feat: Incremental building and simultaneous overloading of object values

So we can start with literal objects whose keys are operator names, and
  whose values are arrays of implementations, and merge them, and then
  replace every value with the overloaded function it specifies.

src/util/overload.ts

@@ -10,7 +10,8 @@ export default function overload<T extends readonly [...any[]]>(
     const impTypes = reflect(callSite).parameters[0].elements
     return <any>((...a: any[]) => {
         for (let i = 0; i < imps.length; ++i) {
-            const paramTypes = impTypes[i].type.parameters
+            const paramTypes = imps[i].functionType.parameters
+                || impTypes[i].type.parameters
             let match = true
             const haveArgs = a.length
             let onArg = 0
@@ -40,3 +41,77 @@ export default function overload<T extends readonly [...any[]]>(
             + 'did not match any implementation')
     })
 }
+
+type AVO = Record<string, readonly [...any[]]>
+
+type MergeArrayValues<L extends AVO, R extends AVO> =
+    Pick<L, Exclude<keyof L, keyof R>>
+    & Pick<R, Exclude<keyof R, keyof L>>
+    & { [P in (keyof L & keyof R)]: [...L[P], ...R[P]] }
+
+function mergeImps<T extends AVO, U extends AVO>(
+    impT: T, impU: U): MergeArrayValues<T, U> {
+    const dummy = Object.assign({}, impT, impU)
+    const result = {} as AVO
+    for (const key in dummy) {
+        if (key in impT) {
+            if (key in impU) {
+                const k = key as Extract<keyof T & keyof U, string>
+                result[k] = [...impT[k], ...impU[k]]
+            } else {
+                result[key] = impT[key]
+            }
+        } else {
+            result[key] = impU[key]
+        }
+    }
+    return result as MergeArrayValues<T, U>
+}
+
+class ImpMerger<T extends AVO> {
+    implementations: T
+    constructor(imps: T) {
+        this.implementations = imps
+    }
+    with<U extends AVO>(
+        moreImps: U, callSite?: CallSite): ImpMerger<MergeArrayValues<T,U>> {
+        const Utype = reflect(callSite).parameters[0]
+        // Annotate the implementations with their RTTI while we have it
+        for (const [key, imps] of Object.entries(moreImps)) {
+            if (!(imps[0].functionType)) {
+                const tuple = Utype.members.find(m => m.name === key)
+                for (let i = 0; i < imps.length; ++i) {
+                    imps[i].functionType = tuple.type.elements[i].type
+                }
+            }
+        }
+        return new ImpMerger(mergeImps<T,U>(this.implementations, moreImps))
+    }
+    imps(): T {
+        return this.implementations
+    }
+}
+
+function merge<T extends AVO>(impsObject: T, callSite?: CallSite) {
+    const Ttype = reflect(callSite).parameters[0]
+    // Annotate the implementations with their RTTI while we have it
+    for (const [key, imps] of Object.entries(impsObject)) {
+        if (!(imps[0].functionType)) {
+            const tuple = Ttype.members.find(m => m.name === key)
+            for (let i = 0; i < imps.length; ++i) {
+                imps[i].functionType = tuple.type.elements[i].type
+            }
+        }
+    }
+    return new ImpMerger(impsObject)
+}
+
+type OverloadedValues<T extends AVO> = {
+    [P in keyof T]: UnionToIntersection<T[P][number]>}
+
+function overloadValues<T extends AVO>(impObject: T) : OverloadedValues<T> {
+    return Object.fromEntries(Object.entries(impObject).map(
+        ([k, v]) => [k, overload(v)])) as OverloadedValues<T>
+}
+
+export {merge, mergeImps, overloadValues}