Many program optimizations and analyses, such as arraybounds checking, termination analysis, depend on knowing the size of a function's input and output. However, size information can be difficult to compute. Firstly, accurate size computation requires detecting a size relation between different inputs of a function. Secondly, size information may also be contained inside a collection (data structure with multiple elements). In this paper, we introduce some techniques to derive universal and existential size properties over collections of elements of recursive data structures. We shall show how a mixed constraint system could support the enhanced size type, and highlight examples where collection analysis are useful.

It is an established notion among financial analysts that price moves in patterns and these patterns can be used to forecast future price. As the definitions of these patterns are often subjective, every analyst has a need to define and search meaningful patterns from historical time series quickly and efficiently. However, such discovery process can be extremely laborious and technically challenging in the absence of a high level pattern definition language. In this paper, we propose a chart-pattern language (CPL for short) to facilitate pattern discovery process. Our language enables financial analysts to (1) define patterns with subjective criteria, through introduction of fuzzy constraints, and (2) incrementally compose complex patterns from simpler patterns. We demonstrate through an array of examples how real life patterns can be expressed in CPL. In short, CPL provides a high-level platform upon which analysts can define and search patterns easily and without any programming expertise.CPL is a domain-specific language embedded in Haskell. We show how various features of a functional language, such as pattern matching, higher-order functions, lazy evaluation, facilitate pattern definitions and implementation. Furthermore, Haskell's type system frees the programmers from annotating the programs with types.

Cooperative statistical debugging is an effective approach for diagnosing production-run failures. To quickly identify failure predictors from the huge program predicate space, existing techniques rely on random or heuristics-guided predicate sampling at the user side. However, none of them can satisfy the requirements of low cost, low diagnosis latency, and high diagnosis quality simultaneously, which are all indispensable for statistical debugging to be practical. This paper presents a new technique that tackles the above challenges. We formulate the technique as an instance of abstraction refinement, where efficient abstract-level profiling is first applied to the whole program and its execution brings information that can pinpoint suspicious coarse-grained entities that need to be refined. The refinement profiles a corresponding set of fine-grained entities, and generates feedback that determines what to prune and what to refine next. The process is fully automated, and more importantly, guided by a mathematically rigorous analysis that guarantees that our approach produces the same debugging results as an exhaustive analysis in deterministic settings. We have implemented this technique for both C and Java on both single machine and distributed system. A thorough evaluation demonstrates that our approach yields (1) an order of magnitude reduction in the user-side runtime overhead even compared to a sampling-based approach and (2) two orders of magnitude reduction in the size of data transferred over the network, completely automatically without sacrificing any debugging capability.

A promising approach for type-safe generic codes in the objectoriented paradigm is variant parametric type, which allows covariant and contravariant subtyping on fields where appropriate. Previous approaches formalise variant type as a special case of the existential type system. In this paper, we present a new framework based on flow analysis and modular type checking to provide a simple but accurate model for capturing generic types. Our scheme stands to benefit from past (and future) advances in flow analysis and subtyping constraints. Furthermore, it fully supports casting for variant types with a special reflection mechanism, called cast capture, to handle objects with unknown types. We have built a constraint-based type checker and have proven its soundness. We have also successfully annotated a suite of Java libraries and client code with our flow-based variant type system.