total-map: Finitely represented total maps

[ bsd3, data, library ] [ Propose Tags ]

Finitely represented total maps. Represented by as a partial map and a default value. Has Applicative and Monad instances (unlike Data.Map).

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Versions [RSS] 0.0.0, 0.0.1, 0.0.2, 0.0.3, 0.0.4, 0.0.5, 0.0.6, 0.0.7, 0.0.8, 0.1.0, 0.1.3
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Dependencies base (<5), containers, semiring-num (>= [details]
License BSD-3-Clause
Copyright (c) 2012--2019 by Conal Elliott
Author Conal Elliott
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Source repo head: git clone git://
Uploaded by ConalElliott at 2019-11-23T22:02:17Z
Reverse Dependencies 1 direct, 0 indirect [details]
Downloads 6966 total (7 in the last 30 days)
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Status Docs available [build log]
Last success reported on 2019-11-23 [all 1 reports]

Readme for total-map-0.1.3

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The usual finite map type (Map from Data.Map) is not an applicative functor, as it doesn't have a pure. Consequently, it's also not a monad. On the other hand, we can decompose Map into two parts: a total map, and Maybe, i.e.,

type Map k v = TMap k (Maybe v)

The type TMap of total maps does have Applicative and Monad instances, and hence this hypothetically rebuilt Map would as well.

The idea for TMap is introduced in the paper Denotational design with type class morphisms. The meaning Map k v is given by its semantic function

(!) :: Map k v -> (k -> v)

The type class morphism (TCM) principle then exactly dictates the meanings of several class instances for TMap, including Functor, Applicative, Monad, and Monoid. For instance, (!) must be a monoid (homo)morphism, i.e.,

(!) mempty == mempty
(!) (s `mappend` t) == (!) s `mappend` (!) t

The current implementation of TMap is via Data.Map.