Algebraic Programming System APS was developed by the department 100/105 of Glushkov
Institute of Cybernetics of National Academy of Science of Ukraine in 1987. It was the first
system of term rewriting which used the systems of rewriting rules and rewriting strategies separately.

The APS v1 has been developed in 1989 (A. Letichevsky, S. Konozenko). During the years before 2004 a lot of experimental works has been done using this system in computer algebra, artificial intelligence, modeling parallel computations etc. The system was used for the development of application systems in City University (London, UK), Kherson State University, Kirovograd Technical University etc. A system ADS (Algebraic Development System) has been developed for Motorola (A.Letichevsky, O. Letichevkyi, A.Chugayenko) as a tool for the development of software in the area of software verification.

APS v2 was developed in 2004 (A. Letichevsky, M. Lvov, V. Peschanenko). APS v2 uses Smart Pointers technology to avoid memory leaks discovered in the previous versions of APS. It is used in TerM project (Kherson: M.Lvov, V. Peschanenko), STG (Kiev: A. Letichevsky, A. Letichevsky Jr., V. Volkov, S. Potienko, A. Kolchin, V. Peschanenko)
APS v3 was developed in 2009 (A. Letichevsky, O. Letichevkyi, V. Peschanenko). What is new:
1. Optimized rewriting machine.
2. Dynamically add and remove function in the system of rewriting rules without it recompilation in REM language.
3. APLANC language (using APLAN language on C).
4. Non-deterministic rewriting strategy

APS v4 was implemented in 2013 (A. Letichevsky, O. Letichevkyi, V. Peschanenko):
1. Clew library is optimized in 4 times in speed and 10 times in memory in general case.
2. Interfaces were added for next external tools: Presburger - omega, Fourier–Motzkin - reallib (our tool), cvc3, z3.
3. Integration was made for Eclipse plug-in of transitional system description.

Insertional Modelling System IMS is APS with insertional model driver. It was used for the development of the Symbolic Trace Generator of the Verification of Requirements System and Generic Trace Generator (2007 - 2018). it was used as a base system for the development of Algebraic Virtual Machine (PE LitSoft, 2018 - till now).