Add pattern matching documentation

README.md

@@ -191,6 +191,7 @@ Other features are described in the following documentation files:
 
 - 📗 Lazy definitions: [Making recursive definitions lazy](docs/lazy-definitions.md)
 - 📗 Data types: [Defining data types](docs/defining-data-types.md)
+- 📗 Pattern matching: [Pattern matching](docs/pattern-matching.md)
 - 📗 Native numbers and operations: [Native numbers](docs/native-numbers.md)
 - 📗 Builtin definitions: [Builtin definitions](docs/builtin-defs.md)
 - 📙 Duplications and superpositions: [Dups and sups](docs/dups-and-sups.md)

docs/pattern-matching.md

@@ -0,0 +1,152 @@
+# Pattern Matching
+
+HVM-Lang offers pattern matching capabilities. You can use pattern matching in defining rules and with the `match` expression.
+
+In example, definitions are a syntax sugar to match expressions:
+```rust
+(Foo 0 false (Cons h1 (Cons h2 t))) = (A h1 h2 t)
+(Foo 0 * *) = B
+(Foo 1+n false *) = n
+(Foo 1+n true *) = 0
+
+Foo = @arg1 @arg2 @arg3 match arg1 arg2 arg3 {
+  (Foo 0 false (Cons h1 (Cons h2 t))): (A h1 h2 t)
+  (Foo 0 * *): B
+  (Foo 1+n false *): n
+  (Foo 1+n true *): 0
+}
+```
+
+Pattern matching on numers has two forms.
+With the successor pattern it will expect a sequence of numbers up to the `n+var` pattern:
+```rust
+match n {
+  0: A
+  1: B
+  ...
+  n+var: (N var)
+}
+
+// Becomes:
+match n {
+  0: A
+  1+p: match p {
+    ...
+    1+var: (N var)
+  }
+}
+```
+
+With the wildcard pattern you can use any number freely:
+```rust
+match n {
+  23: A
+  6343: B
+  0: C
+  ...
+  var: (N var)
+}
+
+// Becomes:
+match (- n 32) {
+  0: A
+  1+n:
+    let n = (+ (+ n 1) 23); match (- n 6453) {
+    ...
+    1+var: let n = (+ (+ n 1) N-1); (N var)
+  }
+}
+```
+
+Match on tuples become let tuple destructors, which are compiled to a native tuple destructor in hvm-core.
+```rust
+match x {
+  (f, s): s
+}
+
+// Becomes:
+let (f, s) = (1, 2); s
+```
+
+Match on vars becomes a rebinding of the variable with a let expression.
+```rust
+match x {
+  c: (Some c)
+}
+
+// Becomes:
+let c = x; (Some c)
+```
+
+Pattern matching on strings and lists desugars to a list of matches on List/String.cons and List.String.nil
+```rust
+Hi "hi" = 1
+Hi _ = 0
+
+Foo [] = 0
+Foo [x] = x
+Foo _ = 3
+
+// Becomes:
+Hi (String.cons 'h' (String.cons 'i' String.nil)) = 2
+Hi _ = 0
+
+Foo List.nil = 0
+Foo (List.cons x List.nil) = x
+Foo _ = 3
+```
+
+Match on ADT constructors can change based on the current encoding.
+```rust
+data Maybe = (Some val) | None
+
+match x {
+  (Some val): val
+  None: 0
+}
+
+// If the current encoding is 'adt-tagged-scott' it becomes:
+#Maybe (x #Maybe.Some.val λval val 0)
+
+// Otherwise, if the current encoding is 'adt-scott' it becomes:
+(x @val val 0)
+```
+
+If constructor fields are not specified, we implicitly bind them based on the name given in the ADT declaration.
+```rust
+data Maybe = (Some value) | None
+
+match x {
+  Some: x.value
+  None: 0
+}
+
+// Becomes:
+match x {
+  (Some x.value): x.value
+  (None): 0
+}
+```
+
+Nested pattern matching allows for matching and deconstructing data within complex structures.
+```rust
+data Tree = (Leaf value) | (Node left right)
+
+match tree {
+  (Node (Leaf a) (Leaf b)): (Combine a b)
+  (Node left right): (Merge left right)
+  Leaf: (Single tree.value)
+}
+
+// Becomes:
+match tree {
+  (Node left right): match left {
+    (Leaf a): match right {
+      (Leaf b): (Combine a b)
+      _: (Merge left right)
+    }
+    _: (Merge left right)
+  }
+  (Leaf value): (Single value)
+}
+```