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Daniel Hillerström
2021-05-26 21:41:59 +01:00
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@@ -15027,10 +15027,10 @@ third-order function.
\[ \Count_n : ((\Nat \to \Bool) \to \Bool) \to \Nat \] \[ \Count_n : ((\Nat \to \Bool) \to \Bool) \to \Nat \]
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A \naive implementation strategy is simply to apply $P$ to each of the A \naive implementation strategy is simply to apply $P$ to each of the
$2^n$ vectors in turn. A much less obvious, but still purely $2^n$ vectors in turn. However, one can do better with an arcane
`functional', approach due to \citet{Berger90} achieves the effect of approach due to \citet{Berger90}, which achieves the effect of `pruned
`pruned search' where the predicate allows it (serving as a warning search' where the predicate allows it. This should be taken as a
that counter-intuitive phenomena can arise in this territory). warning that counter-intuitive phenomena can arise in this territory.
Nonetheless, under the mild condition that $P$ must inspect all $n$ Nonetheless, under the mild condition that $P$ must inspect all $n$
components of the given vector before returning, both these approaches components of the given vector before returning, both these approaches
will have a $\Omega(n 2^n)$ runtime. Moreover, we shall show that in will have a $\Omega(n 2^n)$ runtime. Moreover, we shall show that in
@@ -15054,7 +15054,7 @@ asymptotic gain of a factor of $n$.
% $\BigO(2^n)$ runtime for generic count with effect handlers also % $\BigO(2^n)$ runtime for generic count with effect handlers also
% transfers to generic search. % transfers to generic search.
The idea behind the speedup is easily explained and will already be The idea behind the speedup is readily explained and will already be
familiar, at least informally, to programmers who have worked with familiar, at least informally, to programmers who have worked with
multi-shot continuations. multi-shot continuations.
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