feat: Introduce BooleanT and boolean functions (#17)

This PR adds a boolean section, as well as an isNaN predicate on numbers. In a TypeDispatcher, when BooleanT is present, isNaN returns a BooleanT. However, in a numbers-only TypeDispatcher, it returns 1 or 0 instead. Moreover, when booleans are subsequently added to a numbers-only instance, isNaN properly reconfigures itself to return BooleanT.

No predicates that depend on approximate equality testing or a configuration object are implemented in this PR.

This PR also implements type matching and dispatching with implicit conversions, and adds an implicit conversion from BooleanT to NumberT.

Reviewed-on: #17
Co-authored-by: Glen Whitney <glen@studioinfinity.org>
Co-committed-by: Glen Whitney <glen@studioinfinity.org>

package.json5

@@ -18,4 +18,7 @@
   devDependencies: {
     mocha: '^11.1.0',
   },
+  dependencies: {
+    'array-keyed-map': '^2.1.3',
+  },
 }

pnpm-lock.yaml

@@ -7,6 +7,10 @@ settings:
 importers:
 
   .:
+    dependencies:
+      array-keyed-map:
+        specifier: ^2.1.3
+        version: 2.1.3
     devDependencies:
       mocha:
         specifier: ^11.1.0
@@ -49,6 +53,9 @@ packages:
   argparse@2.0.1:
     resolution: {integrity: sha512-8+9WqebbFzpX9OR+Wa6O29asIogeRMzcGtAINdpMHHyAg10f05aSFVBbcEqGf/PXw1EjAZ+q2/bEBg3DvurK3Q==}
 
+  array-keyed-map@2.1.3:
+    resolution: {integrity: sha512-JIUwuFakO+jHjxyp4YgSiKXSZeC0U+R1jR94bXWBcVlFRBycqXlb+kH9JHxBGcxnVuSqx5bnn0Qz9xtSeKOjiA==}
+
   balanced-match@1.0.2:
     resolution: {integrity: sha512-3oSeUO0TMV67hN1AmbXsK4yaqU7tjiHlbxRDZOpH0KW9+CeX4bRAaX0Anxt0tx2MrpRpWwQaPwIlISEJhYU5Pw==}
 
@@ -398,6 +405,8 @@ snapshots:
 
   argparse@2.0.1: {}
 
+  array-keyed-map@2.1.3: {}
+
   balanced-match@1.0.2: {}
 
   binary-extensions@2.3.0: {}

src/__test__/numbers.spec.js

@@ -0,0 +1,13 @@
+import assert from 'assert'
+import math from '../numbers.js'
+
+describe('the numbers-only bundle', () => {
+   it('works like regular on number-only functions', () => {
+      assert.strictEqual(math.quotient(5, 3), 1)
+      assert.strictEqual(math.square(-3), 9)
+   })
+   it('uses 1 and 0 instead of true and false', () => {
+      assert.strictEqual(math.isnan(-16.5), 0)
+      assert.strictEqual(math.isnan(NaN), 1)
+   })
+})

src/boolean/BooleanT.js

@@ -0,0 +1,3 @@
+import {Type} from '#core/Type.js'
+
+export const BooleanT = new Type(n => typeof n === 'boolean')

src/boolean/__test__/BooleanT.spec.js

@@ -0,0 +1,24 @@
+import assert from 'assert'
+import {BooleanT} from '../BooleanT.js'
+import math from '#nanomath'
+
+describe('BooleanT Type', () => {
+   it('correctly recognizes booleans', () => {
+      assert(BooleanT.test(true))
+      assert(BooleanT.test(false))
+      assert(!BooleanT.test(null))
+      assert(!BooleanT.test(1))
+   })
+   it('autoconverts to number type', () => {
+      assert.strictEqual(math.abs(false), 0)
+      assert.strictEqual(math.absquare(true), 1)
+      assert.strictEqual(math.add(true, true), 2)
+      assert.strictEqual(math.divide(false, true), 0)
+      assert.strictEqual(math.cbrt(true), 1)
+      assert.strictEqual(math.invert(true), 1)
+      assert.strictEqual(math.multiply(false, false), 0)
+      assert.strictEqual(math.negate(false), -0)
+      assert.strictEqual(math.subtract(false, true), -1)
+      assert.strictEqual(math.quotient(true, true), 1)
+   })
+})

src/boolean/__test__/type.spec.js

@@ -0,0 +1,25 @@
+import assert from 'assert'
+import math from '#nanomath'
+import {Type} from '#core/Type.js'
+
+const boolean = math.boolean
+
+describe('boolean type functions', () => {
+   it('properly converts to boolean', () => {
+      assert.strictEqual(boolean(false), false)
+      assert.strictEqual(boolean(true), true)
+      assert.strictEqual(boolean(0), false)
+      assert.strictEqual(boolean(-0), false)
+      assert.strictEqual(boolean(NaN), false)
+      assert.strictEqual(boolean(Infinity), true)
+      assert.strictEqual(boolean(1e-30), true)
+      assert.strictEqual(boolean(undefined), false)
+      assert.strictEqual(boolean(), false)
+      assert.strictEqual(boolean(math.types.NumberT), true)
+   })
+   it('converts any type to boolean', () => {
+      for (const T in math.types) {
+         if (T instanceof Type) assert(boolean.resolve([T]))
+      }
+   })       
+})

src/boolean/all.js

@@ -0,0 +1,2 @@
+export * as typeDefinition from './BooleanT.js'
+export * as type from './type.js'

src/boolean/type.js

@@ -0,0 +1,14 @@
+import {BooleanT} from './BooleanT.js'
+import {onType} from '#core/helpers.js'
+import {Returns, Type, TypeOfTypes, Undefined} from '#core/Type.js'
+import {NumberT} from '#number/NumberT.js'
+
+const bool = f => Returns(BooleanT, f)
+
+export const boolean = onType(
+   BooleanT, bool(p => p),
+   NumberT, bool(a => !!a),
+   TypeOfTypes, bool(() => true),
+   Undefined, bool(() => false),
+   [], bool(() => false)
+)

src/core/Type.js

@@ -1,10 +1,10 @@
-const typeObject = {} // have to make sure there is only one
-
-export const types = () => typeObject
-
 export class Type {
-   constructor(f) {
+   constructor(f, options = {}) {
       this.test = f
+      this.from = options.from ?? {patterns: []} // mock empty Implementations
+   }
+   toString() {
+      return this.name || `[Type ${this.test}]`
    }
 }
 
@@ -13,8 +13,8 @@ export const TypeOfTypes = new Type(t => t instanceof Type)
 
 export const Returns = (type, f) => (f.returns = type, f)
 
-export const typeOf = Returns(TypeOfTypes, item => {
-   for (const type of Object.values(typeObject)) {
+export const whichType = typs => Returns(TypeOfTypes, item => {
+   for (const type of Object.values(typs)) {
       if (!(type instanceof Type)) continue
       if (type.test(item)) return type
    }
@@ -27,10 +27,12 @@ export const typeOf = Returns(TypeOfTypes, item => {
    throw new TypeError(errorMsg)
 })
 
+export const typeOf = math => whichType(math.types)
+
 // bootstrapping order matters, but order of exports in a module isn't
 // simply the order that the items are listed in the module. So we make
 // an explicitly ordered export of implementations for this sake:
 
 export const bootstrapTypes = {
-   types, Type, Undefined, TypeOfTypes, typeOf
+   Type, Undefined, TypeOfTypes, typeOf
 }

src/core/TypeDispatcher.js

@@ -1,27 +1,20 @@
-import {typeOf, Type, bootstrapTypes} from './Type.js'
+import ArrayKeyedMap from 'array-keyed-map'
 
 import {
    Implementations, isPlainFunction, isPlainObject, onType
 } from './helpers.js'
-import {alwaysMatches, Any, Multiple} from './TypePatterns.js'
-
-// helper that organizes a list into the same chunks as a pattern is
-const collectLike = (list, pattern, state = {pos: 0}) => {
-   const result = []
-   for (const elt of pattern) {
-      if (Array.isArray(elt)) result.push(collectLike(list, elt, state))
-      else result.push(list[state.pos++])
-   }
-   return result
-}
+import {bootstrapTypes, Returns, whichType, Type} from './Type.js'
+import {matched, needsCollection, Passthru} from './TypePatterns.js'
 
 export class TypeDispatcher {
    constructor(...specs) {
+      this._types = {} // stores all the types registered in this dispatcher
       this._implementations = {} // maps key to list of [pattern, result] pairs
       this._dependencies = {} // maps key to a map from type vectors to...
       // ...a set of [key, types] that depend on it.
       this._behaviors = {} // maps key to a map from type vectors to results
       this._fallbacks = {} // maps key to a catchall result
+      this.merge({types: () => this._types})
       this.merge(bootstrapTypes) // bootstrap the instance
       for (const spec of specs) this.merge(spec)
    }
@@ -39,37 +32,57 @@ export class TypeDispatcher {
       for (const key in spec) {
          let val = spec[key]
          if (val instanceof Type) {
-            // TODO: Need to wipe out any dependencies on types[key]!
+            // The design here is that we have set up the `types` property to
+            // be watched like any other, so the following assignment will
+            // cause any behaviors that depend on the type named `key` in the
+            // list of types to be cleared out automagically. Seems to work
+            // so far.
             this.types[key] = val
+            val.name = key
             continue
          }
          if (typeof val === 'function') {
-            val = onType(Multiple(Any), val)
+            val = onType(Passthru, val)
          }
          if (val instanceof Implementations) {
             if (!(key in this)) {
-               // need to set up the item
+               // Need to "bootstrap" the item:
+               // We initially define it with a temporary getter, only
+               // because we don't know whether ultimately it will produce
+               // a function or a non-callable value, and the "permanent"
+               // getter we want depends on which it turns out to be. This
+               // situation means it's not supported to replace a key
+               // corresponding to a method, after it's been fetched once,
+               // with a definition that produces a non-callable value;
+               // the TypeDispatcher will go on returning a function, and
+               // even if you call that function, it will throw an error
+               // when it tries to call the non-callable value.
+               // Conversely, if you try to replace a key corresponding
+               // to a non-callable value, after it's been fetched once,
+               // with a function, it will work, but it will not be able to
+               // perform type dispatch on that function.
                Object.defineProperty(this, key, {
                   enumerable: true,
                   configurable: true,
                   get: () => {
                      let tryValue
-                     let tryTypes = []
                      try {
                         tryValue = this.resolve(key, [])
                      } catch {
-                        // Has no value for the empty type list, so
-                        // find a type list it will have a value for
-                        tryTypes =
-                           this._implementations[key][0][0].sampleTypes()
-                        tryValue = this.resolve(key, tryTypes)
+                        // Has no value for the empty type list, so therefore
+                        // it must be a method, as there is no way to supply
+                        // any types for a non-function value. Hence, we can
+                        // just make tryValue any plain function, since it is
+                        // never actually used, just its type analyzed.
+                        tryValue = () => undefined
                      }
                      // Redefine the property according to what sort of
                      // entity it is:
                      if (isPlainFunction(tryValue)) {
+                        const thisTypeOf = whichType(this.types)
                         // the usual case: a method of the dispatcher
                         const standard = (...args) => {
-                           const types = args.map(typeOf)
+                           const types = args.map(thisTypeOf)
                            return this.resolve(key, types)(...args)
                         }
                         standard.resolve = (types) => this.resolve(key, types)
@@ -81,7 +94,7 @@ export class TypeDispatcher {
                         })
                         return standard
                      }
-                     if (tryTypes.length) tryValue = undefined
+
                      if (typeof tryValue === 'object') {
                         if (!('resolve' in tryValue)) {
                            tryValue.resolve = types => this.resolve(key, types)
@@ -99,6 +112,7 @@ export class TypeDispatcher {
                         })
                         return get()
                      }
+
                      Object.defineProperty(this, key, {
                         enumerable: true,
                         configurable: true,
@@ -107,13 +121,16 @@ export class TypeDispatcher {
                      return tryValue
                   }
                })
+
+               // Finally, initialize the other data for this key:
                this._implementations[key] = []
-               this._behaviors[key] = new Map()
-               this._dependencies[key] = new Map()
+               this._behaviors[key] = new ArrayKeyedMap()
+               this._dependencies[key] = new ArrayKeyedMap()
             }
+
             // Now add all of the patterns of this implementation:
             for (const [pattern, result] of val.patterns) {
-               if (alwaysMatches(pattern)) {
+               if (pattern === Passthru) {
                   if (key in this._fallbacks) this._disengageFallback(key)
                   this._fallbacks[key] = result
                } else {
@@ -135,7 +152,7 @@ export class TypeDispatcher {
          }
 
          // install value as a catchall value
-         this.merge({[key]: onType(Multiple(Any), val)})
+         this.merge({[key]: onType(Passthru, val)})
       }
    }
 
@@ -146,6 +163,29 @@ export class TypeDispatcher {
       for (const pair of this.resolve._genDepsOf) depSet.add(pair)
    }
 
+   // produces and returns a function that takes a list of arguments and
+   // transforms them per the given template, to massage them into the form
+   // expected by a behavior associated with the TypePattern that produced
+   // the template.
+   _generateCollectFunction(template, state = {pos: 0}) {
+      const extractors = []
+      for (const elt of template) {
+         if (Array.isArray(elt)) {
+            extractors.push(this._generateCollectFunction(elt, state))
+         } else {
+            const from = state.pos++
+            if ('actual' in elt) { // incorporate conversion
+               let convert = elt.convertor
+               if (!convert.returns) { // it's a factory that produces convert
+                  convert = convert(this, elt.actual)
+               }
+               extractors.push(args => convert(args[from]))
+            } else extractors.push(args => args[from])
+         }
+      }
+      return args => extractors.map(f => f(args))
+   }
+
    resolve(key, types) {
       if (!(key in this)) {
          throw new ReferenceError(`no method or value for key '${key}'`)
@@ -154,64 +194,84 @@ export class TypeDispatcher {
       if (this.resolve._genDepsOf?.length) this._addToDeps(key, types)
 
       const behave = this._behaviors[key]
+      // Return the cached resolution if it's there
       if (behave.has(types)) return behave.get(types)
+
+      // Otherwise, perform the resolution and cache the result
       const imps = this._implementations[key]
       let needItem = true
       let item
-      let pattern
       let template
       if (imps.length) {
-         for ([pattern, item] of imps) {
-            let finalIndex
-            ;[finalIndex, template] = pattern.match(types)
-            if (finalIndex === types.length) {
-               needItem = false
-               break
+         for (const options of [{}, {convert: true}]) {
+            let pattern
+            for ([pattern, item] of imps) {
+               let finalIndex
+               ;[finalIndex, template] = pattern.match(types, options)
+               if (finalIndex === types.length) {
+                  needItem = false
+                  break
+               }
             }
+            if (!needItem) break
          }
       }
       if (needItem && key in this._fallbacks) {
          needItem = false
          item = this._fallbacks[key]
-         template = [types]
+         template = types
       }
       if (needItem) {
          throw new TypeError(`no matching definition of '${key}' on '${types}'`)
       }
-      if (!isPlainFunction(item) || 'returns' in item) {
+      // If this key is producing a non-function value, we're done
+      if (!isPlainFunction(item)) {
          behave.set(types, item)
          return item
       }
-      // item is a Factory. We have to use it to build the behavior
+
+      // item is a function, either a direct behavior or
+      // a factory. We have to use it to build the final behavior
       // First set up to record dependencies
       if (!('_genDepsOf' in this.resolve)) {
          this.resolve._genDepsOf = []
       }
-      this.resolve._genDepsOf.push([key, types])
+
       let theBehavior = () => undefined
-      try {
-         theBehavior = item(DependencyRecorder(this, [], this), template)
-      } catch {
-         behave.set(types, item)
-         return item
-      } finally {
-         this.resolve._genDepsOf.pop()
-      }
-      if (typeof theBehavior === 'function'
-          && theBehavior.length
-          && Array.isArray(template)
-          && template.some(elt => Array.isArray(elt))
-      ) {
-         // have to wrap the behavior to collect the actual arguments
-         // in the way corresponding to the template
-         const wrappedBehavior = (...args) => {
-            const collectedArgs = collectLike(args, template)
-            return theBehavior(...collectedArgs)
+      this.resolve._genDepsOf.push([key, types]) // Important: make sure
+      // not to return without popping _genDepsOf
+      if (!('returns' in item)) {
+         // looks like a factory
+         try {
+            theBehavior = item(
+               DependencyRecorder(this, [], this), matched(template))
+         } catch {
+            // Oops, didn't work as a factory, so guess we were wrong.
+            // Just make it the direct value for this key on these types:
+            theBehavior = item
+         }
+      } else theBehavior = item
+
+      let finalBehavior = theBehavior
+      if (typeof theBehavior === 'function') {
+         const returning = theBehavior.returns
+         if (!returning) {
+            throw new TypeError(
+               `No return type specified for ${key} on ${types}`)
+         }
+         if (theBehavior.length && needsCollection(template)) {
+            // have to wrap the behavior to collect the actual arguments
+            // in the way corresponding to the template. Generating that
+            // argument transformer may generate more dependencies.
+            const morph = this._generateCollectFunction(template)
+            finalBehavior =
+               Returns(returning, (...args) => theBehavior(...morph(args)))
          }
-         theBehavior = wrappedBehavior
       }
-      behave.set(types, theBehavior)
-      return theBehavior
+
+      this.resolve._genDepsOf.pop()  // OK, now it's safe to return
+      behave.set(types, finalBehavior)
+      return finalBehavior
    }
 
    // Method called to invalidate a set of behaviors
@@ -267,7 +327,11 @@ const DependencyRecorder = (object, path, repo) => new Proxy(object, {
    get(target, prop, receiver) {
       const result = Reflect.get(target, prop, receiver)
       // pass resolve calls through, since we record dependencies therein:
-      if (prop === 'resolve' || 'isDispatcher' in result) return result
+      if (prop === 'resolve'
+          || (typeof result === 'function' && 'isDispatcher' in result)
+      ) {
+         return result
+      }
 
       // OK, it's not a method on a TypeDispatcher, it's some other kind of
       // value. So first record the dependency on prop at this path:
@@ -278,8 +342,9 @@ const DependencyRecorder = (object, path, repo) => new Proxy(object, {
       repo._addToDeps(key, subpath)
       // Now, if the result is an object, we may need to record further
       // dependencies on its properties (e.g. math.config.predictable)
-      // So proxy the return value:
-      if (typeof result === 'object') {
+      // So proxy the return value, except for types, which must maintain
+      // strict referential identity:
+      if (typeof result === 'object' && !(result instanceof Type)) {
          return DependencyRecorder(result, newPath, repo)
       } else return result
    }
@@ -292,7 +357,7 @@ const DependencyWatcher = (object, path, repo) => new Proxy(object, {
       // First see if this setting has any dependencies:
       const newPath = path.slice()
       newPath.push(prop)
-      const key = newPath.unshift()
+      const key = newPath.shift()
       const depSet = repo._dependencies[key]?.get(newPath)
       if (depSet?.size) {
          // It does. So if we are changing it, invalidate them:
@@ -305,7 +370,7 @@ const DependencyWatcher = (object, path, repo) => new Proxy(object, {
    get(target, prop, receiver) {
       // Only thing we need to do is push the watching down
       const result = Reflect.get(target, prop, receiver)
-      if (typeof result === 'object') {
+      if (typeof result === 'object' && !(result instanceof Type)) {
          const newPath = path.slice()
          newPath.push(prop)
          return DependencyWatcher(result, newPath, repo)

src/core/TypePatterns.js

@@ -1,7 +1,7 @@
 import {Type, Undefined} from './Type.js'
 
 export class TypePattern {
-   match(typeSequence, position = 0) {
+   match(typeSequence, options={}) {
       throw new Error('Specific TypePatterns must implement match')
    }
    sampleTypes() {
@@ -15,11 +15,19 @@ class MatchTypePattern extends TypePattern {
       super()
       this.type = typeToMatch
    }
-   match(typeSequence, position = 0) {
-      if (position < typeSequence.length
-         && typeSequence[position] === this.type
-      ) {
-         return [position + 1, typeSequence[position]]
+   match(typeSequence, options={}) {
+      const position = options.position ?? 0
+      const actual = typeSequence[position]
+      if (position < typeSequence.length) {
+         if (actual === this.type) return [position + 1, actual]
+         if (options.convert) {
+            for (const [pattern, convertor] of this.type.from.patterns) {
+               const [pos] = pattern.match([actual])
+               if (pos === 1) {
+                  return [position + 1, {actual, convertor, matched: this.type}]
+               }
+            }
+         }
       }
       return [-1, Undefined]
    }
@@ -32,15 +40,19 @@ class SequencePattern extends TypePattern {
       super()
       this.patterns = itemsToMatch.map(pattern)
    }
-   match(typeSequence, position = 0) {
+   match(typeSequence, options={_internal: true}) {
+      options = options._internal
+         ? options
+         : Object.assign({_internal: true}, options)
+      options.position ??= 0
       const matches = []
       for (const pat of this.patterns) {
-         const [newPos, newMatch] = pat.match(typeSequence, position)
+         const [newPos, newMatch] = pat.match(typeSequence, options)
          if (newPos < 0) return [-1, Undefined]
-         position = newPos
+         options.position = newPos
          matches.push(newMatch)
       }
-      return [position, matches]
+      return [options.position, matches]
    }
    sampleTypes() {
       return this.patterns.map(pat => pat.sampleTypes()).flat()
@@ -62,7 +74,8 @@ export const pattern = patternOrSpec => {
 }
 
 class AnyPattern extends TypePattern {
-   match(typeSequence, position = 0) {
+   match(typeSequence, options={}) {
+      const position = options.position ?? 0
       return position < typeSequence.length
          ? [position + 1, typeSequence[position]]
          : [-1, Undefined]
@@ -77,14 +90,18 @@ class OptionalPattern extends TypePattern {
       super()
       this.pattern = pattern(item)
    }
-   match(typeSequence, position = 0) {
+   match(typeSequence, options={_internal: true}) {
+      options = options._internal
+         ? options
+         : Object.assign({_internal: true}, options)
+      options.position ??= 0
       const matches = []
-      const [newPos, newMatch] = this.pattern.match(typeSequence, position)
+      const [newPos, newMatch] = this.pattern.match(typeSequence, options)
       if (newPos >= 0) {
-         position = newPos
+         options.position = newPos
          matches.push(newMatch)
       }
-      return [position, matches]
+      return [options.position, matches]
    }
    sampleTypes() {return []}
    equal(other) {
@@ -99,12 +116,16 @@ class MultiPattern extends TypePattern {
       super()
       this.pattern = pattern(item)
    }
-   match(typeSequence, position = 0) {
+   match(typeSequence, options={_internal: true}) {
+      options = options._internal
+         ? options
+         : Object.assign({_internal: true}, options)
+      options.position ??= 0
       const matches = []
       while (true) {
-         const [newPos, newMatch] = this.pattern.match(typeSequence, position)
-         if (newPos < 0) return [position, matches]
-         position = newPos
+         const [newPos, newMatch] = this.pattern.match(typeSequence, options)
+         if (newPos < 0) return [options.position, matches]
+         options.position = newPos
          matches.push(newMatch)
       }
    }
@@ -115,5 +136,30 @@ class MultiPattern extends TypePattern {
 }
 
 export const Multiple = item => new MultiPattern(item)
-export const alwaysMatches =
-   pat => pat instanceof MultiPattern && pat.pattern instanceof AnyPattern
+
+// Like Multiple(Any) except leaves the argument list alone; it doesn't
+// chunk it into a single Array of all arguments
+class PassthruPattern extends TypePattern {
+   match(typeSequence, options={}) {
+      const position = options.position ?? 0
+      return [typeSequence.length, typeSequence.slice(position)]
+   }
+   sampleTypes() {return []}
+}
+
+export const Passthru = new PassthruPattern()
+
+// returns the template just of matched types, dropping any actual types
+export const matched = (template) => {
+   if (Array.isArray(template)) return template.map(matched)
+   return template.matched ?? template
+}
+
+// checks if the template is just pass-through or needs collection
+export const needsCollection = (template) => {
+   if (Array.isArray(template)) {
+      return template.some(
+         elt => Array.isArray(elt) || needsCollection(elt))
+   }
+   return 'actual' in template
+}

src/core/__test__/Type.spec.js

@@ -1,14 +1,14 @@
 import assert from 'assert'
 import math from '#nanomath'
-import {Number} from '#number/Number.js'
+import {NumberT} from '#number/NumberT.js'
 
 import {Returns} from '../Type.js'
 import {isPlainFunction} from '../helpers.js'
 
 describe('Core types', () => {
    it('creates an object with all of the types', () => {
-      assert('Number' in math.types)
-      assert.strictEqual(math.types.Number, Number)
+      assert('NumberT' in math.types)
+      assert.strictEqual(math.types.NumberT, NumberT)
       assert('Undefined' in math.types)
       assert(!('Type' in math.types))
       assert(math.types.Undefined.test(undefined))
@@ -18,9 +18,9 @@ describe('Core types', () => {
 
    it('supports a typeOf operator', () => {
       const tO = math.typeOf
-      assert.strictEqual(tO(7), Number)
+      assert.strictEqual(tO(7), NumberT)
       assert.strictEqual(tO(undefined), math.types.Undefined)
-      assert.strictEqual(tO(Number), math.types.TypeOfTypes)
+      assert.strictEqual(tO(NumberT), math.types.TypeOfTypes)
       assert.throws(() => tO(Symbol()), TypeError)
    })
 

src/core/__test__/TypeDispatcher.spec.js

@@ -1,7 +1,8 @@
 import assert from 'assert'
 import {TypeDispatcher} from '../TypeDispatcher.js'
-import {numbers} from '../../numbers.js'
-import {generics} from '../../generics.js'
+import * as booleans from '#boolean/all.js'
+import * as generics from '#generic/all.js'
+import * as numbers from '#number/all.js'
 import {onType} from "#core/helpers.js"
 import {Any} from "#core/TypePatterns.js"
 import {Returns} from "#core/Type.js"
@@ -13,8 +14,8 @@ describe('TypeDispatcher', () => {
       assert.strictEqual(
          incremental.typeOf(undefined), incremental.types.Undefined)
       incremental.merge(numbers)
-      const {Number, TypeOfTypes, Undefined} = incremental.types
-      assert(Number.test(7))
+      const {NumberT, TypeOfTypes, Undefined} = incremental.types
+      assert(NumberT.test(7))
       assert.strictEqual(incremental.add(-1.5, 0.5), -1)
       // Make Undefined act like zero:
       incremental.merge({add: onType(
@@ -27,18 +28,22 @@ describe('TypeDispatcher', () => {
          TypeOfTypes)
       assert.strictEqual(incremental.add(undefined, -3.25), -3.25)
       assert.strictEqual(
-         incremental.add.resolve([Undefined, Number]).returns,
-         Number)
+         incremental.add.resolve([Undefined, NumberT]).returns,
+         NumberT)
       // Oops, changed my mind, make it work like NaN with numbers:
-      const alwaysNaN = Returns(Number, () => NaN)
+      const alwaysNaN = Returns(NumberT, () => NaN)
       incremental.merge({add: onType(
-         [Undefined, Number], alwaysNaN,
-         [Number, Undefined], alwaysNaN
+         [Undefined, NumberT], alwaysNaN,
+         [NumberT, Undefined], alwaysNaN
       )})
       assert(isNaN(incremental.add(undefined, -3.25)))
       assert.strictEqual(
-         incremental.add.resolve([Undefined, Number]).returns,
-         Number)
+         incremental.add.resolve([Undefined, NumberT]).returns,
+         NumberT)
+      assert.strictEqual(incremental.isnan(NaN), 1)
+      incremental.merge(booleans)
+      assert.strictEqual(incremental.boolean(undefined), false)
+      assert.strictEqual(incremental.isnan(NaN), true)
    })
    it('changes methods when their dependencies change', () => {
       const gnmath = new TypeDispatcher(generics, numbers)
@@ -47,4 +52,15 @@ describe('TypeDispatcher', () => {
       gnmath.merge({multiply: plain((a,b) => Math.floor(a) * b)})
       assert.strictEqual(gnmath.square(-2.5), 7.5)
    })
+   it('detects dependencies on conversion operations', () => {
+      const bgn = new TypeDispatcher(booleans, generics, numbers)
+      const {BooleanT, NumberT} = bgn.types
+      assert(!bgn._behaviors.negate.has([BooleanT]))
+      assert.strictEqual(bgn.negate(true), -1)
+      assert(bgn._behaviors.negate.has([BooleanT]))
+      const deps = bgn._dependencies.negate
+      bgn.merge({number: onType([BooleanT], Returns(NumberT, b => b ? 2 : 0))})
+      assert(!bgn._behaviors.negate.has([BooleanT]))
+      assert.strictEqual(bgn.negate(true), -2)
+   })
 })

src/core/__test__/TypePatterns.spec.js

@@ -1,5 +1,7 @@
 import assert from 'assert'
-import {pattern, Any, Multiple, Optional} from '../TypePatterns.js'
+import {
+   pattern, Any, Multiple, Optional, needsCollection
+} from '../TypePatterns.js'
 import {Undefined, TypeOfTypes} from '../Type.js'
 
 describe('Type patterns', () => {
@@ -93,4 +95,10 @@ describe('Type patterns', () => {
          whyNot.sampleTypes(), [Undefined, TypeOfTypes])
       assert(whyNot.equal(whyNot))
    })
+   it('determines whether a template needs a collection function', () => {
+      assert(!needsCollection([Undefined]))
+      assert(needsCollection([Undefined, [Undefined, Undefined]]))
+      assert(needsCollection(
+         [Undefined, {actual: Undefined, matched: TypeOfTypes}]))
+   })
 })

src/core/__test__/helpers.spec.js

@@ -9,8 +9,8 @@ describe('Core helpers', () => {
    it('defines what Implementations are', () => {
       const imps = onType(Undefined, 7, [TypeOfTypes, Undefined], -3)
       assert(imps instanceof Implementations)
-      assert(imps.patterns instanceof Map)
-      assert(imps.patterns.keys().every(k => k instanceof TypePattern))
+      assert(imps.patterns instanceof Array)
+      assert(imps.patterns.every(([k]) => k instanceof TypePattern))
    })
 
    it('detects plain objects', () => {

src/core/helpers.js

@@ -1,13 +1,18 @@
-import {Type} from './Type.js'
 import {pattern} from './TypePatterns.js'
 
 export class Implementations {
    constructor(imps) {
-      this.patterns = new Map()
+      this.patterns = []
+      this._add(imps)
+   }
+   _add(imps) {
       for (let i = 0; i < imps.length; ++i) {
-         this.patterns.set(pattern(imps[i]), imps[++i])
+         this.patterns.push([pattern(imps[i]), imps[++i]])
       }
    }
+   also(...imps) {
+      this._add(imps)
+   }
 }
 
 export const onType = (...imps) => new Implementations(imps)

src/generic/__test__/arithmetic.spec.js

@@ -5,7 +5,7 @@ describe('generic arithmetic', () => {
    it('squares anything', () => {
       assert.strictEqual(math.square(7), 49)
       assert.strictEqual(
-         math.square.resolve([math.types.Number]).returns,
-         math.types.Number)
+         math.square.resolve([math.types.NumberT]).returns,
+         math.types.NumberT)
    })
 })

src/generics.js

@@ -1 +0,0 @@
-export * as generics from './generic/all.js'

src/nanomath.js

@@ -1,7 +1,8 @@
-import {generics} from './generics.js'
-import {numbers} from './numbers.js'
+import * as booleans from './boolean/all.js'
+import * as generics from './generic/all.js'
+import * as numbers from './number/all.js'
 import {TypeDispatcher} from '#core/TypeDispatcher.js'
 
-const math = new TypeDispatcher(generics, numbers)
+const math = new TypeDispatcher(booleans, generics, numbers)
 
 export default math

src/number/Number.js

@@ -1,3 +0,0 @@
-import {Type} from '#core/Type.js'
-
-export const Number = new Type(n => typeof n === 'number')

src/number/NumberT.js

@@ -0,0 +1,7 @@
+import {Type} from '#core/Type.js'
+import {onType} from '#core/helpers.js'
+import {BooleanT} from '#boolean/BooleanT.js'
+
+export const NumberT = new Type(n => typeof n === 'number', {
+    from: onType(BooleanT, math => math.number.resolve([BooleanT])),
+})

src/number/__test__/Number.spec.js

@@ -1,11 +0,0 @@
-import assert from 'assert'
-import {Number} from '../Number.js'
-
-describe('Number Type', () => {
-   it('correctly recognizes numbers', () => {
-      assert(Number.test(3))
-      assert(Number.test(NaN))
-      assert(Number.test(Infinity))
-      assert(!Number.test("3"))
-   })
-})

src/number/__test__/NumberT.spec.js

@@ -0,0 +1,26 @@
+import assert from 'assert'
+import {NumberT} from '../NumberT.js'
+import {BooleanT} from '#boolean/BooleanT.js'
+import math from '#nanomath'
+
+describe('NumberT Type', () => {
+   it('correctly recognizes numbers', () => {
+      assert(NumberT.test(3))
+      assert(NumberT.test(NaN))
+      assert(NumberT.test(Infinity))
+      assert(!NumberT.test("3"))
+   })
+
+   it('can convert from BooleanT to NumberT', () => {
+      const convertImps = NumberT.from
+      let cnvBtoN
+      for (const [pattern, convFactory] of convertImps.patterns) {
+         if (pattern.match([BooleanT])) {
+            cnvBtoN = convFactory(math)
+            break
+         }
+      }
+      assert.strictEqual(cnvBtoN(true), 1)
+      assert.strictEqual(cnvBtoN(false), 0)
+   })
+})

src/number/__test__/type.spec.js

@@ -4,5 +4,9 @@ import math from '#nanomath'
 describe('number type operations', () => {
    it('converts to number', () => {
       assert.strictEqual(math.number(2.637), 2.637)
+      assert(isNaN(math.number(NaN)))
+      assert.strictEqual(math.number(true), 1)
+      assert.strictEqual(math.number(false), 0)
+      assert.strictEqual(math.number(), 0)
    })
 })

src/number/__test__/utils.spec.js

@@ -5,4 +5,9 @@ describe('number utilities', () => {
    it('clones a number', () => {
       assert.strictEqual(math.clone(2.637), 2.637)
    })
+   it('tests if a number is NaN', () => {
+      assert.strictEqual(math.isnan(NaN), true)
+      assert.strictEqual(math.isnan(Infinity), false)
+      assert.strictEqual(math.isnan(43), false)
+   })
 })

src/number/all.js

@@ -1,4 +1,4 @@
-export * as typeDefinition from './Number.js'
+export * as typeDefinition from './NumberT.js'
 export * as arithmetic from './arithmetic.js'
 export * as type from './type.js'
 export * as utils from './utils.js'

src/number/helpers.js

@@ -1,7 +1,9 @@
-import {Number} from './Number.js'
+import {NumberT} from './NumberT.js'
 
 import {onType} from '#core/helpers.js'
 import {Returns} from '#core/Type.js'
 
 export const plain = f => onType(
-   Array(f.length).fill(Number), Returns(Number, f))
+   Array(f.length).fill(NumberT), Returns(NumberT, f))
+
+export const boolnum = Returns(NumberT, p => p ? 1 : 0)

src/number/type.js

@@ -1,4 +1,12 @@
-import {plain} from './helpers.js'
+import {plain, boolnum} from './helpers.js'
+import {BooleanT} from '#boolean/BooleanT.js'
+import {Returns} from '#core/Type.js'
+import {NumberT} from '#number/NumberT.js'
+
+const num = f => Returns(NumberT, f)
 
-// Not much to do so far when there is only one type
 export const number = plain(a => a)
+number.also(
+   BooleanT, boolnum,
+   [], num(() => 0)
+)

src/number/utils.js

@@ -1,3 +1,12 @@
-import {plain} from './helpers.js'
+import {plain, boolnum} from './helpers.js'
+import {NumberT} from './NumberT.js'
+
+import {Returns} from '#core/Type.js'
+import {onType} from '#core/helpers.js'
 
 export const clone = plain(a => a)
+export const isnan = onType(NumberT, math => {
+    const {BooleanT} = math.types
+    if (BooleanT) return Returns(BooleanT, a => isNaN(a))
+    return Returns(NumberT, a => boolnum(isNaN(a)))
+})

src/numbers.js

@@ -1 +1,7 @@
-export * as numbers from './number/all.js'
+import * as numbers from './number/all.js'
+import * as generics from './generic/all.js'
+import {TypeDispatcher} from '#core/TypeDispatcher.js'
+
+const math = new TypeDispatcher(numbers, generics)
+
+export default math

src/package.json

@@ -1,7 +1,9 @@
 {
     "imports" : {
         "#nanomath": "./nanomath.js",
+        "#boolean/*.js": "./boolean/*.js",
         "#core/*.js": "./core/*.js",
+        "#generic/*.js": "./generic/*.js",
         "#number/*.js": "./number/*.js"
     },
     "type" : "module"