Refactor semantics logic into separate files. (#2819)

This echoes #2818 and the philosophy is mostly covered there.

Versus parsing, semantics uses fewer separate handler files (for now) because the logic has been shorter. However, the design is still intended to make it easy to split files along boundaries similar to the parser, as I've done for a couple more complex/inter-related sections.

toolchain/semantics/semantics_ir.cpp

@@ -5,10 +5,11 @@
 #include "toolchain/semantics/semantics_ir.h"
 
 #include "common/check.h"
+#include "toolchain/common/pretty_stack_trace_function.h"
 #include "toolchain/parser/parse_tree_node_location_translator.h"
 #include "toolchain/semantics/semantics_builtin_kind.h"
+#include "toolchain/semantics/semantics_context.h"
 #include "toolchain/semantics/semantics_node.h"
-#include "toolchain/semantics/semantics_parse_tree_handler.h"
 
 namespace Carbon {
 
@@ -52,8 +53,37 @@ auto SemanticsIR::MakeFromParseTree(const SemanticsIR& builtin_ir,
   ParseTreeNodeLocationTranslator translator(&tokens, &parse_tree);
   ErrorTrackingDiagnosticConsumer err_tracker(consumer);
   DiagnosticEmitter<ParseTree::Node> emitter(translator, err_tracker);
-  SemanticsParseTreeHandler(tokens, emitter, parse_tree, semantics, vlog_stream)
-      .Build();
+
+  SemanticsContext context(tokens, emitter, parse_tree, semantics, vlog_stream);
+  PrettyStackTraceFunction context_dumper(
+      [&](llvm::raw_ostream& output) { context.PrintForStackDump(output); });
+
+  // Add a block for the ParseTree.
+  context.node_block_stack().Push();
+  context.PushScope();
+
+  // Loops over all nodes in the tree. On some errors, this may return early,
+  // for example if an unrecoverable state is encountered.
+  for (auto parse_node : parse_tree.postorder()) {
+    switch (auto parse_kind = parse_tree.node_kind(parse_node)) {
+#define CARBON_PARSE_NODE_KIND(Name)                   \
+  case ParseNodeKind::Name: {                          \
+    if (!SemanticsHandle##Name(context, parse_node)) { \
+      semantics.has_errors_ = true;                    \
+      return semantics;                                \
+    }                                                  \
+    break;                                             \
+  }
+#include "toolchain/parser/parse_node_kind.def"
+    }
+  }
+
+  // Pop information for the file-level scope.
+  semantics.top_node_block_id_ = context.node_block_stack().Pop();
+  context.PopScope();
+
+  context.VerifyOnFinish();
+
   semantics.has_errors_ = err_tracker.seen_error();
   return semantics;
 }