diff --git a/src/Complex/type.ts b/src/Complex/type.ts
index a174c40..b0bb5b7 100644
--- a/src/Complex/type.ts
+++ b/src/Complex/type.ts
@@ -19,9 +19,10 @@ export const Complex_type = {
    }
 }
 
-type Binary<B> = [B, B]
-
 export interface ComplexReturn<Params> {
+   // Sadly, I can't think of a way to make some nice abbreviation operators
+   // for these generic type specifications because TypeScript generics
+   // can't take and use generic parameters, only fully instantiated types.
    complex: Params extends [infer U] ? Complex<U> // unary case
       : Params extends BBinary<infer B> ? Complex<B> // binary case
       : never 
diff --git a/src/core/Dispatcher.ts b/src/core/Dispatcher.ts
index 46a8bff..b8d7c60 100644
--- a/src/core/Dispatcher.ts
+++ b/src/core/Dispatcher.ts
@@ -9,7 +9,7 @@
 
 type TypeName = string
 type Parameter = TypeName
-type Signature = Parameter[]
+type InputSignature = Parameter[]
 type DependenciesType = Record<string, Function>
 
 export type typeOfDependency = {typeOf: (x: unknown) => TypeName}
@@ -62,7 +62,11 @@ export interface ReturnTypes<Params> {}
 
 // Helpers for specifying signatures
 
-// A homogenous binary operation (comes up a lot)
+// A basic signature with concrete types
+export type Signature<CandidateParams, ActualParams, Returns> =
+   CandidateParams extends ActualParams ? Returns : never
+
+// A homogenous binary operation (comes up a lot, needs a better name?)
 // Typical usage: `foo_impl: Params extends BBinary<infer B> ? B : never`
 // says that this implementation takes two arguments, both of type B, and
 // returns the same type.
@@ -118,9 +122,9 @@ type SpecificationsGroup = Record<string, SpecObject>
 export class Dispatcher {
    installSpecification(
       name: string,
-      signature: Signature,
+      signature: InputSignature,
       returns: TypeName,
-      dependencies: Record<string, Signature>,
+      dependencies: Record<string, InputSignature>,
       behavior: Function // possible todo: constrain this type based
       // on the signature, return type, and dependencies. Not sure if
       // that's really possible, though.
diff --git a/src/numbers/arithmetic.ts b/src/numbers/arithmetic.ts
index bc9b862..9bca0ab 100644
--- a/src/numbers/arithmetic.ts
+++ b/src/numbers/arithmetic.ts
@@ -1,5 +1,5 @@
 import {configDependency} from '../core/Config.js'
-import {BBinary, Dependency, ImpType} from '../core/Dispatcher.js'
+import {Signature, Dependency, ImpType} from '../core/Dispatcher.js'
 import type {Complex} from '../Complex/type.js'
 
 declare module "./type" {
@@ -7,7 +7,7 @@ declare module "./type" {
       // This description loses information: some subtypes like NumInt or
       // Positive are closed under addition, but this says that the result
       // of add is just a number, not still of the reduced type
-      add: Params extends BBinary<number> ? number : never
+      add: Signature<Params, [number, number], number>
       // Whereas this one would preserve information, but would lie
       // because it claims all subtypes of number are closed under addition,
       // which is not true for `1 | 2 | 3`, for example.
@@ -16,15 +16,15 @@ declare module "./type" {
       //    : never
       //
       // Not sure how this will need to go when we introduce NumInt.
-      unaryMinus: Params extends [number] ? number : never
-      subtract: Params extends BBinary<number> ? number : never
-      multiply: Params extends BBinary<number> ? number : never
-      divide: Params extends BBinary<number> ? number : never
+      unaryMinus: Signature<Params, [number], number>
+      subtract: Signature<Params, [number, number], number>
+      multiply: Signature<Params, [number, number], number>
+      divide: Signature<Params, [number, number], number>
       // Best we can do for sqrt at compile time, since actual return
       // type depends on config. Not sure how this will play out
       // when we make a number-only bundle, but at least the import type
       // above for Complex<> does not lead to any emitted JavaScript.
-      sqrt: Params extends [number] ? (number | Complex<number>) : never
+      sqrt: Signature<Params, [number], number | Complex<number>>
    }
 }
 
diff --git a/src/numbers/type.ts b/src/numbers/type.ts
index a32b791..105ca46 100644
--- a/src/numbers/type.ts
+++ b/src/numbers/type.ts
@@ -21,6 +21,10 @@ export interface NumbersReturn<Params> {
    zero: Params extends [infer T]
       ? T extends number ? 0 extends T ? 0 : never : never
       : never
+   // Note that in any case the simple
+   // zero: Signature<Params, [number], 0>
+   // makes complex fail to compile, because it worries that you might be
+   // making `Complex<Small>` where zero would not return the right type.
 }
 
 export const zero: ImpType<'zero', [number]> = a => 0