fix(templates): Enhance the catchall to call the correct specialization

Also enhances type inference in preparation for template types.

src/complex/native.mjs

@@ -4,8 +4,8 @@ export {abs} from './abs.mjs'
 export {absquare} from './absquare.mjs'
 export {add} from './add.mjs'
 export {associate} from './associate.mjs'
-export {conjugate} from './conjugate.mjs'
 export {complex} from './complex.mjs'
+export {conjugate} from './conjugate.mjs'
 export {equal} from './equal.mjs'
 export {gcd} from './gcd.mjs'
 export {invert} from './invert.mjs'

src/core/PocomathInstance.mjs

@@ -27,6 +27,7 @@ export default class PocomathInstance {
       'importDependencies',
       'install',
       'installType',
+      'joinTypes',
       'name',
       'typeOf',
       'Types',
@@ -293,7 +294,20 @@ export default class PocomathInstance {
       }
       this._typed.addTypes([{name: type, test: testFn}], beforeType)
       this.Types[type] = spec
+      this._subtypes[type] = new Set()
       this._priorTypes[type] = new Set()
+      // Update all the subtype sets of supertypes up the chain, and
+      // while we are at it add trivial conversions from subtypes to supertypes
+      // to help typed-function match signatures properly:
+      let nextSuper = spec.refines
+      while (nextSuper) {
+         this._typed.addConversion(
+            {from: type, to: nextSuper, convert: x => x})
+         this._invalidateDependents(':' + nextSuper)
+         this._priorTypes[nextSuper].add(type)
+         this._subtypes[nextSuper].add(type)
+         nextSuper = this.Types[nextSuper].refines
+      }
       /* Now add conversions to this type */
       for (const from in (spec.from || {})) {
          if (from in this.Types) {
@@ -304,13 +318,20 @@ export default class PocomathInstance {
                   {from, to: nextSuper, convert: spec.from[from]})
                this._invalidateDependents(':' + nextSuper)
                this._priorTypes[nextSuper].add(from)
+               /* And all of the subtypes of from are now prior as well: */
+               for (const subtype of this._subtypes[from]) {
+                  this._priorTypes[nextSuper].add(subtype)
+               }
                nextSuper = this.Types[nextSuper].refines
             }
          }
       }
       /* And add conversions from this type */
       for (const to in this.Types) {
-         if (type in (this.Types[to].from || {})) {
+         for (const fromtype in this.Types[to].from) {
+            if (type == fromtype
+                || (fromtype in this._subtypes
+                    && this._subtypes[fromtype].has(type))) {
                if (spec.refines == to || spec.refines in this._subtypes[to]) {
                   throw new SyntaxError(
                      `Conversion of ${type} to its supertype ${to} disallowed.`)
@@ -320,7 +341,7 @@ export default class PocomathInstance {
                   this._typed.addConversion({
                      from: type,
                      to: nextSuper,
-                  convert: this.Types[to].from[type]
+                     convert: this.Types[to].from[fromtype]
                   })
                   this._invalidateDependents(':' + nextSuper)
                   this._priorTypes[nextSuper].add(type)
@@ -328,26 +349,50 @@ export default class PocomathInstance {
                }
             }
          }
-      // Update all the subtype sets of supertypes up the chain, and
-      // while we are at it add trivial conversions from subtypes to supertypes
-      // to help typed-function match signatures properly:
-      this._subtypes[type] = new Set()
-      let nextSuper = spec.refines
-      while (nextSuper) {
-         this._typed.addConversion(
-            {from: type, to: nextSuper, convert: x => x})
-         this._invalidateDependents(':' + nextSuper)
-         this._priorTypes[nextSuper].add(type)
-         this._subtypes[nextSuper].add(type)
-         nextSuper = this.Types[nextSuper].refines
       }
-
       // update the typeOf function
       const imp = {}
       imp[type] = {uses: new Set(), does: () => () => type}
+      console.log('Adding', type, 'to typeOf')
       this._installFunctions({typeOf: imp})
    }
 
+   /* Returns the most refined type of all the types in the array, with
+    * '' standing for the empty type for convenience. If the second
+    * argument `convert` is true, a convertible type is considered a
+    * a subtype (defaults to false).
+    */
+   joinTypes(types, convert) {
+      let join = ''
+      for (const type of types) {
+         join = this._joinTypes(join, type, convert)
+      }
+      return join
+   }
+   /* helper for above */
+   _joinTypes(typeA, typeB, convert) {
+      if (!typeA) return typeB
+      if (!typeB) return typeA
+      if (typeA === typeB) return typeA
+      const subber = convert ? this._priorTypes : this._subtypes
+      if (subber[typeB].has(typeA)) return typeB
+      /* OK, so we need the most refined supertype of A that contains B:
+       */
+      let nextSuper = typeA
+      while (nextSuper) {
+         if (subber[nextSuper].has(typeB)) return nextSuper
+         nextSuper = this.Types[nextSuper].refines
+      }
+      /* And if conversions are allowed, we have to search the other way too */
+      if (convert) {
+         nextSuper = typeB
+         while (nextSuper) {
+            if (subber[nextSuper].has(typeA)) return nextSuper
+            nextSuper = this.Types[nextSuper].refines
+         }
+      }
+      return 'any'
+   }
    /* Returns a list of all types that have been mentioned in the
     * signatures of operations, but which have not actually been installed:
     */
@@ -530,30 +575,94 @@ export default class PocomathInstance {
          const signature = substituteInSig(
             trimSignature, theTemplateParam, 'any')
          /* The catchall signature has to detect the actual type of the call
-          * and add the new instantiations
+          * and add the new instantiations. We should really be using the
+          * typed-function parser to do the manipulations below, but we don't
+          * have access. The firs section prepares the type inference data:
           */
-         const argTypes = trimSignature.split(',')
+         const parTypes = trimSignature.split(',')
-         let exemplar = -1
+         const inferences = []
-         for (let i = 0; i < argTypes.length; ++i) {
+         const typer = entity => this.typeOf(entity)
-            const argType = argTypes[i].trim()
+         let ambiguous = true
-            if (argType === theTemplateParam) {
+         for (let parType of parTypes) {
-               exemplar = i
+            parType = parType.trim()
-               break
+            if (parType.slice(0,3) === '...') {
+               parType = parType.slice(3).trim()
+            }
+            if (parType === theTemplateParam) {
+               inferences.push(typer)
+               ambiguous = false
+            } else {
+               inferences.push(false)
             }
          }
-         if (exemplar < 0) {
+         if (ambiguous) {
             throw new SyntaxError(
                `Cannot find template parameter in ${rawSignature}`)
          }
+         /* Now build the catchall implementation */
          const self = this
          const patch = (refs) => (...args) => {
-            const example = args[exemplar]
+            /* First infer the type we actually should have been called for */
-            const instantiateFor = self.typeOf(example)
+            let i = -1
+            let j = -1
+            /* collect the arg types */
+            const argTypes = []
+            for (const arg of args) {
+               ++j
+               // in case of rest parameter, reuse last parameter type:
+               if (i < inferences.length - 1) ++i
+               if (inferences[i]) {
+                  const argType = inferences[i](arg)
+                  if (!argType || argType === 'any') {
+                     throw TypeError(
+                        `Type inference failed for argument ${j} of ${name}`)
+                  }
+                  argTypes.push(argType)
+               }
+            }
+            if (argTypes.length === 0) {
+               throw TypeError('Type inference failed for' + name)
+            }
+            let usedConversions = false
+            let instantiateFor = self.joinTypes(argTypes)
+            if (instantiateFor === 'any') {
+               usedConversions = true
+               instantiateFor = self.joinTypes(argTypes, usedConversions)
+               if (instantiateFor === 'any') {
+                  throw TypeError('No common type for arguments to ' + name)
+               }
+            }
+            /* Transform the arguments if we used any conversions: */
+            if (usedConversions) {
+               i = - 1
+               for (j = 0; j < args.length; ++j) {
+                  if (i < parTypes.length - 1) ++i
+                  const wantType = substituteInSig(
+                     parTypes[i], theTemplateParam, instantiateFor)
+                  if (wantType !== parTypes[i]) {
+                     args[j] = self._typed.convert(args[j], wantType)
+                  }
+               }
+            }
+            /* Arrange that the desired instantiation will be there next
+             * time so we don't have to go through that again for this type
+             */
             refs[theTemplateParam] = instantiateFor
             behavior.instantiations.add(instantiateFor)
             self._invalidate(name)
-            // And for now, we have to rely on the "any" implementation. Hope
+            // And update refs because we now know the type we're instantiating
-            // it matches the instantiated one!
+            // for:
+            for (const dep of behavior.uses) {
+               let [func, needsig] = dep.split(/[()]/)
+               if (needsig && self._typed.isTypedFunction(refs[dep])) {
+                  const subsig = substituteInSig(
+                     needsig, theTemplateParam, instantiateFor)
+                  if (subsig !== needsig) {
+                     refs[dep] = self._typed.find(refs[dep], subsig)
+                  }
+               }
+            }
+            // Finally ready to make the call.
             return behavior.does(refs)(...args)
          }
          this._addTFimplementation(

test/custom.mjs

@@ -8,6 +8,7 @@ import * as complex from '../src/complex/all.mjs'
 import * as complexAdd from '../src/complex/add.mjs'
 import * as complexNegate from '../src/complex/negate.mjs'
 import * as complexComplex from '../src/complex/complex.mjs'
+import * as bigintAdd from '../src/bigint/add.mjs'
 import * as concreteSubtract from '../src/generic/subtract.concrete.mjs'
 import * as genericSubtract from '../src/generic/subtract.mjs'
 import extendToComplex from '../src/complex/extendToComplex.mjs'
@@ -112,4 +113,25 @@ describe('A custom instance', () => {
          math.complex(1n, -3n))
    })
 
+   it("instantiates templates correctly", () => {
+      const inst = new PocomathInstance('InstantiateTemplates')
+      inst.install(numberAdd)
+      inst.install({typeMerge: {'T,T': ({T}) => (t,u) => 'Merge to ' + T }})
+      assert.strictEqual(inst.typeMerge(7,6.28), 'Merge to number')
+      assert.strictEqual(inst.typeMerge(7,6), 'Merge to NumInt')
+      assert.strictEqual(inst.typeMerge(7.35,6), 'Merge to number')
+      inst.install(complexAdd)
+      inst.install(complexComplex)
+      inst.install(bigintAdd)
+      assert.strictEqual(
+         inst.typeMerge(6n, inst.complex(3n, 2n)),
+         'Merge to GaussianInteger')
+      assert.strictEqual(
+         inst.typeMerge(3, inst.complex(4.5,2.1)),
+         'Merge to Complex')
+      // The following is the current behavior, since both `3+0i` and `3n + 0ni`
+      // are Complex, but it is unfortunate and hopefully it will be fixed
+      // with templates:
+      assert.strictEqual(inst.typeMerge(3, 3n), 'Merge to Complex')
+   })
 })