## Section: New Results

### A two-level logic approach for reasoning about typed specification languages

Participants : Kaustuv Chaudhuri, Mary Southern [University of Minnesota, USA] .

The *two-level logic approach* (*2LLA*) to reasoning about
computational specifications, as implemented by the Abella theorem
prover, represents derivations of a *specification language* as
an inductive definition in a *reasoning logic*.
This approach has traditionally been formulated with the
specification and reasoning logics having the *same* type
system, and only the formulas being translated.
However, requiring identical type systems limits the approach in two
important ways: (1) every change in the specification language's
type system requires a corresponding change in that of the reasoning
logic, and (2) the same reasoning logic cannot be used with two
specification languages at once if they have incompatible type
systems.
InĀ [27] , we propose a technique based on
*adequate* encodings of the types and judgments of a typed
specification language in terms of a simply typed higher-order logic
program, which is then used for reasoning about the specification
language in the usual *2LLA*.
Moreover, a single specification logic implementation can be used as
a basis for a number of other specification languages just by varying
the encoding.
We illustrate our technique with an implementation of the LF
dependent type theory as a new specification language for Abella,
co-existing with its current simply typed higher-order hereditary
Harrop specification logic, without modifying the type system of its
reasoning logic.