## Section: New Software and Platforms

### Redlog

*Reduce Logic System*

Keywords: Computer algebra system (CAS) - First-order logic - Constraint solving

Scientific Description: Redlog is an integral part of the interactive computer algebra system Reduce. It supplements Reduce's comprehensive collection of powerful methods from symbolic computation by supplying more than 100 functions on first-order formulas.

Redlog generally works with interpreted first-order logic in contrast to free first-order logic. Each first-order formula in Redlog must exclusively contain atoms from one particular Redlog-supported theory, which corresponds to a choice of admissible functions and relations with fixed semantics. Redlog-supported theories include Nonlinear Real Arithmetic (Real Closed Fields), Presburger Arithmetic, Parametric QSAT, and many more.

News Of The Year: Parts of the Redlog code are 25 years old now. Version 1 of the underlying computer algebra system Reduce has been published even 50 years ago. In 2018 we therefore started to go for major revisions and improvements of Redlog's software architecture, which are still under way.

Redlog, as well as the underlying Reduce, depends on a quite minimalistic Lisp 1 dialect called Standard Lisp. Today, there are two independent implementations of Standard Lisp left, which are supported only on the basis of private commitment of essentially one individual per Lisp. With the large code base of Redlog plus the necessary algebraic algorithms from Reduce, a migration to a different language or computer algebra system is not feasible. We are therefore experimenting with the realization of a Standard Lisp on the basis of ANSI Common Lisp.

Scientifically we are currently improving on Parametric Gaussian Elimination in Reduce/Redlog, which has various applications in our bilateral interdisciplinary ANR/DFG project SYMBIONT (Symbolic Methods for Biological Networks), e.g., classification of real singularities of systems of implicit ordinary differential equations.