https://github.com/kamirus/purescript-functional-concepts

Elaborated examples concerning functional concepts e.g. gadt, eadt, church encodings
https://github.com/kamirus/purescript-functional-concepts

church-encoding eadt exists gadt gadts higher-order-functions leibniz-equality row-polymorphism tagless typeclasses

Last synced: 4 days ago
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Elaborated examples concerning functional concepts e.g. gadt, eadt, church encodings

• Host: GitHub
• URL: https://github.com/kamirus/purescript-functional-concepts
• Owner: Kamirus
• Created: 2018-10-28T11:46:06.000Z (about 6 years ago)
• Default Branch: master
• Last Pushed: 2024-10-16T10:06:43.000Z (22 days ago)
• Last Synced: 2024-10-17T22:18:15.508Z (21 days ago)
• Topics: church-encoding, eadt, exists, gadt, gadts, higher-order-functions, leibniz-equality, row-polymorphism, tagless, typeclasses
• Language: PureScript
• Homepage:
• Size: 32.2 KB
• Stars: 5
• Watchers: 3
• Forks: 1
• Open Issues: 0
• Metadata Files:
  • Readme: README.md

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README

        
# Purescript - functional concepts

How to run?

 - using pulp: `$ pulp run --main `

## Files

#### Equal

Leibniz equality pure implementation

#### Exists and Exists.Example

Exists implementation without GADTs nor cheats

Example shows simple uses, and points out that sometimes we need some constraints for 'hidden' type.

That would require to write new Exists data type for such use case. Further research is needed in this field.

#### GADTs/ExprLeibnizTagless

Express `Expr a` GADT without this extension

 - using Leibniz equality 

 - using tagless approach 

```haskell

data Expr a where

  I   ∷ Int  → Expr Int

  B   ∷ Bool → Expr Bool

  Add ∷ Expr Int → Expr Int → Expr Int

  Eq  ∷ Eq a ⇒ Expr a → Expr a → Expr Bool

eval ∷ Expr a → a

eval (I n) = n

eval (B b) = b

eval (Add e1 e2) = eval e1 + eval e2

eval (Eq  e1 e2) = eval e1 == eval e2

```

#### GADTs/ExprIf

Simple tagless form for operations: `+` and `if`

#### Tagless

[tagless-final embedding of the simply-typed lambda-calculus with integers and constants, and its uniform interpretations with three different evaluation strategies: call-by-name, call-by-value and call-by-need](http://okmij.org/ftp/tagless-final/cookbook.html#call-by-any)

On why tagless final is better than Leibniz - https://hgiasac.github.io/posts/2018-12-18-PureScript-GADTs-Alternatives---Recap.html