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* Start implementing a Number moduleHEADmasterGravatar Benjamin Barenblat2015-05-23
| | | | | | | | | | | | | | | | | | | | | The nascent Number module also serves as a proof of concept for dealing with records in the Agda standard library that are parameterized by levels instead of sets, like those in the Algebra hierarchy. These records are difficult to use as type classes, because Agda’s normal mechanism for generating type classes ('open SomeRecord ⦃...⦄') will make the levels the instance arguments, rather than the actual set the record’s functions operate on. To work around this, I defined wrapper records (effectively just named dependent pairs) parameterized in the way I desire. Each contains an underlying algebraic structure and a proof of type equality (usually just 'refl') between the parameter and the structure’s carrier. Then, I define functions over my wrapper record to rewrite with the type equality and use the underlying structure’s code. This work is related to standard library bug #35 <https://github.com/agda/agda-stdlib/issues/35>; fixing this bug would obviate the need for my workaround.
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* Initial commit of BGravatar Benjamin Barenblat2015-04-23