  The Curry-Howard correspondence is about a relationship between types and
programs on the one hand and propositions and proofs on the other. The
implications for programming language design and program verification is an
active field of research.
  Transformer-like semantics of internal definitions that combine a defining
computation and an application will be presented. By specialisation for a given
defining computation one can derive inference rules for applications of defined
operations.
  With semantics of that kind for every operation, each application identifies
an axiom in a logic defined by the programming language, so a language can be
considered a theory.
