Friends with benefits: implementing corecursion in foundational proof assistants

We introduce AmiCo, a tool that extends a proof assistant, Isabelle/HOL, with flexible function definitions well beyond primitive corecursion. All definitions are certified by the assistant’s inference kernel to guard against inconsistencies. A central notion is that of friends: functions that preserve the productivity of their arguments and that are allowed in corecursive call contexts. As new friends are registered, corecursion benefits by becoming more expressive. We describe this process and its implementation, from the user’s specification to the synthesis of a higher-order definition to the registration of a friend. We show some substantial case studies where our approach makes a difference

Foundational (co)datatypes and (co)recursion for higher-order logic

We describe a line of work that started in 2011 towards enriching Isabelle/HOL's language with coinductive datatypes, which allow infinite values, and with a more expressive notion of inductive datatype than previously supported by any system based on higher-order logic. These (co)datatypes are complemented by definitional principles for (co)recursive functions and reasoning principles for (co)induction. In contrast with other systems offering codatatypes, no additional axioms or logic extensions are necessary with our approach

Strengthening and weakening by repeated dynamic impact in microcrystals and nanocrystals

International audienceExperiments on micrograined (mg) and nanocrystalline (nc) Ni revealed strengthening and weakening following repeated dynamic impact. The strengthening in mg-Ni arises from intragranular dislocations without a significant change in grain size, whereas the weakening in nc-Ni is due to concurrent grain growth. The strength of mg and nc-Ni samples after deformation settles at similar to 900 MPa, with differing contributions from intragranular dislocations and grain sizes

Monte-Carlo Proof-Number Search for Computer Go

Abstract. In the last decade, proof-number search and Monte-Carlo methods have successfully been applied to the combinatorial-games domain. Proof-number search is a reliable algorithm. It requires a well defined goal to prove. This can be seen as a disadvantage. In contrast to proof-number search, Monte-Carlo evaluation is a flexible stochastic evaluation for game-tree search. In order to improve the efficiency of proof-number search, we introduce a new algorithm, Monte-Carlo Proof-Number search. It enhances proof-number search by adding the flexible Monte-Carlo evaluation. We present the new algorithm and evaluate it on a sub-problem of Go, the Life-and-Death problem. The results show a clear improvement in time efficiency and memory usage: the test problems are solved two times faster and four times less nodes are expanded on average. Future work will assess the possibility of applying this method to enhanced proof-number techniques.

System for creating orientation maps using TEM

International audienceElectron back-scattered diffraction (EBSD) in scanning electron microscopy (SEM) is already extensively used for creating orientationbased microstructure images of polycrystalline materials. In an analogous way, Kikuchi patterns have been recently applied for creating polycrystalline orientation maps using a transmission electron microscope. Main components of the new system are similar to those of the SEM-based systems. The first steps are pattern acquisition and correction of the images. They are subsequently followed by automatic indexing of the patterns. Finally, from orientations obtained in a grid of points, a map is created. The system using transmission electron microscopy (TEM) has a good spatial resolution of about 10 nm. Its accuracy in orientation determination (≈0.1 •) is better than the accuracy of EBSD systems

Polycrystal orientation maps from TEM

International audienceDetermination of topography of crystallite orientations is an important technique of investigation of polycrystalline materials. A system for creating orientation maps using transmission electron microscope (TEM) Kikuchi patterns and Convergent beam electron diffraction patterns is presented. The orientation maps are obtained using a step-by-step beam scan on a computer-controlled TEM equipped with a CCD camera. At each step, acquired diffraction patterns are indexed and orientations are determined. Although, the approach used is similar to that applied in SEM/electron back scattered diffraction (EBSD) orientation imaging setups, the TEM-based system considerably differs from its SEM counterpart. The main differences appear due to specific features of TEM and SEM diffraction patterns. Also, the resulting maps are not equivalent. On these generated by TEM, the accuracy of orientation determination can be better than 0.1. The spatial resolution is estimated to be about 10 nm. The latter feature makes the TEM orientation mapping system an important tool for studies at fine scale unreachable by SEM/EBSD systems. The automatic orientation mapping is expected to be a useful complement of the conventional TEM contrast images. The new technique will be essential for characterization of fine structure materials. To illustrate that, example maps of an aluminum sample produced by severe plastic deformation are included

EP – a program for determination of crystallite orientations from TEM Kikuchi and CBED diffraction patterns

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