Functionalities of the interface at level 1

We focus on the changes brought by the level 1 w.r.t. the level 0.

Variables and Environments

Variables

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.

Semantics and Representation of an abstract value

Semantics and Representation of an abstract value

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;
};

Operations on environments

Operations on environments

• creation, merging, destruction
• addition/removal/renaming of variables

Dynamic typing w.r.t. environments

Dynamic typing w.r.t. environments

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 variables in abstract values

Operations on variables in abstract values

Operations on dimensions are lifted to operations on variables:

• Projection/Elimination of one or several variables with constant environment;
• Addition/Removal/Renaming of variables with corresponding change of environment;
• Change of environment (possibly combining removal and addition of variables);
• Expansion and folding of variables.