Rewriting and narrowing for constructor systems with call-time choice semantics

Non-confluent and non-terminating constructor-based term rewrite systems are useful for the purpose of specification and programming. In particular, existing functional logic languages use such kind of rewrite systems to define possibly non-strict non-deterministic functions. The semantics adopted for non-determinism is call-time choice, whose combination with non-strictness is a non trivial issue, addressed years ago from a semantic point of view with the Constructor-based Rewriting Logic (CRWL), a well-known semantic framework commonly accepted as suitable semantic basis of modern functional logic languages. A drawback of CRWL is that it does not come with a proper notion of one-step reduction, which would be very useful to understand and reason about how computations proceed. In this paper we develop thoroughly the theory for the first order version of letrewriting, a simple reduction notion close to that of classical term rewriting, but extended with a let-binding construction to adequately express the combination of call-time choice with non-strict semantics. Let-rewriting can be seen as a particular textual presentation of term graph rewriting. We investigate the properties of let-rewriting, most remarkably their equivalence with respect to a conservative extension of the CRWL-semantics coping with let-bindings, and we show by some case studies that having two interchangeable formal views (reduction/semantics) of the same language is a powerful reasoning tool. After that, we provide a notion of let-narrowing which is adequate for call-time choice as proved by soundness and completeness results of let-narrowing with respect to letre writing. Moreover, we relate those let-rewriting and let-narrowing relations (and hence CRWL) with ordinary term rewriting and narrowing, providing in particular soundness and completeness of let-rewriting with respect to term rewriting for a class of programs which are deterministic in a semantic sense

Independent AND-parallel implementation of narrowing

We present a parallel graph narrowing machine, which is used to implement a functional logic language on a shared memory multiprocessor. It is an extensión of an abstract machine for a purely functional language. The result is a programmed graph reduction machine which integrates the mechanisms of unification, backtracking, and independent and-parallelism. In the machine, the subexpressions of an expression can run in parallel. In the case of backtracking, the structure of an expression is used to avoid the reevaluation of subexpressions as far as possible. Deterministic computations are detected. Their results are maintained and need not be reevaluated after backtracking

Getting Narrower at the Base: The American Curriculum After NCLB

Examines curriculum changes in elementary, middle, and high schools since No Child Left Behind (NCLB) was enacted, requiring regular testing in reading and math. Analyzes shifts in time allocations to four subjects, contributing factors, and implications

Improved Conflict Detection for Graph Transformation with Attributes

In graph transformation, a conflict describes a situation where two alternative transformations cannot be arbitrarily serialized. When enriching graphs with attributes, existing conflict detection techniques typically report a conflict whenever at least one of two transformations manipulates a shared attribute. In this paper, we propose an improved, less conservative condition for static conflict detection of graph transformation with attributes by explicitly taking the semantics of the attribute operations into account. The proposed technique is based on symbolic graphs, which extend the traditional notion of graphs by logic formulas used for attribute handling. The approach is proven complete, i.e., any potential conflict is guaranteed to be detected.Comment: In Proceedings GaM 2015, arXiv:1504.0244

Changes over time in socioeconomic inequalities in breast and rectal cancer survival in England and Wales during a 32-year period (1973-2004): the potential role of health care.

BACKGROUND: Socioeconomic inequalities in cancer survival are well documented but they vary for different cancers and over time. Reasons for these differences are poorly understood. PATIENTS AND METHODS: For England and Wales, we examined trends in socioeconomic survival inequalities for breast cancer in women and rectal cancer in men during the 32-year period 1973-2004. We used a theoretical framework based on Victora's 'inverse equity' law, under which survival inequalities could change with the advent of successive new treatments, of varying effectiveness, which are disseminated with different speed among patients of different socioeconomic groups. We estimated 5-year relative survival for patients of different deprivation quintiles and examined trends in survival inequalities in light of major treatment innovations. RESULTS: Inequalities in breast cancer survival (921,611 cases) narrowed steadily during the study (from -10% to -6%). In contrast, inequalities in rectal cancer survival (187,104 cases) widened overall (form -5% to -11%) with fluctuating periods of narrowing inequality. CONCLUSIONS: Trends in socioeconomic differences in tumour or patient factors are unlikely explanations of observed changes over time in survival inequalities. The sequential introduction into clinical practice of new treatments of progressively smaller incremental benefit may partly explain the reduction in inequality in breast cancer survival

Guided Unfoldings for Finding Loops in Standard Term Rewriting

In this paper, we reconsider the unfolding-based technique that we have introduced previously for detecting loops in standard term rewriting. We improve it by guiding the unfolding process, using distinguished positions in the rewrite rules. This results in a depth-first computation of the unfoldings, whereas the original technique was breadth-first. We have implemented this new approach in our tool NTI and compared it to the previous one on a bunch of rewrite systems. The results we get are promising (better times, more successful proofs).Comment: Pre-proceedings paper presented at the 28th International Symposium on Logic-Based Program Synthesis and Transformation (LOPSTR 2018), Frankfurt am Main, Germany, 4-6 September 2018 (arXiv:1808.03326

Needed Computations Shortcutting Needed Steps

We define a compilation scheme for a constructor-based, strongly-sequential, graph rewriting system which shortcuts some needed steps. The object code is another constructor-based graph rewriting system. This system is normalizing for the original system when using an innermost strategy. Consequently, the object code can be easily implemented by eager functions in a variety of programming languages. We modify this object code in a way that avoids total or partial construction of the contracta of some needed steps of a computation. When computing normal forms in this way, both memory consumption and execution time are reduced compared to ordinary rewriting computations in the original system.Comment: In Proceedings TERMGRAPH 2014, arXiv:1505.0681