We revisit parallel-innermost term rewriting as a model of parallel computation on inductive data structures and provide a corresponding notion of runtime complexity parametric in the size of the start term. We propose automatic techniques to derive both upper and lower bounds on parallel complexity of rewriting that enable a direct reuse of existing techniques for sequential complexity. Our approach to find lower bounds requires confluence of the parallel-innermost rewrite relation, thus we also provide effective sufficient criteria for proving confluence. The applicability and the precision of the method are demonstrated by the relatively light effort in extending the program analysis tool APROVE and by experiments on numerous benchmarks from the literature.

Initially present only in functional languages such as OCaml and Haskell, Algebraic Data Types (ADTs) have now become pervasive in mainstream languages, providing nice data abstractions and an elegant way to express functions through pattern matching. Unfortunately, ADTs remain seldom used in low-level programming. One reason is that their increased convenience comes at the cost of abstracting away the exact memory layout of values. Even Rust, which tries to optimize data layout, severely limits control over memory representation. In this article, we present a new approach to specify the data layout of rich data types based on a dual view: a source type, providing a high-level description available in the rest of the code, along with a memory type, providing full control over the memory layout. This dual view allows for better reasoning about memory layout, both for correctness, with dedicated validity criteria linking the two views, and for optimizations that manipulate the memory view. We then provide algorithms to compile constructors and destructors, including pattern matching, to their low-level memory representation. We prove our compilation algorithms correct, implement them in a tool called ribbit that compiles to LLVM IR, and show some early experimental results.

We revisit parallel-innermost term rewriting as a model of parallel computation on inductive data structures and provide a corresponding notion of runtime complexity parametric in the size of the start term. We propose automatic techniques to derive both upper and lower bounds on parallel complexity of rewriting that enable a direct reuse of existing techniques for sequential complexity. The applicability and the precision of the method are demonstrated by the relatively light effort in extending the program analysis tool AProVE and by experiments on numerous benchmarks from the literature.