aljebra
Toy implementations of the algebraic structures defined in the Fantasy Land specification, mostly borrowed from Haskell libraries.
npm install aljebra
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Version  0.0.2 last updated a year ago 
Keywords  algebraic, semigroup, monoid, functor, applicative, monad 
Repository  https://github.com/markandrus/aljebra (git) 
Homepage  https://github.com/markandrus/aljebra 
Dependencies  None 
About
Aljebra provides toy implementations of the algebraic structures defined in the Fantasy Land specification, mostly borrowed from Haskell libraries.
Algebraic Structures
The following objects each implement a constructor allowing you to lift values into these base objects. Many of the other instances in this library are built on top of these base objects. As such, they implement a similar constructor pattern.
Constructor  Description 

new Id(a) 
A value (Identity) 
new Optional() or new Optional(a) 
An optional value 
new (new Default(a)) or new (new Default(a))() 
An optional with a default value 
new Either('left', a) or new Either('right', b) 
One of two types of values 
Note that new Default(a)
actually returns a constructor for an Optional
that defaults to a
. In the following sections, such constructorsforconstructors will be listed under the heading “Constructors” and all other simple constructors will be listed under “Instances”.
Semigroup
Constructors
Constructor  Description 

new Semigroup(concat) 
Given associative binary function concat , return a Semigroup constructor. 
new Dual(s) 
Given Semigroup s , flip s.concat and return a constructor for the resulting Semigroup. 
Instances
Constructor  concat 

new Either('left', a) or new Either('right', b) 
Takes the first value labelled 'right' . 
new First(a) 
Takes the first a . 
new Last(a) 
Takes the last a . 
new Max(a) 
> 
new Min(a) 
< 
This module reexports all Monoid instances.
Monoid
Constructors
Constructor  Description 

new Monoid(zero, concat) 
Given value zero and binary function concat , return a Monoid constructor. 
new Dual(m) 
Given Monoid m , flip m.concat and return a constructor for the resulting Monoid. 
new OptionalSemigroup(s) 
Lift Semigroup s into Optional and return a constructor for the resulting Monoid. 
Instances
Constructor  zero 
concat 
Notes 

new All(a) 
true 
&& 

new Any(a) 
false 
││ 

new Array(a) 
[] 
concat 

new Endo(a) 
identity function  function composition  a must be a function from values of type b to b . 
new Product(a) 
1 
* 

new Sum(a) 
0 
+ 
Functor
Instances
Instance  map(f) 

new Id(a) 
Apply f to the value. 
new Optional(a) or new Optional() 
If the value exists, apply f to it. 
new Either('left', a) or new Either('right', b) 
If the value is labelled 'right' , apply f to it. 
This module reexports all Applicative instances.
Applicative
Instances
This module reexports all Monad instances.
Monad
Instances
Constructor  of 
chain 

new Id(a) 
new Id(a) 

new Optional(a) 
new Optional(a) 
A missing value shortcircuits the chain. 
new Either('left', a) or new Either('right', b) 
new Either('right', a) 
A 'left' vale shortcircuits the chain. 
Safety
 All of the algebraic operations defined above are pure.
 Each constructor
freeze
s its resulting object.  Source code includes
'use strict'
, so attempting to mutate any of the structures throws a type error.  Most argument calls are annotated with helpers from
./lib/common.js
. These throw errors, for example, when arguments are of the wrong type or wrong number are provided.
Testing
Note: the test suite itself could be better tested!
The test suite attempts to verify that the instances of algebraic structures defined in this library satisfy the laws defined in the Fantasy Land specification. Additionally, it includes a number of noninstance "sanity checks".
Before running, make sure you have installed the package with npm install
, as the test suite relies on Mocha.
$ make abouttesting
Testing
make test # Run all instance tests
make testinstances # Run all instance tests
make testnoninstances # Run all noninstance tests
make testall # Run all tests
make testallverbose # Run all tests in verbose mode
make testing # Run all tests continuosly
Instance Tests
Example
Id:
✓ Identity (Functor)
✓ Composition (Functor)
✓ Identity (Applicative)
✓ Composition (Applicative)
✓ Homomorphism (Applicative)
✓ Interchange (Applicative)
✓ Associativity (Chain)
✓ Left Identity (Monad)
✓ Right Identity (Monad)
Noninstance Tests
Example
Difference:
✓ is not a Semigroup
Rock, Paper, Scissors:
✓ is not a Semigroup