## Section: New Results

### Automatically deriving schematic theorems for dynamic contexts

Participants : Kaustuv Chaudhuri, Olivier Savary-Bélanger [Princeton University, USA] .

Hypothetical judgments go hand-in-hand with higher-order abstract syntax for
meta-theoretic reasoning.
Such judgments have two kinds of assumptions: those that are statically known
from the specification, and the *dynamic assumptions* that result from
building derivations out of the specification clauses.
These dynamic assumptions often have a simple regular structure of repetitions
of *blocks* of related assumptions, with each block generally involving
one or several variables and their properties, that are added to the context
in a single backchaining step.
Reflecting on this regular structure can let us derive a number of structural
properties about the elements of the context.

In [26] , we present an extension of
the Abella theorem prover, which is based on a simply typed
intuitionistic reasoning logic supporting (co-)inductive
definitions and generic quantification.
Dynamic contexts are represented in Abella using lists of formulas for the
assumptions and quantifier nesting for the variables, together with an
inductively defined *context relation* that specifies their structure.
We add a new mechanism for defining particular kinds of regular context
relations, called *schemas*, and *tacticals* to derive theorems from
these schemas as needed.
Importantly, our extension leaves the trusted kernel of Abella unchanged.
We show that these tacticals can eliminate many commonly encountered kinds of
administrative lemmas that would otherwise have to be proven manually, which
is a common source of complaints from Abella users.