diff --git a/PocomathInstance.mjs b/PocomathInstance.mjs
new file mode 100644
index 0000000..a28744d
--- /dev/null
+++ b/PocomathInstance.mjs
@@ -0,0 +1,90 @@
+/* Core of pocomath: create an instance */
+import typed from 'typed-function'
+
+export default class PocomathInstance {
+   constructor(name) {
+      this.name = name
+      this._imps = {}
+   }
+    
+   /**
+    * (Partially) define one or more operations of the instance:
+    *
+    * @param {Object<string, Object<Signature, [string[], function]>>} ops
+    *    The only parameter ops gives the semantics of the operations to install.
+    *    The keys are operation names. The value for a key is an object
+    *    mapping (typed-function) signature strings to pairs of dependency
+    *    lists and implementation functions.
+    *
+    *    A dependency list is a list of strings. Each string can either be the
+    *    name of a function that the corresponding implementation has to call,
+    *    or a specification of a particular signature of a function that it has
+    *    to call, in the form 'FN(SIGNATURE)'. Note the function name can be
+    *    the special value 'self' to indicate a recursive call to the given
+    *    operation (either with or without a particular signature.
+    *
+    *    There are two cases for the implementation function. If the dependency
+    *    list is empty, it should be a function taking the arguments specified
+    *    by the signature and returning the value. Otherwise, it should be
+    *    a function taking an object with the dependency lists as keys and the
+    *    requested functions as values, to a function taking the arguments
+    *    specified by the signature and returning the value
+    */
+   install(ops) {
+      for (const key in ops) this._installOp(key, ops[key])
+   }
+
+   /* Used internally by install, see the documentation there */
+   _installOp(name, implementations) {
+      // new implementations, so set the op up to lazily recreate itself
+      this._invalidate(name)
+      const opImps = this._imps[name]
+      for (const signature in implementations) {
+         if (signature in opImps) {
+            if (implemenatations[signature] === opImps[signature]) continue
+            throw new SyntaxError(
+               `Conflicting definitions of ${signature} for ${name}`)
+         } else {
+            opImps[signature] = implementations[signature]
+         }
+      }
+   }
+
+   /**
+    * Reset an operation to require creation of typed-function,
+    * and if it has no implementations so far, set them up.
+    */
+   _invalidate(name) {
+      const self = this
+      this[name] = function () {
+         return self._bundle(name).apply(self, arguments)
+      }
+      if (!(name in this._imps)) {
+         this._imps[name] = {}
+      }
+   }
+
+   /**
+    * Create a typed-function from the signatures for the given name and
+    * assign it to the property with that name, returning it as well
+    */
+   _bundle(name) {
+      const imps = this._imps[name]
+      if (!imps || Object.keys(imps).length === 0) {
+         throw new SyntaxError(`No implementations for ${name}`)
+      }
+      const tf_imps = {}
+      // TODO: handle nonempty dependencies
+      for (const signature in imps) {
+         const [deps, imp] = imps[signature]
+         if (deps.length === 0) {
+            tf_imps[signature] = imp
+         } else {
+            throw new Error('Unimplemented')
+         }
+      }
+      const tf = typed(name, tf_imps)
+      this[name] = tf
+      return tf
+   }
+}
diff --git a/number/add.mjs b/number/add.mjs
new file mode 100644
index 0000000..49c1f40
--- /dev/null
+++ b/number/add.mjs
@@ -0,0 +1,3 @@
+export const add = {
+   '...number': [[], addends => addends.reduce((x,y) => x+y, 0)],
+}
diff --git a/package.json5 b/package.json5
index 4898bc0..517eefb 100644
--- a/package.json5
+++ b/package.json5
@@ -21,4 +21,7 @@
   devDependencies: {
     mocha: '^10.0.0',
   },
+  dependencies: {
+    'typed-function': '^3.0.0',
+  },
 }
diff --git a/pnpm-lock.yaml b/pnpm-lock.yaml
index 1b227fd..22e3de7 100644
--- a/pnpm-lock.yaml
+++ b/pnpm-lock.yaml
@@ -2,6 +2,10 @@ lockfileVersion: 5.4
 
 specifiers:
   mocha: ^10.0.0
+  typed-function: ^3.0.0
+
+dependencies:
+  typed-function: 3.0.0
 
 devDependencies:
   mocha: 10.0.0
@@ -465,6 +469,11 @@ packages:
       is-number: 7.0.0
     dev: true
 
+  /typed-function/3.0.0:
+    resolution: {integrity: sha512-mKJKkt2xYxJUuMD7jyfgUxfn5KCsCxkEKBVjep5yYellJJ5aEDO2QUAmIGdvcZmfQnIrplkzELIaG+5b1475qg==}
+    engines: {node: '>= 14'}
+    dev: false
+
   /workerpool/6.2.1:
     resolution: {integrity: sha512-ILEIE97kDZvF9Wb9f6h5aXK4swSlKGUcOEGiIYb2OOu/IrDU9iwj0fD//SsA6E5ibwJxpEvhullJY4Sl4GcpAw==}
     dev: true
diff --git a/pocomath.mjs b/pocomath.mjs
new file mode 100644
index 0000000..c8f5b18
--- /dev/null
+++ b/pocomath.mjs
@@ -0,0 +1,8 @@
+/* Core of pocomath: generates the default instance */
+import PocomathInstance from './PocomathInstance.mjs'
+import * as numberAdd from './number/add.mjs'
+
+const math = new PocomathInstance('math')
+math.install(numberAdd)
+
+export default math
diff --git a/test/_pocomath.mjs b/test/_pocomath.mjs
new file mode 100644
index 0000000..756a8c0
--- /dev/null
+++ b/test/_pocomath.mjs
@@ -0,0 +1,10 @@
+import assert from 'assert'
+import math from '../pocomath.mjs'
+
+describe('The default full pocomath instance "math"', () => {
+   it('can add numbers', () => {
+      assert.strictEqual(math.add(3, 4), 7)
+      assert.strictEqual(math.add(1.5, 2.5, 3.5), 7.5)
+      assert.strictEqual(math.add(Infinity), Infinity)
+   })
+})