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FYI: A suggestion for an additional simplification

From: Chimezie Ogbuji <ogbujic@ccf.org>
Date: Tue, 08 May 2007 08:54:51 -0400
To: public-rdf-dawg@w3.org
Message-ID: <1178628891.6621.35.camel@otherland>

I recently began an attempt to implement the mechanics of "12.2.1
Converting Graph Patterns" as a reduce function (a functional
programming idiom [1]) and came across an additional simplification that
might be useful to list in Step 5: Simplification

OPTIONAL graph patterns juxtaposed against an empty pattern can be
reduced to just the graph pattern:

Replace LeftJoin({},A,expr) with Filter(expr,A)


This seems to follow from:

LeftJoin(Omega1, Omega2, expr) = Filter(expr, Join(Omega1, Omega2))
set-union Diff(Omega1, Omega2, expr)

Omega1 -> [] - an empty multiset of solution  mappings (an empty graph
pattern will not have any solutions)

Filter(expr, Join([], Omega2)) set-union Diff([], Omega2, expr)

Join({}, A) -> A

Filter(expr, Omega2) set-union Diff([], Omega2, expr)

Diff([],.. any solution mapping multiset ..,expr) => [] (by definition)

Filter(expr, Omega2) set-union []

Filter(expr, Omega2) 

[1] http://en.wikipedia.org/wiki/Fold_%28higher-order_function%29 

Chimezie Ogbuji
Lead Systems Analyst
Thoracic and Cardiovascular Surgery
Cleveland Clinic Foundation
9500 Euclid Avenue/ W26
Cleveland, Ohio 44195
Office: (216)444-8593


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Received on Tuesday, 8 May 2007 12:55:35 UTC

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