https://github.com/phadej/free-applicative-agda

Free applicatives in agda
https://github.com/phadej/free-applicative-agda

Last synced: about 7 hours ago
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Free applicatives in agda

• Host: GitHub
• URL: https://github.com/phadej/free-applicative-agda
• Owner: phadej
• Created: 2014-07-15T13:27:17.000Z (over 10 years ago)
• Default Branch: master
• Last Pushed: 2014-12-23T11:05:50.000Z (almost 10 years ago)
• Last Synced: 2024-10-11T23:53:32.189Z (26 days ago)
• Language: Agda
• Size: 148 KB
• Stars: 1
• Watchers: 3
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.agda

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README

        
module README where

-- Free applicatives and related

-- Defined as in Haskell's free package

--

-- Harder to define in Agda

-- Easier to reason about, if you want to prove some facts

import Free

-- More dynamic languages like definition

--

-- Applicative functor is functor from monoidal category to another together

-- with natural transformation η (pure) and morphism φ : F A × F B → F (A × B)

--

-- As product (×) is monoid operation, it is natural to "remember" φ using

-- free monoid structure, i.e. list.

--

-- Though in this case we need heterogenous list, it is easy with dependent types.

--

-- Not requiring F to be functor itself, is quite natural.  We use similar

-- construction as with Coyoneda.  We could use the fact F is a functor, but

-- using this fact will only make implementation more complex.

--

--

-- Definition is very natural after machinery is introduced

-- Yet proving anything (e.g. interchange or composition law) about this variant

-- is tedious

import Monoidal

-- Which is (kind of) extension of Coyoneda from kan-extensions package

import Coyoneda

-- And we are using own definition of well-founded recursion in Free module

-- More universe polymorphism, we can define recursive functions using measures

-- IMHO more flexible than sized-types.

import WellFounded