feat: Template types for Pocomath

Tuple<T> and a couple of functions on it are now working according to
  the target spec. As desired, no instantiations of a template type
  are made until some function that takes an instantiation is called.

src/core/PocomathInstance.mjs

@@ -184,6 +184,9 @@ export default class PocomathInstance {
          if (type === 'any' || this._templateParam(type)) continue
          this.installType(type, spec)
       }
+      for (const [base, info] of Object.entries(other._templateTypes)) {
+         this._installTemplateType(info.type, info.spec)
+      }
       const migrateImps = {}
       for (const operator in other._imps) {
          if (operator != 'typeOf') { // skip the builtin, we already have it
@@ -380,6 +383,7 @@ export default class PocomathInstance {
    _joinTypes(typeA, typeB, convert) {
       if (!typeA) return typeB
       if (!typeB) return typeA
+      if (typeA === 'any' || typeB === 'any') return 'any'
       if (typeA === typeB) return typeA
       const subber = convert ? this._priorTypes : this._subtypes
       if (subber[typeB].has(typeA)) return typeB
@@ -612,12 +616,13 @@ export default class PocomathInstance {
                }
                return behavior.does(innerRefs)
             }
-            this._addTFimplementation(tf_imps, signature, {uses, does: patch})
+            this._addTFimplementation(
+               tf_imps, signature, {uses, does: patch})
          }
          /* Now add the catchall signature */
          let templateCall = `<${theTemplateParam}>`
          /* Relying here that the base of 'Foo<T>' is 'Foo': */
-         let baseSignature = substituteInSig(trimSignature, templateCall, '')
+         let baseSignature = trimSignature.replaceAll(templateCall, '')
          /* Any remaining template params are top-level */
          const signature = substituteInSig(
             baseSignature, theTemplateParam, 'any')
@@ -626,6 +631,7 @@ export default class PocomathInstance {
           * First, prepare the type inference data:
           */
          const parTypes = trimSignature.split(',')
+         const restParam = (parTypes[parTypes.length-1].slice(0,3) === '...')
          const topTyper = entity => this.typeOf(entity)
          const inferences = parTypes.map(
             type => generateTypeExtractor(
@@ -638,10 +644,31 @@ export default class PocomathInstance {
             throw new SyntaxError(
                `Cannot find template parameter in ${rawSignature}`)
          }
+         /* And eliminate template parameters from the dependencies */
+         const simplifiedUses = {}
+         for (const dep of behavior.uses) {
+            let [func, needsig] = dep.split(/[()]/)
+            if (needsig) {
+               const subsig = substituteInSig(needsig, theTemplateParam, '')
+               if (subsig === needsig) {
+                  simplifiedUses[dep] = dep
+               } else {
+                  simplifiedUses[dep] = func
+               }
+            } else {
+               simplifiedUses[dep] = dep
+            }
+         }
          /* Now build the catchall implementation */
          const self = this
          const patch = (refs) => (...args) => {
-            /* First infer the type we actually should have been called for */
+            /* We unbundle the rest arg if there is one */
+            const regLength = args.length - 1
+            if (restParam) {
+               const restArgs = args.pop()
+               args = args.concat(restArgs)
+            }
+            /* Now infer the type we actually should have been called for */
             let i = -1
             let j = -1
             /* collect the arg types */
@@ -652,10 +679,15 @@ export default class PocomathInstance {
                if (i < inferences.length - 1) ++i
                if (inferences[i]) {
                   const argType = inferences[i](arg)
-                  if (!argType || argType === 'any') {
+                  if (!argType) {
                      throw TypeError(
                         `Type inference failed for argument ${j} of ${name}`)
                   }
+                  if (argType === 'any') {
+                     throw TypeError(
+                        `In call to ${name}, incompatible template arguments: `
+                           + args.map(a => JSON.stringify(a)).join(', '))
+                  }
                   argTypes.push(argType)
                }
             }
@@ -669,7 +701,11 @@ export default class PocomathInstance {
                instantiateFor = self.joinTypes(argTypes, usedConversions)
                if (instantiateFor === 'any') {
                   // Need a more informative error message here
-                  throw TypeError('No common type for arguments to ' + name)
+                  throw TypeError(
+                     `In call to ${name}, no type unifies arguments `
+                        + args.toString() + '; of types ' + argTypes.toString()
+                        + '; note each consecutive pair must unify to a '
+                        + 'supertype of at least one of them')
                }
             }
             /* Generate the list of actual wanted types */
@@ -681,9 +717,9 @@ export default class PocomathInstance {
              * by instantiateFor, and for all of instantiateFor's "prior types"
              */
             for (j = 0; j < parTypes.length; ++j) {
-               if (wantTypes[i] !== parTypes[i] && wantTypes.includes('<')) {
+               if (wantTypes[j] !== parTypes[j] && wantTypes[j].includes('<')) {
                   // actually used the param and is a template
-                  self._ensureTemplateTypes(parTypes[i], instantiateFor)
+                  self._ensureTemplateTypes(parTypes[j], instantiateFor)
                }
             }
             /* Transform the arguments if we used any conversions: */
@@ -691,13 +727,23 @@ export default class PocomathInstance {
                i = - 1
                for (j = 0; j < args.length; ++j) {
                   if (i < parTypes.length - 1) ++i
-                  const wantType = substituteInSig(
+                  let wantType = parTypes[i]
-                     parTypes[i], theTemplateParam, instantiateFor)
+                  if (wantType.slice(0,3) === '...') {
+                     wantType = wantType.slice(3)
+                  }
+                  wantType = substituteInSig(
+                     wantType, theTemplateParam, instantiateFor)
                   if (wantType !== parTypes[i]) {
                      args[j] = self._typed.convert(args[j], wantType)
                   }
                }
             }
+            /* Finally reassemble the rest args if there were any */
+            if (restParam) {
+               const restArgs = args.slice(regLength)
+               args = args.slice(0,regLength)
+               args.push(restArgs)
+            }
             /* Arrange that the desired instantiation will be there next
              * time so we don't have to go through that again for this type
              */
@@ -706,22 +752,32 @@ export default class PocomathInstance {
             self._invalidate(name)
             // And update refs because we now know the type we're instantiating
             // for:
-            for (const dep of behavior.uses) {
+            const innerRefs = {}
+            for (const dep in simplifiedUses) {
+               const simplifiedDep = simplifiedUses[dep]
+               if (dep === simplifiedDep) {
+                  innerRefs[dep] = refs[dep]
+               } else {
                   let [func, needsig] = dep.split(/[()]/)
-               if (needsig && self._typed.isTypedFunction(refs[dep])) {
+                  if (self._typed.isTypedFunction(refs[simplifiedDep])) {
                      const subsig = substituteInSig(
                         needsig, theTemplateParam, instantiateFor)
-                  if (subsig !== needsig) {
+                     innerRefs[dep] = self._typed.find(
-                     refs[dep] = self._typed.find(refs[dep], subsig)
+                        refs[simplifiedDep], subsig)
+                  } else {
+                     innerRefs[dep] = refs[simplifiedDep]
                   }
                }
             }
             // Finally ready to make the call.
-            return behavior.does(refs)(...args)
+            return behavior.does(innerRefs)(...args)
          }
+         // The actual uses value needs to be a set:
+         const outerUses = new Set(Object.values(simplifiedUses))
          this._addTFimplementation(
-            tf_imps, signature, {uses: behavior.uses, does: patch})
+            tf_imps, signature, {uses: outerUses, does: patch})
       }
+      this._correctPartialSelfRefs(tf_imps)
       const tf = this._typed(name, tf_imps)
       Object.defineProperty(this, name, {configurable: true, value: tf})
       return tf
@@ -742,9 +798,17 @@ export default class PocomathInstance {
       let part_self_references = []
       for (const dep of uses) {
          let [func, needsig] = dep.split(/[()]/)
-         const needTypes = needsig ? typesOfSignature(needsig) : new Set()
+         /* Safety check that can perhaps be removed:
-         /* For now, punt on template parameters */
+          * Verify that the desired signature has been fully grounded:
-         if (needTypes.has(theTemplateParam)) needsig = ''
+          */
+         if (needsig) {
+            const trysig = substituteInSig(needsig, theTemplateParam, '')
+            if (trysig !== needsig) {
+               throw new Error(
+                  'Attempt to add a template implementation: ' +
+                     `${signature} with dependency ${dep}`)
+            }
+         }
          if (func === 'self') {
             if (needsig) {
                if (full_self_referential) {
@@ -791,17 +855,77 @@ export default class PocomathInstance {
          return
       }
       if (part_self_references.length) {
-         imps[signature] = this._typed.referTo(
+         /* There is an obstruction here. The list part_self_references
-            ...part_self_references, (...impls) => {
+          * might contain a signature that requires conversion for self to
+          * handle. But I advocated this not be allowed in typed.referTo, which
+          * made sense for human-written functions, but is unfortunate now.
+          * So we have to defer creating these and correct them later, at
+          * least until we can add an option to typed-function.
+          */
+         imps[signature] = {
+            deferred: true,
+            builtRefs: refs,
+            sigDoes: does,
+            psr: part_self_references
+         }
+         return
+      }
+      imps[signature] = does(refs)
+   }
+
+   _correctPartialSelfRefs(imps) {
+      for (const aSignature in imps) {
+         if (!(imps[aSignature].deferred)) continue
+         const part_self_references = imps[aSignature].psr
+         const corrected_self_references = []
+         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)
+               continue
+            }
+            // No exact match, have to try to get one that matches with
+            // subtypes since the whole conversion thing in typed-function
+            // is too complicated to reproduce
+            let foundSig = false
+            const typeList = typesOfSignature(neededSig)
+            for (const otherSig in imps) {
+               const otherTypeList = typesOfSignature(otherSig)
+               if (typeList.length !== otherTypeList.length) continue
+               const allMatch = true
+               for (let k = 0; k < typeList.length; ++k) {
+                  if (this._subtypes[otherTypeList[k]].has(typeList[k])) {
+                     continue
+                  }
+                  allMatch = false
+                  break
+               }
+               if (allMatch) {
+                  foundSig = otherSig
+                  break
+               }
+            }
+            if (foundSig) {
+               corrected_self_references.push(foundSig)
+            } else {
+               throw new Error(
+                  'Implement inexact self-reference in typed-function for '
+                     + neededSig)
+            }
+         }
+         const refs = imps[aSignature].builtRefs
+         const does = imps[aSignature].sigDoes
+         imps[aSignature] = this._typed.referTo(
+            ...corrected_self_references, (...impls) => {
                for (let i = 0; i < part_self_references.length; ++i) {
                   refs[`self(${part_self_references[i]})`] = impls[i]
                }
                return does(refs)
             }
          )
-         return
       }
-      imps[signature] = does(refs)
    }
 
    /* This function analyzes the template and makes sure the
@@ -817,7 +941,7 @@ export default class PocomathInstance {
       }
       let instantiations
       if (this._templateParam(arg)) { // 1st-level template
-         instantiations = new Set(this._priorTypes(type))
+         instantiations = new Set(this._priorTypes[type])
          instantiations.add(type)
       } else { // nested template
          instantiations = this._ensureTemplateTypes(arg, type)
@@ -825,7 +949,7 @@ export default class PocomathInstance {
       const resultingTypes = new Set()
       for (const iType of instantiations) {
          const resultType = this._maybeAddTemplateType(base, iType)
-         if (resultType) resultingTypes.push(resultType)
+         if (resultType) resultingTypes.add(resultType)
       }
       return resultingTypes
    }
@@ -840,7 +964,7 @@ export default class PocomathInstance {
       // OK, need to generate the type from the template
       // Set up refines, before, test, and from
       const newTypeSpec = {}
-      const template = this._templateTypes[base]
+      const template = this._templateTypes[base].spec
       if (!template) {
          throw new Error(
             `Implementor error in _maybeAddTemplateType ${base} ${instantiator}`)
@@ -848,6 +972,7 @@ export default class PocomathInstance {
       const instantiatorSpec = this.Types[instantiator]
       if (instantiatorSpec.refines) {
          // Assuming all templates are covariant, for now
+         this._maybeAddTemplateType(base, instantiatorSpec.refines)
          newTypeSpec.refines = `${base}<${instantiatorSpec.refines}>`
       }
       let beforeTypes = []
@@ -867,9 +992,10 @@ export default class PocomathInstance {
       if (template.from) {
          newTypeSpec.from = {}
          for (let source in template.from) {
-            source = substituteInSig(source, theTemplateParam, instantiator)
+            const instSource = substituteInSig(
-            const usesFromParam = false
+               source, theTemplateParam, instantiator)
-            for (const word of source.split(/[<>]/)) {
+            let usesFromParam = false
+            for (const word of instSource.split(/[<>]/)) {
                if (word === templateFromParam) {
                   usesFromParam = true
                   break
@@ -878,12 +1004,12 @@ export default class PocomathInstance {
             if (usesFromParam) {
                for (const iFrom in instantiatorSpec.from) {
                   const finalSource = substituteInSig(
-                     source, templateFromParam, iFrom)
+                     instSource, templateFromParam, iFrom)
-                  newTypeSpec[finalSource] = template.from[source](
+                  newTypeSpec.from[finalSource] = template.from[source](
                      instantiatorSpec.from[iFrom])
                }
             } else {
-               newTypeSpec[source] = template.from[source]
+               newTypeSpec.from[instSource] = template.from[source]
             }
          }
       }

src/core/extractors.mjs

@@ -32,9 +32,9 @@ export function generateTypeExtractor(
    if (!(base in templates)) return false // unknown template
    const arg = type.slice(base.length+1, -1)
    const argExtractor = generateTypeExtractor(
-      arg, param, topTyper, typeJointer, templates)
+      arg, param, topTyper, typeJoiner, templates)
    if (!argExtractor) return false
-   return templates[base].infer({
+   return templates[base].spec.infer({
       typeOf: argExtractor,
       joinTypes: typeJoiner
    })

src/pocomath.mjs

@@ -8,6 +8,7 @@ import * as tuple from './tuple/native.mjs'
 const tupleReady = {
     Tuple: tuple.Tuple,
     equal: tuple.equal,
+    isZero: tuple.isZero,
     length: tuple.length,
     tuple: tuple.tuple
 }

src/tuple/Types/Tuple.mjs

@@ -8,13 +8,11 @@ Tuple.installType('Tuple', {
 })
 // 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
+   // We are assuming 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 => {
+   infer: ({typeOf, joinTypes}) => t => joinTypes(t.elts.map(typeOf)),
-      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>

src/tuple/isZero.mjs

@@ -1,6 +1,8 @@
 export {Tuple} from './Types/Tuple.mjs'
 
 export const isZero = {
-   'Tuple<T>': ({'self(T)': me}) => t => t.elts.every(isZero)
+   'Tuple<T>': ({'self(T)': me}) => 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

@@ -3,4 +3,4 @@ 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})}
+export const tuple = {'...T': () => args => ({elts: args})}

test/tuple/_native.mjs

@@ -3,7 +3,26 @@ 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)
+      assert.strictEqual(math.length(math.tuple(3, 5.2, 2)), 3)
+   })
+
+   it('does not allow unification by converting consecutive arguments', () => {
+      assert.throws(() => math.tuple(3, 5.2, 2n), /TypeError.*unif/)
+      // Hence, the order matters in a slightly unfortunate way,
+      // but I think being a little ragged in these edge cases is OK:
+      assert.throws(
+         () => math.tuple(3, 2n, math.complex(5.2)),
+         /TypeError.*unif/)
+      assert.deepStrictEqual(
+         math.tuple(3, math.complex(2n), 5.2),
+         {elts: [math.complex(3), math.complex(2n), math.complex(5.2)]})
+   })
+
+   it('can be tested for zero', () => {
+      assert.strictEqual(math.isZero(math.tuple(0,1)), false)
+      assert.strictEqual(math.isZero(math.tuple(0n,0n,0n,0n)), true)
+      assert.strictEqual(math.isZero(math.tuple(0,0.001,0)), false)
+      assert.strictEqual(math.isZero(math.tuple(0,math.complex(0,0))), true)
    })
 
 })