Improve README with framework introduction, philosophy, effect system explanation, and comprehensive examples

README.md

@@ -8,9 +8,221 @@
 <a href="[https://codecov.io/gh/field4s/field4s](https://codecov.io/gh/scafi/scafi3)"><img src="https://codecov.io/gh/scafi/scafi3/graph/badge.svg?token=5ZT5AEMNDF" alt="codecov"></a>
 </p>
 
-# Scafi 3
+# ScaFi 3
 
-**scafi3** is a Scala 3 DSL for _Aggregate Programming_. 
+**ScaFi 3** (Scala Fields 3) is a modern Scala 3 DSL and toolkit for **Aggregate Programming**, a paradigm for designing resilient and self-organizing distributed systems.
 
-Roots its foundations on the concept of **computational fields**:
-a _distributed data structure_ manipulated by _aggregate_ functions implementing the business logic for **large-scale distributed systems**. 
+## What is Aggregate Programming?
+
+Aggregate Programming enables you to program collective behaviors across networks of devices—from IoT sensors to robot swarms—by thinking in terms of **computational fields**: distributed data structures that span across the entire system. Instead of programming individual devices, you express global behaviors that automatically adapt to the network topology and evolve over time.
+
+## Philosophy and Design
+
+ScaFi 3 embraces a **functional, composable, and type-safe** approach to distributed programming:
+
+### Computational Fields First
+At its core, ScaFi operates on **fields**: values mapped across space and time in a distributed network. A field might represent temperatures across sensors, distances from a source, or any aggregate value. Fields are first-class citizens that you can manipulate with aggregate operators.
+
+### Effect System Integration
+ScaFi 3 leverages Scala 3's advanced type system and **effect tracking** to provide compile-time safety guarantees:
+
+- **Safer Exceptions**: Using Scala 3's `throws` clauses, functions explicitly declare what exceptions they can throw, enabling better error handling at compile time
+- **Context Functions**: The framework uses `using`/`given` for implicit context passing, making the aggregate computation context available without boilerplate
+- **Type-Level Guarantees**: Strong typing ensures that field operations are correctly aligned and serialization is properly configured
+
+### Programming Style
+
+ScaFi programs are:
+- **Declarative**: Express *what* the system should compute, not *how* each device should behave
+- **Composable**: Build complex behaviors from simple, reusable building blocks
+- **Resilient**: Automatically handle device failures and network topology changes
+- **Pure**: Computation logic is separated from side effects and device-specific concerns
+
+## Installation
+
+### With SBT
+
+Add ScaFi 3 to your `build.sbt`:
+
+```scala
+libraryDependencies ++= Seq(
+  "it.unibo.scafi" %%% "scafi3-core" % "1.0.5",
+  // For distributed systems support
+  "it.unibo.scafi" %%% "scafi3-distributed" % "1.0.5"
+)
+```
+
+ScaFi 3 supports **JVM**, **JavaScript**, and **Native** platforms through Scala's cross-platform compilation:
+
+```scala
+// For a specific platform, use %% instead of %%%
+libraryDependencies += "it.unibo.scafi" %% "scafi3-core" % "1.0.5"
+```
+
+### With Mill
+
+Add ScaFi 3 to your `build.sc`:
+
+```scala
+import mill._, scalalib._
+
+object myproject extends ScalaModule {
+  def scalaVersion = "3.7.3"
+
+  def ivyDeps = Agg(
+    mvn"it.unibo.scafi::scafi3-core:1.0.5",
+    // For distributed systems support
+    mvn"it.unibo.scafi::scafi3-distributed:1.0.5"
+  )
+}
+```
+
+For cross-platform projects with Mill:
+
+```scala
+import mill._, scalalib._, scalajslib._, scalanativelib._
+
+object myproject extends Cross[MyProjectModule](JVMPlatform, JSPlatform, NativePlatform)
+
+class MyProjectModule(val platform: Platform) extends CrossPlatformScalaModule {
+  def scalaVersion = "3.7.3"
+
+  def ivyDeps = Agg(
+    mvn"it.unibo.scafi::scafi3-core:1.0.5",
+  )
+}
+```
+
+## Quick Start
+
+### Basic Field Operations
+
+The foundation of ScaFi is the **field calculus**, which provides three core primitives:
+
+```scala
+import it.unibo.scafi.language.xc.ExchangeLanguage
+import it.unibo.scafi.language.xc.calculus.ExchangeCalculus
+import it.unibo.scafi.libraries.All.*
+
+// Define your aggregate program using context functions
+def myProgram(using context: ExchangeCalculus & ExchangeLanguage): Int =
+  // neighborValues: share a value with neighbors and get their values back
+  val neighborIds = neighborValues(localId)
+
+  // evolve: maintain state across rounds (like a distributed variable)
+  val roundCount = evolve(0)(count => count + 1)
+
+  // share: compute values while sharing them with neighbors
+  val consensus = share(0)(neighborValues => 
+    (neighborValues.toIterable.sum + roundCount) / (neighborValues.size + 1)
+  )
+
+  consensus
+```
+
+### Distance Gradient
+
+A classic aggregate programming example—computing hop count distance from a source:
+
+```scala
+import it.unibo.scafi.libraries.All.*
+
+def gradient(using context: ExchangeCalculus & ExchangeLanguage { type DeviceId = Int }): Double =
+  // Compute distance from source using neighbor distance + edge cost
+  distanceTo[Double, Double](
+    source = localId == 0, // Device 0 is the source
+    distances = neighborValues(1.0) // Each hop costs 1.0
+  )
+```
+
+### Domain Splitting with Branching
+
+Control information flow with domain branching:
+
+```scala
+import it.unibo.scafi.libraries.All.*
+
+def conditionalBehavior(gradient: Double)(using context: ExchangeCalculus & ExchangeLanguage { type DeviceId = Int }): String =
+  val distanceFromSource = gradient
+
+  // Split the network into two independent computational domains
+  branch(distanceFromSource < 5.0)(
+    "Close to source: " + distanceFromSource
+  )(
+    "Far from source: " + distanceFromSource
+  )
+```
+
+### Exchange Calculus: The Foundation
+
+Under the hood, ScaFi implements the **Exchange Calculus**, a more expressive variant of field calculus:
+
+```scala
+import it.unibo.scafi.libraries.All.*
+
+def exchangeExample(using context: ExchangeCalculus & ExchangeLanguage): Int =
+  // exchange: send and receive different values
+  exchange(0) { receivedValues =>
+    val maxFromNeighbors = receivedValues.withoutSelf.max
+    val myValue = 1 + maxFromNeighbors
+
+    // Return one value but send another to neighbors
+    returning(myValue) send (myValue + 1)
+  }(localId)
+```
+
+### Complete Example: Self-Healing Gradient
+
+Here's a complete example showing ScaFi's resilience:
+
+```scala
+import it.unibo.scafi.language.xc.{ExchangeLanguage, ExchangeCalculus}
+import it.unibo.scafi.libraries.All.*
+
+// Define an aggregate program that computes a self-healing gradient
+def selfHealingGradient(
+  isSource: Boolean, 
+  hopDistance: Double = 1.0
+)(using context: ExchangeCalculus & ExchangeLanguage): Double =
+
+  // Automatically computes and maintains shortest distance from source
+  // Adapts to topology changes and device failures
+  distanceTo[Double, Double](isSource, neighborValues(hopDistance))
+
+// In practice, this would be executed by the ScaFi engine across devices
+// Each device runs the same program but operates on its local context
+```
+
+## Key Concepts
+
+### Shared Data Types
+`SharedData[T]` represents a field value—a mapping from device IDs to values of type `T`. It includes:
+- The local value on the current device
+- Values received from aligned neighbors
+- Combinators for field manipulation (map, flatMap, etc.)
+
+### Alignment
+ScaFi automatically manages **alignment**: ensuring that values from different parts of a computation are correctly associated across devices. The alignment mechanism uses tokens derived from the program structure.
+
+### Context Functions
+The `using` syntax provides implicit access to the aggregate computation context, which includes:
+- Device ID and neighbor information
+- Message history for state evolution
+- Network communication primitives
+
+## Advanced Features
+
+- **Multi-platform**: Run on JVM, JavaScript (browser/Node.js), and Native targets
+- **Type-safe serialization**: Automatic codecs with compile-time guarantees using the `CodableFromTo` type class
+- **Modular libraries**: Compose pre-built libraries for common patterns (gradients, broadcasting, leader election)
+- **Integration ready**: Distributed module for real network deployments with socket-based communication
+
+## Learn More
+
+- **Examples**: Check the test suite for comprehensive examples
+- **API Documentation**: [ScalaDoc](https://scafi.github.io/scafi3/)
+- **Research**: Based on [Aggregate Computing](https://doi.org/10.1109/MC.2015.261) and [XC calculus](https://doi.org/10.1016/j.jss.2024.111976)
+
+## License
+
+ScaFi 3 is released under the [Apache 2.0 License](./LICENSE).