Table of Contents
This chapter will introduce you to the basic strategies for working with lists. The strategies provide functionality for composing and decomposing, sorting, filtering, mering as well as constructing new abstractions from basic lists, such as associative lists.
Every value in Stratego is a term. This is also the case for lists.
You can write the list 1, 2, 3 as
Cons(1,Cons(2,Cons(3,Nil))), which is clearly a term.
Fortunately, Stratego also provides some convenient syntactic sugar
that makes lists more readable and easy to work with. We can write
the same list as [1,2,3], which will be desugared
internally in the the term above.
The most fundamental operations on lists is the ability
compose and decompose lists. In Stratego, list composition on
"sugared" lists, that is, lists writen in the sugared form,
has some sugar of its own. Assume xs is the list
[1,2,3]. The code [0|xs] will prepend a
0 to it, yielding [0,1,2,3]. List decomposition is done using
the match operator. The code ![0,1,2,3] ; ?[y|ys]
will bind y to the head of the list, 0,
and ys to the tail of the list, [1,2,3].
The module collection/list contains a lot of convenience
functions for dealing with lists. (collection/list is
contained in the liblib library.) For example, the strategy
elem will check if a given value is in a list. If it
is, the identity of the list will be returned.
stratego>import liblibstratego><elem> (1, [2,3,1,4]) [2,3,1,4]
Continuing on the above Stratego Shell session, we can exercise some of the other strategies:
stratego><length> [1,2,3,4,5] 5stratego><last> [5,6,7,8,9] 9stratego><reverse> [1,2,3,4,5] [5,4,3,2,1]
There are two strategies for concatenating lists. If the lists
are given as a tuple, use conc. If you have a list
of lists, use concat:
stratego><conc> ([1,2,3],[4,5,6],[7,8,9]) [1,2,3,4,5,6,7,8,9]stratego><concat> [[1,2,3],[4,5,6],[7,8,9]] [1,2,3,4,5,6,7,8,9]
The sublist of the first n elements can be
picked out with the take(|n) strategy:
stratego> <take(|3)> [1,2,3,4,5]
[1,2,3]
Finally, the fetch(s) strategy can be used to find
the first element for which s succeeds:
stratego> <fetch(?2)> [1,2,3]
2
The Stratego library contains many other convenient functions, which are documented in the API documentation.
The list sorting function is called qsort(s), and
implements the Quicksort algorithm. The strategy parameter
s is the comparator function.
stratego> <qsort(gt)> [2,3,5,1,9,7]
[9,7,5,3,2,1]
Stratego also has library support for associative lists, sometimes known
as assoc lists. There are essentially lists of (key, value)
pairs, and work like a poor man's hash table. The primary strategy for
working with these lists is lookup. This strategy looks up
the first value associated with a particular key, and returns it.
stratego> <lookup> (2, [(1, "a"), (2, "b"), (3, "c")]) => "b"
The library also contains some useful strategies for
combining multiple lists. The cart(s) strategy
makes a cartesian product of two lists. For each pair,
the parameter strategy s will be called. In
the second case below, each pair will be summed by
add.
stratego><cart(id)> ([1,2,3],[4,5,6]) [(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)]stratego><cart(add)> ([1,2,3],[4,5,6]) [5,6,7,6,7,8,7,8,9]
Two lists can be paired using zip(s). It takes
a tuple of two lists, and will successively pick out the head
of the lists and pair them into a tuple, and apply
s to the tuple. zip is equivalent
to zip(id).
stratego><zip> ([1,2,3],[4,5,6]) [(1,4),(2,5),(3,6)]stratego><zip(add)> ([1,2,3],[4,5,6]) [5,6,7]
The inverse function of zip is unzip.
stratego> <unzip> [(1,4),(2,5),(3,6)]
([1,2,3],[4,5,6])
There is also unzip(s) which like unzip
takes a list of two-element tuples , and applies s
to each tuple before unzipping them into two lists.
In Stratego, lightweight sets are implemented as lists. A set differs
from a list in that a given element (value) can only occur once. The
strategy nub (also known as make-set)
can be use to make a list into a set. It will remove duplicate
elements. The normal functions on sets are provided, among
them union, intersection, difference and equality:
stratego><nub> [1,1,2,2,3,4,5,6,6] [1,2,3,4,5,6]stratego><union> ([1,2,3],[3,4,5]) [1,2,3,4,5]stratego><diff> ([1,2,3],[3,4,5]) [1,2]stratego><isect> ([1,2,3],[3,4,5]) [3]stratego><set-eq> ([1,2,3],[1,2,3]) ([1,2,3],[1,2,3])
Elementwise transformation of a list is normally done with the
map(s) strategy. It must be applied to a list.
When used, it will apply the strategy s to each
element in the list, as shown here. It will return a list of equal
length to the input. If the application of s fails
on one of the elements map(s) fails.
stratego> <map(inc)> [1,2,3,4]
[2,3,4,5]
mapconcat(s) is another variant of the
elementwise strategy application, equivalent to
map(s) ; concat. It takes a strategy
s which will be applied to each element.
The strategy s must always result in a list,
thus giving a list of lists, which will be concatenated.
A slightly more convoluted version of the above mapping.
If we want to remove
elements from the list, we can use filter(s).
The filter strategy will apply s
to each element of a list, and keep whichever elements
it succeeds on:
stratego> <filter(?2 ; !6)> [1,2,3,2]
[6,6]
stratego> <mapconcat(\ x -> [ <inc> x ] \)> [1,2,3,4]
List folding is a somewhat flexible technique primarily intended
for reducing a list of elements to a single value. Think of it
as applying an operator between any two elements in the list,
e.g. going from [1,2,3,4] to the result of
1 + 2 + 3 + 4. If the operator is not commutative,
that is x <op> y is not the same as
y <op> x, folding from the left will not be
the same as folding from the right, hence the need for both
foldl and foldr.
The foldr(init, oper) strategy takes a list of
elements and starts folding them from the right. It starts
after the rightmost element of the list. This means that
if we use the + operator with
foldr on the list [1,2,3,4],
we get the expression 1 + 2 + 3 + 4 + , which
obviously has a dangling +. The strategy
argument init is used to supply the missing
argument on the right hand side of the last plus. If the
init supplied is id,
[] will be supplied by default. We can see
this from the this trial run:
stratego> <foldr>(id, debug)
(4,[])
(3,(4,[]))
(2,(3,(4,[])))
(1,(2,(3,(4,[]))))
(1,(2,(3,(4,[]))))
With this in mind, it should be obvious how we can sum a list
of numbers using foldr:
stratego> <foldr(!0, add)> [1,2,3,4]
10
The related strategy foldl(s) works similarly to
foldr. It takes a two-element tuple with a list
and a single element, i.e. ([x | xs], elem). The
folding will start in the left end of the list. The first
application is s on (elem, x), as
we can see from the following trial run:
stratego> <foldl(debug)> ([1,2,3,4], 0)
(1,0)
(2,(1,0))
(3,(2,(1,0)))
(4,(3,(2,(1,0))))
(4,(3,(2,(1,0))))
Again, summing the elements of the list is be pretty easy:
stratego> <foldl(add)> ([1,2,3,4], 0)
10
In this chapter we got a glimpse of the most important strategies for manipulating lists. We saw how to construct and deconstruct lists, using build and match. We also saw how we can sort, merge, split and otherwise transform lists. The strategies for associative lists and sets gave an impression of how we can construct new abstractions from basic lists.
More information about list strategies available can be found in
the collections/list module, in the
library reference documentation.