Higher-order Transformations with Nested Concrete Syntax

ABSTRACT Transformations play an important role in grammar-based applications such as program generation. In this domain, the use of the concrete syntax technology is particularly beneficial as it substantially simplifies the development and maintenance of the transformations. Further benefits could be achieved by the use of higherorder transformations to generate program transformations. However, both technologies cannot be combined easily because of the difficulties in merging the different object, meta, and meta-meta languages. Here we propose an approach to higher-order transformations with nested concrete syntax. We use Stratego as meta-meta language and allow the embedding of arbitrary object languages into arbitrary meta languages. We describe the implementation of the approach and give two examples for its application, the embedding of Stratego in itself to generate WebDSL program transformations, and the use of Stratego to generate Prolog-clauses with embedded object syntax

Solving the TTC 2011 Reengineering Case with MOLA and Higher-Order Transformations

The Reengineering Case of the Transformation Tool Contest 2011 deals with automatic extraction of state machine from Java source code. The transformation task involves complex, non-local matching of model elements. This paper contains the solution of the task using model transformation language MOLA. The MOLA solution uses higher-order transformations (HOT-s) to generate a part of the required MOLA program. The described HOT approach allows creating reusable, complex model transformation libraries for generic tasks without modifying an implementation of a model transformation language. Thus model transformation users who are not the developers of the language can achieve the desired functionality more easily.Comment: In Proceedings TTC 2011, arXiv:1111.440

Retractions in comparing PROLOG semantics

We present an operational model O and a continuation based denotational model D for a uniform variant of PROLOG, including the cut operator. The two semantical definitions make use of higher order transformations Phi and Psi, respectively. We prove O and D equivalent in a novel way by comparing yet another pair of higher order transformations Phi~ and Psi~, that yield Phi and Psi, respectively, by application of a suitable abstraction operator

Agile Validation of Higher Order Transformations Using F-Alloy

Model transformations play a key role in model driven software engineering approaches. Validation of model transformations is crucial for the quality assurance of software systems to be constructed. The relational logic based specification language Alloy and its accompanying tool the Alloy Analyzer have been used in the past to validate properties of model transformations. However Alloy based analysis of transformations suffers from time complexity and scalability issues. The problem becomes even more severe when it comes to higher order transformations that are inherently more complex. In previous work, we proposed a sub-language of Alloy, called F-Alloy, that is tailored for model transformation specifications. Instead of pure analysis based validation, F-Alloy speeds up the validation of model transformations by applying a hybrid strategy that combines analysis with interpretation. In this paper, we show how the F-Alloy approach can be extended to also support efficient validation of higher order transformations

Spatial transformations of diffusion tensor magnetic resonance images

The authors address the problem of applying spatial transformations (or “image warps”) to diffusion tensor magnetic resonance images. The orientational information that these images contain must be handled appropriately when they are transformed spatially during image registration. The authors present solutions for global transformations of three-dimensional images up to 12-parameter affine complexity and indicate how their methods can be extended for higher order transformations. Several approaches are presented and tested using synthetic data. One method, the preservation of principal direction algorithm, which takes into account shearing, stretching and rigid rotation, is shown to be the most effective. Additional registration experiments are performed on human brain data obtained from a single subject, whose head was imaged in three different orientations within the scanner. All of the authors' methods improve the consistency between registered and target images over naive warping algorithms

Joint use of the Weniger transformation and hyperasymptotics for accurate asymptotic evaluations of a class of saddle-point integrals. II. Higher-order transformations

The use of hyperasymptotics and the Weniger transformation has been proposed, in a joint fashion, for decoding the divergent asymptotic series generated by the steepest descent on a wide class of saddle-point integrals {evaluated across Stokes sets} [R. Borghi, Phys. Rev. E {\bf 78,} 026703 (2008)]. In the present sequel, the full development of the H-WT up to the second order in H is derived. Numerical experiments, carried out on several classes of saddle-point integrals, including the swallowtail diffraction catastrophe, show the effectiveness of the 2nd-level H-WT, in particular when the integrals are evaluated beyond the asymptotic realm