iscc tutorial

iscc is an interactive tool for manipulating special kinds of sets of integer tuples and binary relations over such sets. In particular, all constraints in the descriptions of the sets and relations have to be affine (linear + constant), but may involve parameters and existentially quantified variables. A distinguishing feature of iscc is that it provides a cardinality operation on sets and relations that computes a symbolic expression (in terms of the parameters and domain variables) for the number of elements in the set or the image of the relation. These expressions are piecewise quasipolynomials, which can be further manipulated in iscc. Besides basic operations on sets and piecewise quasipolynomials, iscc also provides an interface to code generation, lexicographic optimization, dependence analysis, transitive closures and the symbolic computation of upper bounds and sums of piecewise quasipolynomials over their domains. This tutorial does not involve any theory, but instead introduces some concepts and operations through examples. These operations are then combined to solve a small number of non-trivial problems. All examples are inspired by the polyhedral model for program analysis and transformation. No prior knowledge of this model is required. As most of the operations supported by iscc take abstract integer sets or related objects as input, they should also be useful outside this context.status: publishe