From f61026119df4700f69eb73e95620bc5928ca0fcb Mon Sep 17 00:00:00 2001
From: User <bnewbold@daemon.robocracy.org>
Date: Tue, 13 Oct 2009 02:52:09 +0000
Subject: Grand rename for gitit transfer

---
 software/functional programming.page | 52 ++++++++++++++++++++++++++++++++++++
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 create mode 100644 software/functional programming.page

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+===================================
+Functional Programming
+===================================
+
+Recursion
+--------------
+**Partial** functions can recurse endlessly over a finite input. **Total**
+functions will terminate/halt over a finite input. (TODO: check this
+definition)
+
+Collectors
+--------------
+The collector concept/pattern/paradigm is the one I am least familiar with
+in functional programming.
+
+My current understanding is that they essentially allow allow recursive
+functions to maintain something like state by wrapping immutable functions
+or variables in layer after layer of functions and just holding on to
+the outermost layer. For instance, the typical way to write a ``length``
+function in python would be::
+
+>>> def how-long(x):
+>>>     l = 0
+>>>     while x.has_next()
+>>>         l = l+1;
+>>>         x.pop()
+>>>     return l
+
+Using recursion, we could do::
+
+>>> def how-long-recurse(x):
+>>>     if x.has_next()
+>>>         x.pop()
+>>>         return how-long-recurse(x) + 1
+>>>     else
+>>>         return 0
+
+Using the collector paradigm, we could do::
+
+>>> def add1(x): return a+1;
+>>> def how-long-col(x, col):
+>>>     if x.has_next()
+>>>         return col(0)
+>>>     else
+>>>         x.pop()
+>>>         return how-long-col(x, lambda a: col(add1(a)))
+
+The first two ways, the plus one operation is actually executed at any given
+time, while with the collector implementation we're really creating a
+function step by step which will give the answer at the end when it is all
+executed.
+
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