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author | Jakob Kaivo <jkk@ung.org> | 2022-03-04 12:32:20 -0500 |
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committer | Jakob Kaivo <jkk@ung.org> | 2022-03-04 12:32:20 -0500 |
commit | 55f277e77428d7423ae906a8e1f1324d35b07a7d (patch) | |
tree | 5c1c04703dff89c46b349025d2d3ec88ea9b3819 /miralib/manual/13 |
import Miranda 2.066 from upstream
Diffstat (limited to 'miralib/manual/13')
-rw-r--r-- | miralib/manual/13/1 | 22 | ||||
-rw-r--r-- | miralib/manual/13/2 | 68 | ||||
-rw-r--r-- | miralib/manual/13/3 | 33 | ||||
-rw-r--r-- | miralib/manual/13/contents | 6 |
4 files changed, 129 insertions, 0 deletions
diff --git a/miralib/manual/13/1 b/miralib/manual/13/1 new file mode 100644 index 0000000..c5e9198 --- /dev/null +++ b/miralib/manual/13/1 @@ -0,0 +1,22 @@ +_D_o_t_d_o_t_ _n_o_t_a_t_i_o_n + +The following abbreviations are provided for denoting lists, of type +[num], whose members form a finite or infinite arithmetic series. Let +`a', `b', `c' stand for arbitrary numeric expressions. + + [a..b] list of numbers from a to b inclusive, interval = 1 + [a..] infinite list starting at a and increasing by 1 + [a,b..c] arithmetic series, first member a, second member b, + last member not greater than c (if b-a non-negative) + or not less than c (if b-a negative). + [a,b..] infinite series starting at a, interval = (b-a) + +So the notation [1..10] has as value the list [1,2,3,4,5,6,7,8,9,10]. +Here are some more examples + + nats = [0..] + evens = [0,2..] + odds_less_than_100 = [1,3..99] + neg_odds = [-1,-3..] + tenths = [1.0,1.1 .. 2.0] + diff --git a/miralib/manual/13/2 b/miralib/manual/13/2 new file mode 100644 index 0000000..2e86d88 --- /dev/null +++ b/miralib/manual/13/2 @@ -0,0 +1,68 @@ +_L_i_s_t_ _c_o_m_p_r_e_h_e_n_s_i_o_n_s + + [exp | qualifiers] + +List of all `exp' such that `qualifiers'. If there are two or more +qualifiers they are separated by semicolons. Each qualifier is either a +generator, of which the allowed forms are + + pattern-list <- exp (first form) + + pattern <- exp, exp .. (second form) + +or else a filter, which is a boolean expression restricting the range of +the variables introduced by preceding generators. The variables +introduced on the left of each `<-' are local to the list comprehension. + +Some examples + + sqs = [ n*n | n<-[1..] ] + + factors n = [ r | r<-[1..n div 2]; n mod r = 0 ] + + knights_moves [i,j] = [ [i+a,j+b] | a,b<-[-2..2]; a^2+b^2=5 ] + +Notice that a list of variables on the lhs of a `<-' is shorthand for +multiple generators, e.g. `i,j<-thing' expands to `i<-thing; j<-thing'. + +The variables introduced by the generators come into scope from left to +right, so later generators can make use of variables introduced by +earlier ones. An example of this is shown by the following definition +of a function for generating all the permutations of a given list. + + perms [] = [[]] + perms x = [ a:p | a<-x; p<-perms(x--[a]) ] + +The second form of generator allows the construction of lists from +arbitrary recurrence relations, thus + x <- a, f x .. +causes x to assume in turn the values `a', `f a', `f(f a)', etc. + +An example of its use is in the following definition of the fibonacci +series + + fibs = [ a | (a,b) <- (1,1), (b,a+b) .. ] + +Another example is given by the following expression which lists the +powers of two + + [ n | n <- 1, 2*n .. ] + +The order of enumeration of a list comprehension with multiple +generators is like that of nested for-loops, with the rightmost +generator as the innermost loop. For example the value of the +comprehension [ f x y | x<-[1..4]; y<-[1..4] ] is + + [ f 1 1, f 1 2, f 1 3, f 1 4, f 2 1, f 2 2, f 2 3, f 2 4, + f 3 1, f 3 2, f 3 3, f 3 4, f 4 1, f 4 2, f 4 3, f 4 4 ] + +As a consequence of this order of enumeration of multiple generators, if +any generator other than the first (leftmost) is infinite, some +combinations of values will never be reached in the enumeration. To +overcome this a second, _d_i_a_g_o_n_a_l_i_s_i_n_g, form of list comprehension is +provided (see separate manual section). + +Note that list comprehensions do NOT remove duplicates from the result +list. To remove duplicates from a list, apply the standard function +`mkset'. + diff --git a/miralib/manual/13/3 b/miralib/manual/13/3 new file mode 100644 index 0000000..9cfbf11 --- /dev/null +++ b/miralib/manual/13/3 @@ -0,0 +1,33 @@ +_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. + diff --git a/miralib/manual/13/contents b/miralib/manual/13/contents new file mode 100644 index 0000000..543af82 --- /dev/null +++ b/miralib/manual/13/contents @@ -0,0 +1,6 @@ +_I_t_e_r_a_t_i_v_e_ _e_x_p_r_e_s_s_i_o_n_s + + 1. Dotdot expression + 2. List comprehensions + 3. Diagonalising list comprehensions + |