Redo introduction of design overview (#2017)

Previous overview is changed to an introduction that includes a modified first example, and adding a brief tour of Carbon in the form of an explanation of the features demonstrated in that example. Also update to reflect that we expect `Print` to be available in some package imported by default, which we are currently calling `Carbon`.

Co-authored-by: Wolff Dobson <wolffg@users.noreply.github.com>
Co-authored-by: Chandler Carruth <chandlerc@gmail.com>

docs/design/README.md

@@ -13,9 +13,9 @@ SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
 
 ## Table of contents
 
--   [Overview](#overview)
+-   [Introduction](#introduction)
     -   [This document is provisional](#this-document-is-provisional)
--   [Hello, Carbon](#hello-carbon)
+    -   [Tour of the basics](#tour-of-the-basics)
 -   [Code and comments](#code-and-comments)
 -   [Build modes](#build-modes)
 -   [Types are values](#types-are-values)
@@ -120,7 +120,7 @@ SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
 
 <!-- tocstop -->
 
-## Overview
+## Introduction
 
 This documentation describes the design of the Carbon language, and the
 rationale for that design. This documentation is an overview of the Carbon
@@ -139,37 +139,201 @@ design have things that have not been decided through the Carbon process. This
 preliminary material fills in gaps until aspects of the design can be filled in.
 Features that are provisional have been marked as such on a best-effort basis.
 
-## Hello, Carbon
+### Tour of the basics
 
 Here is a simple function showing some Carbon code:
 
 ```carbon
-import Console;
+import Math;
 
-// Prints the Fibonacci numbers less than `limit`.
-fn Fibonacci(limit: i64) {
-  var (a: i64, b: i64) = (0, 1);
-  while (a < limit) {
-    Console.Print(a, " ");
-    let next: i64 = a + b;
-    a = b;
-    b = next;
+// Returns the smallest factor of `n` > 1, and
+// whether `n` itself is prime.
+fn SmallestFactor(n: i32) -> (i32, bool) {
+  let limit: i32 = Math.Sqrt(n) as i32;
+  var i: i32 = 2;
+  while (i <= limit) {
+    let remainder: i32 = n % i;
+    if (remainder == 0) {
+      Carbon.Print("{0} is a factor of {1}", i, n);
+      return (i, false);
+    }
+    if (i == 2) {
+      i = 3;
+    } else {
+      // Skip even numbers once we get past `2`.
+      i += 2;
+    }
   }
-  Console.Print("\n");
+  return (n, true);
 }
 ```
 
 Carbon is a language that should feel familiar to C++ and C developers. This
 example has familiar constructs like [imports](#imports),
-[function definitions](#functions), [typed arguments](#binding-patterns), and
-[curly braces](#blocks-and-statements).
+[comments](#code-and-comments), [function definitions](#functions),
+[typed arguments](#binding-patterns), and [expressions](#expressions).
+[Statements](#blocks-and-statements) and
+[declarations](#declarations-definitions-and-scopes) are terminated with a `;`
+or something in curly braces `{`...`}`.
 
 A few other features that are unlike C or C++ may stand out. First,
 [declarations](#declarations-definitions-and-scopes) start with introducer
 keywords. `fn` introduces a function declaration, and `var` introduces a
-[variable declaration](#variable-var-declarations). You can also see a
-[_tuple_](#tuples), a composite type written as a comma-separated list inside
-parentheses. Unlike, say, Python, these types are strongly-typed as well.
+[variable declaration](#variable-var-declarations).
+
+The example starts with an [`import` declaration](#imports). Carbon imports are
+more like [C++ modules](https://en.cppreference.com/w/cpp/language/modules) than
+[textual inclusion during preprocessing using `#include`](https://en.cppreference.com/w/cpp/preprocessor/include).
+The `import` declaration imports a
+[library from a package](#files-libraries-packages). It must appear at the top
+of a Carbon source file, the first thing after the
+[optional `package` declaration](#package-declaration). Libraries can optionally
+be split into [api and implementation files](#files-libraries-packages), like
+C++'s header and source files but without requiring a source file in any cases.
+This declaration from the example:
+
+```carbon
+import Math;
+```
+
+imports the default library from package `Math`. The names from this library are
+accessible as members of `Math`, like `Math.Sqrt`. The `Carbon.Print` function
+comes from the `Carbon` package's prelude library which is
+[imported by default](#name-lookup-for-common-types). Unlike C++, the namespaces
+of different packages are kept separate, so there are no name conflicts.
+
+Carbon [comments](#code-and-comments) must be on a line by themselves starting
+with `//`:
+
+```carbon
+// Returns the smallest factor of `n` > 1, and
+// whether `n` itself is prime.
+...
+      // Skip even numbers once we get past `2`.
+```
+
+A [function definition](#functions) consists of:
+
+-   the `fn` keyword introducer,
+-   the function's name,
+-   a parameter list in round parens `(`...`)`,
+-   an optional `->` and return type, and
+-   a body inside curly braces `{`...`}`.
+
+```carbon
+fn SmallestFactor(n: i32) -> (i32, bool) {
+  ...
+      return (i, false);
+  ...
+  return (n, true);
+}
+```
+
+The body of the function is an ordered sequence of
+[statements](#blocks-and-statements) and
+[declarations](#declarations-definitions-and-scopes). Function execution ends
+when it reaches a `return` statement or the end of the function body. `return`
+statements can also specify an expression whose value is returned.
+
+Here `i32` refers to a signed [integer type](#integer-types), with 32 bits, and
+`bool` is the [boolean type](#bool). Carbon also has
+[floating-point types](#floating-point-types) like `f32` and `f64`, and
+[string types](#string-types).
+
+A [variable declaration](#variable-var-declarations) has three parts:
+
+-   the `var` keyword introducer,
+-   the name followed by a `:` and a type, declared the same way as a parameter
+    in a function signature, and
+-   an optional initializer.
+
+```carbon
+  var i: i32 = 2;
+```
+
+You can modify the value of a variable with an
+[assignment statement](#assignment-statements):
+
+```carbon
+      i = 3;
+      ...
+      i += 2;
+```
+
+[Constants are declared](#constant-let-declarations) with the `let` keyword
+introducer. The syntax parallels variable declarations except the initializer is
+required:
+
+```carbon
+  let limit: i32 = Math.Sqrt(n) as i32;
+  ...
+    let remainder: i32 = n % i;
+```
+
+The initializer `Math.Sqrt(n) as i32` is an [expression](#expressions). It first
+calls the `Math.Sqrt` function with `n` as the argument. Then, the `as` operator
+casts the floating-point return value to `i32`. Lossy conversions like that must
+be done explicitly.
+
+Other expressions include `n % i`, which applies the binary `%` modulo operator
+with `n` and `i` as arguments, and `remainder == 0`, which applies the `==`
+comparison operator producing a `bool` result. Expression return values are
+ignored when expressions are used as statements, as in this call to the
+`Carbon.Print` function:
+
+```carbon
+      Carbon.Print("{0} is a factor of {1}", i, n);
+```
+
+Function calls consist of the name of the function followed by the
+comma-separated argument list in round parentheses `(`...`)`.
+
+Control flow statements, including `if`, `while`, `for`, `break`, and
+`continue`, change the order that statements are executed, as they do in C++:
+
+```carbon
+  while (i <= limit) {
+    ...
+    if (remainder == 0) {
+      ...
+    }
+    if (i == 2) {
+      ...
+    } else {
+      ...
+    }
+  }
+```
+
+Every code block in curly braces `{`...`}` defines a scope. Names are visible
+from their declaration until the end of innermost scope containing it. So
+`remainder` in the example is visible until the curly brace `}` that closes the
+`while`.
+
+The example function uses a [_tuple_](#tuples), a
+[composite type](#composite-types), to return multiple values. Both tuple values
+and types are written using a comma-separated list inside parentheses. So
+`(i, false)` and `(n, true)` are tuple values, and `(i32, bool)` is their type.
+
+[Struct types](#struct-types) are similar, except their members are referenced
+by name instead of position. The example could be changed to use structs instead
+as follows:
+
+```carbon
+// Return type of `{.factor: i32, .prime: bool}` is a struct
+// with an `i32` field named `.factor`, and a `bool` field
+// named `.prime`.
+fn SmallestFactor(n: i32) -> {.factor: i32, .prime: bool} {
+  ...
+    if (remainder == 0) {
+      // Return a struct value.
+      return {.factor = i, .prime = false};
+    }
+  ...
+  // Return a struct value.
+  return {.factor = n, .prime = true};
+}
+```
 
 ## Code and comments
 
@@ -190,7 +354,7 @@ required to be the only non-whitespace on the line.
 > References:
 >
 > -   [Source files](code_and_name_organization/source_files.md)
-> -   [lexical conventions](lexical_conventions)
+> -   [Lexical conventions](lexical_conventions)
 > -   Proposal
 >     [#142: Unicode source files](https://github.com/carbon-language/carbon-lang/pull/142)
 > -   Proposal
@@ -213,10 +377,26 @@ The behavior of the Carbon compiler depends on the _build mode_:
 
 Expressions compute values in Carbon, and these values are always strongly typed
 much like in C++. However, an important difference from C++ is that types are
-themselves modeled as values; specifically, compile-time constant values. This
-means that the grammar for writing a type is the [expression](#expressions)
-grammar. Expressions written where a type is expected must be able to be
-evaluated at compile-time and must evaluate to a type value.
+themselves modeled as values; specifically, compile-time-constant values. This
+has a number of consequences:
+
+-   Names for types are in the same namespace shared with functions, variables,
+    namespaces, and so on.
+-   The grammar for writing a type is the [expression](#expressions) grammar,
+    not a separate grammar for types. As a result, Carbon doesn't use angle
+    brackets `<`...`>` in types, since `<` and `>` are used for comparison in
+    expressions.
+-   Function call syntax is used to specify parameters to a type, like
+    `HashMap(String, i64)`.
+
+Some values, such as `()` and `{}`, may even be used as types, but only act like
+types when they are in a type position, like after a `:` in a variable
+declaration or the return type after a `->` in a function declaration. Any
+expression in a type position must be
+[a constants or symbolic value](#value-categories-and-value-phases) so the
+compiler can resolve whether the value can be used as a type. This also puts
+limits on how much operators can do different things for types. This is good for
+consistency, but is a significant restriction on Carbon's design.
 
 ## Primitive types
 
@@ -567,7 +747,7 @@ Elements of an array may be accessed using square brackets (`[`...`]`), as in
 
 ```carbon
 a[i] = 2;
-Console.Print(a[0]);
+Carbon.Print(a[0]);
 ```
 
 > **TODO:** Slices
@@ -689,9 +869,11 @@ are two kinds of patterns:
 -   _Irrefutable_ patterns are guaranteed to match, so long as the code
     type-checks.
 
-Irrefutable patterns are used in [function parameters](#functions),
+In the [introduction](#tour-of-the-basics), [function parameters](#functions),
 [variable `var` declarations](#variable-var-declarations), and
-[constant `let` declarations](#constant-let-declarations).
+[constant `let` declarations](#constant-let-declarations) use a "name `:` type"
+construction. That construction is an example of an irrefutable pattern, and in
+fact any irrefutable pattern may be used in those positions.
 [`match` statements](#match) can include both refutable patterns and irrefutable
 patterns.
 
@@ -1051,11 +1233,11 @@ For example:
 
 ```carbon
 if (fruit.IsYellow()) {
-  Console.Print("Banana!");
+  Carbon.Print("Banana!");
 } else if (fruit.IsOrange()) {
-  Console.Print("Orange!");
+  Carbon.Print("Orange!");
 } else {
-  Console.Print("Vegetable!");
+  Carbon.Print("Vegetable!");
 }
 ```
 
@@ -1084,10 +1266,10 @@ example, this prints `0`, `1`, `2`, then `Done!`:
 ```carbon
 var x: i32 = 0;
 while (x < 3) {
-  Console.Print(x);
+  Carbon.Print(x);
   ++x;
 }
-Console.Print("Done!");
+Carbon.Print("Done!");
 ```
 
 > References:
@@ -1103,7 +1285,7 @@ example, this prints each `String` value in `names`:
 
 ```carbon
 for (var name: String in names) {
-  Console.Print(name);
+  Carbon.Print(name);
 }
 ```
 
@@ -1123,7 +1305,7 @@ processed):
 ```carbon
 for (var step: Step in steps) {
   if (step.IsManual()) {
-    Console.Print("Reached manual step!");
+    Carbon.Print("Reached manual step!");
     break;
   }
   step.Process();
@@ -1152,7 +1334,7 @@ while (!f.EOF()) {
   if (line.IsEmpty()) {
     continue;
   }
-  Console.Print(line);
+  Carbon.Print(line);
 }
 ```
 
@@ -1181,7 +1363,7 @@ fn PrintFirstN(n: i32) {
       // executed after a `return`.
       return;
     }
-    Console.Print(i);
+    Carbon.Print(i);
   }
 }
 ```
@@ -2021,7 +2203,7 @@ class C {
     // ✅ Allowed: unambiguous
     C.F();
     // ❌ Error: ambiguous whether `P` means
-    // `package.P` or `package.P.F`.
+    // `package.P` or `package.C.P`.
     P.H();
     // ✅ Allowed
     package.P.H();
@@ -2266,6 +2448,9 @@ imported automatically into every `api` file. Dedicated type literal syntaxes
 like `i32` and `bool` refer to types defined within this package, based on the
 ["all APIs are library APIs" principle](/docs/project/principles/library_apis_only.md).
 
+> **TODO:** Prelude provisionally imports the `Carbon` package which includes
+> common facilities, like `Print` and the interfaces for operator overloading.
+
 > References:
 >
 > -   [Name lookup](name_lookup.md)
@@ -2420,7 +2605,7 @@ class Circle {
 
   impl as Printable {
     fn Print[me: Self]() {
-      Console.WriteLine("Circle with radius: {0}", me.radius);
+      Carbon.Print("Circle with radius: {0}", me.radius);
     }
   }
 }