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authorJakob Kaivo <jkk@ung.org>2022-03-04 12:32:20 -0500
committerJakob Kaivo <jkk@ung.org>2022-03-04 12:32:20 -0500
commit55f277e77428d7423ae906a8e1f1324d35b07a7d (patch)
tree5c1c04703dff89c46b349025d2d3ec88ea9b3819 /miralib/manual/13/3
import Miranda 2.066 from upstream
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+_D_i_a_g_o_n_a_l_i_s_i_n_g_ _l_i_s_t_ _c_o_m_p_r_e_h_e_n_s_i_o_n_s
+
+ [ exp // qualifiers ]
+
+Syntax and scope rules exactly as for standard list comprehensions, the
+only difference being the use of `//' in place of the vertical bar. The
+order of enumeration of the generators is such that it is guaranteed
+that every possible combination of values will be reached eventually.
+The diagonalisation algorithm used is "fair" in the sense that it gives
+equal priority to all of the generators.
+
+For example the value of [f x y//x<-[1..4]; y<-[1..4]] is
+
+ [ f 1 1, f 1 2, f 2 1, f 1 3, f 2 2, f 3 1, f 1 4, f 2 3,
+ f 3 2, f 4 1, f 2 4, f 3 3, f 4 2, f 3 4, f 4 3, f 4 4 ]
+
+The algorithm used used is "Cantorian diagonalisation" - imagine the
+possible combinations of values from the two generators laid out in a
+(perhaps infinite) rectangular array, and traverse each diagonal in turn
+starting from the origin. The appropriate higher-dimensional analogue
+of this algorithm is used for the case of a list comprehension with
+three or more generators.
+
+As an example of an enumeration that could not be defined at all using a
+standard list comprehension, because of the presence of several infinite
+generators, here is a definition of the list of all pythagorean
+triangles (right-angled triangles with integer sides)
+
+ pyths = [(a,b,c)//a,b,c<-[1..];a^2+b^2=c^2]
+
+In the case that there is only one generator, the use of `//' instead of
+`|' makes no difference to the meaning of the list comprehension.
+