Transformation of Applicative Specifications into Imperative ...

6.4. TRANSFORMING EXPLICIT FUNCTION DEFINITIONS
The transformation of an explicit function definition can be done in four
steps:
1. Transformation of the single typing, also known as the function signature.
2. Transformation of the formal function application.
3. Transformation of the value expression.
4. Transformation of the possible pre-condition.
These steps are described below.
6.4.1 Transforming Single Typings
When transforming a single typing the single typing keeps its id. Only single
typings in which the type expression is a function type expression are allowed.
The function type expression is transformed in the following way:
• The type of the arrow, either total or partial, of the type expression is
preserved.
• If the applicative function takes the type of interest T as argument,
this is removed from the left hand side of the arrow and replaced by
an access descriptor read t at the right hand side of the arrow, where
t is the variable name of the type of interest.
• If the applicative function returns the type of interest, this is replaced
by an access descriptor write t.
• Any gaps in the single typing after the above transformation are filled
with Unit, that is if the whole left or right hand side of the arrow are
removed.
Examples of transformations of single typings are given in Table 6.1 on
the following page.
Furthermore, if the value expression of the function contains hidden observers
or generators or implicit observers or generators, read/write access
descriptors matching those of the observers/generators have to be included
in the single typing. This has to be done recursively, such that if a function
contains an application of a function containing observers and/or generators
the appropriate read and write access descriptors matching these observers
and generators have to be included in the single typing of the original function,
and so on.
The inclusion of both read and write access descriptors of the same
variable is not necessary due to the fact that write implies read. The
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