On Static and Dynamic Control-Flow Information in Program Analysis and Transformation

This thesis addresses several aspects of static and dynamic control-flow information in programming languages, by investigating its interaction with program transformation and program analysis. Control-flow information indicates for each point in a program the possible program points to be executed next. Control-flow information in a program may be static, as when the syntax of the program directly determines which parts of the program may be executed next. Control-flow information may be dynamic, as when run-time values and inputs of the program are required to determine which parts of the program may be executed next. A control-flow analysis approximates the dynamic control-flow information with conservative static control-flow information. We explore the impact of a continuation-passing-style (CPS) transformation on the result of a constraint-based control-flow analysis over Moggi’s computational metalanguage. A CPS transformation makes control-flow explicitly available to the program by abstracting the remainder of the computation into a continuation. Moggi’s computational metalanguage supports reasoning about higher-order programs in the presence of computational effects. We show that a non-duplicating CPS transformation does not alter the result of a monovariant constraint-based control-flow analysis. Building on control-flow analysis, we show that traditional constraint-based binding-time analysis and traditional partial evaluation benefit from the effects of a CPS transformation, while the same CPS transformation does not affect continuation-based partial evaluation and its corresponding binding-time analysis. As an intermediate result, we show that reducing a program in the computational metalanguage to monadic normal form also improves binding times for traditional partial evaluation while it does not affect continuation-based partial evaluation. In addition, we show that linear β-reductions have no effect on controlflow analysis. As a corollary, we solve a problem left open in Palsberg and Wand’s CPS transformation of flow information. Furthermore, using Danvy and Nielsen’s first-order, one-pass CPS transformation, we present a simpler CPS transformation of flow information with a simpler correctness proof. We continue by exploring Shivers’s time-stamps-based technique for approximating program analyses over programs with dynamic control flow. We formalize a time-stamps-based algorithm for approximating the least fixed point