Transformation of Applicative Specifications into Imperative ...

CHAPTER 6. TRANSFORMATIONS
Applicative single typing ✄ Imperative single typing
U → V ✄ U → V
T → V ✄ Unit → read t V
U → T ✄ U → write t Unit
T → T ✄ Unit → read t write t Unit
T × U → V ✄ U → read t V
U → T × V ✄ U → write t V
T × U → T × V ✄ U → read t write t V
Table 6.1: Transformation of single typings. T is a type of interest with
associated variable t, U and V are not of the type of interest.
superfluous read access descriptor is included in order to ease the verification
of the transformation rules, see Chapter 7.
The reason for these transformations is that instead of referring to the
type of interest using parameters, you refer to the corresponding variable of
the type of interest, and instead of returning a type of interest, you assign
the results to the variable of the type of interest.
6.4.2 Transforming Formal Function Applications
When transforming formal function applications all occurrences of parameters
of the type of interest are removed as in the following example where t
is a parameter of the type of interest:
f(u, t, v) ≡ ...
✄
f(u, v) ≡ ...
If the type of interest is an abbreviation type and this is exploited in the
formal function application, all parameters forming the type of interest are
removed as in the following example where (u, v) is of the type of interest:
f(p, (u, v), q) ≡ ...
✄
f(p, q) ≡ ...
When this is done it is necessary to establish a let expression in the transformation
of the value expression at the right hand side of the equivalence
operator ≡:
f(p, q) ≡ let (u, v) = t in ... end
This is done in order to be able to refer to the parameters removed as
these are not variables that can be referred to as t can.
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