src/bigint/negate.mjs

@@ -1,3 +1,4 @@
+import Returns from '../core/Returns.mjs'
 export * from './Types/bigint.mjs'
 
-export const negate = {bigint: () => b => -b}
+export const negate = {bigint: () => Returns('bigint', b => -b)}

src/complex/Types/Complex.mjs

@@ -1,3 +1,4 @@
+import {Returns, returnTypeOf} from '../../core/Returns.mjs'
 import PocomathInstance from '../../core/PocomathInstance.mjs'
 
 const Complex = new PocomathInstance('Complex')
@@ -21,7 +22,12 @@ Complex.installType('Complex<T>', {
 })
 
 Complex.promoteUnary = {
-   'Complex<T>': ({'self(T)': me, complex}) => z => complex(me(z.re), me(z.im))
+   'Complex<T>': ({
+      T,
+      'self(T)': me,
+      complex
+   }) => Returns(
+      `Complex<${returnTypeOf(me)}>`, z => complex(me(z.re), me(z.im)))
 }
 
 export {Complex}

src/complex/add.mjs

@@ -1,8 +1,10 @@
+import Returns from '../core/Returns.mjs'
 export * from './Types/Complex.mjs'
 
 export const add = {
    'Complex<T>,Complex<T>': ({
+      T,
       'self(T,T)': me,
       'complex(T,T)': cplx
-   }) => (w,z) => cplx(me(w.re, z.re), me(w.im, z.im))
+   }) => Returns(`Complex<${T}>`, (w,z) => cplx(me(w.re, z.re), me(w.im, z.im)))
 }

src/complex/complex.mjs

@@ -1,3 +1,4 @@
+import Returns from '../core/Returns.mjs'
 export * from './Types/Complex.mjs'
 export * from '../generic/Types/generic.mjs'
 
@@ -6,15 +7,16 @@ export const complex = {
     * have a numeric/scalar type, e.g. by implementing subtypes in
     * typed-function
     */
-   'undefined': () => u => u,
-   'undefined,any': () => (u, y) => u,
-   'any,undefined': () => (x, u) => u,
-   'undefined,undefined': () => (u, v) => u,
-   'T,T': () => (x, y) => ({re: x, im: y}),
+   'undefined': () => Returns('undefined', u => u),
+   'undefined,any': () => Returns('undefined', (u, y) => u),
+   'any,undefined': () => Returns('undefined', (x, u) => u),
+   'undefined,undefined': () => Returns('undefined', (u, v) => u),
+   'T,T': ({T}) => Returns(`Complex<${T}>`, (x, y) => ({re: x, im: y})),
    /* Take advantage of conversions in typed-function */
    // 'Complex<T>': () => z => z
    /* But help out because without templates built in to typed-function,
     * type inference turns out to be too hard
     */
-   'T': ({'zero(T)': zr}) => x => ({re: x, im: zr(x)})
+   'T': ({T, 'zero(T)': zr}) => Returns(
+      `Complex<${T}>`, x => ({re: x, im: zr(x)}))
 }

src/core/PocomathInstance.mjs

@@ -8,14 +8,15 @@ import {typeListOfSignature, typesOfSignature, subsetOfKeys} from './utils.mjs'
 const anySpec = {} // fixed dummy specification of 'any' type
 
 const theTemplateParam = 'T' // First pass: only allow this one exact parameter
+const restTemplateParam = `...${theTemplateParam}`
 const templateFromParam = 'U' // For defining covariant conversions
 
 /* Returns a new signature just like sig but with the parameter replaced by
  * the type
  */
-const upperBounds = /\s*[(]=\s*(\w*)\s*/g
+const upperBounds = /\s*(\S*)\s*:\s*(\w*)\s*/g
 function substituteInSignature(signature, parameter, type) {
-   const sig = signature.replaceAll(upperBounds, '')
+   const sig = signature.replaceAll(upperBounds, '$1')
    const pattern = new RegExp("\\b" + parameter + "\\b", 'g')
    return sig.replaceAll(pattern, type)
 }
@@ -53,6 +54,14 @@ export default class PocomathInstance {
       this._typed = typed.create()
       this._typed.clear()
       this._typed.addTypes([{name: 'ground', test: () => true}])
+      const me = this
+      const myTyped = this._typed
+      this._typed.onMismatch = (name, args, sigs) => {
+         if (me._invalid.has(name)) {
+            return me[name](...args) // rebuild implementation and try again
+         }
+         myTyped.throwMismatchError(name, args, sigs)
+      }
       /* List of types installed in the instance. We start with just dummies
        * for the 'any' type and for type parameters:
        */
@@ -201,11 +210,13 @@ export default class PocomathInstance {
 
    /* Determine the return type of an operation given an input signature */
    returnTypeOf(operation, signature) {
-      if (typeof operation === 'string') {
-         operation = this[operation]
+      for (const type of typeListOfSignature(signature)) {
+         this._maybeInstantiate(type)
       }
-      if (!(this._typed.isTypedFunction(operation))) return 'any'
-      const details = this._typed.findSignature(operation, signature)
+      if (typeof operation !== 'string') {
+         operation = operation.name
+      }
+      const details = this._pocoFindSignature(operation, signature)
       return returnTypeOf(details.fn, signature, this)
    }
 
@@ -650,7 +661,7 @@ export default class PocomathInstance {
          /* Check if it's an ordinary non-template signature */
          let explicit = true
          for (const type of typesOfSignature(rawSignature)) {
-            for (const word of type.split(/[<>(=\s]/)) {
+            for (const word of type.split(/[<>:\s]/)) {
                if (this._templateParam(word)) {
                   explicit = false
                   break
@@ -667,7 +678,7 @@ export default class PocomathInstance {
          upperBounds.lastIndex = 0
          let ubType = upperBounds.exec(rawSignature)
          if (ubType) {
-            ubType = ubType[1]
+            ubType = ubType[2]
             if (!ubType in this.Types) {
                throw new TypeError(
                   `Unknown type upper bound '${ubType}' in '${rawSignature}'`)
@@ -681,7 +692,9 @@ export default class PocomathInstance {
          let instantiationSet = new Set()
          for (const instType of behavior.instantiations) {
             instantiationSet.add(instType)
-            for (const other of this.subtypesOf(instType)) {
+            const otherTypes =
+                  ubType ? this.subtypesOf(instType) : this._priorTypes[instType]
+            for (const other of otherTypes) {
                instantiationSet.add(other)
             }
          }
@@ -828,6 +841,7 @@ export default class PocomathInstance {
             /* Generate the list of actual wanted types */
             const wantTypes = parTypes.map(type => substituteInSignature(
                type, theTemplateParam, instantiateFor))
+            const wantSig = wantTypes.join(',')
             /* Now we have to add any actual types that are relevant
              * to this invocation. Namely, that would be every formal parameter
              * type in the invocation, with the parameter template instantiated
@@ -890,9 +904,22 @@ export default class PocomathInstance {
             }
             // Finally ready to make the call.
             const implementation = behavior.does(innerRefs)
-            // Could do something with return type information here
+            // We can access return type information here
+            // And in particular, if it's a template, we should try to
+            // instantiate it:
+            const returnType = returnTypeOf(implementation, wantSig, self)
+            const instantiated = self._maybeInstantiate(returnType)
+            if (instantiated) {
+               const tempBase = instantiated.split('<',1)[0]
+               self._invalidateDependents(':' + tempBase)
+            }
             return implementation(...args)
          }
+         Object.defineProperty(patch, 'name', {value: `${name}(${signature})`})
+         // TODO: Decorate patch with a function that calculates the
+         // correct return type a priori. Deferring because unclear what
+         // aspects will be merged into typed-function.
+         //
          // The actual uses value needs to be a set:
          const outerUses = new Set(Object.values(simplifiedUses))
          this._addTFimplementation(
@@ -905,19 +932,11 @@ export default class PocomathInstance {
       const badSigs = new Set()
       for (const sig in tf_imps) {
          for (const type of typeListOfSignature(sig)) {
-            if (type.includes('<')) {
-               // 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)
-               if (base.slice(0,3) === '...') {
-                  base = base.slice(3)
-               }
-               if (this.instantiateTemplate(base, arg) === undefined) {
+            if (this._maybeInstantiate(type) === undefined) {
                badSigs.add(sig)
             }
          }
       }
-      }
       for (const badSig of badSigs) {
          delete tf_imps[badSig]
       }
@@ -926,6 +945,29 @@ export default class PocomathInstance {
       return tf
    }
 
+   /* Takes an arbitrary type and performs an instantiation if necessary.
+    * @param {string} type  The type to instantiate
+    * @param {string | bool | undefined }
+    *     Returns the name of the type if an instantiation occurred, false
+    *     if the type was already present, and undefined if the type can't
+    *     be satisfied (because it is not the name of a type or it is nested
+    *     too deep.
+    */
+   _maybeInstantiate(type) {
+      if (type.slice(0,3) === '...') {
+         type = type.slice(3)
+      }
+      if (!(type.includes('<'))) {
+         // Not a template, so just check if type exists
+         if (type in this.Types) return false // already there
+         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)
+      return this.instantiateTemplate(base, arg)
+   }
+
    /* Adapts Pocomath-style behavior specification (uses, does) for signature
     * to typed-function implementations and inserts the result into plain
     * object imps
@@ -985,7 +1027,7 @@ export default class PocomathInstance {
             } else {
                // can bundle up func, and grab its signature if need be
                let destination = this[func]
-               if (destination &&needsig) {
+               if (destination && needsig) {
                   destination = this._pocoresolve(func, needsig)
                }
                refs[dep] = destination
@@ -996,6 +1038,7 @@ export default class PocomathInstance {
          imps[signature] = this._typed.referToSelf(self => {
             refs.self = self
             const implementation = does(refs)
+            Object.defineProperty(implementation, 'name', {value: does.name})
             // What are we going to do with the return type info in here?
             return implementation
          })
@@ -1171,16 +1214,17 @@ export default class PocomathInstance {
          const otherTypeList = typeListOfSignature(otherSig)
          if (typeList.length !== otherTypeList.length) continue
          let allMatch = true
+         let paramBound = 'ground'
          for (let k = 0; k < typeList.length; ++k) {
             let myType = typeList[k]
             let otherType = otherTypeList[k]
             if (otherType === theTemplateParam) {
-               otherTypeList[k] = 'ground'
-               otherType = 'ground'
+               otherTypeList[k] = paramBound
+               otherType = paramBound
             }
-            if (otherType === '...T') {
-               otherTypeList[k] = '...ground'
-               otherType = 'ground'
+            if (otherType === restTemplateParam) {
+               otherTypeList[k] = `...${paramBound}`
+               otherType = paramBound
             }
             const adjustedOtherType = otherType.replaceAll(
                `<${theTemplateParam}>`, '')
@@ -1190,6 +1234,13 @@ export default class PocomathInstance {
             }
             if (myType.slice(0,3) === '...') myType = myType.slice(3)
             if (otherType.slice(0,3) === '...') otherType = otherType.slice(3)
+            const otherBound = upperBounds.exec(otherType)
+            if (otherBound) {
+               paramBound = otherBound[2]
+               otherType = paramBound
+               otherTypeList[k] = otherBound[1].replaceAll(
+                  theTemplateParam, paramBound)
+            }
             if (otherType === 'any') continue
             if (otherType === 'ground') continue
             if (!(otherType in this.Types)) {
@@ -1218,25 +1269,49 @@ export default class PocomathInstance {
       return foundSig
    }
 
-   _pocoresolve(name, sig, typedFunction) {
+   _pocoFindSignature(name, sig, typedFunction) {
       if (!this._typed.isTypedFunction(typedFunction)) {
          typedFunction = this[name]
       }
       let result = undefined
+      if (!this._typed.isTypedFunction(typedFunction)) {
+         return result
+      }
       try {
-         result = this._typed.find(typedFunction, sig, {exact: true})
+         result = this._typed.findSignature(typedFunction, sig, {exact: true})
       } catch {
       }
       if (result) return result
       const foundsig = this._findSubtypeImpl(name, this._imps[name], sig)
-      if (foundsig) return this._typed.find(typedFunction, foundsig)
-      // Make sure bundle is up-to-date:
+      if (foundsig) return this._typed.findSignature(typedFunction, foundsig)
+      const wantTypes = typeListOfSignature(sig)
+      for (const [implSig, details]
+           of typedFunction._typedFunctionData.signatureMap) {
+         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
+         }
+         if (allMatched) return details
+      }
+      // Hmm, no luck. Make sure bundle is up-to-date and retry:
       typedFunction = this[name]
       try {
-         result = this._typed.find(typedFunction, sig)
+         result = this._typed.findSignature(typedFunction, sig)
       } catch {
       }
-      if (result) return result
+      return result
+   }
+   
+   _pocoresolve(name, sig, typedFunction) {
+      if (!this._typed.isTypedFunction(typedFunction)) {
+         typedFunction = this[name]
+      }
+      const result = this._pocoFindSignature(name, sig, typedFunction)
+      if (result) return result.implementation
       // total punt, revert to typed-function resolution on every call;
       // hopefully this happens rarely:
       return typedFunction

src/core/utils.mjs

@@ -8,6 +8,8 @@ export function subsetOfKeys(set, obj) {
 
 /* Returns a list of the types mentioned in a typed-function signature */
 export function typeListOfSignature(signature) {
+   signature = signature.trim()
+   if (!signature) return []
    return signature.split(',').map(s => s.trim())
 }
 

src/number/add.mjs

@@ -1,3 +1,8 @@
+import Returns from '../core/Returns.mjs'
 export * from './Types/number.mjs'
 
-export const add = {'number,number': () => (m,n) => m+n}
+export const add = {
+    // Note the below assumes that all subtypes of number that will be defined
+    // are closed under addition!
+    'T:number, T': ({T}) => Returns(T, (m,n) => m+n)
+}

src/number/negate.mjs

@@ -2,5 +2,5 @@ import Returns from '../core/Returns.mjs'
 export * from './Types/number.mjs'
 
 export const negate = {
-   'T (= number': ({T}) => Returns(T, n => -n)
+   'T:number': ({T}) => Returns(T, n => -n)
 }

src/number/zero.mjs

@@ -1,3 +1,4 @@
+import Returns from '../core/Returns.mjs'
 export * from './Types/number.mjs'
 
-export const zero = {number: () => () => 0}
+export const zero = {number: () => Returns('NumInt', () => 0)}

src/ops/floor.mjs

@@ -1,3 +1,4 @@
+import Returns from '../core/Returns.mjs'
 import {Complex} from '../complex/Types/Complex.mjs'
 
 /* Note we don't **export** any types here, so that only the options
@@ -5,17 +6,20 @@ import {Complex} from '../complex/Types/Complex.mjs'
  */
 
 export const floor = {
-   bigint: () => x => x,
-   NumInt: () => x => x, // Because Pocomath isn't part of typed-function, or
-   'Complex<bigint>': () => x => x, // at least have access to the real
-   // typed-function parse, we unfortunately can't coalesce these into one
-   // entry with type `bigint|NumInt|GaussianInteger` because they couldn't
-   // be separately activated then
+   /* Because Pocomath isn't part of typed-function, nor does it have access
+    * to the real typed-function parse, we unfortunately can't coalesce the
+    * first several implementations into one entry with type
+    * `bigint|NumInt|GaussianInteger` because then they couldn't
+    * be separately activated
+    */
+   bigint: () => Returns('bigint', x => x),
+   NumInt: () => Returns('NumInt', x => x), 
+   'Complex<bigint>': () => Returns('Complex<bigint>', x => x), 
 
-   number: ({'equalTT(number,number)': eq}) => n => {
+   number: ({'equalTT(number,number)': eq}) => Returns('NumInt', n => {
       if (eq(n, Math.round(n))) return Math.round(n)
       return Math.floor(n)
-   },
+   }),
 
    'Complex<T>': Complex.promoteUnary['Complex<T>'],
 
@@ -25,6 +29,6 @@ export const floor = {
    BigNumber: ({
       'round(BigNumber)': rnd,
       'equal(BigNumber,BigNumber)': eq
-   }) => x => eq(x,round(x)) ? round(x) : x.floor()
+   }) => Returns('BigNumber', x => eq(x,round(x)) ? round(x) : x.floor())
 
 }

test/_pocomath.mjs

@@ -23,6 +23,17 @@ describe('The default full pocomath instance "math"', () => {
    it('can determine the return types of operations', () => {
       assert.strictEqual(math.returnTypeOf('negate', 'number'), 'number')
       assert.strictEqual(math.returnTypeOf('negate', 'NumInt'), 'NumInt')
+      math.negate(math.complex(1.2, 2.8)) // TODO: make this call unnecessary
+      assert.strictEqual(
+         math.returnTypeOf('negate', 'Complex<number>'), 'Complex<number>')
+      assert.strictEqual(math.returnTypeOf('add', 'number,number'), 'number')
+      assert.strictEqual(math.returnTypeOf('add', 'NumInt,NumInt'), 'NumInt')
+      assert.strictEqual(math.returnTypeOf('add', 'NumInt,number'), 'number')
+      assert.strictEqual(math.returnTypeOf('add', 'number,NumInt'), 'number')
+      assert.deepStrictEqual(  // TODO: ditto
+         math.add(3, math.complex(2.5, 1)), math.complex(5.5, 1))
+      assert.strictEqual(
+         math.returnTypeOf('add', 'Complex<number>,NumInt'), 'Complex<number>')
    })
 
    it('can subtract numbers', () => {

test/core/_utils.mjs

@@ -0,0 +1,8 @@
+import assert from 'assert'
+import * as utils from '../../src/core/utils.mjs'
+
+describe('typeListOfSignature', () => {
+   it('returns an empty list for the empty signature', () => {
+      assert.deepStrictEqual(utils.typeListOfSignature(''), [])
+   })
+})