src/complex/native.mjs

@@ -9,9 +9,11 @@ export {conjugate} from './conjugate.mjs'
 export {equalTT} from './equalTT.mjs'
 export {gcd} from './gcd.mjs'
 export {invert} from './invert.mjs'
+export {isReal} from './isReal.mjs'
 export {isZero} from './isZero.mjs'
 export {multiply} from './multiply.mjs'
 export {negate} from './negate.mjs'
+export {polynomialRoot} from './polynomialRoot.mjs'
 export {quaternion} from './quaternion.mjs'
 export {quotient} from './quotient.mjs'
 export {roundquotient} from './roundquotient.mjs'

src/core/PocomathInstance.mjs

@@ -87,6 +87,7 @@ function substituteInSignature(signature, parameter, type) {
    return sig.replaceAll(pattern, type)
 }
 
+const UniversalType = 'ground' // name for a type that matches anything
 let lastWhatToDo = null // used in an infinite descent check
 
 export default class PocomathInstance {
@@ -128,12 +129,13 @@ export default class PocomathInstance {
       // its onMismatch function, below:
       this._metaTyped = typed.create()
       this._metaTyped.clear()
+      this._metaTyped.addTypes([{name: UniversalType, test: () => true}])
+
       // And these are the meta bindings: (I think we don't need separate
       // invalidation for them as they are only accessed through a main call.)
       this._meta = {} // The resulting typed-functions
       this._metaTFimps = {} // and their implementations
       const me = this
-      const myTyped = this._typed
       this._typed.onMismatch = (name, args, sigs) => {
          if (me._invalid.has(name)) {
             // rebuild implementation and try again
@@ -523,6 +525,10 @@ export default class PocomathInstance {
             }
          }
       }
+      // Need to metafy ground types
+      if (type === base) {
+         this._metafy(type)
+      }
       // update the typeOf function
       const imp = {}
       imp[type] = {uses: new Set(), does: () => Returns('string', () => type)}
@@ -640,7 +646,7 @@ export default class PocomathInstance {
       }
 
       // install the "base type" in the meta universe:
-      let beforeType = 'any'
+      let beforeType = UniversalType
       for (const other of spec.before || []) {
          if (other in this.templates) {
             beforeType = other
@@ -648,6 +654,13 @@ export default class PocomathInstance {
          }
       }
       this._metaTyped.addTypes([{name: base, test: spec.base}], beforeType)
+      // Add conversions to the base type:
+      if (spec.from && spec.from[theTemplateParam]) {
+         for (const ground of this._metafiedTypes) {
+            this._metaTyped.addConversion(
+               {from: ground, to: base, convert: spec.from[theTemplateParam]})
+         }
+      }
       this._instantiationsOf[base] = new Set()
 
       // update the typeOf function
@@ -881,7 +894,7 @@ export default class PocomathInstance {
                      basesig, theTemplateParam, '')
                   if (testsig === basesig) {
                      // that is not also top-level
-                     for (const templateType of typeListOfSignature(basesig)) {
+                     for (let templateType of typeListOfSignature(basesig)) {
                         if (templateType.slice(0,3) === '...') {
                            templateType = templateType.slice(3)
                         }
@@ -908,7 +921,7 @@ export default class PocomathInstance {
          let baseSignature = rawSignature.replaceAll(templateCall, '')
          /* Any remaining template params are top-level */
          const signature = substituteInSignature(
-            baseSignature, theTemplateParam, 'any')
+            baseSignature, theTemplateParam, UniversalType)
          const hasTopLevel = (signature !== baseSignature)
          if (!ubType && hasTopLevel) {
             for (const othersig in imps) {
@@ -939,7 +952,6 @@ export default class PocomathInstance {
                }
             }
          }
-
          for (const instType of instantiationSet) {
             this._instantiateTemplateImplementation(name, rawSignature, instType)
          }
@@ -1018,9 +1030,10 @@ export default class PocomathInstance {
                   usedConversions = true
                   instantiateFor = self.joinTypes(argTypes, usedConversions)
                   if (instantiateFor === 'any') {
+                     let argDisplay = args.map(toString).join(', ')
                      throw TypeError(
                         `In call to ${name}, no type unifies arguments `
-                           + args.toString() + '; of types ' + argTypes.toString()
+                           + argDisplay + '; of types ' + argTypes.toString()
                            + '; note each consecutive pair must unify to a '
                            + 'supertype of at least one of them')
                   }
@@ -1042,7 +1055,9 @@ export default class PocomathInstance {
                for (j = 0; j < parTypes.length; ++j) {
                   if (wantTypes[j] !== parTypes[j] && parTypes[j].includes('<')) {
                      // actually used the param and is a template
-                     self._ensureTemplateTypes(parTypes[j], instantiateFor)
+                     const strippedType = parTypes[j].substr(
+                        parTypes[j].lastIndexOf('.') + 1)
+                     self._ensureTemplateTypes(strippedType, instantiateFor)
                   }
                }
 
@@ -1117,11 +1132,13 @@ export default class PocomathInstance {
       if (Object.keys(tf_imps).length > 0) {
          tf = this._typed(name, tf_imps)
          tf.fromInstance = this
+         tf.isMeta = false
       }
       let metaTF
       if (Object.keys(meta_imps).length > 0) {
          metaTF = this._metaTyped(name, meta_imps)
          metaTF.fromInstance = this
+         metaTF.isMeta = true
       }
       this._meta[name] = metaTF
 
@@ -1325,6 +1342,14 @@ export default class PocomathInstance {
                if (destination && needsig) {
                   destination = this.resolve(func, needsig)
                }
+               if (!destination) {
+                  // Unresolved reference. This is allowed so that
+                  // you can bundle up just some portions of the library,
+                  // but let's warn.
+                  console.log(
+                     'WARNING: No definition found for dependency',
+                     dep, 'needed by a function with signature', signature)
+               }
                refs[dep] = destination
             }
          }
@@ -1364,76 +1389,85 @@ export default class PocomathInstance {
    }
 
    _correctPartialSelfRefs(name, imps) {
-      for (const aSignature in imps) {
-         if (!(imps[aSignature].deferred)) continue
-         const deferral = imps[aSignature]
-         const part_self_references = deferral.psr
-         const corrected_self_references = []
-         const remaining_self_references = []
-         const refs = deferral.builtRefs
-         for (const neededSig of part_self_references) {
-            // Have to find a match for neededSig among the other signatures
-            // of this function. That's a job for typed-function, but we will
-            // try here:
-            if (neededSig in imps) { // the easy case
-               corrected_self_references.push(neededSig)
-               remaining_self_references.push(neededSig)
-               continue
-            }
-            // No exact match, try to get one that matches with
-            // subtypes since the whole conversion thing in typed-function
-            // is too complicated to reproduce
-            let foundSig = this._findSubtypeImpl(name, imps, neededSig)
-            if (foundSig) {
-               corrected_self_references.push(foundSig)
-               remaining_self_references.push(neededSig)
-            } else {
-               // Maybe it's a template instance we don't yet have
-               foundSig = this._findSubtypeImpl(
-                  name, this._imps[name], neededSig)
+      let sawDeferral = true
+      while (sawDeferral) {
+         // We might generate some new partial self references in resolving
+         // the previously existing ones, so looping through the signatures
+         // once is not enough; we have to keep looping until there are no
+         // more deferrals
+         sawDeferral = false
+         for (const aSignature in imps) {
+            if (!(imps[aSignature].deferred)) continue
+            sawDeferral = true
+            const deferral = imps[aSignature]
+            const part_self_references = deferral.psr
+            const corrected_self_references = []
+            const remaining_self_references = []
+            const refs = deferral.builtRefs
+            for (const neededSig of part_self_references) {
+               // Have to find a match for neededSig among the other signatures
+               // of this function. That's a job for typed-function, but we will
+               // try here:
+               if (neededSig in imps) { // the easy case
+                  corrected_self_references.push(neededSig)
+                  remaining_self_references.push(neededSig)
+                  continue
+               }
+               // No exact match, try to get one that matches with
+               // subtypes since the whole conversion thing in typed-function
+               // is too complicated to reproduce
+               let foundSig = this._findSubtypeImpl(name, imps, neededSig)
                if (foundSig) {
-                  const match = this._pocoFindSignature(name, neededSig)
-                  const neededTemplate = match.fn._pocoSignature
-                  const neededInstance = whichSigInstance(
-                     neededSig, neededTemplate)
-                  const neededImplementation =
-                     this._instantiateTemplateImplementation(
-                        name, neededTemplate, neededInstance)
-                  if (!neededImplementation) {
-                     refs[`self(${neededSig})`] = match.implementation
-                  } else {
-                     if (typeof neededImplementation === 'function') {
-                        refs[`self(${neededSig})`] = neededImplementation
-                     } else {
-                        corrected_self_references.push(neededSig)
-                        remaining_self_references.push(neededSig)
-                     }
-                  }
+                  corrected_self_references.push(foundSig)
+                  remaining_self_references.push(neededSig)
                } else {
-                  throw new Error(
-                     'Implement inexact self-reference in typed-function for '
-                        + `${name}(${neededSig})`)
+                  // Maybe it's a template instance we don't yet have
+                  foundSig = this._findSubtypeImpl(
+                     name, this._imps[name], neededSig)
+                  if (foundSig) {
+                     const match = this._pocoFindSignature(name, neededSig)
+                     const neededTemplate = match.fn._pocoSignature
+                     const neededInstance = whichSigInstance(
+                        neededSig, neededTemplate)
+                     const neededImplementation =
+                           this._instantiateTemplateImplementation(
+                              name, neededTemplate, neededInstance)
+                     if (!neededImplementation) {
+                        refs[`self(${neededSig})`] = match.implementation
+                     } else {
+                        if (typeof neededImplementation === 'function') {
+                           refs[`self(${neededSig})`] = neededImplementation
+                        } else {
+                           corrected_self_references.push(neededSig)
+                           remaining_self_references.push(neededSig)
+                        }
+                     }
+                  } else {
+                     throw new Error(
+                        'Implement inexact self-reference in typed-function for '
+                           + `${name}(${neededSig})`)
+                  }
                }
             }
-         }
-         const does = deferral.sigDoes
-         if (remaining_self_references.length > 0) {
-            imps[aSignature] = this._typed.referTo(
-               ...corrected_self_references, (...impls) => {
-                  for (let i = 0; i < remaining_self_references.length; ++i) {
-                     refs[`self(${remaining_self_references[i]})`] = impls[i]
+            const does = deferral.sigDoes
+            if (remaining_self_references.length > 0) {
+               imps[aSignature] = this._typed.referTo(
+                  ...corrected_self_references, (...impls) => {
+                     for (let i = 0; i < remaining_self_references.length; ++i) {
+                        refs[`self(${remaining_self_references[i]})`] = impls[i]
+                     }
+                     const implementation = does(refs)
+                     // What will we do with the return type info in here?
+                     return implementation
                   }
-                  const implementation = does(refs)
-                  // What will we do with the return type info in here?
-                  return implementation
-               }
-            )
-         } else {
-            imps[aSignature] = does(refs)
+               )
+            } else {
+               imps[aSignature] = does(refs)
+            }
+            imps[aSignature]._pocoSignature = deferral._pocoSignature
+            imps[aSignature]._pocoInstance = deferral._pocoInstance
+            imps[aSignature].fromInstance = deferral.fromInstance
          }
-         imps[aSignature]._pocoSignature = deferral._pocoSignature
-         imps[aSignature]._pocoInstance = deferral._pocoInstance
-         imps[aSignature].fromInstance = deferral.fromInstance
       }
    }
 
@@ -1550,7 +1584,7 @@ export default class PocomathInstance {
          const otherTypeList = typeListOfSignature(otherSig)
          if (typeList.length !== otherTypeList.length) continue
          let allMatch = true
-         let paramBound = 'any'
+         let paramBound = UniversalType
          for (let k = 0; k < typeList.length; ++k) {
             let myType = typeList[k]
             let otherType = otherTypeList[k]
@@ -1577,6 +1611,7 @@ export default class PocomathInstance {
                   theTemplateParam, paramBound)
             }
             if (otherType === 'any') continue
+            if (otherType === UniversalType) continue
             if (myType === otherType) continue
             if (otherType in this.Templates) {
                const [myBase] = splitTemplate(myType)
@@ -1608,6 +1643,7 @@ export default class PocomathInstance {
          typedFunction = this[name]
       }
       const haveTF = this._typed.isTypedFunction(typedFunction)
+                     && !(typedFunction.isMeta)
       if (haveTF) {
          // First try a direct match
          let result

src/tuple/tuple.mjs

@@ -6,5 +6,5 @@ export {Tuple} from './Types/Tuple.mjs'
  * are convertible to the same type.
  */
 export const tuple = {
-    '...T': ({T}) => Returns(`Tuple<${T}>`, args => ({elts: args}))
+   '...T': ({T}) => Returns(`Tuple<${T}>`, args => ({elts: args}))
 }

test/complex/_all.mjs

@@ -45,6 +45,11 @@ describe('complex', () => {
       assert.ok(!(math.equal(math.complex(45n, 3n), 45n)))
    })
 
+   it('tests for reality', () => {
+      assert.ok(math.isReal(math.complex(3, 0)))
+      assert.ok(!(math.isReal(math.complex(3, 2))))
+   })
+
    it('computes gcd', () => {
       assert.deepStrictEqual(
          math.gcd(math.complex(53n, 56n), math.complex(47n, -13n)),