smash: Combinators for Maybe types

This is a package candidate release! Here you can preview how this package release will appear once published to the main package index (which can be accomplished via the 'maintain' link below). Please note that once a package has been published to the main package index it cannot be undone! Please consult the package uploading documentation for more information.

[maintain] [Publish]

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

[Skip to Readme]

Properties

Versions	0.1.0.0, 0.1.1.0, 0.1.2, 0.1.3, 0.1.3
Change log	CHANGELOG.md
Dependencies	base (>=4.12 && <4.17), bifunctors (>=5.5 && <5.6), binary (>=0.8 && <0.9), deepseq (>=1.4 && <1.5), hashable (>=1.3 && <1.4), mtl, template-haskell (>=2.2 && <3.0) [details]
License	BSD-3-Clause
Copyright	(c) 2020-2021 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 2022-04-27T00:44:51Z

Modules

[Index] [Quick Jump]

Control
- Monad
  - Trans
Data

Downloads

smash-0.1.3.tar.gz [browse] (Cabal source package)
Package description (as included in the package)

Maintainer's Corner

Package maintainers

topos

For package maintainers and hackage trustees

edit package information

Readme for smash-0.1.3

[back to package description]

smash: Combinators for Maybe types

This package consists of 3 interesting datatypes and their respective monad transformers:

Wedge: Isomorphic to Maybe (Either a b). The Wedge datatype represents the coproduct in the category Hask* of pointed Hask types, called a wedge sum. One can derive this type as follows:
```
Either (Maybe a) (Maybe b)
~ (1 + a) + (1 + b)
-- units are the same via pushout
~ 1 + a + b
~ Maybe (Either a b)
~ Wedge a b
```

Can: Isomorphic to Maybe (These a b). The Can datatype represents the product in Hask*. One can derive this as follows:

(Maybe a, Maybe a)
~ (1 + a) * (1 + b)
-- products distribute over coproducts
~ 1 + b + a + a*b
-- coproducts are associative
~ 1 + (b + a + a*b)
~ 1 + These a b
~ Maybe (These a b)
~ Can a b

Smash: Isomorphic to Maybe (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 is the quotient of Can over Wedge. It can be derived as follows:
```
Can a b / Wedge a b
~ 1 + a + b + a*b / 1 + a + b
-- reassoc coproduct
~ (1 + a + b) + a*b / 1 + a + b
-- def. of quotient: (1 + a + b) ~ 1
~ 1 + a * b
~ Maybe (a,b)
~ Smash a b
```