active terms, of nearly orthogonal infinitary
term rewriting systems. Nearly orthogonal systems allow certain root
overlaps, but no non-root overlaps. Using a slightly more complicated method we also show confluence modulo equivalence of
hypercollapsing terms. The condition we impose on root overlaps is
similar to the condition used by Toyama in the context of finitary
rewriting
Proof nets and the call-by-value λ-calculus
International audienceThis paper gives a detailed account of the relationship between (a variant of) the call-by-value lambda calculus and linear logic proof nets. The presentation is carefully tuned in order to realize an isomorphism between the two systems: every single rewriting step on the calculus maps to a single step on proof nets, and viceversa. In this way, we obtain an algebraic reformulation of proof nets. Moreover, we provide a simple correctness criterion for our proof nets, which employ boxes in an unusual way, and identify a subcalculus that is shown to be as expressive as the full calculus
SMT Sampling via Model-Guided Approximation
We investigate the domain of satisfiable formulas in satisfiability modulo
theories (SMT), in particular, automatic generation of a multitude of
satisfying assignments to such formulas. Despite the long and successful
history of SMT in model checking and formal verification, this aspect is
relatively under-explored. Prior work exists for generating such assignments,
or samples, for Boolean formulas and for quantifier-free first-order formulas
involving bit-vectors, arrays, and uninterpreted functions (QF_AUFBV). We
propose a new approach that is suitable for a theory T of integer arithmetic
and to T with arrays and uninterpreted functions. The approach involves
reducing the general sampling problem to a simpler instance of sampling from a
set of independent intervals, which can be done efficiently. Such reduction is
carried out by expanding a single model - a seed - using top-down propagation
of constraints along the original first-order formula
Semi-continuous Sized Types and Termination
Some type-based approaches to termination use sized types: an ordinal bound
for the size of a data structure is stored in its type. A recursive function
over a sized type is accepted if it is visible in the type system that
recursive calls occur just at a smaller size. This approach is only sound if
the type of the recursive function is admissible, i.e., depends on the size
index in a certain way. To explore the space of admissible functions in the
presence of higher-kinded data types and impredicative polymorphism, a
semantics is developed where sized types are interpreted as functions from
ordinals into sets of strongly normalizing terms. It is shown that upper
semi-continuity of such functions is a sufficient semantic criterion for
admissibility. To provide a syntactical criterion, a calculus for
semi-continuous functions is developed.Comment: 33 pages, extended version of CSL'0