Discovering program specifications automatically for heap-manipulating programs is a challenging task due to the complexity of aliasing and mutability of data structures. This task is further complicated by an expressive domain that combines shape, numerical and bag information. In this paper, we propose a compositional analysis framework that would derive the summary for each method in the expressive abstract domain, independently from its callers. We propose a novel abstraction method with a bi-abduction technique in the combined domain to discover pre-/post-conditions that could not be automatically inferred before. The analysis does not only infer memory safety properties, but also finds relationships between pure and shape domains towards full functional correctness of programs. A prototype of the framework has been implemented and initial experiments have shown that our approach can discover interesting properties for non-trivial programs.