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6 Iteration  6.1 The LOOP Facility 6.1.2 Variable Initialization and Stepping Clauses 6.1.2.1 Iteration Control
6.1.2.1.1 The for-as-arithmetic subclause
In the for-as-arithmetic subclause, the for
or as construct iterates from the value supplied by
form1 to the value supplied by form2 in increments or
decrements denoted by form3. Each
expression is evaluated only once and must evaluate to a number.
The variable var is bound to the value of
form1 in the first iteration and is stepped1
by the value of form3 in each succeeding iteration,
or by 1 if form3 is not provided.
The following loop keywords serve as valid prepositions within this
syntax.
At least one of the
prepositions must be used;
and at most one from each line may be used in a single subclause.
- from | downfrom | upfrom
- to | downto | upto | below | above
- by
The prepositional phrases in each subclause may appear in any order.
For example, either "from x by y" or "by y from x" is permitted.
However, because left-to-right order of evaluation is preserved,
the effects will be different in the case of side effects.
Consider:
(let ((x 1)) (loop for i from x by (incf x) to 10 collect i))
 (1 3 5 7 9)
(let ((x 1)) (loop for i by (incf x) from x to 10 collect i))
(2 4 6 8 10)
The descriptions of the prepositions follow:
- from
The loop keyword from specifies the value from which
stepping1 begins, as supplied by form1.
Stepping1 is incremental by default. If
decremental stepping1 is desired,
the preposition downto
or above must be used with form2. For incremental
stepping1, the default from value is 0.
- downfrom, upfrom
The loop keyword downfrom
indicates that the variable var is decreased in decrements
supplied by form3; the loop keyword upfrom indicates that
var is increased in increments supplied by form3.
- to
The loop keyword to marks the end value
for stepping1 supplied in form2.
Stepping1 is incremental by default.
If decremental stepping1 is desired,
the preposition downfrom must be used with form1,
or else the preposition downto or above should be used instead
of to with form2.
- downto, upto
The loop keyword downto specifies decremental stepping;
the loop keyword upto specifies incremental stepping.
In both cases, the amount of change on each step is specified by form3,
and the loop terminates when the variable var passes
the value of form2.
Since there is no default for form1 in decremental stepping1,
a form1 value must be supplied (using from or downfrom)
when downto is supplied.
- below, above
The loop keywords below and above are analogous to
upto and downto respectively. These keywords stop
iteration just before the value of the variable var reaches the value
supplied by form2; the end value of form2 is not included.
Since there is no default for form1 in decremental stepping1,
a form1 value must be supplied (using from or downfrom)
when above is supplied.
- by
The loop keyword by marks the increment or decrement supplied by
form3. The value of form3 can be any
positive
number.
The default value is 1.
In an iteration control clause, the for or as construct
causes termination when the supplied limit is reached. That is,
iteration continues until the value var is stepped to the
exclusive or inclusive limit supplied by form2. The range is
exclusive if form3 increases or decreases var
to the value of form2 without reaching that value; the loop
keywords below and above provide exclusive limits. An
inclusive limit allows var to attain the value of
form2; to, downto, and upto provide inclusive
limits.
6.1.2.1.1.1 Examples of for-as-arithmetic subclause
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