Numeric Types in Formal Synthesis

The Formal Synthesis methodology can be considered as the application of the transformational approach to circuit synthesis by logical transformations performed in a theorem prover. Additionally to the implementation of the circuit, the proof that the result is a correct implementation of a given specification is obtained automatically. In this paper, a higher-order formalisation for the arithmetic of bound numeric data types is given. We provide correct transformations implemented in the theorem prover HOL [4], to register-transfer level descriptions of arithmetic operations. For a restricted class of specifications, a correct transformation is described which eliminates the type num and replaces arithmetic operations by its bound variants.