With the digitalization of society, the interest, the debates and the research efforts concerning "code", "law", "artificial intelligence", and their various relationships, have been widely increasing. Yet, most arguments primarily focus on contemporary computational methods and artifacts (inferential models constructed via machine-learning methods, rule-based systems, smart contracts), rather than attempting to identify more fundamental mechanisms. Aiming to go beyond this conceptual limitation, this paper introduces and elaborates on "normware" as an explicit additional stance -- complementary to software and hardware -- for the interpretation and the design of artificial devices. By means of a few examples, I will argue that a normware-centred perspective provides a more adequate abstraction to study and design interactions between computational systems and human institutions, and may help with the design and development of technical interventions within wider socio-technical views.