We introduce a formal semantics of P4 for the HOL4 interactive theorem prover. We exploit properties of the language, like the absence of call by reference and the copy-in/copy-out mechanism, to define a heapless small-step semantics that is abstract enough to simplify verification, but that covers the main aspects of the language: interaction with the architecture via externs, table match, and parsers. Our formalization is written in the Ott metalanguage, which allows us to export definitions to multiple interactive theorem provers. The exported HOL4 semantics allows us to establish machine-checkable proofs regarding the semantics, properties of P4 programs, and soundness of analysis tools.