A Denotational Semantics for Handel-C Hardware Compilation

Mechanised Wire-wise Verification of Handel-C Synthesis

“…As in [10], we define two auxiliary functions: ΔEnv : env → Action → env and f lattenEnv : env → env. The former updates the environment according to the action passed as argument by means of rewriting the appropriate function using λ-abstractions.…”

“…The existing denotational semantics for the synthesis process [10] is based on the notion of "branching sequences", where non-branching sequences denote the execution of actions in which no information from the persistent part of the state (i.e., memory locations) is required. Branching nodes, on the other hand, model a choice point (such as the condition in a while construct), where the state must be accessed in order to evaluate the condition.…”

“…Given the fact that we focus on the correctness of the synthesis process, we also exclude any efficiency/optimisation analysis from this work. The rest of the paper is organised as follows: we first propose a reformulation of the semantic domain in [10] in terms of a slightly higher level semantic domain that allows us to capture parallelism at the sequence level. We then redefine the semantics in terms of the new domain and prove the existence of fix-point solutions for the recursive equations.…”

“…The semantics is based on the assumption that the start signal will be given to a circuit only if all the previous circuits have already finished. A formal model of the compilation and denotational semantics for the generated hardware has been proposed as a first step towards verifying the compilation scheme [10]. The semantics relies on the concept of state-transformers and uses branching sequences of atomic hardware actions as its semantic domain.…”