Mendler-style Iso-(Co)inductive predicates: a strongly normalizing approach

We present an extension of the second-order logic AF2 with iso-style inductive and coinductive definitions specifically designed to extract programs from proofs a la Krivine-Parigot by means of primitive (co)recursion principles. Our logic includes primitive constructors of least and greatest fixed points of predicate transformers, but contrary to the common approach, we do not restrict ourselves to positive operators to ensure monotonicity, instead we use the Mendler-style, motivated here by the concept of monotonization of an arbitrary operator on a complete lattice. We prove an adequacy theorem with respect to a realizability semantics based on saturated sets and saturated-valued functions and as a consequence we obtain the strong normalization property for the proof-term reduction, an important feature which is absent in previous related work.Comment: In Proceedings LSFA 2011, arXiv:1203.542

On a New Notion of Partial Refinement

Formal specification techniques allow expressing idealized specifications, which abstract from restrictions that may arise in implementations. However, partial implementations are universal in software development due to practical limitations. Our goal is to contribute to a method of program refinement that allows for partial implementations. For programs with a normal and an exceptional exit, we propose a new notion of partial refinement which allows an implementation to terminate exceptionally if the desired results cannot be achieved, provided the initial state is maintained. Partial refinement leads to a systematic method of developing programs with exception handling.Comment: In Proceedings Refine 2013, arXiv:1305.563

Healthiness from Duality

Healthiness is a good old question in program logics that dates back to Dijkstra. It asks for an intrinsic characterization of those predicate transformers which arise as the (backward) interpretation of a certain class of programs. There are several results known for healthiness conditions: for deterministic programs, nondeterministic ones, probabilistic ones, etc. Building upon our previous works on so-called state-and-effect triangles, we contribute a unified categorical framework for investigating healthiness conditions. We find the framework to be centered around a dual adjunction induced by a dualizing object, together with our notion of relative Eilenberg-Moore algebra playing fundamental roles too. The latter notion seems interesting in its own right in the context of monads, Lawvere theories and enriched categories.Comment: 13 pages, Extended version with appendices of a paper accepted to LICS 201

MintHint: Automated Synthesis of Repair Hints

Being able to automatically repair programs is an extremely challenging task. In this paper, we present MintHint, a novel technique for program repair that is a departure from most of today's approaches. Instead of trying to fully automate program repair, which is often an unachievable goal, MintHint performs statistical correlation analysis to identify expressions that are likely to occur in the repaired code and generates, using pattern-matching based synthesis, repair hints from these expressions. Intuitively, these hints suggest how to rectify a faulty statement and help developers find a complete, actual repair. MintHint can address a variety of common faults, including incorrect, spurious, and missing expressions. We present a user study that shows that developers' productivity can improve manyfold with the use of repair hints generated by MintHint -- compared to having only traditional fault localization information. We also apply MintHint to several faults of a widely used Unix utility program to further assess the effectiveness of the approach. Our results show that MintHint performs well even in situations where (1) the repair space searched does not contain the exact repair, and (2) the operational specification obtained from the test cases for repair is incomplete or even imprecise

Code Prediction by Feeding Trees to Transformers

We advance the state-of-the-art in the accuracy of code prediction (next token prediction) used in autocomplete systems. First, we report that using the recently proposed Transformer architecture even out-of-the-box outperforms previous neural and non-neural systems for code prediction. We then show that by making the Transformer architecture aware of the syntactic structure of code, we further increase the margin by which a Transformer-based system outperforms previous systems. With this, it outperforms the accuracy of an RNN-based system (similar to Hellendoorn et al. 2018) by 18.3\%, the Deep3 system (Raychev et al 2016) by 14.1\%, and an adaptation of Code2Seq (Alon et al., 2018) for code prediction by 14.4\%. We present in the paper several ways of communicating the code structure to the Transformer, which is fundamentally built for processing sequence data. We provide a comprehensive experimental evaluation of our proposal, along with alternative design choices, on a standard Python dataset, as well as on a Facebook internal Python corpus. Our code and data preparation pipeline will be available in open source

A Mission of the Heart: What Does It Take to Transform a School? 2008

Based on interviews and focus group discussions with principals and superintendents, examines the leadership skills, commitments, resources, and supports needed to turn around low-performing schools and how to recruit and retain qualified principals