Abstract

Relational languages such as Ruby are used to derive hardware circuits from abstract specifications of their behaviour. Much reasoning is done informally in Ruby using pictorial representations of relational terms. We formalise this use of pictures in circuit design. We show that pictures naturally form a unitary pretabular allegory. Homomorphisms of pictures correspond to adding new wires or circuit components. Two pictures are mutually homomorphic if and only if they represent equal allegorical terms. We prove soundness and completeness results which guarantee that deriving circuits using pictures does not lead to errors. We illustrate the use of pictures by deriving the ripple adder implementation from a high level, behavioural specification. 1: Introduction Hardware circuit design involves translating abstract specifications of programs into efficient circuits which compute those programs. Pictures are widely used as an informal means of translating a specification into an imple...

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