ترغب بنشر مسار تعليمي؟ اضغط هنا

Logical Reasoning for Higher-Order Functions with Local State

173   0   0.0 ( 0 )
 نشر من قبل Nobuko Yoshida Dr
 تاريخ النشر 2008
  مجال البحث الهندسة المعلوماتية
والبحث باللغة English




اسأل ChatGPT حول البحث

We introduce an extension of Hoare logic for call-by-value higher-order functions with ML-like local reference generation. Local references may be generated dynamically and exported outside their scope, may store higher-order functions and may be used to construct complex mutable data structures. This primitive is captured logically using a predicate asserting reachability of a reference name from a possibly higher-order datum and quantifiers over hidden references. We explore the logics descriptive and reasoning power with non-trivial programming examples combining higher-order procedures and dynamically generated local state. Axioms for reachability and local invariant play a central role for reasoning about the examples.



قيم البحث

اقرأ أيضاً

129 - Fabrizio Montesi 2018
Classical Processes (CP) is a calculus where the proof theory of classical linear logic types communicating processes with mobile channels, a la pi-calculus. Its construction builds on a recent propositions as types correspondence between session typ es and propositions in linear logic. Desirable properties such as type preservation under reductions and progress come for free from the metatheory of linear logic. We contribute to this research line by extending CP with code mobility. We generalise classical linear logic to capture higher-order (linear) reasoning on proofs, which yields a logical reconstruction of (a variant of) the Higher-Order pi-calculus (HOpi). The resulting calculus is called Classical Higher-Order Processes (CHOP). We explore the metatheory of CHOP, proving that its semantics enjoys type preservation and progress (terms do not get stuck). We also illustrate the expressivity of CHOP through examples, derivable syntax sugar, and an extension to multiparty sessions. Lastly, we define a translation from CHOP to CP, which encodes mobility of process code into reference passing.
We show that the techniques for resource control that have been developed in the so-called light logics can be fruitfully applied also to process algebras. In particular, we present a restriction of Higher-Order pi-calculus inspired by Soft Linear Lo gic. We prove that any soft process terminates in polynomial time. We argue that the class of soft processes may be naturally enlarged so that interesting processes are expressible, still maintaining the polynomial bound on executions.
This paper studies the logical properties of a very general class of infinite ranked trees, namely those generated by higher-order recursion schemes. We consider, for both monadic second-order logic and modal mu-calculus, three main problems: model-c hecking, logical reflection (aka global model-checking, that asks for a finite description of the set of elements for which a formula holds) and selection (that asks, if exists, for some finite description of a set of elements for which an MSO formula with a second-order free variable holds). For each of these problems we provide an effective solution. This is obtained thanks to a known connection between higher-order recursion schemes and collapsible pushdown automata and on previous work regarding parity games played on transition graphs of collapsible pushdown automata.
173 - Tom Hirschowitz 2013
We propose a semantics for permutation equivalence in higher-order rewriting. This semantics takes place in cartesian closed 2-categories, and is proved sound and complete.
97 - Francesco Gavazzo 2018
This paper studies the quantitative refinements of Abramskys applicative similarity and bisimilarity in the context of a generalisation of Fuzz, a call-by-value $lambda$-calculus with a linear type system that can express programs sensitivity, enrich ed with algebraic operations emph{`a la} Plotkin and Power. To do so a general, abstract framework for studying behavioural relations taking values over quantales is defined according to Lawveres analysis of generalised metric spaces. Barrs notion of relator (or lax extension) is then extended to quantale-valued relations adapting and extending results from the field of monoidal topology. Abstract notions of quantale-valued effectful applicative similarity and bisimilarity are then defined and proved to be a compatible generalised metric (in the sense of Lawvere) and pseudometric, respectively, under mild conditions.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا