pure-lang-svn Mailing List for Pure (Page 8)

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Revision: 695
          http://pure-lang.svn.sourceforge.net/pure-lang/?rev=695&view=rev
Author:   agraef
Date:     2008-09-04 01:18:14 +0000 (Thu, 04 Sep 2008)

Log Message:
-----------
Update documentation.

Modified Paths:
--------------
    pure/trunk/pure.1.in

Modified: pure/trunk/pure.1.in
===================================================================

--- pure/trunk/pure.1.in	2008-09-04 00:45:30 UTC (rev 694)
+++ pure/trunk/pure.1.in	2008-09-04 01:18:14 UTC (rev 695)
@@ -411,7 +411,7 @@
 lambdas, conditional expressions and ``catmaps'' (a list operation which
 combines list concatenation and mapping a function over a list, defined in the
 prelude), but they are often much easier to write. Some examples of list
-comprehensions can be found below at the end of this section.
+comprehensions can be found in the EXAMPLES section below.
 .TP
 .B Function applications: \fRfoo\ x\ y\ z
 As in other modern FPLs, these are written simply as juxtaposition (i.e., in
@@ -520,9 +520,11 @@
 .PP
 The & operator does
 .IR "lazy evaluation" .
-More precisely, it turns its operand into a kind of parameterless anonymous
-closure, deferring its evaluation. These kinds of objects are commonly known
-as
+This is the only postfix operator defined in the standard prelude, written as
+`x&', where x is an arbitrary Pure expression. The & operator binds stronger
+than any other operation except function application. It turns its operand
+into a kind of parameterless anonymous closure, deferring its
+evaluation. These kinds of objects are also commonly known as
 .I thunks
 or
 .IR futures .
@@ -535,22 +537,9 @@
 structures in Pure, in particular: lazy lists a.k.a.
 .IR streams .
 A stream is simply a list with a thunked tail, which allows it to be
-infinite. E.g.:
-.sp
-.nf
-> ints n = n : ints (n+1) &; let nats = ints 1;
-> nats;
-1:<<thunk 0xb6033528>>
-> take 10 nats;
-[1,2,3,4,5,6,7,8,9,10]
-> nats;
-1:2:3:4:5:6:7:8:9:10:11:<<thunk 0xb5fb1a08>>
-> nats!9999;
-10000
-.fi
-.sp
-Note that the prelude defines & as a postfix operator which binds stronger
-than any other operation except function application.
+infinite. The Pure prelude defines many functions for creating and
+manipulating these kinds of objects; further details and examples can be found
+in the EXAMPLES section below.
 .PP
 .B Toplevel.
 At the toplevel, a Pure program basically consists of rewriting rules (which
@@ -699,8 +688,7 @@
 symbols needed in an evaluation
 .I before
 entering the expression to be evaluated.
-.PP
-.B Examples.
+.SH EXAMPLES
 Here are a few examples of simple Pure programs (see the following section for
 a closer discussion of the rule syntax).
 .PP
@@ -756,7 +744,8 @@
 6.28318530717958
 .fi
 .PP
-A little list comprehension example (Erathosthenes' classical prime sieve):
+.B List comprehensions.
+Erathosthenes' classical prime sieve:
 .sp
 .nf
 primes n        = sieve (2..n) \fBwith\fP
@@ -796,6 +785,136 @@
                 = i1==i2 || j1==j2 || i1+j1==i2+j2 || i1-j1==i2-j2;
 \fBend\fP;
 .fi
+.PP
+.B Lazy evaluation and streams.
+As already mentioned, lists can also be evaluated in a ``lazy'' fashion, by
+just turning the tail of a list into a
+.IR future .
+This special kind of list is also called a
+.IR stream .
+Streams enable you to work with infinite lists (or finite lists which are so
+huge that we would never want to keep them in memory). E.g., here's one way to
+create the infinite list of all positive integers:
+.sp
+.nf
+> ones = 1:ones&;
+> integers = 1 : zipwith (+) ones integers&;
+> \fBlet\fP ints = integers; ints;
+1:<<thunk 0xb5fdd5b8>>
+.fi
+.PP
+(Note that we use machine integers in this example, so in fact the list will
+wrap around to the smallest negative integer at some point.)
+.PP
+Of course, care must be taken not to invoke ``eager'' operations such as `#'
+(which computes the size of a list) on infinite streams, since this never
+terminates. However, many list operations work with infinite streams just
+fine, and return the appropriate stream results. E.g., the `take' function
+(which retrieves a given number of elements from the front of a list) works
+with streams just as well as with ``eager'' lists:
+.sp
+.nf
+> take 10 ints;
+1:<<thunk 0xb5fdd5e8>>
+.fi
+.PP
+Hmm, not much progress there, but that's just how streams work (or rather
+don't, they're lazy bums indeed!). But the stream computed with `take' is in
+fact finite and we can readily convert it to an ordinary list, forcing its
+evaluation:
+.sp
+.nf
+> (list) (take 10 ints);
+[1,2,3,4,5,6,7,8,9,10]
+.fi
+.PP
+(Note that we typed `(list)' instead of just `list' here, so that the
+interpreter does not mistake this for the interactive
+.B list
+command. This is only necessary at the interactive command prompt, see
+INTERACTIVE USAGE.)
+.PP
+For interactive usage it's often convenient to define an eager variation of
+`take' which combines `take' and `list'. Let's do this now, so that we can use
+this operation in the following examples.
+.sp
+.nf
+> takel n xs = list (take n xs);
+> takel 10 ints;
+[1,2,3,4,5,6,7,8,9,10]
+.fi
+.PP
+Let's take another look at the `ints' stream now:
+.sp
+.nf
+> ints;
+1:2:3:4:5:6:7:8:9:10:<<thunk 0xb5fddcd8>>
+.fi
+.PP
+As you can see, the invokation of `list' on the result of `take' forced the
+corresponding prefix of the `ints' stream to be computed. The result of this
+is memoized, so that this portion of the stream is now readily available in
+case we need to have another look at it again later. By these means, possibly
+costly reevaluations are avoided, trading memory for execution speed.
+.PP
+A number of convenience operations are available for generating stream values.
+The prelude defines infinite arithmetic sequences, using
+.B inf
+or
+.B -inf
+to denote an upper (or lower) infinite bound for the sequence, e.g.:
+.sp
+.nf
+> let u = 1..inf; let v = -1.0,-1.2..-inf;
+> takel 10 u; takel 10 v;
+[1,2,3,4,5,6,7,8,9,10]
+[-1.0,-1.2,-1.4,-1.6,-1.8,-2.0,-2.2,-2.4,-2.6,-2.8]
+.fi
+.PP
+Other useful stream generator functions are `iterate', `repeat' and `cycle',
+which have been adopted from Haskell. Moreover, list comprehensions can draw
+values from streams and return the appropriate stream result:
+.sp
+.nf
+> \fBlet\fP pairs = [i,j; i=1..inf; j=1..i]; pairs;
+(1,1):<<thunk 0xb5f28818>>
+> takel 10 pairs;
+[(1,1),(2,1),(2,2),(3,1),(3,2),(3,3),(4,1),(4,2),(4,3),(4,4)]
+.fi
+.PP
+Finally, let's rewrite our prime sieve so that it generates the infinite
+stream of
+.I all
+prime numbers:
+.sp
+.nf
+all_primes      = sieve (2..inf) \fBwith\fP
+  sieve []      = [];
+  sieve (p:qs)  = p : sieve [q; q = qs; q mod p] &;
+\fBend\fP;
+.fi
+.sp
+Example:
+.sp
+.nf
+> \fBlet\fP P = all_primes;
+> takel 20 P;
+[2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71]
+> P!299;
+1987
+.fi
+.PP
+You can also just print the entire stream. This will run forever, so hit
+Ctrl-C when you get bored.
+.sp
+.nf
+> \fBusing\fP system;
+> do (printf "%d\en") all_primes;
+2
+3
+5
+  ...
+.fi
 .SH RULE SYNTAX
 Basically, the same rule syntax is used in all kinds of global and local
 definitions. However, some constructs (specifically, \fBwhen\fP, \fBlet\fP,
@@ -1689,8 +1808,9 @@
 See the DEFINITION LEVELS section below for details.
 .PP
 Note that these special commands are only recognized at the beginning of the
-interactive command line. (Thus you can escape a symbol looking like a command
-by prefixing it with a space.)
+interactive command line. (Thus you can escape an identifier at the beginning
+of the command line, which looks like a command, by prefixing it with a space
+or by wrapping it up in parentheses.)
 .PP
 Some commands which are especially important for effective operation of the
 interpreter are discussed in more detail in the following sections.


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