Program representation size in an intermediate language with intersection and union types

The CIL compiler for core Standard ML compiles whole programs using a novel typed intermediate language (TIL) with intersection and union types and flow labels on both terms and types. The CIL term representation duplicates portions of the program where intersection types are introduced and union types are eliminated. This duplication makes it easier to represent type information and to introduce customized data representations. However, duplication incurs compile-time space costs that are potentially much greater than are incurred in TILs employing type-level abstraction or quantification. In this paper, we present empirical data on the compile-time space costs of using CIL as an intermediate language. The data shows that these costs can be made tractable by using sufficiently fine-grained flow analyses together with standard hash-consing techniques. The data also suggests that non-duplicating formulations of intersection (and union) types would not achieve significantly better space complexity.National Science Foundation (CCR-9417382, CISE/CCR ESS 9806747); Sun grant (EDUD-7826-990410-US); Faculty Fellowship of the Carroll School of Management, Boston College; U.K. Engineering and Physical Sciences Research Council (GR/L 36963, GR/L 15685

Computer programs simplify optical system analysis

The optical ray-trace computer program performs geometrical ray tracing. The energy-trace program calculates the relative monochromatic flux density on a specific target area. This program uses the ray-trace program as a subroutine to generate a representation of the optical system

Provably Correct Control-Flow Graphs from Java Programs with Exceptions

We present an algorithm to extract flow graphs from Java bytecode, focusing on exceptional control flows. We prove its correctness, meaning that the behaviour of the extracted control-flow graph is an over-approximation of the behaviour of the original program. Thus any safety property that holds for the extracted control-flow graph also holds for the original program. This makes control-flow graphs suitable for performing different static analyses. For precision and efficiency, the extraction is performed in two phases. In the first phase the program is transformed into a BIR program, where BIR is a stack-less intermediate representation of Java bytecode; in the second phase the control-flow graph is extracted from the BIR representation. To prove the correctness of the two-phase extraction, we also define a direct extraction algorithm, whose correctness can be proven immediately. Then we show that the behaviour of the control-flow graph extracted via the intermediate representation is an over-approximation of the behaviour of the directly extracted graphs, and thus of the original program

Program Synthesis and Linear Operator Semantics

For deterministic and probabilistic programs we investigate the problem of program synthesis and program optimisation (with respect to non-functional properties) in the general setting of global optimisation. This approach is based on the representation of the semantics of programs and program fragments in terms of linear operators, i.e. as matrices. We exploit in particular the fact that we can automatically generate the representation of the semantics of elementary blocks. These can then can be used in order to compositionally assemble the semantics of a whole program, i.e. the generator of the corresponding Discrete Time Markov Chain (DTMC). We also utilise a generalised version of Abstract Interpretation suitable for this linear algebraic or functional analytical framework in order to formulate semantical constraints (invariants) and optimisation objectives (for example performance requirements).Comment: In Proceedings SYNT 2014, arXiv:1407.493

Representation theory and cohomology of Khovanov-Lauda-Rouquier algebras

This expository paper is based on the lectures given at the program `Modular Representation Theory of Finite and $p$-adic Groups' at the National University of Singapore. We are concerned with recent results on representation theory and cohomology of KLR algebras, with emphasis on standard module theory.Comment: arXiv admin note: text overlap with arXiv:1210.655