diff --git a/src/Complex/arithmetic.ts b/src/Complex/arithmetic.ts
index e11d91e..0d403f4 100644
--- a/src/Complex/arithmetic.ts
+++ b/src/Complex/arithmetic.ts
@@ -1,6 +1,6 @@
 import {Complex} from './type.js'
 import type {
-   Dependencies, Signature, Returns, RealType, ZeroType
+   Dependencies, Signature, Returns, RealType, AliasOf
 } from '../interfaces/type.js'
 
 declare module "../interfaces/type" {
@@ -9,8 +9,8 @@ declare module "../interfaces/type" {
       // after removing any `_...` suffixes; the following should be
       // additional dispatches for add and divide, not separate
       // operations, in the final mathjs bundle.
-      add_real:    {params: [T, RealType<T>], returns: T}
-      divide_real: {params: [T, RealType<T>], returns: T}
+      addReal: AliasOf<'add', (a: T, b: RealType<T>) => T>
+      divideReal: AliasOf<'divide', (a: T, b: RealType<T>) => T>
    }
 }
 
@@ -19,9 +19,9 @@ export const add =
    (w, z) => dep.complex(dep.add(w.re, z.re), dep.add(w.im, z.im))
 
 export const add_real =
-   <T>(dep: Dependencies<'add_real' | 'complex', T>):
-      Signature<'add_real', Complex<T>> =>
-   (z, r) => dep.complex(dep.add_real(z.re, r), z.im)
+   <T>(dep: Dependencies<'addReal' | 'complex', T>):
+      Signature<'addReal', Complex<T>> =>
+   (z, r) => dep.complex(dep.addReal(z.re, r), z.im)
 
 export const unaryMinus =
    <T>(dep: Dependencies<'unaryMinus' | 'complex', T>):
@@ -58,14 +58,14 @@ export const absquare =
    z => dep.add(dep.absquare(z.re), dep.absquare(z.im))
 
 export const divideByReal =
-   <T>(dep: Dependencies<'divide_real' | 'complex', T>):
-      Signature<'divide_real', Complex<T>> =>
-   (z, r) => dep.complex(dep.divide_real(z.re, r), dep.divide_real(z.im, r))
+   <T>(dep: Dependencies<'divideReal' | 'complex', T>):
+      Signature<'divideReal', Complex<T>> =>
+   (z, r) => dep.complex(dep.divideReal(z.re, r), dep.divideReal(z.im, r))
 
 export const reciprocal =
-   <T>(dep: Dependencies<'conj' | 'absquare' | 'divide_real', Complex<T>>):
+   <T>(dep: Dependencies<'conj' | 'absquare' | 'divideReal', Complex<T>>):
       Signature<'reciprocal', Complex<T>> =>
-   z => dep.divide_real(dep.conj(z), dep.absquare(z))
+   z => dep.divideReal(dep.conj(z), dep.absquare(z))
 
 export const divide =
    <T>(dep: Dependencies<'multiply' | 'reciprocal', Complex<T>>):
@@ -78,11 +78,14 @@ export const divide =
 // in fact, we need `add_real` on both T and Complex<T>, hence the dependency
 // with a custom name, not generated via Dependencies<...>
 export const sqrt =
-   <T>(dep: Dependencies<'add' | 'equal' | 'conservativeSqrt' | 'unaryMinus',
-                         RealType<T>>
-       & Dependencies<'zero' | 'add_real' | 'complex', T>
-       & Dependencies<'absquare' | 're' | 'divide_real', Complex<T>>
-       & {add_complex_real: Signature<'add_real', Complex<T>>}):
+   <T>(dep: Dependencies<'equal' | 'conservativeSqrt' | 'unaryMinus', RealType<T>>
+       & Dependencies<'zero' | 'complex', T>
+       & Dependencies<'absquare' | 're' | 'divideReal', Complex<T>>
+       & {
+         addNumber: Signature<'addReal', T>, // TODO: should use Signature<'add'> here
+         addReal: Signature<'add', RealType<T>>,
+         addComplex: Signature<'addReal', Complex<T>> // TODO: should use Signature<'add'> here
+      }):
       Signature<'sqrt', Complex<T>> =>
    z => {
       const myabs = dep.conservativeSqrt(dep.absquare(z))
@@ -91,12 +94,12 @@ export const sqrt =
       if (dep.equal(myabs, negr)) {
          // pure imaginary square root; z.im already zero
          return dep.complex(
-            dep.zero(z.re), dep.add_real(z.im, dep.conservativeSqrt(negr)))
+            dep.zero(z.re), dep.addNumber(z.im, dep.conservativeSqrt(negr)))
       }
-      const num = dep.add_complex_real(z, myabs)
-      const denomsq = dep.add(dep.add(myabs, myabs), dep.add(r, r))
+      const num = dep.addComplex(z, myabs)
+      const denomsq = dep.addReal(dep.addReal(myabs, myabs), dep.addReal(r, r))
       const denom = dep.conservativeSqrt(denomsq)
-      return dep.divide_real(num, denom)
+      return dep.divideReal(num, denom)
    }
 
 export const conservativeSqrt = sqrt
diff --git a/src/Complex/type.ts b/src/Complex/type.ts
index 43c79fe..50a1314 100644
--- a/src/Complex/type.ts
+++ b/src/Complex/type.ts
@@ -32,7 +32,7 @@ declare module "../interfaces/type" {
    }
 
    interface Signatures<T> {
-      complex: {params: [T] | [T,T], returns: Complex<T>}
+      complex: ((re: T) => Complex<T>) | ((re: T, im: T) => Complex<T>)
    }
 }
 
diff --git a/src/interfaces/arithmetic.ts b/src/interfaces/arithmetic.ts
index f77ceb1..df2d765 100644
--- a/src/interfaces/arithmetic.ts
+++ b/src/interfaces/arithmetic.ts
@@ -1,23 +1,18 @@
 import type {Complex} from '../Complex/type.js'
 import type {RealType} from './type.js'
 
-type UnaryOperator<T>  = {params: [T], returns: T}
-type BinaryOperator<T> = {params: [T, T], returns: T}
 declare module "./type" {
    interface Signatures<T> {
-      add:              BinaryOperator<T>
-      unaryMinus:       UnaryOperator<T>
-      conj:             UnaryOperator<T>
-      subtract:         BinaryOperator<T>
-      multiply:         BinaryOperator<T>
-      square:           UnaryOperator<T>
-      absquare:         {params: [T], returns: RealType<T>}
-      reciprocal:       UnaryOperator<T>
-      divide:           BinaryOperator<T>
-      conservativeSqrt: UnaryOperator<T>
-      sqrt: {
-         params: [T],
-         returns: T extends Complex<any> ? T : T | Complex<T>
-      }
+      add:              (a: T, b: T) => T
+      unaryMinus:       (a: T) => T
+      conj:             (a: T) => T
+      subtract:         (a: T, b: T) => T
+      multiply:         (a: T, b: T) => T
+      square:           (a: T) => T
+      absquare:         (a: T) => RealType<T>
+      reciprocal:       (a: T) => T
+      divide:           (a: T, b: T) => T
+      conservativeSqrt: (a: T) => T
+      sqrt: (a: T)=> T extends Complex<unknown> ? T : T | Complex<T>
    }
 }
diff --git a/src/interfaces/predicate.ts b/src/interfaces/predicate.ts
index b4c7393..93d3b4a 100644
--- a/src/interfaces/predicate.ts
+++ b/src/interfaces/predicate.ts
@@ -1,9 +1,10 @@
 // Warning: a module must have something besides just a "declare module"
 // section; otherwise it is ignored.
-export type UnaryPredicate<T> = {params: [T], returns: boolean}
+export type UnaryPredicate<T> = (a: T) => boolean
+
 declare module "./type" {
    interface Signatures<T> {
-      isReal:   UnaryPredicate<T>
-      isSquare: UnaryPredicate<T>
+      isReal:   (a: T) => boolean
+      isSquare: (a: T) => boolean
    }
 }
diff --git a/src/interfaces/relational.ts b/src/interfaces/relational.ts
index 9b511b0..e2aa3a1 100644
--- a/src/interfaces/relational.ts
+++ b/src/interfaces/relational.ts
@@ -1,9 +1,9 @@
 // Warning: a module must have something besides just a "declare module"
 // section; otherwise it is ignored.
-export type BinaryPredicate<T> = {params: [T, T], returns: boolean}
+export type BinaryPredicate<T> = (a: T, b: T) => T
 declare module "./type" {
    interface Signatures<T> {
-      equal:   BinaryPredicate<T>
-      unequal: BinaryPredicate<T>
+      equal:   (a: T, b: T) => boolean
+      unequal: (a: T, b: T) => boolean
    }
 }
diff --git a/src/interfaces/type.ts b/src/interfaces/type.ts
index 4596d7f..9e6870d 100644
--- a/src/interfaces/type.ts
+++ b/src/interfaces/type.ts
@@ -58,17 +58,18 @@ export type RealType<T> = ALookup<T, 'real'>
  * key 're' in the interface.
  ****/
 export interface Signatures<T> {
-   zero: {params: [T], returns: ZeroType<T>}
-   one:  {params: [T], returns: OneType<T>}
+   zero: (a: T) => ZeroType<T>
+   one:  (a: T) => OneType<T>
    // nan needs to be able to operate on its own output for everything
    // else to compile. That's why its parameter type is widened:
-   nan:  {params: [T | NaNType<T>], returns: NaNType<T>}
-   re:   {params: [T], returns: RealType<T>}
+   nan:  (a: T | NaNType<T>) => NaNType<T>
+   re:   (a: T) => RealType<T>
 }
 
-type SignatureKey = keyof Signatures<unknown>
+type SignatureKey<T> = keyof Signatures<T>
 
-export type Returns<Name extends SignatureKey, T> = Signatures<T>[Name]['returns']
-export type Signature<Name extends SignatureKey, T> =
-   (...args: Signatures<T>[Name]['params']) => Returns<Name, T>
-export type Dependencies<Name extends SignatureKey, T> = {[K in Name]: Signature<K, T>}
+export type Signature<Name extends SignatureKey<T>, T> = Signatures<T>[Name]
+export type Returns<Name extends SignatureKey<T>, T> = ReturnType<Signatures<T>[Name]>
+export type Dependencies<Name extends SignatureKey<T>, T> = {[K in Name]: Signature<K, T>}
+
+export type AliasOf<Name extends string, T> = T & {aliasOf?: Name}