Multilisp: A Language for Concurrent Symbolic Computation by Robert H. Halstead. (ACM Transactions on Programming Languages and Systems, Vol. 7, No. 4, October 1985, Pages 501-538.)

Abstract:

Multilisp is a version of the Lisp dialect Scheme extended with constructs for parallel execution. Like Scheme, Multilisp is oriented toward symbolic computation. Unlike some parallel programming languages, Multilisp incorporates constructs for causing side effects and for explicitly introducing parallelism. The potential complexity of dealing with side effects in a parallel context is mitigated by the nature of the parallelism constructs and by support for abstract data types: a recommended Multilisp programming style is presented which, if followed, should lead to highly parallel, easily understandable programs. Multilisp is being implemented on the 32-processor Concert multiprocessor; however, it is ulti-mately intended for use on larger multiprocessors. The current implementation, called Concert Multilisp, is complete enough to run the Multilisp compiler itself and has been run on Concert prototypes including up to eight processors. Concert Multilisp uses novel techniques for task scheduling and garbage collection. The task scheduler helps control excessive resource utilization by means of an unfair scheduling policy; the garbage collector uses a multiprocessor algorithm based on the incremental garbage collector of Baker.

Of particular interest:

Multilisp’s principal construct for both creating tasks and synchronizing among them is the *future*. The construct ( *future ***X** ) immediately returns a future for the value of the expression **X** and concurrently begins evaluating **X**. When the evaluation of **X** yields a value, that value replaces the future. The future is said to be initially *undetermined*; it becomes *determined* when its value has been computed. An operation (such as addition) that needs to know the value of an undetermined future will be suspended until the future becomes determined, but many operations, such as assignment and parameter passing, do not need to know anything about the values of their operands and may be performed quite comfortably on undetermined futures. The use of futures often exposes surprisingly large amounts of parallelism in a program, as illustrated by a Quicksort program given in Figure 1.

The use of a *future* value for merge operations, which could avoid re-processing a topic map for each cycle of merging, sounds promising.

Deferral of the results isn’t just an old Lisp idea as you will find in: Counting complex disordered states by efficient pattern matching: chromatic polynomials and Potts partition functions by Marc Timme, Frank van Bussel, Denny Fliegner, and Sebastian Stolzenberg.

Abstract:

Counting problems, determining the number of possible states of a large system under certain constraints, play an important role in many areas of science. They naturally arise for complex disordered systems in physics and chemistry, in mathematical graph theory, and in computer science. Counting problems, however, are among the hardest problems to access computationally. Here, we suggest a novel method to access a benchmark counting problem, finding chromatic polynomials of graphs. We develop a vertex-oriented symbolic pattern matching algorithm that exploits the equivalence between the chromatic polynomial and the zero-temperature partition function of the Potts antiferromagnet on the same graph. Implementing this bottom-up algorithm using appropriate computer algebra, the new method outperforms standard top-down methods by several orders of magnitude, already for moderately sized graphs. As a first application, we compute chromatic polynomials of samples of the simple cubic lattice, for the first time computationally accessing three-dimensional lattices of physical relevance. The method offers straightforward generalizations to several other counting problems.

In lay person’s terms the work by Timme and company visits each node in a graph and records an expression that includes unkowns (futures?), that is the values at other nodes in the graph. Using pattern matching techniques, the algorithm then solves all of the unknowns and replaces them with appropriate values. How effective is this?

“The existing algorithm copies the whole network for each stage of the calculation and only changes one aspect of it each time,” explains Frank van Bussel of the Max Planck Institute for Dynamics and Self-Organization (MPIDS). Increasing the number of nodes dramatically increases the calculation time. For a square lattice the size of a chess board, this is estimated to be many billions of years. The new algorithm developed by the Göttingen-based scientists is significantly faster. “Our calculation for the chess board lattice only takes seven seconds,” explains Denny Fliegner from MPIDS. (A New Kind of Counting)

Hmmm, “many billions of years” versus “seven seconds.”

For further details on the pattern matching work see the project page at: Complex Disordered Systems: Statistical Physics and Symbolic Computation

Deferral of results looks like a fruitful area for research for topic maps in general and parallel processing of topic maps in particular.

I first saw the Multilisp paper in a tweet by Mom of Finland.