51,113 research outputs found
On Graph Refutation for Relational Inclusions
We introduce a graphical refutation calculus for relational inclusions: it
reduces establishing a relational inclusion to establishing that a graph
constructed from it has empty extension. This sound and complete calculus is
conceptually simpler and easier to use than the usual ones.Comment: In Proceedings LSFA 2011, arXiv:1203.542
A Uniform Substitution Calculus for Differential Dynamic Logic
This paper introduces a new proof calculus for differential dynamic logic
(dL) that is entirely based on uniform substitution, a proof rule that
substitutes a formula for a predicate symbol everywhere. Uniform substitutions
make it possible to rely on axioms rather than axiom schemata, substantially
simplifying implementations. Instead of nontrivial schema variables and
soundness-critical side conditions on the occurrence patterns of variables, the
resulting calculus adopts only a finite number of ordinary dL formulas as
axioms. The static semantics of differential dynamic logic is captured
exclusively in uniform substitutions and bound variable renamings as opposed to
being spread in delicate ways across the prover implementation. In addition to
sound uniform substitutions, this paper introduces differential forms for
differential dynamic logic that make it possible to internalize differential
invariants, differential substitutions, and derivations as first-class axioms
in dL
First Class Call Stacks: Exploring Head Reduction
Weak-head normalization is inconsistent with functional extensionality in the
call-by-name -calculus. We explore this problem from a new angle via
the conflict between extensionality and effects. Leveraging ideas from work on
the -calculus with control, we derive and justify alternative
operational semantics and a sequence of abstract machines for performing head
reduction. Head reduction avoids the problems with weak-head reduction and
extensionality, while our operational semantics and associated abstract
machines show us how to retain weak-head reduction's ease of implementation.Comment: In Proceedings WoC 2015, arXiv:1606.0583
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