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smash: Combinators for Maybe types

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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 [RSS] 0.1.0.0, 0.1.1.0, 0.1.2, 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]
Tested with ghc ==8.6.5 || ==8.8.4 || ==8.10.7 || ==9.0.2 || ==9.2.2
License BSD-3-Clause
Copyright (c) 2020-2022 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 2022-04-27T00:57:59Z
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Reverse Dependencies 6 direct, 0 indirect [details]
Downloads 1007 total (6 in the last 30 days)
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Status Docs available [build log]
Last success reported on 2022-04-27 [all 1 reports]

Readme for smash-0.1.3

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smash: Combinators for Maybe types

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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