Well, you can define a combinational circuit as something that has n inputs and m outputs and it is one of: * a gate, * a circuit that takes two inputs and pr

Well, you can define a combinational circuit as something that has n inputs and m outputs and it is one of: * a gate, * a circuit that takes two inputs and produces two outputs by swapping the order, * a circuit that takes one input and produces one output, * a circuit that takes one input and produces no outputs, * the circuit obtained by taking two circuits and composing them in serial, * the circuit obtained by taking two circuits and composing them in parallel. This produces a simple inductive definition for combinational circuits. Synchronous, sequential circuits can be obtained by taking a combinational circuit and connecting the first n outputs to the first n inputs via D flip-flops. If you want asynchronous circuits, you can add another combinator that takes a circuit and a connects the first n outputs to the first n inputs without the flip-flops. With these definitions, it's quite straight forward to manipulate circuits in a functional manner.