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TL;DR: This paper shows how contexts can be represented using the notion of projection from domain theory, which means that recursive context equations can be solved using standard fixpoint techniques, instead of the algebraic manipulation previously used.
Abstract: Contexts have been proposed as a means of performing strictness analysis on non-flat domains. Roughly speaking, a context describes how much a sub-expression will be evaluated by the surrounding program. This paper shows how contexts can be represented using the notion of projection from domain theory. This is clearer than the previous explanation of contexts in terms of continuations. In addition, this paper describes finite domains of contexts over the non-flat list domain. This means that recursive context equations can be solved using standard fixpoint techniques, instead of the algebraic manipulation previously used.
TL;DR: The three instruction machine Tim is described, an abstract machine for the execution of supercombinators that usually executes programmes faster than the G-machine style of abstract machine while being at least as easy to implement as an S-K combinator reducer.
Abstract: This paper is a description of the three instruction machine Tim, an abstract machine for the execution of supercombinators. Tim usually executes programmes faster than the G-machine style of abstract machine while being at least as easy to implement as an S-K combinator reducer. It has a lower overhead for passing unevaluated arguments than the G-machine, resulting in good performance even without strictness analysis, and is probably easier to implement in hardware.
TL;DR: A set-theoretic abstract interpretation framework is formulated in a way which is independent of both the programming language and the method used to specify its semantics, starting from its standard denotational semantics.
Abstract: The original formulation of abstract interpretation represents program properties by sets. A property is understood as the set of semantic values satisfying it. Strongest program properties are defined by the collecting semantics which extends the standard semantics to powersets of semantic values. The approximation relation corresponding to the logical implication of program properties is subset inclusion. This was expressed using set and lattice theory in the context of transition systems. Some applications of abstract interpretation, such as strictness analysis for lazy functional languages, require infinite behaviours of higher-order functions to be taken into account. We solve the problem by returning to the sources of abstract interpretation, which consists in considering collecting semantics. By using Galois connections, properties of the standard semantics naturally transfer to the collecting and then to the abstract semantics. This set-theoretic abstract interpretation framework is formulated in a way which is independent of both the programming language and the method used to specify its semantics. It is illustrated for a higher-order monomorphically typed lazy functional language starting from its standard denotational semantics. >
TL;DR: Data or program flow analysis is concerned with the static analysis of programs, to obtain as much information as possible about their possible run time behavior without actually having to run the programs.
Abstract: Data or program flow analysis is concerned with the static analysis of programs, to obtain as much information as possible about their possible run time behavior without actually having to run the programs. Due to the unsolvability of the halting problem (and nearly any other question concerning program behavior), such analyses are necessarily only approximate whenever the analysis algorithm is guaranteed to terminate. Further, exact analysis may be impossible due to the lack of knowledge of input data values, so the analysis can at best yield information about sets of possible computations.