Transformation of Applicative Specifications into Imperative ...

CHAPTER 8. SPECIFICATIONS
8.5.2 Changing from Maps to Lists
The idea is illustrated in the case of CONC1 being a map. The map type has
to be changed into a list type as done several times in the actual translation
of the transformer specification from RSL into RSL1. The operators on maps
are turned into functions. Only the operators used in the specifications of
the transformer are considered here.
As the type of the elements in the map is not important at this stage the
elements of the map are defined as sorts, see Specification 8.3.
Specification 8.3 – Specification of an element
scheme ELEMENT = class type Elem end
The concrete specification of the map CONC_MAP can be found in
Specification 8.4. The functions are defined using map operators.
Specification 8.4 – Concrete specification of a map
scheme CONC_MAP(T1 : ELEMENT, T2 : ELEMENT) =
class
type Map = T1.Elem ∼ →m T2.Elem
value
/∗ generators ∗/
empty : Map = [ ],
override : Map × Map → Map
override(m1, m2) ≡ m1 † m2,
restrict_by : Map × T1.Elem-infset → Map
restrict_by(m, t1) ≡ m \ t1,
/∗ observers ∗/
domain : Map → T1.Elem-infset
domain(m) ≡ dom m,
range : Map → T2.Elem-infset
range(m) ≡ rng m,
get_map_value : Map × T1.Elem ∼ → T2.Elem
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