Head-Order Techniques and Other Pragmatics of Lambda Calculus Graph Reduction

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Head-Order Techniques and Other Pragmatics of Lambda Calculus Graph Reduction

Available in Paperback Available in eBook editions (PDF format)
Institution:
Syracuse University (Syracuse, NY, USA)
Advisor(s):
Prof. Klaus J. Berkling
Degree:
Ph.D.... Viac o knihe

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O knihe

Available in Paperback Available in eBook editions (PDF format)
Institution:
Syracuse University (Syracuse, NY, USA)
Advisor(s):
Prof. Klaus J. Berkling
Degree:
Ph.D. in Computer and Information Science
Year:
1993
Book Information:
248 pages
Publisher:
Dissertation.com
ISBN-10:
1612337570
ISBN-13:
9781612337579
View First 25 pages:
(free download)
Abstract
The operational aspects of Lambda Calculus are studied as a fundamental basis for high-order functional computation. We consider systems having full reduction semantics, i.e., equivalence-preserving transformations of functions. The historic lineage from Eval-Apply to SECD to RTNF/RTLF culminates in the techniques of normal-order graph Head Order Reduction (HOR). By using a scalar mechanism to artificially bind relatively free variables, HOR makes it relatively effortless to reduce expressions beyond weak normal form and to allow expression-level results while exhibiting a well-behaved linear self-modifying code structure. Several variations of HOR are presented and compared to other efficient reducers, with and without sharing, including a conservative breadth-first one which mechanically takes advantage of the inherent, fine-grained parallelism of the head normal form. We include abstract machine and concrete implementations of all the reducers in pure functional code. Benchmarking comparisons are made through a combined time-space efficiency metric. The original results indicate that circa 2010 reduction rates of 10-100 million reductions per second can be achieved in software interpreters and a billion reductions per second can be achieved by a state-of-the art custom VLSI implementation.