feat: Implement subtypes

This should eventually be moved into typed-function itself, but for
  now it can be implemented on top of the existing typed-function.

  Uses subtypes to define (and error-check) gcd and lcm, which are only
  defined for integer arguments.

  Resolves #36.

src/generic/arithmetic.mjs

@@ -1,7 +1,10 @@
 export * from './Types/generic.mjs'
 
+export {lcm} from './lcm.mjs'
+export {mod} from './mod.mjs'
 export {multiply} from './multiply.mjs'
 export {divide} from './divide.mjs'
 export {sign} from './sign.mjs'
 export {sqrt} from './sqrt.mjs'
+export {square} from './square.mjs'
 export {subtract} from './subtract.mjs'

src/generic/gcdType.mjs

@@ -0,0 +1,18 @@
+/* Returns a object that defines the gcd for the given type */
+export default function(type) {
+   const producer = refs => {
+      const modder = refs[`mod(${type},${type})`]
+      const zeroTester = refs[`isZero(${type})`]
+      return (a,b) => {
+         while (!zeroTester(b)) {
+            const r = modder(a,b)
+            a = b
+            b = r
+         }
+         return a
+      }
+   }
+   const retval = {}
+   retval[`${type},${type}`] = producer
+   return retval
+}

src/generic/lcm.mjs

@@ -0,0 +1,6 @@
+export const lcm = {
+   'any,any': ({
+      multiply,
+      quotient,
+      gcd}) => (a,b) => multiply(quotient(a, gcd(a,b)), b)
+}

src/generic/mod.mjs

@@ -0,0 +1,6 @@
+export const mod = {
+   'any,any': ({
+      subtract,
+      multiply,
+      quotient}) => (a,m) => subtract(a, multiply(m, quotient(a,m)))
+}

src/generic/multiply.mjs

@@ -4,9 +4,9 @@ export const multiply = {
    'undefined': () => u => u,
    'undefined,...any': () => (u, rest) => u,
    'any,undefined': () => (x, u) => u,
-   'any,undefined,...any': () => (x, u, rest) => u,
-   'any,any,undefined': () => (x, y, u) => u,
-   'any,any,undefined,...any': () => (x, y, u, rest) => u
-   // Bit of a hack since this should go on indefinitely...
+   'any,any,...any': ({self}) => (a,b,rest) => {
+      const later = [b, ...rest]
+      return later.reduce((x,y) => self(x,y), a)
+   }
 }
 

src/generic/square.mjs

@@ -0,0 +1,3 @@
+export const square = {
+   any: ({multiply}) => x => multiply(x,x)
+}