feat(Tuple): Stub for a template type

This adds the target initial definition of a homogeneous Tuple<T>
  type, and just enough processing that the type can be defined and
  non-template methods that deal with the generic base type Tuple can
  be called. Still has no actual template instantiation.

src/core/PocomathInstance.mjs

@@ -45,6 +45,8 @@ export default class PocomathInstance {
        */
       this.Types = {any: anySpec}
       this.Types[theTemplateParam] = anySpec
+      // All the template types that have been defined
+      this._templateTypes = {}
       this._subtypes = {} // For each type, gives all of its (in)direct subtypes
       /* The following gives for each type, a set of all types that could
        * match in typed-function's dispatch algorithm before the given type.
@@ -263,10 +265,15 @@ export default class PocomathInstance {
     * the corresponding changes to the _typed object immediately
     */
    installType(type, spec) {
-      if (this._templateParam(type)) {
+      const parts = type.split(/[<,>]/)
+      if (this._templateParam(parts[0])) {
          throw new SyntaxError(
             `Type name '${type}' reserved for template parameter`)
       }
+      if (parts.some(this._templateParam.bind(this))) {
+         // It's a template, deal with it separately
+         return this._installTemplateType(type, spec)
+      }
       if (type in this.Types) {
          if (spec !== this.Types[type]) {
             throw new SyntaxError(`Conflicting definitions of type ${type}`)
@@ -353,7 +360,6 @@ export default class PocomathInstance {
       // update the typeOf function
       const imp = {}
       imp[type] = {uses: new Set(), does: () => () => type}
-      console.log('Adding', type, 'to typeOf')
       this._installFunctions({typeOf: imp})
    }
 
@@ -393,6 +399,7 @@ export default class PocomathInstance {
       }
       return 'any'
    }
+
    /* Returns a list of all types that have been mentioned in the
     * signatures of operations, but which have not actually been installed:
     */
@@ -400,6 +407,23 @@ export default class PocomathInstance {
       return Array.from(this._usedTypes).filter(t => !(t in this.Types))
    }
 
+   /* Used internally to install a template type */
+   _installTemplateType(type, spec) {
+      const base = type.split('<')[0]
+      /* For now, just allow a single template per base type; that
+       * might need to change later:
+       */
+      if (base in this._templateTypes) {
+         if (spec !== this._templateTypes[base].spec) {
+            throw new SyntaxError(
+               `Conflicting definitions of template type ${type}`)
+         }
+         return
+      }
+      // Nothing actually happens until we match a template parameter
+      this._templateTypes[base] = {type, spec}
+   }
+
    /* Used internally by install, see the documentation there */
    _installFunctions(functions) {
       for (const [name, spec] of Object.entries(functions)) {
@@ -509,6 +533,7 @@ export default class PocomathInstance {
             `Every implementation for ${name} uses an undefined type;\n`
                + `    signatures: ${Object.keys(imps)}`)
       }
+      // Mark this method as being in the midst of being reassembled
       Object.defineProperty(this, name, {configurable: true, value: 'limbo'})
       const tf_imps = {}
       for (const [rawSignature, behavior] of usableEntries) {

src/pocomath.mjs

@@ -3,10 +3,18 @@ import PocomathInstance from './core/PocomathInstance.mjs'
 import * as numbers from './number/native.mjs'
 import * as bigints from './bigint/native.mjs'
 import * as complex from './complex/native.mjs'
+import * as tuple from './tuple/native.mjs'
+// Most of tuple is not ready yet:
+const tupleReady = {
+    Tuple: tuple.Tuple,
+    equal: tuple.equal,
+    length: tuple.length,
+    tuple: tuple.tuple
+}
 import * as generic from './generic/all.mjs'
 import * as ops from './ops/all.mjs'
 
 const math = PocomathInstance.merge(
-    'math', numbers, bigints, complex, generic, ops)
+    'math', numbers, bigints, complex, tupleReady, generic, ops)
 
 export default math

src/tuple/Types/Tuple.mjs

@@ -0,0 +1,82 @@
+/* A template type representing a homeogeneous tuple of elements */
+import PocomathInstance from '../../core/PocomathInstance.mjs'
+
+const Tuple = new PocomathInstance('Tuple')
+// First a base type that will generally not be used directly
+Tuple.installType('Tuple', {
+   test: t => t && typeof t === 'object' && 'elts' in t && Array.isArray(t.elts)
+})
+// Now the template type that is the primary use of this
+Tuple.installType('Tuple<T>', {
+   // For now we will assume that any 'Type<T>' refines 'Type', so this is
+   // not necessary:
+   // refines: 'Tuple',
+   // But we need there to be a way to determine the type of a tuple:
+   infer: ({typeOf, joinTypes}) => t => {
+      return joinTypes(t.elts.map(typeOf))
+   },
+   // For the test, we can assume that t is already a base tuple,
+   // and we get the test for T as an input and we have to return
+   // the test for Tuple<T>
+   test: testT => t => t.elts.every(testT),
+   // These are only invoked for types U such that there is already
+   // a conversion from U to T, and that conversion is passed as an input
+   // and we have to return the conversion to Tuple<T>:
+   from: {
+      'Tuple<U>': convert => tu => ({elts: tu.elts.map(convert)}),
+      // Here since there is no U it's a straight conversion:
+      T: t => ({elts: [u]}), // singleton promotion
+      // Whereas the following will let you go directly from an element
+      // convertible to T to a singleton Tuple<T>. Not sure if we really
+      // want that, but we'll try it just for kicks.
+      U: convert => u => ({elts: [convert(u)]})
+   }
+})
+
+Tuple.promoteUnary = {
+   'Tuple<T>': ({'self(T)': me}) => t => ({elts: t.elts.map(me)})
+}
+
+Tuple.promoteBinaryUnary = {
+   'Tuple<T>,Tuple<T>': ({'self(T,T)': meB, 'self(T)': meU}) => (s,t) => {
+      let i = -1
+      let result = []
+      while (true) {
+         i += 1
+         if (i < s.elts.length) {
+            if (i < t.elts.length) result.append(meB(s.elts[i], t.elts[i]))
+            else results.append(meU(s.elts[i]))
+            continue
+         }
+         if (i < t.elts.length) result.append(meU(t.elts[i]))
+         else break
+      }
+      return {elts: result}
+   }
+}
+
+Tuple.promoteBinary = {
+   'Tuple<T>,Tuple<T>': ({'self(T,T)': meB}) => (s,t) => {
+      const lim = Math.max(s.elts.length, t.elts.length)
+      const result = []
+      for (let i = 0; i < lim; ++i) {
+         result.append(meB(s.elts[i], t.elts[i]))
+      }
+      return {elts: result}
+   }
+}
+
+Tuple.promoteBinaryStrict = {
+   'Tuple<T>,Tuple<T>': ({'self(T,T)': meB}) => (s,t) => {
+      if (s.elts.length !== t.elts.length) {
+         throw new RangeError('Tuple length mismatch') // get name of self ??
+      }
+      const result = []
+      for (let i = 0; i < s.elts.length; ++i) {
+         result.append(meB(s.elts[i], t.elts[i]))
+      }
+      return {elts: result}
+   }
+}
+
+export {Tuple}

src/tuple/equal.mjs

@@ -0,0 +1,14 @@
+export * from './Types/Tuple.mjs'
+
+export const equal = {
+   // Change this to a template implementation (or maybe add template
+   // implementation to handle matching types, and have mixed template-base
+   // method returning false to catch test of two tuples of different types.
+   'Tuple,Tuple': ({self, length}) => (s,t) => {
+      if (length(s) !== length(t)) return false
+      for (let i = 0; i < length(s); ++i) {
+         if (!self(s.elts[i], t.elts[i])) return false
+      }
+      return true
+   }
+}

src/tuple/isZero.mjs

@@ -0,0 +1,6 @@
+export {Tuple} from './Types/Tuple.mjs'
+
+export const isZero = {
+   'Tuple<T>': ({'self(T)': me}) => t => t.elts.every(isZero)
+}
+

src/tuple/length.mjs

@@ -0,0 +1,3 @@
+export {Tuple} from './Types/Tuple.mjs'
+
+export const length = {Tuple: () => t => t.elts.length}

src/tuple/native.mjs

@@ -0,0 +1,20 @@
+import {Tuple} from './Types/Tuple.mjs'
+
+export const add = Tuple.promoteBinaryUnary
+export const complex = Tuple.promoteBinaryStrict
+export const conjugate = Tuple.promoteUnary
+// May want to replace equal with compare based on lexicographic ordering?
+export {equal} from './equal.mjs'
+export const invert = Tuple.promoteUnary
+export {isZero} from './isZero.mjs'
+export {length} from './length.mjs'
+export const multiply = Tuple.promoteBinaryUnary
+export const negate = Tuple.promoteUnary
+export const one = Tuple.promoteUnary
+export const quotient = Tuple.promoteBinaryStrict
+export const roundquotient = Tuple.promoteBinaryStrict
+export const sqrt = Tuple.promoteUnary
+export {tuple} from './tuple.mjs'
+export const zero = Tuple.promoteUnary
+
+export {Tuple}

src/tuple/tuple.mjs

@@ -0,0 +1,6 @@
+export {Tuple} from './Types/Tuple.mjs'
+
+/* The purpose of the template argument is to ensure that all of the args
+ * are convertible to the same type.
+ */
+export const tuple = {'...any': () => args => ({elts: args})}

test/tuple/_native.mjs

@@ -0,0 +1,9 @@
+import assert from 'assert'
+import math from '../../src/pocomath.mjs'
+
+describe('tuple', () => {
+   it('can be created and provide its length', () => {
+      assert.strictEqual(math.length(math.tuple(3,5.2,2n)), 3)
+   })
+
+})