AbstractArchitectural design of software systems deals with high level configuration structuring. Checking that a system belongs to a software architecture style (or shape) implies that the architecture is an instance of a structurally defined class. On the other side, hierarchies allow modeling at different levels of detail: subsystems may be represented as single components to abstract structure and behavior. This paper proposes a type-based approach for representing hierarchical SA shapes using types. Typing proofs define a general framework based on inference rules where shape rules and graphs representing systems are type judgements. Hierarchy constructors are defined in the type system to construct proof terms capturing hierarchical structure. We claim that proof terms provide more information than just graphs about the process of constructing systems, and allow the specification of reconfigurations as proof term rewritings. Reconfiguration consistency is obtained as subject reduction: as long as cutting and pasting typing proofs still yields typing proofs, subject reduction is guaranteed. As a possible instantiation of the approach, we present the type system for shapes (and hierarchies) with global references.