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a_type_system_as_a_model_for_some_concepts [2016/10/16 14:51] nikolaj |
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==== Guide ==== | ==== Guide ==== | ||

We introduce some basic notions of Idris, namely those that can be seen as "semantics" for logic, set theory and category theory (or rather topoi, as discussed in | We introduce some basic notions of Idris, namely those that can be seen as "semantics" for logic, set theory and category theory (or rather topoi, as discussed in | ||

- | [[http://arxiv.org/abs/1212.6543 | Leinster, Rethinking set theory]]). However, we always treat the (chosen subpart of the) language from a syntactical perspective as a programming language, //as is//, and don't "force it into" a known mathematical structure. (In particular, many forms of "equality" often make problems.) | + | [[http://arxiv.org/abs/1212.6543 | Leinster, Rethinking set theory]]). However, we always treat the (chosen subpart of the) language from a syntactical perspective as a programming language, //as is//, and don't "force it into" a known mathematical structure. In particular, many forms of "equality" often make problems. Then again, it's always good to know how to map your stuff //into// mathematical frameworks (e.g. into a well defined category), even if that mapping is neither surjective nor even injective. |

(161013 The code presented below is also all included on the page [[Idris syntax]], but that's just for now.) | (161013 The code presented below is also all included on the page [[Idris syntax]], but that's just for now.) |