.. _SLang2TTK:
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.. |---| unicode:: U+2014 .. em dash, trimming surrounding whitespace
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.. This file is part of the OpenDSA eTextbook project. See
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.. Copyright (c) 2012-13 by the OpenDSA Project Contributors, and
.. distributed under an MIT open source license.
.. avmetadata::
:author: David Furcy and Tom Naps
Tying The Knot
==============
We next consider how to implement recursive functions in SLang 2. In
the lambda calculus and SLang 1, all functions are anonymous and
cannot call themselves. We could use a fixed-point combinator, like
the :math:`Y` combinator.
::
let
Y = fn (h) => (fn (x) => (h (x x)) fn (x) => (h (x x)))
f = fn (g) => fn (n) => if (n === 0) then 1 else (n * (g (n - 1)))
in
((Y f) 5)
end
What is the problem with this approach?
SLang 2:
In SLang 2, we can take advantage of references and the assignment statement to
implement recursion in an efficient way with a technique called "tying
the knot."
To get a sense of how this technique works, ask yourself what is the
value of the following program?
::
let
dummyClosure = fn (n) => (n + 1)
in
let
f = fn (n) => if (n===0) then 1 else (n * (dummyClosure (n - 1)))
in
(f 5)
end
end
How can we modify this program to turn the function **f** above into the
(recursive) function that we know under the name *factorial* so that
the value of the program above is 120?
Hint: add a single assignment statement, but which one? and where?
Answer these questions and you will see why this technique is called
"tying the knot".
Practice TTK
------------
This problem will help you get comfortable with the TTK
technique. To earn credit for it, you must complete this randomized
problem correctly three times in a row.
When you provide your answer, remember to include the full denoted
values, for example **["Num",0]** and not just **0**.
.. avembed:: Exercises/PL/TyingTheKnot.html ka
:module: SLang2TTK
:long_name: Tying the Knot