add basic function implementation

packages/backend-function/.npmignore

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+# Be very careful editing this file. It is crafted to work around [this issue](https://github.com/npm/npm/issues/4479)
+
+# First ignore everything
+**/*
+
+# Then add back in transpiled js and ts declaration files
+!lib/**/*.js
+!lib/**/*.d.ts
+
+# Then ignore test js and ts declaration files
+*.test.js
+*.test.d.ts
+
+# This leaves us with including only js and ts declaration files of functional code

packages/backend-function/API.md

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+## API Report File for "@aws-amplify/backend-function"
+
+> Do not edit this file. It is a report generated by [API Extractor](https://api-extractor.com/).
+
+```ts
+
+import { AmplifyFunction } from '@aws-amplify/function-construct';
+import { AmplifyFunctionProps } from '@aws-amplify/function-construct';
+import { ConstructFactory } from '@aws-amplify/plugin-types';
+import { ConstructFactoryGetInstanceProps } from '@aws-amplify/plugin-types';
+
+// @public (undocumented)
+export type AmplifyFunctionBaseProps = {
+    name: string;
+};
+
+// @public (undocumented)
+export type AmplifyFunctionBuildProps = AmplifyFunctionBaseProps & Omit<AmplifyFunctionProps, 'absoluteCodePath'> & {
+    buildCommand: string;
+    outDir: string;
+};
+
+// @public
+export class AmplifyFunctionFactory implements ConstructFactory<AmplifyFunction> {
+    static build(props: AmplifyFunctionBuildProps): Promise<AmplifyFunctionFactory>;
+    static fromDir(props: AmplifyFunctionFromDirProps): AmplifyFunctionFactory;
+    getInstance({ constructContainer, }: ConstructFactoryGetInstanceProps): AmplifyFunction;
+}
+
+// @public (undocumented)
+export type AmplifyFunctionFromDirProps = AmplifyFunctionBaseProps & Omit<AmplifyFunctionProps, 'absoluteCodePath'> & {
+    codePath: string;
+};
+
+// @public
+export const Func: typeof AmplifyFunctionFactory;
+
+// (No @packageDocumentation comment for this package)
+
+```

packages/backend-function/api-extractor.json

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+{
+  "extends": "../../api-extractor.base.json"
+}

packages/backend-function/package.json

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+{
+  "name": "@aws-amplify/backend-function",
+  "version": "0.1.0",
+  "type": "module",
+  "exports": {
+    ".": {
+      "types": "./lib/index.d.ts",
+      "import": "./lib/index.js",
+      "require": "./lib/index.js"
+    }
+  },
+  "types": "lib/index.d.ts",
+  "scripts": {
+    "update:api": "api-extractor run --local"
+  },
+  "dependencies": {
+    "@aws-amplify/function-construct": "^0.1.0",
+    "execa": "^7.1.1"
+  },
+  "devDependencies": {
+    "@aws-amplify/backend-engine": "^0.1.0",
+    "@aws-amplify/plugin-types": "^0.1.0"
+  },
+  "peerDependencies": {
+    "aws-cdk-lib": "~2.68.0",
+    "constructs": "^10.0.0"
+  }
+}

packages/backend-function/src/factory.test.ts

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+import { beforeEach, describe, it, mock } from 'node:test';
+import { Func } from './factory.js';
+import { App, Stack } from 'aws-cdk-lib';
+import {
+  NestedStackResolver,
+  SingletonConstructContainer,
+  StackMetadataBackendOutputStorageStrategy,
+} from '@aws-amplify/backend-engine';
+import {
+  BackendOutputEntry,
+  BackendOutputStorageStrategy,
+  ConstructContainer,
+} from '@aws-amplify/plugin-types';
+import assert from 'node:assert';
+import { fileURLToPath } from 'url';
+
+describe('AmplifyFunctionFactory', () => {
+  let constructContainer: ConstructContainer;
+  let outputStorageStrategy: BackendOutputStorageStrategy<BackendOutputEntry>;
+
+  beforeEach(() => {
+    const app = new App();
+    const stack = new Stack(app, 'testStack');
+
+    constructContainer = new SingletonConstructContainer(
+      new NestedStackResolver(stack)
+    );
+
+    outputStorageStrategy = new StackMetadataBackendOutputStorageStrategy(
+      stack
+    );
+  });
+
+  it('creates singleton function instance', () => {
+    const functionFactory = Func.fromDir({
+      name: 'testFunc',
+      codePath: '../test-assets/test-lambda',
+    });
+    const instance1 = functionFactory.getInstance({
+      constructContainer,
+      outputStorageStrategy,
+    });
+    const instance2 = functionFactory.getInstance({
+      constructContainer,
+      outputStorageStrategy,
+    });
+    assert.strictEqual(instance1, instance2);
+  });
+
+  it('executes build command from directory where constructor is used', async () => {
+    const commandExecutorMock = mock.fn();
+
+    // Casting to never is necessary because commandExecutor is a private method.
+    // TS yells that it's not a property on Func even though it is there
+    mock.method(Func, 'commandExecutor' as never, commandExecutorMock);
+
+    (
+      await Func.build({
+        name: 'testFunc',
+        outDir: '../test-assets/test-lambda',
+        buildCommand: 'test command',
+      })
+    ).getInstance({ constructContainer, outputStorageStrategy });
+
+    assert.strictEqual(commandExecutorMock.mock.callCount(), 1);
+    assert.deepStrictEqual(commandExecutorMock.mock.calls[0].arguments, [
+      'test command',
+      {
+        cwd: fileURLToPath(new URL('../src', import.meta.url)),
+        stdio: 'inherit',
+      },
+    ]);
+  });
+});