Transformation of Applicative Specifications into Imperative ...

2.1. THE STACK EXAMPLE
both sides without any type expressions Unit is inserted.
Explicit value definitions of the Stack type is transformed into explicit
function definitions, in which the stack variable is assigned the value expression
of the explicit value definition.
This leads to the concrete imperative specification given in Specification
2.2.
Specification 2.2 – Concrete imperative specification of a stack
scheme I_STACK =
class
type
Stack = Element ∗ ,
Element
end
variable
stack : Stack
value
empty : Unit → write stack Unit
empty() ≡ stack := 〈〉,
is_empty : Unit → read stack Bool
is_empty() ≡ stack = 〈〉,
push : Element → write stack Unit
push(elem) ≡ stack := 〈elem〉 stack,
pop : Unit ∼ → write stack Unit
pop() ≡ stack := tl stack
pre ∼ is_empty(),
top : Unit ∼ → read stack Element
top() ≡ hd stack
pre ∼ is_empty()
The following changes have been made:
• The constant empty is transformed into an explicit function definition
in which the stack variable is assigned the empty list.
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