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Line 30: :I am uncertain, myself about this task. Here's what I believe I know: ::"algebraic data type" means that data types are represented by numbers which list the number of possible values that can be represented by that data type. A bit data type would be represented by the number 2. An 8 bit character would be represented by the number 256. A 32 bit integer would be represented by the number 4294967296. AnA type that represents the program being in an error state would be represented by the number 0. This system allows you to use algebra to work with the properties of composite and derived types. ::Implicitly, languages which support types often have syntax rules to prevent certain combinations of types from being used. Typically, these syntax rules get associated with defined words which represent functions, and these syntax rules approximate the domain of those functions. (In some cases you get an exact match , but this cannot be guaranteed without solving the halting problem.) This, I think, is what encourages a proliferation of types.

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