TheoriesAndDataStructures

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TheoriesAndDataStructures

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Showing how some simple mathematical theories naturally give rise to some common data-structures

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<h1> TheoriesAndDataStructures </h1>

Showing how some simple mathematical theories naturally give rise to some common data-structures.

Attempting to answer the following questions:

-   Why do lists pop-up more frequently to the average programmer than, say, their duals: bags?

-   More simply, why do unit and empty types occur so naturally? What about enumerations/sums and records/products?

-   Why is it that dependent sums and products do not pop-up expicitly to the average programmer? They arise naturally all the time as tuples and as classes.

-   How do we get the usual toolbox of functions and helpful combinators for a particular data type? Are they \`\`built into'' the type?

-   Is it that the average programmer works in the category of classical Sets,   with functions and propositional equality? Does this result in some \`\`free constructions'' not easily made computable since mathematicians usually work in the category of Setoids but tend to quotient to arrive in \`Sets\` &#x2014;where quotienting is not computably feasible, in \`Sets\` at-least; and why is that?

And lots of other stuff.

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