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Due on Friday, September 30, 5pm.
The Simple Imperative Language
- Complete this denotational semantics of SIL in
Haskell, in which I have provided the syntax, and you must fill in the
semantics. To
make the syntax look as much like Reynolds as possible, note that I
used "fixity" declarations to the get precedence and associativity right.
To make the semantics look as much like Reynolds as possible, you
should use the following ideas:
 | The fixpoint operator Y can be defined as:
y :: (a -> a) -> a
y f = f (y f)
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| Every domain is automatically lifted in Haskell,
meaning that each of them already has a bottom
element. Furthermore, all Haskell functions are continuous, but
are not
(necessarily) strict.
Therefore the extension of a function f to a
function f
subscripted with the "double bottom" symbol,
amounts to simply making
the Haskell function strict. This is easily done by the predefined
Haskell
function ($!), which behaves as
follows:
f $! _|_ = _|_
f $! e = f e, if e /= _|_
This is not valid Haskell code, but shows how
($!) behaves
semantically.
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| Equations such as this:
/ a, if p1
[[ e ]] = | b, if p2
\
c, if p3
where p1,
p2, and
p3 are arbitrary
predicates, can be written as:
meaning e | p1 = a
meaning e | p2 = b
meaning e | p3 = c
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Do problem 2.1 in Reynolds. Also add the "double
assignment" construct to your interpreter above, with test cases.
Do Exercise 2.4 in Reynolds.
Do Exercise 2.6 in Reynolds.
Solution.
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