Hardware and software co-design is a design technique which delivers computer systems comprising hardware and software components. A critical phase of codesign process is to decompose a program into hardware and software. This paper proposes an algebraic partitioning method whose correctness is verified in the algebra of programs. We introduce the program analysis phase before program partitioning and develop a collection of syntax-based splitting rules, where the former provides the information for moving operations from software to hardware and reducing the interaction between components, and the latter supports a compositional approach to the program partitioning.