src/complex/abs.mjs

@@ -8,13 +8,8 @@ export const abs = {
       'absquare(T)': baseabsq,
       'absquare(Complex<T>)': absq
    }) => {
-      const pm = sqrt.fromInstance
-      if (typeof pm === 'undefined') {
-         // Just checking for the dependencies, return value is irrelevant
-         return undefined
-      }
       const midType = returnTypeOf(baseabsq)
-      const sqrtImp = pm.resolve('sqrt', midType, sqrt)
+      const sqrtImp = sqrt.fromInstance.resolve('sqrt', midType, sqrt)
       let retType = returnTypeOf(sqrtImp)
       if (retType.includes('|')) {
          // This is a bit of a hack, as it relies on all implementations of

src/complex/absquare.mjs

@@ -9,13 +9,9 @@ export const absquare = {
            // we extract the needed implementation below.
       'self(T)': absq
    }) => {
-      const pm = add.fromInstance
-      if (typeof pm === 'undefined') {
-         // Just checking the dependencies, return value irrelevant
-         return undefined
-      }
       const midType = returnTypeOf(absq)
-      const addImp = pm.resolve('add', `${midType},${midType}`, add)
+      const addImp = add.fromInstance.resolve(
+         'add', `${midType},${midType}`, add)
       return Returns(
          returnTypeOf(addImp), z => addImp(absq(z.re), absq(z.im)))
    }

src/core/PocomathInstance.mjs

@@ -7,11 +7,76 @@ import {typeListOfSignature, typesOfSignature, subsetOfKeys} from './utils.mjs'
 
 const anySpec = {} // fixed dummy specification of 'any' type
 
+/* Template/signature parsing stuff; should probably be moved to a
+ * separate file, but it's a bit interleaved at the moment
+ */
+
 const theTemplateParam = 'T' // First pass: only allow this one exact parameter
 const restTemplateParam = `...${theTemplateParam}`
 const templateCall = `<${theTemplateParam}>`
 const templateFromParam = 'U' // For defining covariant conversions
 
+/* returns the pair [base, instance] for a template type. If the type
+ * is not a template, instance is undefined
+ */
+const templatePattern = /^\s*([^<\s]*)\s*<\s*(\S*)\s*>\s*$/
+function splitTemplate(type) {
+   if (!(type.includes('<'))) return [type, undefined]
+   const results = templatePattern.exec(type)
+   return [results[1], results[2]]
+}
+/* Returns the instance such that type is template instantiated for that
+ * instance.
+ */
+function whichInstance(type, template) {
+   if (template === theTemplateParam) return type
+   if (type === template) return ''
+   if (!(template.includes(templateCall))) {
+      throw new TypeError(
+         `Type ${template} is not a template, so can't produce ${type}`)
+   }
+   const [typeBase, typeInstance] = splitTemplate(type)
+   if (!typeInstance) {
+      throw new TypeError(
+         `Type ${type} not from a template, so isn't instance of ${template}`)
+   }
+   const [tempBase, tempInstance] = splitTemplate(template)
+   if (typeBase !== tempBase) {
+      throw new TypeError(
+         `Type ${type} has wrong top-level base to be instance of ${template}`)
+   }
+   return whichInstance(typeInstance, tempInstance)
+}
+/* Same as above, but for signatures */
+function whichSigInstance(sig, tempsig) {
+   const sigTypes = typeListOfSignature(sig)
+   const tempTypes = typeListOfSignature(tempsig)
+   const sigLength = sigTypes.length
+   if (sigLength === 0) {
+      throw new TypeError("No types in signature, so can't determine instance")
+   }
+   if (sigLength !== tempTypes.length) {
+      throw new TypeError(`Signatures ${sig} and ${tempsig} differ in length`)
+   }
+   let maybeInstance = whichInstance(sigTypes[0], tempTypes[0])
+   for (let i = 1; i < sigLength; ++i) {
+      const currInstance = whichInstance(sigTypes[i], tempTypes[i])
+      if (maybeInstance) {
+         if (currInstance && currInstance !== maybeInstance) {
+            throw new TypeError(
+               `Inconsistent instantiation of ${sig} from ${tempsig}`)
+         }
+      } else {
+         maybeInstance = currInstance
+      }
+   }
+   if (!maybeInstance) {
+      throw new TypeError(
+         `Signature ${sig} identical to ${tempsig}, not an instance`)
+   }
+   return maybeInstance
+}
+
 /* Returns a new signature just like sig but with the parameter replaced by
  * the type
  */
@@ -202,7 +267,10 @@ export default class PocomathInstance {
             const stdimps = {}
             for (const [signature, does] of Object.entries(spec)) {
                const uses = new Set()
-               does(dependencyExtractor(uses))
+               try {
+                  does(dependencyExtractor(uses))
+               } catch {
+               }
                stdimps[signature] = {uses, does}
             }
             stdFunctions[item] = stdimps
@@ -334,7 +402,7 @@ export default class PocomathInstance {
     * the corresponding changes to the _typed object immediately
     */
    installType = Returns('void', function(type, spec) {
-      const parts = type.split(/[<,>]/)
+      const parts = type.split(/[<,>]/).map(s => s.trim())
       if (this._templateParam(parts[0])) {
          throw new SyntaxError(
             `Type name '${type}' reserved for template parameter`)
@@ -400,14 +468,14 @@ export default class PocomathInstance {
                }
 
                /* Add the conversion in the metaverse if need be: */
-               const toParts = nextSuper.split('<', 2)
-               if (toParts.length > 1) {
-                  const fromParts = from.split('<', 2)
-                  if (fromParts.length === 1 || fromParts[0] !== toParts[0]) {
+               const [toBase, toInstance] = splitTemplate(nextSuper)
+               if (toInstance) {
+                  const [fromBase, fromInstance] = splitTemplate(from)
+                  if (!fromBase || fromBase !== toBase) {
                      this._metafy(from)
                      try {
                         this._metaTyped.addConversion(
-                           {from, to: toParts[0], convert: spec.from[from]})
+                           {from, to: toBase, convert: spec.from[from]})
                      } catch {
                      }
                   }
@@ -438,12 +506,12 @@ export default class PocomathInstance {
                      })
                      this._invalidateDependents(':' + nextSuper)
                      /* Add the conversion in the metaverse if need be: */
-                     const toParts = nextSuper.split('<', 2)
-                     if (toParts.length > 1 && base !== toParts[0]) {
+                     const [toBase, toInstance] = splitTemplate(nextSuper)
+                     if (toInstance && base !== toBase) {
                         this._metafy(type)
                         this._metaTyped.addConversion({
                            from: type,
-                           to: toParts[0],
+                           to: toBase,
                            convert: this.Types[to].from[fromtype]
                         })
                      }
@@ -559,7 +627,7 @@ export default class PocomathInstance {
 
    /* Used internally to install a template type */
    _installTemplateType(type, spec) {
-      const base = type.split('<')[0]
+      const [base] = splitTemplate(type)
       /* For now, just allow a single template per base type; that
        * might need to change later:
        */
@@ -760,7 +828,7 @@ export default class PocomathInstance {
          let keep = true
          for (const type of typesOfSignature(entry[0])) {
             if (type in this.Types) continue
-            const baseType = type.split('<')[0]
+            const [baseType] = splitTemplate(type)
             if (baseType in this.Templates) continue
             keep = false
             break
@@ -857,7 +925,7 @@ export default class PocomathInstance {
                      othertype, theTemplateParam, '')
                   let otherTypeCollection = [othertype]
                   if (testType !== othertype) {
-                     const base = othertype.split('<',1)[0]
+                     const [base] = splitTemplate(othertype)
                      otherTypeCollection = this._instantiationsOf[base]
                   }
                   for (const possibility of otherTypeCollection) {
@@ -873,43 +941,7 @@ export default class PocomathInstance {
          }
 
          for (const instType of instantiationSet) {
-            if (!(instType in this.Types)) continue
-            if (this.Types[instType] === anySpec) continue
-            if (instType in behavior.hasInstantiations) continue
-            const signature =
-                  substituteInSignature(rawSignature, theTemplateParam, instType)
-            /* Don't override an explicit implementation: */
-            if (signature in imps) continue
-            /* Don't go too deep */
-            let maxdepth = 0
-            for (const argType in typeListOfSignature(signature)) {
-               const depth = argType.split('<').length
-               if (depth > maxdepth) maxdepth = depth
-            }
-            if (maxdepth > this._maxDepthSeen + 1) continue
-            /* All right, go ahead and instantiate */
-            const uses = new Set()
-            for (const dep of behavior.uses) {
-               if (this._templateParam(dep)) continue
-               uses.add(substituteInSignature(dep, theTemplateParam, instType))
-            }
-            const patch = (refs) => {
-               const innerRefs = {}
-               for (const dep of behavior.uses) {
-                  if (this._templateParam(dep)) {
-                     innerRefs[dep] = instType
-                  } else {
-                     const outerName = substituteInSignature(
-                        dep, theTemplateParam, instType)
-                     innerRefs[dep] = refs[outerName]
-                  }
-               }
-               return behavior.does(innerRefs)
-            }
-            this._addTFimplementation(tf_imps, signature, {uses, does: patch})
-            tf_imps[signature]._pocoSignature = rawSignature
-            tf_imps[signature]._pocoInstance = instType
-            behavior.hasInstantiations[instType] = signature
+            this._instantiateTemplateImplementation(name, rawSignature, instType)
          }
          /* Now add the catchall signature */
          /* (Not needed if if it's a bounded template) */
@@ -1031,7 +1063,7 @@ export default class PocomathInstance {
                for (const possibility of returnType.split('|')) {
                   const instantiated = self._maybeInstantiate(possibility)
                   if (instantiated) {
-                     const tempBase = instantiated.split('<',1)[0]
+                     const [tempBase] = splitTemplate(instantiated)
                      self._invalidateDependents(':' + tempBase)
                   }
                }
@@ -1047,6 +1079,7 @@ export default class PocomathInstance {
             }
             Object.defineProperty(
                patchFunc, 'name', {value: `${name}(${signature})`})
+            patchFunc._pocoSignature = rawSignature
             return patchFunc
          }
          Object.defineProperty(
@@ -1083,12 +1116,12 @@ export default class PocomathInstance {
       let tf
       if (Object.keys(tf_imps).length > 0) {
          tf = this._typed(name, tf_imps)
-         Object.defineProperty(tf, 'fromInstance', {value: this})
+         tf.fromInstance = this
       }
       let metaTF
       if (Object.keys(meta_imps).length > 0) {
          metaTF = this._metaTyped(name, meta_imps)
-         Object.defineProperty(metaTF, 'fromInstance', {value: this})
+         metaTF.fromInstance = this
       }
       this._meta[name] = metaTF
 
@@ -1137,11 +1170,58 @@ export default class PocomathInstance {
          return undefined // no such type
       }
       // it's a template type, turn it into a template and an arg
-      let base = type.split('<',1)[0]
-      const arg = type.slice(base.length+1, -1)
+      let [base, arg] = splitTemplate(type)
       return this.instantiateTemplate(base, arg)
    }
 
+   /* Generate and include a template instantiation for operation name
+    * for the template signature templateSignature instantiated for
+    * instanceType, returning the resulting implementation.
+    */
+   _instantiateTemplateImplementation(name, templateSignature, instanceType) {
+      if (!(instanceType in this.Types)) return undefined
+      if (this.Types[instanceType] === anySpec) return undefined
+      const imps = this._imps[name]
+      const behavior = imps[templateSignature]
+      if (instanceType in behavior.hasInstantiations) return undefined
+      const signature = substituteInSignature(
+         templateSignature, theTemplateParam, instanceType)
+      /* Don't override an explicit implementation: */
+      if (signature in imps) return undefined
+      /* Don't go too deep */
+      let maxdepth = 0
+      for (const argType in typeListOfSignature(signature)) {
+         const depth = argType.split('<').length
+         if (depth > maxdepth) maxdepth = depth
+      }
+      if (maxdepth > this._maxDepthSeen + 1) return undefined
+      /* All right, go ahead and instantiate */
+      const uses = new Set()
+      for (const dep of behavior.uses) {
+         if (this._templateParam(dep)) continue
+         uses.add(substituteInSignature(dep, theTemplateParam, instanceType))
+      }
+      const patch = (refs) => {
+         const innerRefs = {}
+         for (const dep of behavior.uses) {
+            if (this._templateParam(dep)) {
+               innerRefs[dep] = instanceType
+            } else {
+               const outerName = substituteInSignature(
+                  dep, theTemplateParam, instanceType)
+               innerRefs[dep] = refs[outerName]
+            }
+         }
+         return behavior.does(innerRefs)
+      }
+      const tf_imps = this._TFimps[name]
+      this._addTFimplementation(tf_imps, signature, {uses, does: patch})
+      tf_imps[signature]._pocoSignature = templateSignature
+      tf_imps[signature]._pocoInstance = instanceType
+      behavior.hasInstantiations[instanceType] = signature
+      return tf_imps[signature]
+   }
+
    /* Adapts Pocomath-style behavior specification (uses, does) for signature
     * to typed-function implementations and inserts the result into plain
     * object imps
@@ -1254,6 +1334,7 @@ export default class PocomathInstance {
             refs.self = self
             const implementation = does(refs)
             Object.defineProperty(implementation, 'name', {value: does.name})
+            implementation.fromInstance = this
             // What are we going to do with the return type info in here?
             return implementation
          })
@@ -1271,11 +1352,13 @@ export default class PocomathInstance {
             deferred: true,
             builtRefs: refs,
             sigDoes: does,
+            fromInstance: this,
             psr: part_self_references
          }
          return
       }
       const implementation = does(refs)
+      implementation.fromInstance = this
       // could do something with return type information here?
       imps[signature] = implementation
    }
@@ -1310,7 +1393,22 @@ export default class PocomathInstance {
                   name, this._imps[name], neededSig)
                if (foundSig) {
                   const match = this._pocoFindSignature(name, neededSig)
-                  refs[`self(${neededSig})`] = match.implementation
+                  const neededTemplate = match.fn._pocoSignature
+                  const neededInstance = whichSigInstance(
+                     neededSig, neededTemplate)
+                  const neededImplementation =
+                     this._instantiateTemplateImplementation(
+                        name, neededTemplate, neededInstance)
+                  if (!neededImplementation) {
+                     refs[`self(${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 '
@@ -1335,6 +1433,7 @@ export default class PocomathInstance {
          }
          imps[aSignature]._pocoSignature = deferral._pocoSignature
          imps[aSignature]._pocoInstance = deferral._pocoInstance
+         imps[aSignature].fromInstance = deferral.fromInstance
       }
    }
 
@@ -1343,8 +1442,7 @@ export default class PocomathInstance {
     * in the instance.
     */
    _ensureTemplateTypes(template, type) {
-      const base = template.split('<', 1)[0]
-      const arg = template.slice(base.length + 1, -1)
+      const [base, arg] = splitTemplate(template)
       if (!arg) {
          throw new Error(
             'Implementation error in _ensureTemplateTypes', template, type)
@@ -1481,7 +1579,7 @@ export default class PocomathInstance {
             if (otherType === 'any') continue
             if (myType === otherType) continue
             if (otherType in this.Templates) {
-               const myBase = myType.split('<',1)[0]
+               const [myBase] = splitTemplate(myType)
                if (myBase === otherType) continue
                if (this.instantiateTemplate(otherType, myType)) {
                   let dummy
@@ -1525,10 +1623,24 @@ export default class PocomathInstance {
             let allMatched = true
             const implTypes = typeListOfSignature(implSig)
             for (let i = 0; i < wantTypes.length; ++i) {
-               if (wantTypes[i] == implTypes[i]
-                   || this.isSubtypeOf(wantTypes[i], implTypes[i])) continue
-               allMatched = false
-               break
+               const implIndex = Math.min(i, implTypes.length - 1)
+               let implType = implTypes[implIndex]
+               if (implIndex < i) {
+                  if (implType.slice(0,3) !== '...') {
+                     // ran out of arguments in impl
+                     allMatched = false
+                     break
+                  }
+               }
+               if (implType.slice(0,3) === '...') {
+                  implType = implType.slice(3)
+               }
+               const hasMatch = implType.split('|').some(
+                  t => (wantTypes[i] === t || this.isSubtypeOf(wantTypes[i], t)))
+               if (!hasMatch) {
+                  allMatched = false
+                  break
+               }
             }
             if (allMatched) return details
          }

src/tuple/Types/Tuple.mjs

@@ -1,5 +1,6 @@
 /* A template type representing a homeogeneous tuple of elements */
 import PocomathInstance from '../../core/PocomathInstance.mjs'
+import {Returns, returnTypeOf} from '../../core/Returns.mjs'
 
 const Tuple = new PocomathInstance('Tuple')
 
@@ -33,50 +34,66 @@ Tuple.promoteUnary = {
    'Tuple<T>': ({
       'self(T)': me,
       tuple
-   }) => t => tuple(...(t.elts.map(x => me(x)))) // NOTE: this must use
-   // the inner arrow function to drop additional arguments that Array.map
-   // supplies, as otherwise the wrong signature of `me` might be used.
+   }) => {
+      const compType = me.fromInstance.joinTypes(
+         returnTypeOf(me).split('|'), 'convert')
+      return Returns(
+         `Tuple<${compType}>`, t => tuple(...(t.elts.map(x => me(x)))))
+   }
 }
 
 Tuple.promoteBinaryUnary = {
-   'Tuple<T>,Tuple<T>': ({'self(T,T)': meB, 'self(T)': meU, tuple}) => (s,t) => {
-      let i = -1
-      let result = []
-      while (true) {
-         i += 1
-         if (i < s.elts.length) {
-            if (i < t.elts.length) result.push(meB(s.elts[i], t.elts[i]))
-            else result.push(meU(s.elts[i]))
-            continue
+   'Tuple<T>,Tuple<T>': ({'self(T,T)': meB, 'self(T)': meU, tuple}) => {
+      const compTypes = returnTypeOf(meB).split('|').concat(
+         returnTypeOf(meU).split('|'))
+      const compType = meU.fromInstance.joinTypes(compTypes, 'convert')
+      return Returns(`Tuple<${compType}>`, (s,t) => {
+         let i = -1
+         let result = []
+         while (true) {
+            i += 1
+            if (i < s.elts.length) {
+               if (i < t.elts.length) result.push(meB(s.elts[i], t.elts[i]))
+               else result.push(meU(s.elts[i]))
+               continue
+            }
+            if (i < t.elts.length) result.push(meU(t.elts[i]))
+            else break
          }
-         if (i < t.elts.length) result.push(meU(t.elts[i]))
-         else break
-      }
-      return tuple(...result)
+         return tuple(...result)
+      })
    }
 }
 
 Tuple.promoteBinary = {
-   'Tuple<T>,Tuple<T>': ({'self(T,T)': meB, tuple}) => (s,t) => {
-      const lim = Math.max(s.elts.length, t.elts.length)
-      const result = []
-      for (let i = 0; i < lim; ++i) {
-         result.push(meB(s.elts[i], t.elts[i]))
-      }
-      return tuple(...result)
+   'Tuple<T>,Tuple<T>': ({'self(T,T)': meB, tuple}) => {
+      const compType = meB.fromInstance.joinTypes(
+         returnTypeOf(meB).split('|'))
+      return Returns(`Tuple<${compType}>`, (s,t) => {
+         const lim = Math.max(s.elts.length, t.elts.length)
+         const result = []
+         for (let i = 0; i < lim; ++i) {
+            result.push(meB(s.elts[i], t.elts[i]))
+         }
+         return tuple(...result)
+      })
    }
 }
 
 Tuple.promoteBinaryStrict = {
-   'Tuple<T>,Tuple<T>': ({'self(T,T)': meB, tuple}) => (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.push(meB(s.elts[i], t.elts[i]))
-      }
-      return tuple(...result)
+   'Tuple<T>,Tuple<T>': ({'self(T,T)': meB, tuple}) => {
+      const compType = meB.fromInstance.joinTypes(
+         returnTypeOf(meB).split('|'))
+      return Returns(`Tuple<${compType}>`, (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.push(meB(s.elts[i], t.elts[i]))
+         }
+         return tuple(...result)
+      })
    }
 }
 

src/tuple/equalTT.mjs

@@ -1,11 +1,16 @@
+import Returns from '../core/Returns.mjs'
+
 export * from './Types/Tuple.mjs'
 
 export const equalTT = {
-   'Tuple<T>,Tuple<T>': ({'self(T,T)': me, 'length(Tuple)': len}) => (s,t) => {
+   'Tuple<T>,Tuple<T>': ({
+      'self(T,T)': me,
+      'length(Tuple)': len
+   }) => Returns('boolean', (s,t) => {
       if (len(s) !== len(t)) return false
       for (let i = 0; i < len(s); ++i) {
          if (!me(s.elts[i], t.elts[i])) return false
       }
       return true
-   }
+   })
 }

src/tuple/isZero.mjs

@@ -1,7 +1,10 @@
+import Returns from '../core/Returns.mjs'
+
 export {Tuple} from './Types/Tuple.mjs'
 
 export const isZero = {
-   'Tuple<T>': ({'self(T)': me}) => t => t.elts.every(e => me(e))
+   'Tuple<T>': ({'self(T)': me}) => Returns(
+      'boolean', t => t.elts.every(e => me(e)))
    // Note we can't just say `every(me)` above since every invokes its
    // callback with more arguments, which then violates typed-function's
    // signature for `me`

src/tuple/tuple.mjs

@@ -1,6 +1,10 @@
+import Returns from '../core/Returns.mjs'
+
 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 = {'...T': () => args => ({elts: args})}
+export const tuple = {
+    '...T': ({T}) => Returns(`Tuple<${T}>`, args => ({elts: args}))
+}

test/tuple/_native.mjs

@@ -54,6 +54,9 @@ describe('tuple', () => {
       assert.deepStrictEqual(
          math.subtract(math.tuple(3n,4n,5n), math.tuple(2n,1n,0n)),
          math.tuple(1n,3n,5n))
+      assert.deepStrictEqual(
+         math.returnTypeOf('subtract', 'Tuple<bigint>,Tuple<bigint>'),
+         'Tuple<bigint>')
       assert.throws(
          () => math.subtract(math.tuple(5,6), math.tuple(7)),
          /RangeError/)
@@ -104,9 +107,16 @@ describe('tuple', () => {
    })
 
    it('supports sqrt', () => {
+      const mixedTuple = math.tuple(2, math.complex(0,2), 1.5)
       assert.deepStrictEqual(
-         math.sqrt(math.tuple(4,-4,2.25)),
-         math.tuple(2, math.complex(0,2), 1.5))
+         mixedTuple,
+         math.tuple(math.complex(2), math.complex(0,2), math.complex(1.5)))
+      assert.strictEqual(
+         math.returnTypeOf('tuple', 'NumInt, Complex<NumInt>, number'),
+         'Tuple<Complex<number>>')
+      assert.deepStrictEqual(math.sqrt(math.tuple(4,-4,2.25)), mixedTuple)
+      assert.strictEqual(
+         math.returnTypeOf('sqrt', 'Tuple<NumInt>'), 'Tuple<Complex<number>>')
    })
 
 })