After Max' introduction to abstract interpretation for the toy optimizer in the last post, I want to present a more complicated abstract domain in this post. This abstract domain reasons about the individual bits of a variable in a trace. Every bit can be either "known zero", "known one" or "unknown". The abstract domain is useful for optimizing integer operations, particularly the bitwise operati
There are lots of interesting little subproblems in compilation like instruction selection, register allocation and instruction scheduling. These can be expressed in declarative interlinked way to constraint solvers. I’ve been fiddling with probably 6 iterations of using constraint solvers for compiler backends over the last 3 years and never written a blog post on it. This is long over due, and s
As far as static analyzers are concerned, one of the most important point to consider is filtering out false positives as much as possible, in order for the reports to be actionable. This is an area on which Coverity did an excellent job, and likely a major reason why they got so popular within the open source community, despite being a closed-source product. LLVM has the LLVM_ENABLE_Z3_SOLVER bui
Solving Wordle with Z3 I've been enjoying this viral new word game eponymously named Wordle. The aim of the game is to guess the day's word in six or less tries. I'll go through an example game to give an idea of the rules. In this particular game: the hidden word was G O R G E, guessed correctly on the fifth try. the first guess was R E N T S, which was incorrect. However it gave us clues: R is f
1. Introduction Satisfiability Modulo Theories (SMT) problem is a decision problem for logical formulas with respect to combinations of background theories such as arithmetic, bit-vectors, arrays, and uninterpreted functions. Z3 is an efficient SMT solver with specialized algorithms for solving background theories. SMT solving enjoys a synergetic relationship with software analysis, verification a
Programming in logic can help you produce better optimized, more secure, bug-free code … if only you knew how to do it. Image created by storiesIt took me about two years to write my first program in Z3. I had done some tutorials, wrote code to solve other people’s example puzzles, but I couldn’t really figure out how to cross over from very abstract “toy” use cases to applications that had actual
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