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P4 is a domain-specific language for programming and specifying packet-processing systems. It is based on an elegant design with high-level abstractions like parsers and match-action pipelines that can be compiled to efficient implementations in software or hardware. Unfortunately, like many industrial languages, P4 has developed without a formal foundation. The P4 Language Specification is a 160-page document with a mixture of informal prose, graphical diagrams, and pseudocode, leaving many aspects of the language semantics up to individual compilation targets. The P4 reference implementation is a complex system, running to over 40KLoC of C++ code, with support for only a few targets. Clearly neither of these artifacts is suitable for formal reasoning about P4 in general. This paper presents a new framework, called Petr4, that puts P4 on a solid foundation. Petr4 consists of a clean-slate definitional interpreter and a core calculus that models a fragment of P4. Petr4 is not tied to any particular target: the interpreter is parameterized over an interface that collects features delegated to targets in one place, while the core calculus overapproximates target-specific behaviors using non-determinism. We have validated the interpreter against a suite of over 750 tests from the P4 reference implementation, exercising our target interface with tests for different targets. We validated the core calculus with a proof of type-preserving termination. While developing Petr4, we reported dozens of bugs in the language specification and the reference implementation, many of which have been fixed.

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The P4 language enables a range of new network applications. However, it is still far from easy to implement and optimize P4 programs for PISA hardware. Programmers must engage in a tedious "trial and error" process wherein they write their program (guessing it will fit within the hardware) and then check by compiling it. If it fails, they repeat the process. In this paper, we argue that programmers should define elastic data structures that stretch automatically to make use of available switch resources. We present P4All, an extension of P4 that supports elastic switch programming. Elastic data structures also make P4All modules reusable across different applications and hardware targets, where resource needs and constraints may vary. Our design is oriented around use of symbolic primitives (integers that may take on a range of possible values at compile time), arrays, and loops. We show how to use these primitive mechanisms to build a range of reusable libraries such as hash tables, Bloom filters, sketches, and key-value stores. We also explain the important role that elasticity plays in modular programming, and we allow programmers to declare utility functions that control the relative share of data-plane resources apportioned to each module.