Projection Based Program Analysis

Projection based program analysis techniques are remarkable for their ability to give highly detailed and useful information not obtainable by other methods The rst proposed projection based analysis techniques were those of Wadler and Hughes for strictness analysis and Launchbury for binding time analysis both techniques are restricted to analysis of rst order monomorphic languages Hughes and Launchbury generalised the strictness analysis technique and Launchbury the binding time analy sis technique to handle polymorphic languages again restricted to rst order Other than a general approach to higher order analysis suggested by Hughes and an ad hoc implementation of higher order binding time analysis by Mogensen neither of which had any formal notion of correctness there has been no successful generalisation to higher order analysis We present a complete redevelopment of monomorphic projection based program analysis from rst principles starting by considering the analysis of functions rather than programs to establish bounds on the intrinsic power of projection based anal ysis showing also that projection based analysis can capture interesting termination properties The development of program analysis proceeds in two distinct steps rst for rst order then higher order Throughout we maintain a rigorous notion of correctness and prove that our techniques satisfy their correctness conditions Our higher order strictness analysis technique is able to capture various so called data structure strictness properties such as head strictness the fact that a function may be safely assumed to evaluate the head of every cons cell in a list for which it evaluates the cons cell Our technique and Hunt s PER based technique originally proposed at about the same time as ours are the rst techniques of any kind to capture such properties at higher order Both the rst order and higher order techniques are the rst projection based techniques to capture joint strictness properties for example the fact that a function may be safely assumed to evaluate at least one of several arguments The rst order binding time analysis technique is essentially the same as Launchbury s the higher order technique is the rst such formally based higher order generalisation Ours are the rst projection based termination analysis techniques and are the rst techniques of any kind that are able to detect termination properties such as head termination the fact that termination of a cons cell implies termination of the head A notable feature of the development is the method by which the rst order analysis semantics are generalised to higher order except for the xed point constant the higher order semantics are all instances of a higher order semantics parameterised by the constants de ning the various rst order semantics