smash: Smash products - like 'These', but with a unit!

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Smash products are like the These datatype, only with a unit. You can think of this type as isomorphic to 'Maybe (These a b)'.

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Versions	0.1.0.0, 0.1.1.0, 0.1.1.0, 0.1.2, 0.1.3
Change log	CHANGELOG.md
Dependencies	base (>=4.10 && <5.0), bifunctors (>=5.5 && <5.6), binary (>=0.8 && <0.9), deepseq (>=1.4 && <1.5), hashable (>=1.3 && <1.4) [details]
License	BSD-3-Clause
Copyright	(c) 2020 Emily Pillmore <emilypi@cohomolo.gy>
Author	Emily Pillmore
Maintainer	emilypi@cohomolo.gy
Category	Data
Home page	https://github.com/emilypi/smash
Bug tracker	https://github.com/emilypi/smash/issues
Source repo	head: git clone https://github.com/emilypi/smash.git
Uploaded	by topos at 2020-04-07T16:10:40Z

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smash: Combinators for Maybe types

This package consists of 3 datatypes: Wedge, Can, and Smash.

You can imagine these three types as Maybe (Either a b), Maybe (Either a (Either b (a,b)), and Maybe (These a b) respectively. It turns out that that each of these datatypes has spcial properties:

the Wedge datatype represents the coproduct (like, Either) in the category Hask* of pointed Hask types, called a wedge sum. One can derive this by noting that units are the same in Haskell, and the sum of two pointed types is (1 + a) + (1 + b) ~ 1 + a + b ~ Wedge a b.
the Can datatype represents the product (like, (,)) in Hask*. You can derive this by considering the product of two pointed types (1 + a) * (1 + b) ~ 1 + a + b + a*b ~ Can a b.
the Smash datatype represents a special type of product, a smash product, in the category Hask*. The smash product is a symmetric, monoidal tensor in Hask* that plays nicely with the product, 'Can', and coproduct, 'Wedge'.

Pictorially, these datatypes look like this:

'Can':
        a
        |
Non +---+---+ (a,b)
        |
        b

'Wedge':
                a
                |
Nowhere +-------+
                |
                b


'Smash':


Nada +--------+ (a,b)