diff --git a/src/generic/Types/adapted.mjs b/src/generic/Types/adapted.mjs
index ba20889..6c54fc5 100644
--- a/src/generic/Types/adapted.mjs
+++ b/src/generic/Types/adapted.mjs
@@ -1,4 +1,6 @@
 import PocomathInstance from '../../core/PocomathInstance.mjs'
+import Returns from '../../core/Returns.mjs'
+
 /* creates a PocomathInstance incorporating a new numeric type encapsulated
  * as a class. (This instance can the be `install()ed` in another to add the
  * type so created.)
@@ -22,15 +24,15 @@ export default function adapted(name, Thing, overrides) {
    // first a creator function, with name depending on the name of the thing:
    const creatorName = overrides.creatorName || name.toLowerCase()
    const creator = overrides[creatorName]
-      ? overrides[creatorName]('')
+      ? overrides[creatorName]['']
       : Thing[creatorName]
          ? (Thing[creatorName])
          : ((...args) => new Thing(...args))
    const defaultCreatorImps = {
-      '': () => () => creator(),
-      '...any': () => args => creator(...args)
+      '': () => Returns(name, () => creator()),
+      '...any': () => Returns(name, args => creator(...args))
    }
-   defaultCreatorImps[name] = () => x => x // x.clone(x)?
+   defaultCreatorImps[name] = () => Returns(name, x => x) // x.clone(x)?
    operations[creatorName] = overrides[creatorName] || defaultCreatorImps
 
    // We make the default instance, just as a place to check for methods
@@ -47,34 +49,35 @@ export default function adapted(name, Thing, overrides) {
       negate: 'neg'
    }
    const binaryOps = {
-      add: 'add',
-      compare: 'compare',
-      divide: 'div',
-      equalTT: 'equals',
-      gcd: 'gcd',
-      lcm: 'lcm',
-      mod: 'mod',
-      multiply: 'mul',
-      subtract: 'sub'
+      add: ['add', name],
+      compare: ['compare', name],
+      divide: ['div', name],
+      equalTT: ['equals', 'boolean'],
+      gcd: ['gcd', name],
+      lcm: ['lcm', name],
+      mod: ['mod', name],
+      multiply: ['mul', name],
+      subtract: ['sub', name]
    }
    for (const [mathname, standardname] of Object.entries(unaryOps)) {
       if (standardname in instance) {
          operations[mathname] = {}
-         operations[mathname][name] = () => t => t[standardname]()
+         operations[mathname][name] = () => Returns(name, t => t[standardname]())
       }
    }
    operations.zero = {}
-   operations.zero[name] = () => t => creator()
+   operations.zero[name] = () => Returns(name, t => creator())
    operations.one = {}
-   operations.one[name] = () => t => creator(1)
+   operations.one[name] = () => Returns(name, t => creator(1))
    operations.conjugate = {}
-   operations.conjugate[name] = () => t => t // or t.clone() ??
+   operations.conjugate[name] = () => Returns(name, t => t) // or t.clone() ??
 
    const binarySignature = `${name},${name}`
-   for (const [mathname, standardname] of Object.entries(binaryOps)) {
-      if (standardname in instance) {
+   for (const [mathname, spec] of Object.entries(binaryOps)) {
+      if (spec[0] in instance) {
          operations[mathname] = {}
-         operations[mathname][binarySignature] = () => (t,u) => t[standardname](u)
+         operations[mathname][binarySignature] = () => Returns(
+            spec[1], (t,u) => t[spec[0]](u))
       }
    }
    if ('operations' in overrides) {
diff --git a/src/generic/all.mjs b/src/generic/all.mjs
index 7132944..45bd9d0 100644
--- a/src/generic/all.mjs
+++ b/src/generic/all.mjs
@@ -1,5 +1,6 @@
 import {adapted} from './Types/adapted.mjs'
 import Fraction from 'fraction.js/bigfraction.js'
+import Returns from '../core/Returns.mjs'
 
 export * from './arithmetic.mjs'
 export * from './relational.mjs'
@@ -8,15 +9,18 @@ export const fraction = adapted('Fraction', Fraction, {
    before: ['Complex'],
    from: {number: n => new Fraction(n)},
    operations: {
-      compare: {'Fraction,Fraction': () => (f,g) => new Fraction(f.compare(g))},
+      compare: {
+         'Fraction,Fraction': () => Returns(
+            'Fraction', (f,g) => new Fraction(f.compare(g)))
+      },
       mod: {
-         'Fraction,Fraction': () => (n,d) => {
+         'Fraction,Fraction': () => Returns('Fraction', (n,d) => {
             // patch for "mathematician's modulus"
             // OK to use full public API of Fraction here
             const fmod = n.mod(d)
             if (fmod.s === -1n) return fmod.add(d.abs())
             return fmod
-         }
+         })
       }
    }
 })
diff --git a/src/generic/divide.mjs b/src/generic/divide.mjs
index 1aee89b..ab1e893 100644
--- a/src/generic/divide.mjs
+++ b/src/generic/divide.mjs
@@ -1,7 +1,10 @@
+import Returns from '../core/Returns.mjs'
+
 export const divide = {
    'T,T': ({
+      T,
       'multiply(T,T)': multT,
       'invert(T)': invT
-   }) => (x, y) => multT(x, invT(y))
+   }) => Returns(T, (x, y) => multT(x, invT(y)))
 }
 
diff --git a/src/generic/lcm.mjs b/src/generic/lcm.mjs
index 04e78b5..26bfbf8 100644
--- a/src/generic/lcm.mjs
+++ b/src/generic/lcm.mjs
@@ -1,10 +1,12 @@
+import Returns from '../core/Returns.mjs'
 import {reducingOperation} from './reducingOperation.mjs'
 
 export const lcm = {
    'T,T': ({
+      T,
       'multiply(T,T)': multT,
       'quotient(T,T)': quotT,
       'gcd(T,T)': gcdT
-   }) => (a,b) => multT(quotT(a, gcdT(a,b)), b)
+   }) => Returns(T, (a,b) => multT(quotT(a, gcdT(a,b)), b))
 }
 Object.assign(lcm, reducingOperation)
diff --git a/src/generic/mean.mjs b/src/generic/mean.mjs
index d12c21b..58cbc19 100644
--- a/src/generic/mean.mjs
+++ b/src/generic/mean.mjs
@@ -1,3 +1,8 @@
+import Returns from '../core/Returns.mjs'
 export const mean = {
-   '...any': ({add, divide}) => args => divide(add(...args), args.length)
+   '...T': ({
+      T,
+      add,
+      'divide(T,NumInt)': div
+   }) => Returns(T, args => div(add(...args), args.length))
 }
diff --git a/src/generic/mod.mjs b/src/generic/mod.mjs
index 84af4e6..e1b5ec6 100644
--- a/src/generic/mod.mjs
+++ b/src/generic/mod.mjs
@@ -1,7 +1,10 @@
+import Returns from '../core/Returns.mjs'
+
 export const mod = {
    'T,T': ({
+      T,
       'subtract(T,T)': subT,
       'multiply(T,T)': multT,
       'quotient(T,T)': quotT
-   }) => (a,m) => subT(a, multT(m, quotT(a,m)))
+   }) => Returns(T, (a,m) => subT(a, multT(m, quotT(a,m))))
 }
diff --git a/src/generic/quotient.mjs b/src/generic/quotient.mjs
index 54e000a..521bd2a 100644
--- a/src/generic/quotient.mjs
+++ b/src/generic/quotient.mjs
@@ -1,3 +1,9 @@
+import Returns from '../core/Returns.mjs'
+
 export const quotient = {
-    'T,T': ({'floor(T)': flr, 'divide(T,T)':div}) => (n,d) => flr(div(n,d))
+    'T,T': ({
+        T,
+        'floor(T)': flr,
+        'divide(T,T)': div
+    }) => Returns(T, (n,d) => flr(div(n,d)))
 }
diff --git a/src/generic/reducingOperation.mjs b/src/generic/reducingOperation.mjs
index e29baf1..3c256f2 100644
--- a/src/generic/reducingOperation.mjs
+++ b/src/generic/reducingOperation.mjs
@@ -1,13 +1,16 @@
+import Returns from '../core/Returns.mjs'
 export * from './Types/generic.mjs'
 
 export const reducingOperation = {
-   'undefined': () => u => u,
-   'undefined,...any': () => (u, rest) => u,
-   'any,undefined': () => (x, u) => u,
-   'undefined,undefined': () => (u,v) => u,
-   any: () => x => x,
+   'undefined': () => Returns('undefined', u => u),
+   'undefined,...any': () => Returns('undefined', (u, rest) => u),
+   'any,undefined': () => Returns('undefined', (x, u) => u),
+   'undefined,undefined': () => Returns('undefined', (u,v) => u),
+   T: ({T}) => Returns(T, x => x),
+   // Unfortunately the type language of Pocomath is not (yet?) expressive
+   // enough to properly type the full reduction signature here:
    'any,any,...any': ({
       self
-   }) => (a,b,rest) => [b, ...rest].reduce((x,y) => self(x,y), a)
+   }) => Returns('any', (a,b,rest) => [b, ...rest].reduce((x,y) => self(x,y), a))
 }
 
diff --git a/src/generic/relational.mjs b/src/generic/relational.mjs
index a1639a1..72de34c 100644
--- a/src/generic/relational.mjs
+++ b/src/generic/relational.mjs
@@ -1,34 +1,45 @@
+import Returns from '../core/Returns.mjs'
+
 export const compare = {
-   'undefined,undefined': () => () => 0
+   'undefined,undefined': () => Returns('NumInt', () => 0)
 }
 
 export const isZero = {
-   'undefined': () => u => u === 0,
-   T: ({'equal(T,T)': eq, 'zero(T)': zr}) => t => eq(t, zr(t))
+   'undefined': () => Returns('boolean', u => u === 0),
+   T: ({
+      T,
+      'equal(T,T)': eq,
+      'zero(T)': zr
+   }) => Returns('boolean', t => eq(t, zr(t)))
 }
 
 export const equal = {
-   'any,any': ({equalTT, joinTypes, Templates, typeOf}) => (x,y) => {
+   'any,any': ({
+      equalTT,
+      joinTypes,
+      Templates,
+      typeOf
+   }) => Returns('boolean', (x,y) => {
       const resultant = joinTypes([typeOf(x), typeOf(y)], 'convert')
       if (resultant === 'any' || resultant in Templates) {
          return false
       }
       return equalTT(x,y)
-   }
+   })
 }
 
 export const equalTT = {
    'T,T': ({
       'compare(T,T)': cmp,
       'isZero(T)': isZ
-   }) => (x,y) => isZ(cmp(x,y)),
+   }) => Returns('boolean', (x,y) => isZ(cmp(x,y)))
    // If templates were native to typed-function, we should be able to
    // do something like:
    // 'any,any': () => () => false // should only be hit for different types
 }
 
 export const unequal = {
-   'any,any': ({equal}) => (x,y) => !(equal(x,y))
+   'any,any': ({equal}) => Returns('boolean', (x,y) => !(equal(x,y)))
 }
 
 export const larger = {
@@ -36,7 +47,7 @@ export const larger = {
       'compare(T,T)': cmp,
       'one(T)' : uno,
       'equalTT(T,T)' : eq
-   }) => (x,y) => eq(cmp(x,y), uno(y))
+   }) => Returns('boolean', (x,y) => eq(cmp(x,y), uno(y)))
 }
 
 export const largerEq = {
@@ -45,10 +56,10 @@ export const largerEq = {
       'one(T)' : uno,
       'isZero(T)' : isZ,
       'equalTT(T,T)': eq
-   }) => (x,y) => {
+   }) => Returns('boolean', (x,y) => {
       const c = cmp(x,y)
       return isZ(c) || eq(c, uno(y))
-   }
+   })
 }
 
 export const smaller = {
@@ -57,10 +68,10 @@ export const smaller = {
       'one(T)' : uno,
       'isZero(T)' : isZ,
       unequal
-   }) => (x,y) => {
+   }) => Returns('boolean', (x,y) => {
       const c = cmp(x,y)
       return !isZ(c) && unequal(c, uno(y))
-   }
+   })
 }
 
 export const smallerEq = {
@@ -68,5 +79,5 @@ export const smallerEq = {
       'compare(T,T)': cmp,
       'one(T)' : uno,
       unequal
-   }) => (x,y) => unequal(cmp(x,y), uno(y))
+   }) => Returns('boolean', (x,y) => unequal(cmp(x,y), uno(y)))
 }
diff --git a/src/generic/roundquotient.mjs b/src/generic/roundquotient.mjs
index 5346882..9c2ba2b 100644
--- a/src/generic/roundquotient.mjs
+++ b/src/generic/roundquotient.mjs
@@ -1,3 +1,9 @@
+import Returns from '../core/Returns.mjs'
+
 export const roundquotient = {
-    'T,T': ({'round(T)': rnd, 'divide(T,T)':div}) => (n,d) => rnd(div(n,d))
+   'T,T': ({
+      T,
+      'round(T)': rnd,
+      'divide(T,T)':div
+   }) => Returns(T, (n,d) => rnd(div(n,d)))
 }
diff --git a/src/generic/sign.mjs b/src/generic/sign.mjs
index 769e2c9..cec73cd 100644
--- a/src/generic/sign.mjs
+++ b/src/generic/sign.mjs
@@ -1,3 +1,9 @@
+import Returns from '../core/Returns.mjs'
+
 export const sign = {
-   T: ({'compare(T,T)': cmp, 'zero(T)': Z}) => x => cmp(x, Z(x))
+   T: ({
+      T,
+      'compare(T,T)': cmp,
+      'zero(T)': Z
+   }) => Returns(T, x => cmp(x, Z(x)))
 }
diff --git a/src/generic/sqrt.mjs b/src/generic/sqrt.mjs
index 21aa1d5..faea759 100644
--- a/src/generic/sqrt.mjs
+++ b/src/generic/sqrt.mjs
@@ -1,3 +1,4 @@
+import Returns from '../core/Returns.mjs'
 export * from './Types/generic.mjs'
 
-export const sqrt = {undefined: () => () => undefined}
+export const sqrt = {undefined: () => Returns('undefined', () => undefined)}
diff --git a/src/generic/subtract.mjs b/src/generic/subtract.mjs
index b048d0c..35dab22 100644
--- a/src/generic/subtract.mjs
+++ b/src/generic/subtract.mjs
@@ -1,3 +1,9 @@
+import Returns from '../core/Returns.mjs'
+
 export const subtract = {
-   'T,T': ({'add(T,T)': addT, 'negate(T)': negT}) => (x,y) => addT(x, negT(y))
+   'T,T': ({
+      T,
+      'add(T,T)': addT,
+      'negate(T)': negT
+   }) => Returns(T, (x,y) => addT(x, negT(y)))
 }
diff --git a/test/_pocomath.mjs b/test/_pocomath.mjs
index 4a63d55..3eff3d3 100644
--- a/test/_pocomath.mjs
+++ b/test/_pocomath.mjs
@@ -34,6 +34,11 @@ describe('The default full pocomath instance "math"', () => {
          math.add(3, math.complex(2.5, 1)), math.complex(5.5, 1))
       assert.strictEqual(
          math.returnTypeOf('add', 'Complex<number>,NumInt'), 'Complex<number>')
+      // The following is not actually what we want, but the Pocomath type
+      // language isn't powerful enough at this point to capture the true
+      // return type:
+      assert.strictEqual(
+         math.returnTypeOf('add', 'number,NumInt,Complex<number>'), 'any')
       assert.strictEqual(
          math.returnTypeOf('chain', 'bigint'), 'Chain<bigint>')
       assert.strictEqual(
diff --git a/test/generic/_all.mjs b/test/generic/_all.mjs
new file mode 100644
index 0000000..94829a4
--- /dev/null
+++ b/test/generic/_all.mjs
@@ -0,0 +1,20 @@
+import assert from 'assert'
+import math from '../../src/pocomath.mjs'
+
+describe('generic', () => {
+   it('calculates mean', () => {
+      assert.strictEqual(math.mean(1,2.5,3.25,4.75), 2.875)
+      assert.strictEqual(
+         math.returnTypeOf('mean', 'number,number,number,number'),
+         'number'
+      )
+   })
+   it('compares things', () => {
+      assert.strictEqual(math.larger(7n, 3n), true)
+      assert.strictEqual(
+         math.returnTypeOf('larger', 'bigint,bigint'), 'boolean')
+      assert.strictEqual(math.smallerEq(7.2, 3), false)
+      assert.strictEqual(
+         math.returnTypeOf('smallerEq', 'number,NumInt'), 'boolean')
+   })
+})
diff --git a/test/generic/fraction.mjs b/test/generic/fraction.mjs
index 9af3b8d..f1fcd97 100644
--- a/test/generic/fraction.mjs
+++ b/test/generic/fraction.mjs
@@ -92,4 +92,10 @@ describe('fraction', () => {
       assert.deepStrictEqual(math.square(tf), math.fraction(9/16))
    })
 
+   it('knows the types of its operations', () => {
+      assert.deepStrictEqual(
+         math.returnTypeOf('ceiling', 'Fraction'), 'Fraction')
+      assert.deepStrictEqual(
+         math.returnTypeOf('multiply', 'Fraction,Fraction'), 'Fraction')
+   })
 })