## Section: Scientific Foundations

### A logic for reasoning about logic specifications

Coming up with the design of a logic that allows reasoning richly over relational specifications involving bindings in syntax has been a long standing problem, dating from at least the early papers by McDowell and Miller [52] [7] , and by Despeyroux, Leleu, Pfenning, and Schürmann [36] , [35] [2] , [1] . Relational specifications are popular among many designers and implementers of programming languages and computing specification languages. Almost invariably since specifications need to deal with syntax containing variable bindings. Finding a logic appropriate for this domain has gone through many attempts. Pioneer work here includes work by Despeyroux, Leleu, Pfenning, and Schürmann [2] , [1] , in the Type Theoretic approach. McDowell and Miller [51] also presented a start at such a logic, with a proof-search approach in mind. Later, Tiu and Miller [55] , [9] developed the -quantifier that provided a significant improvement to the expressiveness of logic. Tiu then went on to enrich the possibilities of such a logic as well allowing for more “nominal” effects to be captured [66] , [67] .

As described in Section 6.1 , the team has recently found completely satisfactory designs for a logic for reasoning about logic specifications.