Connecting Constrained Constructor Patterns and Matching Logic

Matching-Logic-Based Understanding of Polynomial Functors and their Initial/Final Models

“…A possible answer can be obtained by capturing these objects in Matching Logic (ML), the logical foundation of the K Framework, where the program languages and the properties of their programs can be specified in a uniform way (see, e.g., [12,8,13,7,11]). First steps are done in [6], where the initial algebra semantics is captured in ML, and in [7], where it is shown how examples of inductive/coinductive data types are fully specified in ML. We say that ML captures a (inductive/coinductive) data type DT if there is an ML theory Th ML (DT) such that:…”

“…The constant and the identity functors, together with their initial and final models, can be easily captured in ML. Moreover, if we exclude the exponent functor, then the initial algebra can be captured using the approach similar to that from [6]. The exponent functor complicates the things.…”