feat: add architecture doc (#73)

* feat: add architecture doc

* fix: typos

Author: ed255

book/src/SUMMARY.md

@@ -17,4 +17,7 @@
   - [SignedPOD](./signedpod.md)
   - [MainPOD](./mainpod.md)
   - [MockPOD](./mockpod.md)
-- [Examples](./examples.md)
+- [Examples](./examples.md)
+
+# Architecture
+- [Architecture](./architecture.md)

book/src/architecture.md

@@ -0,0 +1,42 @@
+# Architecture
+
+This document explains the architecture of the current implementation.
+
+The main logic of the POD2 implementation is divided into three modules:
+- frontend
+    - compiles user-friendly pod declarations into intermediate representations to be consumed by the backend
+    - internally connects to the backend to get pods built (signed / proved).
+    - presents pods to the user
+- middleware
+    - defines the intermediate representation of Statements, Operations and interfaces of PODs
+    - Statements and Operations are strongly typed here
+    - Both frontend and backend use types defined in the middleware
+    - Does not import types from frontend nor backend
+- backend
+    - takes a middleware POD request representation, signs/proves it and returns a generic POD object
+
+If this was the Rust language compiler:
+- frontend: takes a Rust code and compiles it to LLVM-IR
+- middleware: defines LLVM-IR instructions and blocks
+- backend: Takes LLVM-IR instructions and emits assembly code for a particular CPU
+
+The following diagram shows visually how the components interact with each other:
+
+![](img/frontend-backend.png)
+
+In this organization, the middleware could be defined at arbitrary points:
+- closer to the user would be more high level
+- closer to the target would be more low level
+
+All these positions are OK.  We just need to choose one, and we can try to choose a point that simplifies the implementation.
+
+For example in the middleware we could define `Value = 4 x Goldilock` (making it slightly low level); or `Value = BigUint` and letting the backend choose the maximum representable value, the field encoding, etc. (making it slightly higher level).
+
+In the current iteration we choose `Value = 4 x Goldilock`, but we can revisit it in a future iteration (eg. if we want to support plonky3) by either moving the middleware to a higher level, or by keeping it the same and replacing the `Value` definition.
+
+The diagram above includes an arrow that would show the typical flow followed by a user making a POD.  This is a simplified description of the process.
+1. The user interacts with the frontend API and passes a list of Operations.  The frontend takes those operations and generates the corresponding Statements.  The list of Operations and Statements are transformed into middleware types.  This process can be seen as a compilation step.  The frontend sends this middleware data as a request to the Backend.
+2. The backend receives a request to build a POD from a list of Statements and Operations.  It takes that bundle of data and lays it out in the appropriate format to be proved by a circuit, padding unused slots, etc.  Then it calls a proof system API to generate a proof.
+3. The target (proof system) generates a proof from some circuit description and witness data and gives it back to the backend.
+4. The backend receives the proof and encapsulates it in an object that adheres to the Pod trait and passes it to the frontend
+5. The frontend receives a "blackbox" Pod object and wraps it in a presentation layer in order to show it to the user.