[EMAIL PROTECTED] wrote in article <[EMAIL PROTECTED]> in
gmane.comp.lang.haskell.cafe:
> Conor McBride has posed an interesting problem:
> > implement constructors
> > P v for embedding pure values v
> > O for holes
> > f :$ a for application, left-associative
> > and an interpreting function
> > emmental
> > such that
> > emmental (P (+) :$ (P (*) :$ O :$ P 10) :$ O) 4 2 = 42
Hrm! I don't see the original message where the problem was posed, but
it is indeed interesting. Here is my solution, but I don't need "P",
"O", and ":$" to be constructors, so I rename them to "p", "o", and
"$:", respectively:
emmental m = m id
p x k = k x
o k = k
(m $: n) k = m (\f -> n (\x -> k (f x)))
infixl 0 $:
test = emmental (p (+) $: (p (*) $: o $: p 10) $: o) 4 2 -- 42
All credit is due to Danvy and Filinski (DIKU TR 89/12, Section 3.4;
later Danvy's "functional unparsing" paper, JFP 8(6)). One way to
understand this code is that "o" is like the word "what" in a language
like Mandarin ("shenme") or Japanese ("dare") that does not move any
wh-word to the boundary of a clause. In Japanese, "emmental" would
correspond to the "-ka" that marks the scope of a question and awaits
an answer (in this case the numbers 4 and 2). Or, we have control
inversion: the argument to emmental is a sandboxed user process that
occasionally requests input.
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