diff --git a/src/bigint/absquare.mjs b/src/bigint/absquare.mjs
index 4c2040a..587e8ec 100644
--- a/src/bigint/absquare.mjs
+++ b/src/bigint/absquare.mjs
@@ -1,6 +1,7 @@
+import Returns from '../core/Returns.mjs'
 export * from './Types/bigint.mjs'
 
 /* Absolute value squared */
 export const absquare = {
-    bigint: ({'square(bigint)': sqb}) => b => sqb(b)
+    bigint: ({'square(bigint)': sqb}) => Returns('bigint', b => sqb(b))
 }
diff --git a/src/bigint/add.mjs b/src/bigint/add.mjs
index 1cd296d..c4291ac 100644
--- a/src/bigint/add.mjs
+++ b/src/bigint/add.mjs
@@ -1,3 +1,4 @@
+import Returns from '../core/Returns.mjs'
 export * from './Types/bigint.mjs'
 
-export const add = {'bigint,bigint': () => (a,b) => a+b}
+export const add = {'bigint,bigint': () => Returns('bigint', (a,b) => a+b)}
diff --git a/src/bigint/compare.mjs b/src/bigint/compare.mjs
index ab830ab..097dfca 100644
--- a/src/bigint/compare.mjs
+++ b/src/bigint/compare.mjs
@@ -1,5 +1,7 @@
+import Returns from '../core/Returns.mjs'
 export * from './Types/bigint.mjs'
 
 export const compare = {
-   'bigint,bigint': () => (a,b) => a === b ? 0n : (a > b ? 1n : -1n)
+   'bigint,bigint': () => Returns(
+      'boolean', (a,b) => a === b ? 0n : (a > b ? 1n : -1n))
 }
diff --git a/src/bigint/divide.mjs b/src/bigint/divide.mjs
index 4554457..028d3e6 100644
--- a/src/bigint/divide.mjs
+++ b/src/bigint/divide.mjs
@@ -1,12 +1,13 @@
+import Returns from '../core/Returns.mjs'
 export * from './Types/bigint.mjs'
 
 export const divide = {
    'bigint,bigint': ({config, 'quotient(bigint,bigint)': quot}) => {
       if (config.predictable) return quot
-      return (n, d) => {
+      return Returns('bigint|undefined', (n, d) => {
          const q = n/d
          if (q * d == n) return q
          return undefined
-      }
+      })
    }
 }
diff --git a/src/bigint/isZero.mjs b/src/bigint/isZero.mjs
index 0efa71c..02aca57 100644
--- a/src/bigint/isZero.mjs
+++ b/src/bigint/isZero.mjs
@@ -1,3 +1,4 @@
+import Returns from '../core/Returns.mjs'
 export * from './Types/bigint.mjs'
 
-export const isZero = {bigint: () => b => b === 0n}
+export const isZero = {bigint: () => Returns('boolean', b => b === 0n)}
diff --git a/src/bigint/multiply.mjs b/src/bigint/multiply.mjs
index e19959e..e80cee0 100644
--- a/src/bigint/multiply.mjs
+++ b/src/bigint/multiply.mjs
@@ -1,3 +1,4 @@
+import Returns from '../core/Returns.mjs'
 export * from './Types/bigint.mjs'
 
-export const multiply = {'bigint,bigint': () => (a,b) => a*b}
+export const multiply = {'bigint,bigint': () => Returns('bigint', (a,b) => a*b)}
diff --git a/src/bigint/native.mjs b/src/bigint/native.mjs
index 6cc76d4..b387615 100644
--- a/src/bigint/native.mjs
+++ b/src/bigint/native.mjs
@@ -1,12 +1,12 @@
 import gcdType from '../generic/gcdType.mjs'
-import {identity} from '../generic/identity.mjs'
+import {identityType} from '../generic/identity.mjs'
 
 export * from './Types/bigint.mjs'
 
 export {absquare} from './absquare.mjs'
 export {add} from './add.mjs'
 export {compare} from './compare.mjs'
-export const conjugate = {bigint: () => identity}
+export const conjugate = {bigint: identityType('bigint')}
 export {divide} from './divide.mjs'
 export const gcd = gcdType('bigint')
 export {isZero} from './isZero.mjs'
diff --git a/src/bigint/one.mjs b/src/bigint/one.mjs
index f548a65..8e8a7f2 100644
--- a/src/bigint/one.mjs
+++ b/src/bigint/one.mjs
@@ -1,3 +1,4 @@
+import Returns from '../core/Returns.mjs'
 export * from './Types/bigint.mjs'
 
-export const one = {bigint: () => () => 1n}
+export const one = {bigint: () => Returns('bigint', () => 1n)}
diff --git a/src/bigint/quotient.mjs b/src/bigint/quotient.mjs
index 589adc3..c1a086a 100644
--- a/src/bigint/quotient.mjs
+++ b/src/bigint/quotient.mjs
@@ -1,13 +1,14 @@
+import Returns from '../core/Returns.mjs'
 export * from './Types/bigint.mjs'
 
-/* Returns the best integer approximation to n/d */
+/* Returns the floor integer approximation to n/d */
 export const quotient = {
-   'bigint,bigint': ({'sign(bigint)': sgn}) => (n, d) => {
+   'bigint,bigint': ({'sign(bigint)': sgn}) => Returns('bigint', (n, d) => {
       const dSgn = sgn(d)
       if (dSgn === 0n) return 0n
       if (sgn(n) === dSgn) return n/d
       const quot = n/d
       if (quot * d == n) return quot
       return quot - 1n
-   }
+   })
 }
diff --git a/src/bigint/roundquotient.mjs b/src/bigint/roundquotient.mjs
index c6763a2..57fb941 100644
--- a/src/bigint/roundquotient.mjs
+++ b/src/bigint/roundquotient.mjs
@@ -1,8 +1,9 @@
+import Returns from '../core/Returns.mjs'
 export * from './Types/bigint.mjs'
 
 /* Returns the closest integer approximation to n/d */
 export const roundquotient = {
-   'bigint,bigint': ({'sign(bigint)': sgn}) => (n, d) => {
+   'bigint,bigint': ({'sign(bigint)': sgn}) => Returns('bigint', (n, d) => {
       const dSgn = sgn(d)
       if (dSgn === 0n) return 0n
       const candidate = n/d
@@ -11,5 +12,5 @@ export const roundquotient = {
       if (2n * rem > absd) return candidate + dSgn
       if (-2n * rem >= absd) return candidate - dSgn
       return candidate
-   }
+   })
 }
diff --git a/src/bigint/sign.mjs b/src/bigint/sign.mjs
index af48e05..c811df2 100644
--- a/src/bigint/sign.mjs
+++ b/src/bigint/sign.mjs
@@ -1,9 +1,10 @@
+import Returns from '../core/Returns.mjs'
 export * from './Types/bigint.mjs'
 
 export const sign = {
-   bigint: () => b => {
+   bigint: () => Returns('bigint', b => {
       if (b === 0n) return 0n
       if (b > 0n) return 1n
       return -1n
-   }
+   })
 }
diff --git a/src/bigint/sqrt.mjs b/src/bigint/sqrt.mjs
index 4d34513..01ef0b0 100644
--- a/src/bigint/sqrt.mjs
+++ b/src/bigint/sqrt.mjs
@@ -1,5 +1,6 @@
-export * from './Types/bigint.mjs'
+import Returns from '../core/Returns.mjs'
 import isqrt from 'bigint-isqrt'
+export * from './Types/bigint.mjs'
 
 export const sqrt = {
    bigint: ({
@@ -11,18 +12,18 @@ export const sqrt = {
          // Don't just return the constant isqrt here because the object
          // gets decorated with info that might need to be different
          // for different PocomathInstancss
-         return b => isqrt(b)
+         return Returns('bigint', b => isqrt(b))
       }
       if (!cplx) {
-         return b => {
+         return Returns('bigint|undefined', b => {
             if (b >= 0n) {
                const trial = isqrt(b)
                if (trial * trial === b) return trial
             }
             return undefined
-         }
+         })
       }
-      return b => {
+      return Returns('bigint|Complex<bigint>|undefined', b => {
          if (b === undefined) return undefined
          let real = true
          if (b < 0n) {
@@ -33,6 +34,6 @@ export const sqrt = {
          if (trial * trial !== b) return undefined
          if (real) return trial
          return cplx(0n, trial)
-      }
+      })
    }
 }
diff --git a/src/bigint/zero.mjs b/src/bigint/zero.mjs
index 0c63a1a..e9fe83b 100644
--- a/src/bigint/zero.mjs
+++ b/src/bigint/zero.mjs
@@ -1,3 +1,4 @@
+import Returns from '../core/Returns.mjs'
 export * from './Types/bigint.mjs'
 
-export const zero = {bigint: () => () => 0n}
+export const zero = {bigint: () => Returns('bigint', () => 0n)}
diff --git a/src/generic/gcdType.mjs b/src/generic/gcdType.mjs
index 1ca16ab..ee86b50 100644
--- a/src/generic/gcdType.mjs
+++ b/src/generic/gcdType.mjs
@@ -1,3 +1,5 @@
+import Returns from '../core/Returns.mjs'
+
 /* Note we do not use a template here so that we can explicitly control
  * which types this is instantiated for, namely the "integer" types, and
  * not simply allow Pocomath to generate instances for any type it encounters.
@@ -7,14 +9,14 @@ export default function(type) {
    const producer = refs => {
       const modder = refs[`mod(${type},${type})`]
       const zeroTester = refs[`isZero(${type})`]
-      return (a,b) => {
+      return Returns(type, (a,b) => {
          while (!zeroTester(b)) {
             const r = modder(a,b)
             a = b
             b = r
          }
          return a
-      }
+      })
    }
    const retval = {}
    retval[`${type},${type}`] = producer
diff --git a/src/generic/identity.mjs b/src/generic/identity.mjs
index 2422d2f..fb3853e 100644
--- a/src/generic/identity.mjs
+++ b/src/generic/identity.mjs
@@ -1,3 +1,11 @@
-export function identity(x) {
-   return x
+import Returns from '../core/Returns.mjs'
+
+export function identityType(type) {
+   return () => Returns(type, x => x)
 }
+
+export function identitySubTypes(type) {
+   return ({T}) => Returns(T, x => x)
+}
+
+export const identity = {T: ({T}) => Returns(T, x => x)}
diff --git a/src/number/native.mjs b/src/number/native.mjs
index 6746408..fcebecc 100644
--- a/src/number/native.mjs
+++ b/src/number/native.mjs
@@ -1,5 +1,5 @@
 import gcdType from '../generic/gcdType.mjs'
-import {identity} from '../generic/identity.mjs'
+import {identitySubTypes} from '../generic/identity.mjs'
 
 export * from './Types/number.mjs'
 
@@ -7,7 +7,7 @@ export {abs} from './abs.mjs'
 export {absquare} from './absquare.mjs'
 export {add} from './add.mjs'
 export {compare} from './compare.mjs'
-export const conjugate = {number: () => identity}
+export const conjugate = {'T:number': identitySubTypes('number')}
 export const gcd = gcdType('NumInt')
 export {invert} from './invert.mjs'
 export {isZero} from './isZero.mjs'
diff --git a/test/_pocomath.mjs b/test/_pocomath.mjs
index eb0481b..b49efb6 100644
--- a/test/_pocomath.mjs
+++ b/test/_pocomath.mjs
@@ -38,6 +38,14 @@ describe('The default full pocomath instance "math"', () => {
          math.returnTypeOf('chain', 'bigint'), 'Chain<bigint>')
       assert.strictEqual(
          math.returnTypeOf('returnTypeOf', 'string,string'), 'string')
+      assert.strictEqual(
+         math.returnTypeOf('conjugate', 'bigint'), 'bigint')
+      assert.strictEqual(
+         math.returnTypeOf('gcd', 'bigint,bigint'), 'bigint')
+      math.identity(math.fraction(3,5)) // TODO: ditto
+      assert.strictEqual(math.returnTypeOf('identity', 'Fraction'), 'Fraction')
+      assert.strictEqual(
+         math.returnTypeOf('quotient', 'bigint,bigint'), 'bigint')
    })
 
    it('can subtract numbers', () => {