The C standard formalized in Coq

values hide internal details of the memory such as permissions, padding and object representations. They are therefore used in the external interface of the memory model and throughout the operational semantics. Memory trees, abstract values and bits with permissions can be converted into each other. These conversions are used to define operations internal to the memory model. However, none of these conversions are bijective because different information is materialized in these three data types: Abstract values Memory trees Bits with permissions Permissions X X Padding always E X Variants of union X X Mathematical values Xvalues Memory trees Bits with permissions Permissions X X Padding always E X Variants of union X X Mathematical values X This table indicates that abstract values and sequences of bits are complementary. Memory trees are a middle ground, and therefore suitable to describe both the lowlevel and high-level aspects of the C memory.