Transformation of Applicative Specifications into Imperative ...

12.1. TRANSFORMATIONS OF CONSTRUCTS OUTSIDE RSLA
12.1.8 Axioms
Axioms can be transformed almost as value definitions since value definitions
are a short way of writing axioms. The extension should therefore be almost
straight forward. It is necessary to consider quantified expressions though.
12.1.9 Quantified Expressions
Quantified expressions are of the form:
quantifier typing1, ..., typingn • value_expr
A quantified expression is transformed by transforming the constituent
value expression. If the typings contain types of interest the corresponding
variables must be assigned the values of the value names in the typing. Due
to side effects an equivalence expression must be established, for example:
∃ x : T • obs(x)
✄
∃ x : T • ( t := x ; obs() ≡ t := x ; true )
where T is a type of interest and t is the corresponding variable.
If the quantified expression contains universal quantification over a type
of interest this is replaced by the always combinator ✷, see Example 12.1.
Example 12.1 – Transformation of a quantified expression
type
T = Int
value
f : T → Int
axiom
∀ x : T • f(x) > x
✄
type
T = Int
variable
t : T
value
f : Unit → read t Int
axiom
✷ f() > t
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