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# algebraic-structures
Provides useful algebraic structures for programming using parametric modules in Chicken Scheme.
## Install
Run `chicken-install` in the project's root directory.
```
$ cd algebraic-structures
$ chicken-install
```
## Usage
### Define Semigroup, Monoid and Group
```scheme
(import (algebraic-structures semigroup)
(algebraic-structures monoid)
(algebraic-structures group)
(algebraic-structures monoid fold)
(algebraic-structures list foldable))
(module (mod7 semigroup) = (algebraic-structures semigroup)
(import scheme
(chicken module))
(export op)
(define (op x y)
(assert (integer? x))
(assert (integer? y))
(assert (not (zero? x)))
(assert (not (zero? y)))
(modulo (* x y) 7)))
(module (mod7 monoid) = (algebraic-structures monoid)
(import scheme
(chicken module)
(chicken base)
(only (mod7 semigroup)))
(reexport (mod7 semigroup))
(export unit)
(define unit 1))
(module (mod7 group) = (algebraic-structures group)
(import scheme
(chicken base)
(chicken module)
matchable
(only (mod7 monoid)))
(reexport (mod7 monoid))
(export inv)
(define (inv n)
(assert (integer? n))
(assert (not (zero? n)))
(match (modulo n 7)
(1 1)
(2 4)
(3 5)
(4 2)
(5 3)
(6 6))))
(module (mod7 fold) = ((algebraic-structures monoid fold) (mod7 monoid) (algebraic-structures list foldable)))
(import (prefix (mod7 group) mod7:)
(prefix (mod7 fold) mod7:))
```
In REPL:
```
> (map (cut mod7:pow 3 op) '(0 1 2 3 4 5 6 7 8 9 10 11))
(1 3 2 6 4 5 1 3 2 6 4 5)
> (mod7:fold '(1 2 3 4 5 6))
6
```
### Monad Syntax
```scheme
(import (srfi 41)
(prefix (algebraic-structures stream monad) stream:)
(prefix (algebraic-structures stream alternative) stream:))
(define (pythagorean-triples)
(stream:do (b <- (stream-from 1))
(a <- (stream-range 1 b))
(let c^2 = (+ (* a a) (* b b)))
(let-values (c r) = (exact-integer-sqrt c^2))
(stream:guard (zero? r))
(stream (list a b c))))
```
In REPL:
```
> (stream->list (stream-take 10 (pythagorean-triples)))
((3 4 5) (6 8 10) (5 12 13) (9 12 15) (8 15 17) (12 16 20) (15 20 25) (20 21 29) (7 24 25) (10 24 26))
```
## Supported Features
- Semigroup: `(algebraic-structures semigroup)`
- Number (product): `(algebraic-structures number product semigroup)`
- Number (sum): `(algebraic-structures number sum semigroup)`
- List: `(algebraic-structures list semigroup)`
- Vector: `(algebraic-structures vector semigroup)`
- Stream: `(algebraic-structures stream semigroup)`
- Semigroup.reduce: `(algebraic-structures semigroup reduce)`
- Monoid: `(algebraic-structures monoid)`
- Number (product): `(algebraic-structures number product monoid)`
- Number (sum): `(algebraic-structures number sum monoid)`
- List: `(algebraic-structures list monoid)`
- Vector: `(algebraic-structures vector monoid)`
- Stream: `(algebraic-structures stream monoid)`
- Monoid.fold: `(algebraic-structures monoid fold)`
- Group
- Number (product): `(algebraic-structures number product group)`
- Number (sum): `(algebraic-structures number sum group)`
- Foldable: `(algebraic-structures foldable)`
- List: `(algebraic-structures list foldable)`
- Vector: `(algebraic-structures vector foldable)`
- Stream: `(algebraic-structures stream foldable)`
- Reducible: `(algebraic-structures reducible)`
- List: `(algebraic-structures list reducible)`
- Vector: `(algebraic-structures vector reducible)`
- Stream: `(algebraic-structures stream reducible)`
- Functor: `(algebraic-structures functor)`
- List: `(algebraic-structures list functor)`
- Vector: `(algebraic-structures vector functor)`
- Stream: `(algebraic-structures stream functor)`
- Applicative: `(algebraic-structures applicative)`
- List: `(algebraic-structures list applicative)`
- List (zip): `(algebraic-structures list zip applicative)`
- Vector (zip): `(algebraic-structures vector zip applicative)`
- Stream: `(algebraic-structures stream applicative)`
- Stream (zip): `(algebraic-structures stream zip applicative)`
- Monad: `(algebraic-structures monad)`
- List: `(algebraic-structures list monad)`
- Stream: `(algebraic-structures stream monad)`
- Alternative: `(algebraic-structures alternative)`
- List: `(algebraic-structures list alternative)`
- Stream: `(algebraic-structures stream alternative)`
## Examples
- Group
- [mod7](./examples/mod7.scm)
- Monad
- [optional](./examples/optional.scm)
- [state](./examples/state.scm)
- Monad (`do` syntax)
- [pythagorean-triples](./examples/pythagorean-triples.scm)
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