Stratified synthesis: automatically learning the x86-64 instruction set

The x86-64 ISA sits at the bottom of the software stack of most desktop and server software. Because of its importance, many software analysis and verification tools depend, either explicitly or implicitly, on correct modeling of the semantics of x86-64 instructions. However, formal semantics for the x86-64 ISA are difficult to obtain and often written manually through great effort. We describe an automatically synthesized formal semantics of the input/output behavior for a large fraction of the x86-64 Haswell ISA’s many thousands of instruction variants. The key to our results is stratified synthesis, where we use a set of instructions whose semantics are known to synthesize the semantics of additional instructions whose semantics are unknown. As the set of formally described instructions increases, the synthesis vocabulary expands, making it possible to synthesize the semantics of increasingly complex instructions. Using this technique we automatically synthesized formal semantics for 1,795 instruction variants of the x86-64 Haswell ISA. We evaluate the learned semantics against manually written semantics (where available) and find that they are formally equivalent with the exception of 50 instructions, where the manually written semantics contain an error. We further find the learned formulas to be largely as precise as manually written ones and of similar size.