Make '$' variables globally unique

ir.py

@@ -11,6 +11,12 @@ import types_
 Expression: TypeAlias = 'MonoFunc | Application | Int | Variable | Builtin | LetBinding | ReplHole | Switch'
 Value: TypeAlias = 'MonoFunc | Int | Builtin | ReplHole'
 
+dollar_count: int = 0
+def mk_dollar() -> str:
+	global dollar_count
+	dollar_count += 1
+	return f'${dollar_count-1}'
+
 @dataclass(frozen=True)
 class ReplHole:
 	typ_bindings: types_.Context
@@ -120,18 +126,20 @@ class MonoFunc:
 					case [(var, [])]: # Binds a single variable to the entire input
 						return Ok(MonoFunc(var, body))
 
+		local_variable = mk_dollar()
+
 		# If those special cases fail, we eliminate the pattern matching to produce a
 		# single body:
 		match_trees = tuple( # Construct a match tree for each possible branch
 			pattern.match_tree(
 				EMPTY_STRUCT_PATH,
-				LeafNode.from_value(bindings_to_lets(pattern.bindings(), Variable('$'), body))
+				LeafNode.from_value(bindings_to_lets(pattern.bindings(), Variable(local_variable), body))
 			)
 			for (pattern, body) in forms
 		)
 		unified_match_tree = merge_all_trees(match_trees) # Unify all the trees
-		compiled_tree = compile_tree(unified_match_tree, Variable('$')) # Turn each tree into IR
-		return compiled_tree <= p(MonoFunc, '$')
+		compiled_tree = compile_tree(unified_match_tree, Variable(local_variable)) # Turn each tree into IR
+		return compiled_tree <= p(MonoFunc, local_variable)
 
 	def try_apply(self, v: Expression) -> Option[Expression]:
 		return Some(self.body.subst(v, self.arg))