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We focus on the changes brought by the level 1 w.r.t. the level 0.
• Variables and Environments | ||
• Semantics and Representation of an abstract value | ||
• Operations on environments | ||
• Dynamic typing w.r.t. environments | ||
• Operations on variables in abstract values |
Dimensions are replaced by variables.
In the C interface, variables are defined by a generic type
(char*
, structured type, ...), equipped with the operations
compare
, copy
, free
, to_string
. In the
OCAML, for technical reasons, the type is just the string
type.
Environments manages the correspondance between the numerical dimensions of level 0 and the variables of level 1.
The semantics of an abstract value is a subset
X -> (N+R).
where X is a set of variables. Abstract values are typed according to their environment.
It is represented by a structure
struct ap_abstract1_t { ap_abstract0_t *abstract0; ap_environment_t *env; };
Other datatypes of level 0 are extend in the same way. For instance,
struct ap_linexpr1_t { ap_linexpr0_t *linexpr0; ap_environment_t *env; };
For binary operations on abstract values, the environments should be the same.
For operations involving an abstract value and an other datatype (expression, constraint, ...), one checks that the environment of the expression is a subenvironment of the environment of the abstract value, and one resize if necessary.
Operations on dimensions are lifted to operations on variables:
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