218,638 research outputs found
Probabilistic Rewriting: Normalization, Termination, and Unique Normal Forms
While a mature body of work supports the study of rewriting systems, abstract tools for Probabilistic Rewriting are still limited. We study in this setting questions such as uniqueness of the result (unique limit distribution) and normalizing strategies (is there a strategy to find a result with greatest probability?). The goal is to have tools to analyse the operational properties of probabilistic calculi (such as probabilistic lambda-calculi) whose evaluation is also non-deterministic, in the sense that different reductions are possible
Probabilistic Rewriting: On Normalization, Termination, and Unique Normal Forms
While a mature body of work supports the study of rewriting systems, even
infinitary ones, abstract tools for Probabilistic Rewriting are still limited.
Here, we investigate questions such as uniqueness of the result (unique limit
distribution) and we develop a set of proof techniques to analyze and compare
reduction strategies. The goal is to have tools to support the operational
analysis of probabilistic calculi (such as probabilistic lambda-calculi) whose
evaluation is also non-deterministic, in the sense that different reductions
are possible.
In particular, we investigate how the behavior of different rewrite sequences
starting from the same term compare w.r.t. normal forms, and propose a robust
analogue of the notion of "unique normal form". Our approach is that of
Abstract Rewrite Systems, i.e. we search for general properties of
probabilistic rewriting, which hold independently of the specific structure of
the objects.Comment: Extended version of the paper in FSCD 2019, International Conference
on Formal Structures for Computation and Deductio
XML document design via GN-DTD
Designing a well-structured XML document is important for the sake of readability and maintainability. More importantly, this will avoid data redundancies and update anomalies when maintaining a large quantity of XML based documents. In this paper, we propose a method to improve XML structural design by adopting graphical notations for Document Type Definitions (GN-DTD), which is used to describe the structure of an XML document at the schema level. Multiples levels of normal forms for GN-DTD are proposed on the basis of conceptual model approaches and theories of normalization. The normalization rules are applied to transform a poorly designed XML document into a well-designed based on normalized GN-DTD, which is illustrated through examples
Characterizing normal crossing hypersurfaces
The objective of this article is to give an effective algebraic
characterization of normal crossing hypersurfaces in complex manifolds. It is
shown that a hypersurface has normal crossings if and only if it is a free
divisor, has a radical Jacobian ideal and a smooth normalization. Using K.
Saito's theory of free divisors, also a characterization in terms of
logarithmic differential forms and vector fields is found and and finally
another one in terms of the logarithmic residue using recent results of M.
Granger and M. Schulze.Comment: v2: typos fixed, final version to appear in Math. Ann.; 24 pages, 2
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Derivational Complexity and Context-Sensitive Rewriting
[EN] Context-sensitive rewriting is a restriction of rewriting where reduction steps are allowed on specific arguments mu(f) subset of {1, ..., k} of k-ary function symbols f only. Terms which cannot be further rewritten in this way are called mu-normal forms. For left-linear term rewriting systems (TRSs), the so-called normalization via mu-normalization procedure provides a systematic way to obtain normal forms by the stepwise computation and combination of intermediate mu-normal forms. In this paper, we show how to obtain bounds on the derivational complexity of computations using this procedure by using bounds on the derivational complexity of context-sensitive rewriting. Two main applications are envisaged: Normalization via mu-normalization can be used with non-terminating TRSs where the procedure still terminates; on the other hand, it can be used to improve on bounds of derivational complexity of terminating TRSs as it discards many rewritings.Partially supported by the EU (FEDER), and projects RTI2018-094403-B-C32 and PROMETEO/2019/098.Lucas Alba, S. (2021). Derivational Complexity and Context-Sensitive Rewriting. Journal of Automated Reasoning. 65(8):1191-1229. https://doi.org/10.1007/s10817-021-09603-11191122965
Denotational Aspects of Untyped Normalization by Evaluation
We show that the standard normalization-by-evaluation construction for the simply-typed lambda_{beta eta}-calculus has a natural counterpart for the untyped lambda_beta-calculus, with the central type-indexed logical relation replaced by a "recursively defined'' invariant relation, in the style of Pitts. In fact, the construction can be seen as generalizing a computational-adequacy argument for an untyped, call-by-name language to normalization instead of evaluation. In the untyped setting, not all terms have normal forms, so the normalization function is necessarily partial. We establish its correctness in the senses of soundness (the output term, if any, is in normal form and beta-equivalent to the input term); identification ( beta-equivalent terms are mapped to the same result); and completeness (the function is defined for all terms that do have normal forms). We also show how the semantic construction enables a simple yet formal correctness proof for the normalization algorithm, expressed as a functional program in an ML-like call-by-value language. Finally, we generalize the construction to produce an infinitary variant of normal forms, namely Böhm trees. We show that the three-part characterization of correctness, as well as the proofs, extend naturally to this generalization
Normalization by Evaluation with Typed Abstract Syntax
We present a simple way to implement typed abstract syntax for thelambda calculus in Haskell, using phantom types, and we specify normalization by evaluation (i.e., type-directed partial evaluation) to yield thistyped abstract syntax. Proving that normalization by evaluation preserves types and yields normal forms then reduces to type-checking thespecification
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