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<p class=MsoNormal>New to Haskell, with a mental block about how to represent
this situation efficiently:<o:p></o:p></p>
<p class=MsoNormal><o:p> </o:p></p>
<p class=MsoNormal>I have an unknown function f which is defined on subsets of
some universal set (say integers 1…N). I know the values of f for
some subsets, and using those can infer values on other subsets. <o:p></o:p></p>
<p class=MsoNormal><o:p> </o:p></p>
<p class=MsoNormal>So what I need is a way to manage a collection of subsets
s_i (and the associated values f(s_i)) so that I can efficiently (a) check
whether a subset s is already 'known' in my collection, and (b) find all
subsets t in the collection that intersect s.<o:p></o:p></p>
<p class=MsoNormal><o:p> </o:p></p>
<p class=MsoNormal>In a "traditional" language, I'd likely create a
dictionary with keys s_i containing the f(s_i) as values, along with a separate
dictionary keyed on the elements of the universal set (1…N) in which each
entry is a list of all s_i containing the given element of the universal set.
Together they let me check, given a subset s, whether I know f(s), and also get
the list of all known subsets intersecting s (by the union of the lists of sets
containing each element of s).<o:p></o:p></p>
<p class=MsoNormal><o:p> </o:p></p>
<p class=MsoNormal>I can't quite wrap my head around how to do this efficiently
in Haskell, maybe because of the way the above is duplicating information about
the subsets across two different data structures? <o:p></o:p></p>
<p class=MsoNormal><o:p> </o:p></p>
<p class=MsoNormal>Any thoughts?<o:p></o:p></p>
<p class=MsoNormal><o:p> </o:p></p>
<p class=MsoNormal>Thanks,<br>
Patrick<o:p></o:p></p>
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