Formal Language for Register Machine Design and Abstraction

Key Insight

To manage the complexity of designing large machines, a textual language is introduced as an alternative to diagrams. This language formally describes a machine's data paths by detailing registers, their assignment buttons, and data sources (registers, constants, or operation results), along with operations and their inputs. The machine's control logic is defined as a sequence of instructions, potentially containing labels for entry points, which include pushing data-path buttons, performing tests, conditional branches based on test outcomes, and unconditional branches to specific labels.

The language evolves to improve readability by integrating data-path descriptions directly into controller instructions, replacing abstract button and operation names with their explicit behaviors. For example, instead of a controller instruction 't<-r' and a separate definition for it, the instruction becomes '(assign t (op rem) (reg a) (reg b))'. While this combined form makes individual operations clearer by showing their full context, it can lead to verbosity and obscure the overall data-path structure in more complex machine designs.

The concept of 'actions' extends the language for operations that have an effect but do not produce a value for a register, such as 'print'. These are executed using a 'perform' instruction, e.g., '(perform (op print) (reg a))'. Abstraction is a key design principle, allowing complex operations like 'remainder' to be treated as primitives initially, simplifying the high-level design. These complex 'primitives' can later be elaborated into sequences of simpler, more fundamental operations, such as subtractions and comparisons, demonstrating how machine designs can be refined layer by layer.