An algebraic array shape inference system for MATLAB®
ACM Transactions on Programming Languages and Systems (TOPLAS)
A translator system for the MATLAB language: Research Articles
Software—Practice & Experience
McSAF: a static analysis framework for MATLAB
ECOOP'12 Proceedings of the 26th European conference on Object-Oriented Programming
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This thesis presents techniques for deducing valuable array shape information in typeless array-based languages like MATLAB, even when the shapes may be statically unknown. The approach is based on an algebraical modelling of the language's array shape semantics. The dissertation makes five primary contributions: (1) it shows how to model shape semantics so as to enable precise characterizations that are independent of an array's dimensionality, (2) it presents a rewriting methodology that uses the characterizations to symbolically determine an array expression's shape in O(R||s||3 log||s||) time, where ||s|| is the number of nodes in a rooted ordered tree representation of a shape term s, and R is an upper bound on an array's canonical rank, (3) it presents a shape-tracking optimization that detects equivalent shapes, permitting a translator to eliminate redundant shape checks, and to generate specialized code even when the shapes may be compile-time unknowns, (4) it shows a preallocation optimization that determines the set of all possible shapes that an expression may assume during program execution; and (5) it presents an interference graph-based algorithm that uses type and control-flow information to coalesce array storage. The dissertation also substantiates the techniques by presenting performance numbers of an implementation on a benchmark suite.