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2.5. Lazy Constraint Programs 49

%%%%%%%%%% NOW WE GENERATE AN INFINITE LIST OF LISTS

%%%%%%%%%% CONTAINING THE MAGIC SEQUENCES FROM A NUMBER N

%%%%%%%%%% I.E., THE MAGIC SEQUENCES FROM N,N+1,N+2, ETC.

magicfrom :: int -> [[int]]

magicfrom N = [lazymagic N |magicfrom(N+1)]

Now it is easy to generate a list of N-magic series. For example, the following

goal generates a 3-element list containing, respectively, the solution to the problems of

7-magic, 8-magic and 9-magic series

TOY(FD)> take 3 (magicfrom 7) == L

yes

L == [ [ 3, 2, 1, 1, 0, 0, 0 ], [ 4, 2, 1, 0, 1, 0, 0, 0 ],

[ 5, 2, 1, 0, 0, 1, 0, 0, 0 ] ]

Elapsed time: 20 ms.

More expressiveness is shown by mixing curried functions, HO functions, inﬁnite

lists and function composition (another nice feature from the functional component of

TOY(FD)). For example, consider the TOY(FD) code below: :

from :: int -> [int]

from N = [N|from (N+1)]

lazyseries :: int -> [[int]]

lazyseries = map lazymagic.from

where the operator ‘.’ deﬁnes the composition of functions as follows (again, function

./2 is predeﬁned in the ﬁle misc.toy):

(.):: (B -> C) -> (A -> B) -> (A -> C) (F . G) X = F (G X)

Observe that lazyseries curries the comp osition (map lazymagic).from. Then, it is

easy to generate the 3-element list shown above by just typing the goal

TOY(FD) > take 3 (lazyseries 7) == L

yes

L == [ [ 3, 2, 1, 1, 0, 0, 0 ], [ 4, 2, 1, 0, 1, 0, 0, 0 ],

[ 5, 2, 1, 0, 0, 1, 0, 0, 0 ] ]

This goal is equivalent to the following

TOY(FD)> take 3 (map lazymagic (from 7)) == L

The function take/2 is predeﬁned in the ﬁle misc.toy (see Appendix C).

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