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Computer Science > Logic in Computer Science

arXiv:2103.12811 (cs)
[Submitted on 23 Mar 2021]

Title:Combinators: A Centennial View

Authors:Stephen Wolfram
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    Abstract: We give a modern computational introduction to the S,K
    combinators invented by Moses Schonfinkel in 1920, and present a
    variety of new results and ideas about combinators. We explore
    the spectrum of behavior obtained with small combinator
    expressions, showing a variety of approaches to analysis and
    visualization. We discuss the implications of evaluation
    strategies, and of multiway systems representing all possible
    strategies. We show how causal graphs introduced in recent models
    of fundamental physics can be applied to combinators, as well as
    describing how combinators introduce a new form of treelike
    separation. We give a variety of new results on minimal
    combinator expressions, as well as showing how empirical
    computation theory and computational complexity theory can be
    done with combinators. We also suggest that when viewed in terms
    of ongoing computation, the S combinator alone may be capable of
    universal computation.

Subjects: Logic in Computer Science (cs.LO); Discrete Mathematics
          (cs.DM)
Cite as:  arXiv:2103.12811 [cs.LO]
          (or arXiv:2103.12811v1 [cs.LO] for this version)

Submission history

From: Stephen Wolfram [view email]
[v1] Tue, 23 Mar 2021 19:48:36 UTC (38,006 KB)
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