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# B. Reference Implementations

This appendix contains some `silly` source code for several functions that are mentioned in Virtual Code Semantics, for specifying the virtual machine code semantics, namely `pairwise`, `transition`, `insert` and `replace`.

The intention is to specify the virtual machine mathematically with a minimum of hand waving, by using only simple equations and small fragments of `silly` code, which has a straightforward semantics. However, the `silly` code fragments are more significant in some cases than what could fit into a few lines or be mechanically derived from an equation.

The purpose of this appendix is therefore to avoid leaving any gaps in the construction by demonstrating that everything mentioned can be done. None of this code is needed for any practical purpose, because its functionality is inherent in the virtual machine, but it shows how certain operations would be specified if they were not built in.

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