Transformation of Applicative Specifications into Imperative ...

8.3. SPECIFICATION OF THE TRANSFORMER
The ENV map maps types of interest to the value names under which they
are known at a certain point of execution. The ENV map is related to a
function and not to the entire specification . The initial value of the ENV
map is computed both in CheckValueDef and TRValueDef when dealing
with explicit function definitions,
The ENV map is used to check if the special scope rules defined in Chapter
5 are fulfilled. Furthermore, it is used to decide which value names are
of the type of interest and should be replaced with variables.
When deciding if a value expression is transformable the following idea
is pursued: A type identifier is mapped to a corresponding value name in
ENV map, when the value name is in the scope. When the value name gets
out of scope the entry is removed from the map. A value name can only be
read from when it is in the scope, that is when it is in the range of the ENV
map.
When starting the check for transformability of the value expression of a
function, the ENV map maps any type of interest occurring in the argument
type of the function to the corresponding parameter name.
During the check for transformability of let expressions the ENV map
has to be updated according to the bindings in the let expressions to reflect
the scopes of the value names. The content of the ENV map during a check
for transformability is illustrated in Figure 8.1. By comparing this figure
with Figure 5.1 on page 27 the connection between the scope rules and the
ENV map should be obvious.
type
T
value
gen : ... → ... × T × ...
f : T → ...
f(t1) ≡ t1 + let t2 = t1 + gen(...) in t2 + gen(...) + ... end
↑ ↑ ↑
[ T ↦→ t1 ] [ T ↦→ t2 ] [ ]
Figure 8.1: The ENV during transformability check
The ENV map is a finite map, which means that it can hold at most one
entry per type of interest. This conforms to the fact that there is only one
placeholder for a variable, and that only one value name of a type of interest
can be in scope at a certain point of execution.
The most natural way to represent the ENV map is the reversed way,
that is such that value names are mapped to type identifiers. But it turned
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