diff --git a/mie/include/mie/ctx.h b/mie/include/mie/ctx.h
index b009e29..d5f6a69 100644
--- a/mie/include/mie/ctx.h
+++ b/mie/include/mie/ctx.h
@@ -43,7 +43,6 @@ MIE_API void mie_ctx_destroy(struct mie_ctx *ctx);
 
 MIE_API struct mie_op *mie_ctx_create_op(
 	const struct mie_ctx *ctx, const char *dialect, const char *op);
-MIE_API bool mie_ctx_resolve_op(const struct mie_ctx *ctx, struct mie_op *op);
 
 MIE_API struct mie_dialect *mie_ctx_get_dialect(
 	const struct mie_ctx *ctx, const char *name);
diff --git a/mie/include/mie/ir/block.h b/mie/include/mie/ir/block.h
index 18f1943..0455784 100644
--- a/mie/include/mie/ir/block.h
+++ b/mie/include/mie/ir/block.h
@@ -6,13 +6,26 @@
 #include <mie/name.h>
 #include <mie/vector.h>
 
+#define MIE_BLOCK_ID_INVALID ((size_t)0)
+
 struct mie_op;
 struct mie_register;
 
+struct mie_block_predecessor {
+	struct mie_block *p_block;
+};
+
 struct mie_block {
 	struct mie_name b_name;
 	struct mie_region *b_parent;
+
+	/* immediate predecessor blocks */
+	MIE_VECTOR_DECLARE(struct mie_block_predecessor, b_ipred);
+
 	/* used by struct mie_region */
+	unsigned int b_id;
+	struct mie_block *b_idom;
+	// struct mie_block *b_sdom, *b_dfs_parent;
 	b_queue_entry b_entry;
 
 	MIE_VECTOR_DECLARE(struct mie_register, b_params);
@@ -29,9 +42,33 @@ MIE_API struct mie_op *mie_block_get_next_op(
 	const struct mie_block *block, const struct mie_op *after);
 MIE_API struct mie_op *mie_block_get_last_op(const struct mie_block *block);
 
+MIE_API struct mie_op *mie_block_get_terminator(const struct mie_block *block);
+
+MIE_API struct mie_op_successor *mie_block_get_first_successor(
+	const struct mie_block *block);
+MIE_API struct mie_op_successor *mie_block_get_prev_successor(
+	const struct mie_block *block, const struct mie_op_successor *before);
+MIE_API struct mie_op_successor *mie_block_get_next_successor(
+	const struct mie_block *block, const struct mie_op_successor *after);
+MIE_API struct mie_op_successor *mie_block_get_last_successor(
+	const struct mie_block *block);
+
+MIE_API struct mie_block_predecessor *mie_block_get_first_predecessor(
+	const struct mie_block *block);
+MIE_API struct mie_block_predecessor *mie_block_get_prev_predecessor(
+	const struct mie_block *block, const struct mie_block_predecessor *before);
+MIE_API struct mie_block_predecessor *mie_block_get_next_predecessor(
+	const struct mie_block *block, const struct mie_block_predecessor *after);
+MIE_API struct mie_block_predecessor *mie_block_get_last_predecessor(
+	const struct mie_block *block);
+
 MIE_API struct mie_op *mie_block_add_op(struct mie_block *block);
 MIE_API struct mie_op *mie_block_add_op_after(
 	struct mie_block *block, struct mie_op *after);
 MIE_API struct mie_register *mie_block_add_param(struct mie_block *block);
 
+MIE_API struct mie_register *mie_block_find_register(
+	const struct mie_block *block, const char *name,
+	const struct mie_op *start_point);
+
 #endif
diff --git a/mie/include/mie/ir/op.h b/mie/include/mie/ir/op.h
index 963c757..1893078 100644
--- a/mie/include/mie/ir/op.h
+++ b/mie/include/mie/ir/op.h
@@ -9,8 +9,8 @@
 #include <mie/name.h>
 #include <mie/parse/file-span.h>
 
+struct mie_ctx;
 struct mie_type;
-
 struct mie_value;
 struct mie_block;
 struct mie_region;
@@ -37,6 +37,7 @@ struct mie_op_arg {
 
 struct mie_op_successor {
 	enum mie_op_flags s_flags;
+	struct mie_file_span s_name_span;
 
 	union {
 		/* only valid if F_SUCCESSOR_RESOLVED is set in s_flags; */
@@ -53,8 +54,8 @@ struct mie_op {
 	/* used by struct mie_block */
 	b_queue_entry op_entry;
 
-	/* these pointers are only valid if the F_OP_RESOLVED flag is set */
-	const struct mie_dialect *op_dialect;
+	struct mie_line_source *op_src;
+	/* this pointer is only valid if the F_OP_RESOLVED flag is set */
 	const struct mie_op_definition *op_info;
 
 	struct mie_block *op_container;
@@ -78,6 +79,10 @@ MIE_API void mie_op_cleanup(struct mie_op *op);
 
 MIE_API size_t mie_op_get_name(const struct mie_op *op, char *out, size_t max);
 
+MIE_API bool mie_op_resolve_self(struct mie_op *op, struct mie_ctx *ctx);
+MIE_API bool mie_op_resolve_args(struct mie_op *op, struct mie_ctx *ctx);
+MIE_API bool mie_op_resolve_successors(struct mie_op *op, struct mie_ctx *ctx);
+
 MIE_API struct mie_op_arg *mie_op_add_arg(struct mie_op *op);
 MIE_API struct mie_register *mie_op_add_result(
 	struct mie_op *op, const struct mie_type *ty);
@@ -102,6 +107,8 @@ MIE_API struct mie_region *mie_op_get_next_region(
 MIE_API struct mie_region *mie_op_get_last_region(const struct mie_op *op);
 
 MIE_API struct mie_register *mie_op_get_arg(const struct mie_op *op, size_t index);
+MIE_API struct mie_register *mie_op_get_result_with_name(
+	const struct mie_op *op, const char *name);
 
 MIE_API struct mie_op *mie_op_get_first_child_op(const struct mie_op *op);
 MIE_API struct mie_op *mie_op_get_last_child_op(const struct mie_op *op);
diff --git a/mie/include/mie/ir/region.h b/mie/include/mie/ir/region.h
index dabc140..34456f6 100644
--- a/mie/include/mie/ir/region.h
+++ b/mie/include/mie/ir/region.h
@@ -1,12 +1,14 @@
 #ifndef MIE_IR_REGION_H_
 #define MIE_IR_REGION_H_
 
+#include <blue/core/btree.h>
 #include <blue/core/queue.h>
 #include <mie/misc.h>
 #include <mie/vector.h>
 #include <stddef.h>
 
 struct mie_op;
+struct mie_ctx;
 struct mie_block;
 
 struct mie_region {
@@ -16,6 +18,9 @@ struct mie_region {
 	b_queue_entry r_entry;
 	/* queue of struct mie_block */
 	b_queue r_blocks;
+	/* bst of struct mie_block, as numbered by a depth-first search.
+	 * this ordering is recalculated by mie_region_refresh_dominance */
+	b_btree r_blocks_s;
 };
 
 MIE_API struct mie_block *mie_region_get_first_block(
@@ -29,5 +34,22 @@ MIE_API struct mie_block *mie_region_get_last_block(const struct mie_region *reg
 MIE_API struct mie_block *mie_region_add_block(struct mie_region *region);
 MIE_API struct mie_block *mie_region_add_block_after(
 	struct mie_region *region, struct mie_block *after);
+MIE_API struct mie_block *mie_region_find_block(
+	const struct mie_region *region, const char *name);
+MIE_API struct mie_register *mie_region_find_register(
+	const struct mie_region *region, const char *name);
+
+/* calculate the dominance-tree of all blocks in a region.
+ * this function populates the following attributes of every block in the
+ * region:
+ *   b_id
+ *   b_node
+ *   b_parent
+ * as well as the following attributes of the region itself:
+ *   r_blocks_s
+ * only top-level blocks and ops are considered by this function. if an op
+ * within the region itself contains one/more child regions, these are ignored.
+ */
+MIE_API void mie_region_refresh_dominance(struct mie_region *region);
 
 #endif
diff --git a/mie/include/mie/ir/register.h b/mie/include/mie/ir/register.h
index c4a46af..d24f240 100644
--- a/mie/include/mie/ir/register.h
+++ b/mie/include/mie/ir/register.h
@@ -37,6 +37,7 @@ struct mie_register_use {
 
 struct mie_register {
 	enum mie_register_flags reg_flags;
+	struct mie_file_span reg_span;
 	union {
 		/* only valid if F_VIRTUAL is set. */
 		struct mie_name reg_name;
diff --git a/mie/include/mie/ir/resolve.h b/mie/include/mie/ir/resolve.h
new file mode 100644
index 0000000..5f7350e
--- /dev/null
+++ b/mie/include/mie/ir/resolve.h
@@ -0,0 +1,14 @@
+#ifndef MIE_IR_RESOLVE_H_
+#define MIE_IR_RESOLVE_H_
+
+#include <mie/misc.h>
+#include <stdbool.h>
+
+struct mie_op;
+struct mie_ctx;
+
+MIE_API bool mie_resolve_op_self(struct mie_op *op, struct mie_ctx *ctx);
+MIE_API bool mie_resolve_op_args(struct mie_op *op, struct mie_ctx *ctx);
+MIE_API bool mie_resolve_op_successors(struct mie_op *op, struct mie_ctx *ctx);
+
+#endif
diff --git a/mie/include/mie/name.h b/mie/include/mie/name.h
index 24136e1..1c06410 100644
--- a/mie/include/mie/name.h
+++ b/mie/include/mie/name.h
@@ -59,7 +59,7 @@ struct mie_name {
 
 	/* if this name was read from a file, these structs can be used to
 	 * record the location within the file where the name is found. */
-	struct mie_file_span n_start, n_end;
+	struct mie_file_span n_span;
 };
 
 struct mie_name_map {
diff --git a/mie/include/mie/parse/lex.h b/mie/include/mie/parse/lex.h
index b6a92d6..0434d7d 100644
--- a/mie/include/mie/parse/lex.h
+++ b/mie/include/mie/parse/lex.h
@@ -16,6 +16,7 @@ MIE_API struct mie_lex *mie_lex_create(
 MIE_API void mie_lex_destroy(struct mie_lex *lex);
 
 MIE_API enum mie_status mie_lex_get_status(const struct mie_lex *lex);
+MIE_API struct mie_line_source *mie_lex_get_line_source(const struct mie_lex *lex);
 MIE_API struct mie_token *mie_lex_peek(struct mie_lex *lex);
 MIE_API void mie_lex_advance(struct mie_lex *lex);
 
diff --git a/mie/include/mie/print/printer.h b/mie/include/mie/print/printer.h
index a730126..3128c9f 100644
--- a/mie/include/mie/print/printer.h
+++ b/mie/include/mie/print/printer.h
@@ -23,6 +23,8 @@ enum mie_print_flags {
 	MIE_PRINT_F_INCLUDE_TYPE = 0x04u,
 	MIE_PRINT_F_EXCLUDE_BLOCK_HEADER = 0x08u,
 	MIE_PRINT_F_EXCLUDE_FIRST_BLOCK_HEADER = 0x10u,
+
+	MIE_PRINT_F_MARK_UNRESOLVED_ELEMENTS = 0x20u,
 };
 
 struct mie_printer {
diff --git a/mie/include/mie/vector.h b/mie/include/mie/vector.h
index 8b16e35..9d70be6 100644
--- a/mie/include/mie/vector.h
+++ b/mie/include/mie/vector.h
@@ -49,8 +49,8 @@ struct mie_vector_ops {
 		&(vector.max), ops)
 #define mie_vector_pop_back(vector, ops)                                       \
 	__mie_vector_pop_back(                                                 \
-		(void **)&(vector), sizeof *vector, &(vector.count),           \
-		&(vector.max), ops)
+		(void **)&(vector.items), sizeof *vector.items,                \
+		&(vector.count), &(vector.max), ops)
 #define mie_vector_emplace_back(vector, ops)                                   \
 	__mie_vector_emplace_back(                                             \
 		(void **)&(vector.items), sizeof *vector.items,                \
@@ -86,6 +86,10 @@ struct mie_vector_ops {
 	__mie_vector_destroy(                                                  \
 		(void **)(vector), sizeof **vector, (vector##_count),          \
 		(vector##_max), ops)
+#define mie_vector_ref_get_item(vector, index)     (*vector)[index]
+#define mie_vector_ref_get_item_ptr(vector, index) (&(*vector)[index])
+#define mie_vector_ref_get_count(vector)           *(vector##_count)
+#define mie_vector_ref_get_max(vector)             *(vector##_count)
 
 /* don't use these functions */
 MIE_API int __mie_vector_push_back(
diff --git a/mie/ir/block.c b/mie/ir/block.c
index e8d8ee5..0a91324 100644
--- a/mie/ir/block.c
+++ b/mie/ir/block.c
@@ -52,6 +52,144 @@ struct mie_op *mie_block_get_last_op(const struct mie_block *block)
 	return b_unbox(struct mie_op, entry, op_entry);
 }
 
+struct mie_op *mie_block_get_terminator(const struct mie_block *block)
+{
+	b_queue_entry *op_entry = b_queue_last(&block->b_ops);
+	return b_unbox(struct mie_op, op_entry, op_entry);
+}
+
+struct mie_op_successor *mie_block_get_first_successor(const struct mie_block *block)
+{
+	struct mie_op *op = mie_block_get_terminator(block);
+	if (!op) {
+		return NULL;
+	}
+
+	if (MIE_VECTOR_COUNT(op->op_successors) == 0) {
+		return NULL;
+	}
+
+	return &op->op_successors.items[0];
+}
+
+struct mie_op_successor *mie_block_get_prev_successor(
+	const struct mie_block *block, const struct mie_op_successor *before)
+{
+	struct mie_op *op = mie_block_get_terminator(block);
+	if (!op) {
+		return NULL;
+	}
+
+	if (MIE_VECTOR_COUNT(op->op_successors) == 0) {
+		return NULL;
+	}
+
+	size_t i = before - &op->op_successors.items[0];
+	if (i == 0 || i >= MIE_VECTOR_COUNT(op->op_successors)) {
+		return NULL;
+	}
+
+	return &op->op_successors.items[i - 1];
+}
+
+struct mie_op_successor *mie_block_get_next_successor(
+	const struct mie_block *block, const struct mie_op_successor *after)
+{
+	struct mie_op *op = mie_block_get_terminator(block);
+	if (!op) {
+		return NULL;
+	}
+
+	if (MIE_VECTOR_COUNT(op->op_successors) == 0) {
+		return NULL;
+	}
+
+	size_t i = after - &op->op_successors.items[0];
+	if (i >= MIE_VECTOR_COUNT(op->op_successors)) {
+		return NULL;
+	}
+
+	if (i + 1 >= MIE_VECTOR_COUNT(op->op_successors)) {
+		return NULL;
+	}
+
+	return &op->op_successors.items[i + 1];
+}
+
+struct mie_op_successor *mie_block_get_last_successor(const struct mie_block *block)
+{
+	struct mie_op *op = mie_block_get_terminator(block);
+	if (!op) {
+		return NULL;
+	}
+
+	size_t nr_successors = MIE_VECTOR_COUNT(op->op_successors);
+
+	if (nr_successors == 0) {
+		return NULL;
+	}
+
+	return &op->op_successors.items[nr_successors - 1];
+}
+
+struct mie_block_predecessor *mie_block_get_first_predecessor(
+	const struct mie_block *block)
+{
+	size_t nr_predecessors = MIE_VECTOR_COUNT(block->b_ipred);
+
+	if (nr_predecessors == 0) {
+		return NULL;
+	}
+
+	return &block->b_ipred.items[0];
+}
+
+struct mie_block_predecessor *mie_block_get_prev_predecessor(
+	const struct mie_block *block, const struct mie_block_predecessor *before)
+{
+	if (MIE_VECTOR_COUNT(block->b_ipred) == 0) {
+		return NULL;
+	}
+
+	size_t i = before - &block->b_ipred.items[0];
+	if (i == 0) {
+		return NULL;
+	}
+
+	return &block->b_ipred.items[i - 1];
+}
+
+struct mie_block_predecessor *mie_block_get_next_predecessor(
+	const struct mie_block *block, const struct mie_block_predecessor *after)
+{
+	if (MIE_VECTOR_COUNT(block->b_ipred) == 0) {
+		return NULL;
+	}
+
+	size_t i = after - &block->b_ipred.items[0];
+	if (i >= MIE_VECTOR_COUNT(block->b_ipred)) {
+		return NULL;
+	}
+
+	if (i + 1 >= MIE_VECTOR_COUNT(block->b_ipred)) {
+		return NULL;
+	}
+
+	return &block->b_ipred.items[i + 1];
+}
+
+struct mie_block_predecessor *mie_block_get_last_predecessor(
+	const struct mie_block *block)
+{
+	size_t nr_predecessors = MIE_VECTOR_COUNT(block->b_ipred);
+
+	if (nr_predecessors == 0) {
+		return NULL;
+	}
+
+	return &block->b_ipred.items[nr_predecessors - 1];
+}
+
 struct mie_op *mie_block_add_op(struct mie_block *block)
 {
 	struct mie_op *op = malloc(sizeof *op);
@@ -100,3 +238,31 @@ struct mie_register *mie_block_add_param(struct mie_block *block)
 
 	return result;
 }
+
+struct mie_register *mie_block_find_register(
+	const struct mie_block *block, const char *name,
+	const struct mie_op *start_point)
+{
+	const b_queue_entry *entry = b_queue_last(&block->b_ops);
+	if (start_point) {
+		entry = &start_point->op_entry;
+	}
+
+	for (size_t i = 0; i < MIE_VECTOR_COUNT(block->b_params); i++) {
+		if (!strcmp(block->b_params.items[i].reg_name.n_str, name)) {
+			return &block->b_params.items[i];
+		}
+	}
+
+	while (entry) {
+		struct mie_op *op = b_unbox(struct mie_op, entry, op_entry);
+		struct mie_register *reg = mie_op_get_result_with_name(op, name);
+		if (reg) {
+			return reg;
+		}
+
+		entry = b_queue_prev(entry);
+	}
+
+	return NULL;
+}
diff --git a/mie/ir/op.c b/mie/ir/op.c
index 5fe4b6e..1f5c61a 100644
--- a/mie/ir/op.c
+++ b/mie/ir/op.c
@@ -1,4 +1,8 @@
 #include <assert.h>
+#include <mie/ctx.h>
+#include <mie/diag/diag.h>
+#include <mie/diag/highlight.h>
+#include <mie/dialect/builtin.h>
 #include <mie/dialect/dialect.h>
 #include <mie/ir/block.h>
 #include <mie/ir/op-definition.h>
@@ -260,6 +264,18 @@ struct mie_register *mie_op_get_arg(const struct mie_op *op, size_t index)
 	return arg->arg_value.u_reg;
 }
 
+struct mie_register *mie_op_get_result_with_name(
+	const struct mie_op *op, const char *name)
+{
+	for (size_t i = 0; i < MIE_VECTOR_COUNT(op->op_result); i++) {
+		if (!strcmp(op->op_result.items[i].reg_name.n_str, name)) {
+			return &op->op_result.items[i];
+		}
+	}
+
+	return NULL;
+}
+
 struct mie_op *mie_op_get_first_child_op(const struct mie_op *op)
 {
 	struct mie_region *first_region = mie_op_get_first_region(op);
diff --git a/mie/ir/region.c b/mie/ir/region.c
index b34e214..84a20d5 100644
--- a/mie/ir/region.c
+++ b/mie/ir/region.c
@@ -1,4 +1,9 @@
+#include <limits.h>
+#include <mie/ctx.h>
+#include <mie/diag/diag.h>
+#include <mie/dialect/builtin.h>
 #include <mie/ir/block.h>
+#include <mie/ir/op.h>
 #include <mie/ir/region.h>
 #include <stdlib.h>
 #include <string.h>
@@ -63,6 +68,7 @@ struct mie_block *mie_region_add_block(struct mie_region *region)
 
 	memset(block, 0x0, sizeof *block);
 	block->b_parent = region;
+	block->b_id = MIE_BLOCK_ID_INVALID;
 
 	b_queue_push_back(&region->r_blocks, &block->b_entry);
 
@@ -89,3 +95,38 @@ struct mie_block *mie_region_add_block_after(
 
 	return block;
 }
+
+struct mie_block *mie_region_find_block(
+	const struct mie_region *region, const char *name)
+{
+	b_queue_entry *cur = b_queue_first(&region->r_blocks);
+	while (cur) {
+		struct mie_block *block = b_unbox(struct mie_block, cur, b_entry);
+		if (!strcmp(block->b_name.n_str, name)) {
+			return block;
+		}
+
+		cur = b_queue_next(cur);
+	}
+
+	return NULL;
+}
+
+struct mie_register *mie_region_find_register(
+	const struct mie_region *region, const char *name)
+{
+	b_queue_entry *cur = b_queue_first(&region->r_blocks);
+
+	while (cur) {
+		struct mie_block *block = b_unbox(struct mie_block, cur, b_entry);
+		struct mie_register *reg
+			= mie_block_find_register(block, name, NULL);
+		if (reg) {
+			return reg;
+		}
+
+		cur = b_queue_next(cur);
+	}
+
+	return NULL;
+}
diff --git a/mie/ir/resolve.c b/mie/ir/resolve.c
new file mode 100644
index 0000000..8137a5d
--- /dev/null
+++ b/mie/ir/resolve.c
@@ -0,0 +1,264 @@
+#include <mie/ctx.h>
+#include <mie/diag/diag.h>
+#include <mie/diag/highlight.h>
+#include <mie/dialect/builtin.h>
+#include <mie/dialect/dialect.h>
+#include <mie/ir/block.h>
+#include <mie/ir/op.h>
+#include <mie/ir/region.h>
+#include <mie/ir/register.h>
+
+enum register_find_result {
+	REG_FIND_NONE = 0,
+	REG_FIND_USE_BEFORE_DEFINE,
+	REG_FIND_UNDOMINATED,
+	REG_FIND_ISOLATED,
+};
+
+bool mie_op_resolve_self(struct mie_op *op, struct mie_ctx *ctx)
+{
+	if (op->op_flags & MIE_OP_F_OP_RESOLVED) {
+		return true;
+	}
+
+	const char *dialect_name = NULL, *op_name = NULL;
+
+	char *dot = strchr(op->op_name, '.');
+	if (dot) {
+		*dot = 0;
+		dialect_name = op->op_name;
+		op_name = dot + 1;
+	} else {
+		dialect_name = NULL;
+		op_name = op->op_name;
+	}
+
+	const struct mie_dialect *dialect = mie_ctx_get_dialect(ctx, dialect_name);
+	if (dot) {
+		*dot = '.';
+	}
+
+	/* dialect_name is no longer valid after this point */
+	dialect_name = NULL;
+
+	if (!dialect) {
+		return false;
+	}
+
+	const struct mie_op_definition *op_info
+		= mie_dialect_get_op(dialect, op_name);
+	if (!op_info) {
+		return false;
+	}
+
+	op->op_info = op_info;
+
+	free(op->op_name);
+	op->op_name = NULL;
+
+	op->op_flags |= MIE_OP_F_OP_RESOLVED;
+
+	return true;
+}
+
+static enum register_find_result find_register_wide(
+	struct mie_op *op, const char *name, struct mie_register **out)
+{
+	struct mie_region *region = op->op_container->b_parent;
+	enum register_find_result result = REG_FIND_UNDOMINATED;
+	struct mie_register *reg = NULL;
+
+	while (region) {
+		reg = mie_region_find_register(region, name);
+		if (reg) {
+			*out = reg;
+			break;
+		}
+
+		struct mie_op *op = region->r_parent;
+		if (mie_op_has_trait(op, "builtin", "isolated-from-above")) {
+			result = REG_FIND_ISOLATED;
+		}
+
+		region = op->op_container ? op->op_container->b_parent : NULL;
+	}
+
+	if (!reg) {
+		return result;
+	}
+
+	if (reg->reg_block == op->op_container) {
+		return REG_FIND_USE_BEFORE_DEFINE;
+	}
+
+	return result;
+}
+
+static bool resolve_arg(
+	struct mie_op *op, struct mie_op_arg *arg, struct mie_ctx *ctx)
+{
+	const char *arg_name = arg->arg_unresolved.reg_name;
+	struct mie_block *block = op->op_container;
+	struct mie_op *search_start = op;
+	struct mie_register *reg = NULL;
+
+	while (block) {
+		reg = mie_block_find_register(block, arg_name, search_start);
+		if (reg) {
+			break;
+		}
+
+		search_start = NULL;
+		block = block->b_idom;
+	}
+
+	if (reg) {
+		free(arg->arg_unresolved.reg_name);
+		arg->arg_flags |= MIE_OP_F_ARG_RESOLVED;
+
+		memset(&arg->arg_value, 0x0, sizeof arg->arg_value);
+		arg->arg_value.u_reg = reg;
+		arg->arg_value.u_user = op;
+		b_queue_push_back(&reg->reg_use, &arg->arg_value.u_entry);
+		return true;
+	}
+
+	enum register_find_result find_result
+		= find_register_wide(op, arg_name, &reg);
+
+	struct mie_diag *diag = mie_ctx_push_diag(
+		ctx, op->op_src, &arg->arg_span.s_start, "builtin",
+		MIE_BUILTIN_E_UNRESOLVED_VALUE);
+	mie_diag_push_msg(diag, ctx, "builtin", MIE_BUILTIN_MSG_UNRESOLVED_VALUE);
+
+	struct mie_diag_highlight hl[] = {
+		{
+			.hl_type = MIE_DIAG_HIGHLIGHT_ERROR,
+			.hl_span = arg->arg_span,
+		},
+	};
+
+	mie_diag_push_snippet(
+		diag, arg->arg_span.s_start.c_row, arg->arg_span.s_end.c_row,
+		NULL, 0, hl, 1);
+
+	if (!reg) {
+		return false;
+	}
+
+	struct mie_block *reg_container = reg->reg_block;
+
+	switch (find_result) {
+	case REG_FIND_ISOLATED:
+		mie_diag_push_msg(
+			diag, ctx, "builtin",
+			MIE_BUILTIN_MSG_VALUE_DEFINED_OUTSIDE_ISOLATED_REGION);
+		break;
+	case REG_FIND_UNDOMINATED:
+		mie_diag_push_msg(
+			diag, ctx, "builtin",
+			MIE_BUILTIN_MSG_VALUE_DEFINED_IN_NON_DOMINANT_BLOCK);
+		break;
+	case REG_FIND_USE_BEFORE_DEFINE:
+		mie_diag_push_msg(
+			diag, ctx, "builtin",
+			MIE_BUILTIN_MSG_VALUE_DEFINED_AFTER_USE);
+		break;
+	default:
+		return false;
+	}
+
+	hl[0].hl_type = MIE_DIAG_HIGHLIGHT_HINT;
+	hl[0].hl_span = reg->reg_span;
+
+	mie_diag_push_snippet(
+		diag, reg->reg_span.s_start.c_row, reg->reg_span.s_end.c_row,
+		NULL, 0, hl, 1);
+
+	if (!reg_container) {
+		return false;
+	}
+
+	hl[0].hl_span = reg_container->b_name.n_span;
+
+	mie_diag_push_snippet(
+		diag, reg_container->b_name.n_span.s_start.c_row,
+		reg_container->b_name.n_span.s_end.c_row, NULL, 0, hl, 1);
+
+	return false;
+}
+
+static bool resolve_successor(
+	struct mie_op *op, struct mie_op_successor *s, struct mie_ctx *ctx)
+{
+	if (s->s_flags & MIE_OP_F_SUCCESSOR_RESOLVED) {
+		return true;
+	}
+
+	struct mie_block *container = op->op_container;
+	struct mie_region *region = container ? container->b_parent : NULL;
+	if (!region) {
+		return false;
+	}
+
+	struct mie_diag *diag = NULL;
+	struct mie_block *dest = mie_region_find_block(region, s->s_block_name);
+	if (!dest) {
+		diag = mie_ctx_push_diag(
+			ctx, op->op_src, &s->s_name_span.s_start, "builtin",
+			MIE_BUILTIN_E_UNRESOLVED_SUCCESSOR);
+		mie_diag_push_msg(
+			diag, ctx, "builtin", MIE_BUILTIN_MSG_CANNOT_FIND_BLOCK);
+		const struct mie_diag_highlight hl[] = {
+			{
+				.hl_type = MIE_DIAG_HIGHLIGHT_ERROR,
+				.hl_span = s->s_name_span,
+			},
+		};
+		mie_diag_push_snippet(
+			diag, s->s_name_span.s_start.c_row,
+			s->s_name_span.s_end.c_row, NULL, 0, hl, 1);
+		return false;
+	}
+
+	free(s->s_block_name);
+	s->s_block = dest;
+	s->s_flags |= MIE_OP_F_SUCCESSOR_RESOLVED;
+
+	return true;
+}
+
+bool mie_op_resolve_args(struct mie_op *op, struct mie_ctx *ctx)
+{
+	bool ok = true;
+
+	for (size_t i = 0; i < MIE_VECTOR_COUNT(op->op_args); i++) {
+		if (!resolve_arg(op, &op->op_args.items[i], ctx)) {
+			ok = false;
+		}
+	}
+
+	for (size_t i = 0; i < MIE_VECTOR_COUNT(op->op_successors); i++) {
+		struct mie_op_successor *s = &op->op_successors.items[i];
+		for (size_t k = 0; k < MIE_VECTOR_COUNT(s->s_args); k++) {
+			if (!resolve_arg(op, &s->s_args.items[k], ctx)) {
+				ok = false;
+			}
+		}
+	}
+
+	return ok;
+}
+
+bool mie_op_resolve_successors(struct mie_op *op, struct mie_ctx *ctx)
+{
+	bool ok = true;
+
+	for (size_t i = 0; i < MIE_VECTOR_COUNT(op->op_successors); i++) {
+		if (!resolve_successor(op, &op->op_successors.items[i], ctx)) {
+			ok = false;
+		}
+	}
+
+	return ok;
+}
diff --git a/mie/lt-idom.c b/mie/lt-idom.c
new file mode 100644
index 0000000..86fa787
--- /dev/null
+++ b/mie/lt-idom.c
@@ -0,0 +1,254 @@
+#include <mie/ir/block.h>
+#include <mie/ir/op.h>
+#include <mie/ir/region.h>
+#include <stdio.h>
+
+struct set {
+	MIE_VECTOR_DECLARE(unsigned int, v);
+};
+
+struct dfs_stack_item {
+	struct mie_block *i_parent, *i_node;
+};
+
+struct lt_ctx {
+	size_t nr_nodes;
+	struct mie_block **vertex;
+	struct set *bucket;
+	unsigned int *semi;
+	unsigned int *idom;
+	unsigned int *samedom;
+	unsigned int *parent;
+	unsigned int *ancestor;
+	unsigned int *label;
+
+	MIE_VECTOR_DECLARE(struct dfs_stack_item, dfstack);
+};
+
+#if 0
+static B_BTREE_DEFINE_SIMPLE_INSERT(struct mie_block, b_node, b_id, put_block_by_id);
+static B_BTREE_DEFINE_SIMPLE_GET(
+	struct mie_block, size_t, b_node, b_id, get_block_by_id);
+#endif
+
+static void set_add(struct set *set, unsigned int val)
+{
+	for (size_t i = 0; i < MIE_VECTOR_COUNT(set->v); i++) {
+		if (set->v.items[i] == val) {
+			return;
+		}
+	}
+
+	mie_vector_push_back(set->v, &val, NULL);
+}
+
+static struct mie_block *pop_block_successor(
+	MIE_VECTOR_REF_PARAM(struct mie_block *, successors))
+{
+	size_t count = mie_vector_ref_get_count(successors);
+	if (count == 0) {
+		return false;
+	}
+
+	struct mie_block *out = mie_vector_ref_get_item(successors, count - 1);
+	mie_vector_ref_pop_back(successors, NULL);
+
+	return out;
+}
+
+static void enqueue_block_successors(
+	struct mie_block *block,
+	MIE_VECTOR_REF_PARAM(struct mie_block *, successors))
+{
+	struct mie_op_successor *s = mie_block_get_first_successor(block);
+	struct mie_block_predecessor pred = {.p_block = block};
+
+	while (s) {
+		if (s->s_flags & MIE_OP_F_SUCCESSOR_RESOLVED) {
+			mie_vector_ref_push_back(successors, &s->s_block, NULL);
+			mie_vector_push_back(s->s_block->b_ipred, &pred, NULL);
+		}
+
+		s = mie_block_get_next_successor(block, s);
+	}
+}
+
+static void dfs_stack_pop(
+	struct lt_ctx *ctx, struct mie_block **parent, struct mie_block **node)
+{
+	size_t nr = MIE_VECTOR_COUNT(ctx->dfstack);
+	if (!nr) {
+		return;
+	}
+
+	struct dfs_stack_item *item = &ctx->dfstack.items[nr - 1];
+	*parent = item->i_parent;
+	*node = item->i_node;
+	mie_vector_pop_back(ctx->dfstack, NULL);
+}
+
+static void dfs_stack_push(
+	struct lt_ctx *ctx, struct mie_block *parent, struct mie_block *node)
+{
+	struct dfs_stack_item item = {.i_node = node, .i_parent = parent};
+	mie_vector_push_back(ctx->dfstack, &item, NULL);
+}
+
+static void dfs(struct lt_ctx *ctx, struct mie_block *root)
+{
+	dfs_stack_push(ctx, NULL, root);
+	unsigned int id = 1;
+
+	while (MIE_VECTOR_COUNT(ctx->dfstack) > 0) {
+		struct mie_block *p, *n;
+		dfs_stack_pop(ctx, &p, &n);
+
+		if (n->b_id != MIE_BLOCK_ID_INVALID) {
+			continue;
+		}
+
+#if 0
+		printf("dfs(p=%s, n=%s)\n", p ? p->b_name.n_str : "NA",
+		       n->b_name.n_str);
+#endif
+
+		n->b_id = id++;
+		ctx->vertex[n->b_id] = n;
+		ctx->semi[n->b_id] = n->b_id;
+		ctx->parent[n->b_id] = p ? p->b_id : MIE_BLOCK_ID_INVALID;
+
+		struct mie_op_successor *s = mie_block_get_first_successor(n);
+		while (s) {
+			dfs_stack_push(ctx, n, s->s_block);
+			mie_vector_push_back(s->s_block->b_ipred, &n, NULL);
+			s = mie_block_get_next_successor(n, s);
+		}
+	}
+}
+
+static void link(struct lt_ctx *ctx, unsigned int parent, unsigned int node)
+{
+	ctx->ancestor[node] = parent;
+	ctx->label[node] = node;
+}
+
+static unsigned int eval(struct lt_ctx *ctx, unsigned int v)
+{
+	unsigned int a = ctx->ancestor[v];
+	if (ctx->ancestor[a] > MIE_BLOCK_ID_INVALID) {
+		unsigned int b = eval(ctx, a);
+		ctx->ancestor[v] = ctx->ancestor[a];
+		if (ctx->semi[b] < ctx->semi[ctx->label[v]]) {
+			ctx->label[v] = b;
+		}
+	}
+
+	return ctx->label[v];
+}
+
+static void reset_block_relationship_metadata(struct mie_region *region)
+{
+	b_queue_entry *cur = b_queue_first(&region->r_blocks);
+	while (cur) {
+		struct mie_block *block = b_unbox(struct mie_block, cur, b_entry);
+
+		block->b_id = MIE_BLOCK_ID_INVALID;
+		block->b_idom = NULL;
+		// block->b_sdom   = block->b_dfs_parent = NULL;
+		mie_vector_destroy(block->b_ipred, NULL);
+
+		cur = b_queue_next(cur);
+	}
+
+	memset(&region->r_blocks_s, 0x0, sizeof region->r_blocks_s);
+}
+
+static void lt_ctx_init(struct lt_ctx *ctx, size_t nr_nodes)
+{
+	memset(ctx, 0x0, sizeof *ctx);
+	ctx->idom = calloc(nr_nodes + 1, sizeof(unsigned int));
+	ctx->samedom = calloc(nr_nodes + 1, sizeof(unsigned int));
+	ctx->vertex = calloc(nr_nodes + 1, sizeof(struct mie_block *));
+	ctx->bucket = calloc(nr_nodes + 1, sizeof(struct set));
+	ctx->semi = calloc(nr_nodes + 1, sizeof(unsigned int));
+	ctx->parent = calloc(nr_nodes + 1, sizeof(unsigned int));
+	ctx->ancestor = calloc(nr_nodes + 1, sizeof(unsigned int));
+	ctx->label = calloc(nr_nodes + 1, sizeof(unsigned int));
+}
+
+static void lt_ctx_cleanup(struct lt_ctx *ctx)
+{
+	free(ctx->idom);
+	free(ctx->samedom);
+	free(ctx->vertex);
+	free(ctx->bucket);
+	free(ctx->semi);
+	free(ctx->parent);
+	free(ctx->ancestor);
+	free(ctx->label);
+}
+
+void mie_region_refresh_dominance(struct mie_region *region)
+{
+	struct lt_ctx ctx;
+	size_t nr_nodes = b_queue_length(&region->r_blocks);
+	lt_ctx_init(&ctx, nr_nodes);
+
+	struct mie_block *root = mie_region_get_first_block(region);
+
+	reset_block_relationship_metadata(region);
+	dfs(&ctx, root);
+
+	for (size_t i = nr_nodes; i > 0; i--) {
+		struct mie_block *n = ctx.vertex[i];
+		unsigned int p = ctx.parent[i];
+		unsigned int s = p;
+
+		struct mie_block_predecessor *pred
+			= mie_block_get_first_predecessor(n);
+		while (pred) {
+			struct mie_block *v = pred->p_block;
+			unsigned int s_prime = MIE_BLOCK_ID_INVALID;
+
+			if (v->b_id <= n->b_id) {
+				s_prime = v->b_id;
+			} else {
+				s_prime = eval(&ctx, v->b_id);
+				s_prime = ctx.semi[s_prime];
+			}
+
+			if (s_prime < s) {
+				s = s_prime;
+			}
+
+			pred = mie_block_get_next_predecessor(n, pred);
+		}
+
+		ctx.semi[n->b_id] = s;
+		set_add(&ctx.bucket[s], n->b_id);
+		link(&ctx, p, n->b_id);
+
+		for (size_t k = 0; k < MIE_VECTOR_COUNT(ctx.bucket[p].v); k++) {
+			unsigned int v = ctx.bucket[p].v.items[k];
+			unsigned int y = eval(&ctx, v);
+			if (ctx.semi[y] == ctx.semi[p]) {
+				ctx.idom[v] = p;
+			} else {
+				ctx.samedom[v] = y;
+			}
+		}
+	}
+
+	for (size_t i = 1; i <= nr_nodes; i++) {
+		struct mie_block *n = ctx.vertex[i];
+		if (ctx.samedom[i] > 0) {
+			ctx.idom[i] = ctx.idom[ctx.samedom[i]];
+		}
+
+		n->b_idom = ctx.vertex[ctx.idom[i]];
+		// n->b_sdom = ctx.vertex[ctx.semi[i]];
+		// n->b_dfs_parent = ctx.vertex[ctx.parent[i]];
+	}
+
+	lt_ctx_cleanup(&ctx);
+}
diff --git a/mie/parse/lex.c b/mie/parse/lex.c
index 7b40511..4878432 100644
--- a/mie/parse/lex.c
+++ b/mie/parse/lex.c
@@ -211,6 +211,11 @@ enum mie_status mie_lex_get_status(const struct mie_lex *lex)
 	return lex->lex_status;
 }
 
+struct mie_line_source *mie_lex_get_line_source(const struct mie_lex *lex)
+{
+	return lex->lex_source;
+}
+
 static bool char_can_begin_symbol(char c)
 {
 	for (size_t i = 0; i < nr_symbols; i++) {
@@ -774,8 +779,10 @@ static enum mie_status pump_tokens(struct mie_lex *lex)
 		= mie_line_source_get_cursor(lex->lex_source);
 	unsigned long line = cursor->c_row;
 	const struct mie_diag_highlight hl[] = {
-		{.hl_type = MIE_DIAG_HIGHLIGHT_ERROR,
-	         .hl_span = {.s_start = *cursor, .s_end = *cursor}},
+		{
+			.hl_type = MIE_DIAG_HIGHLIGHT_ERROR,
+			.hl_span = {.s_start = *cursor, .s_end = *cursor},
+		},
 	};
 	const size_t nr_hl = sizeof hl / sizeof hl[0];
 	mie_diag_push_snippet(diag, line, line, NULL, 0, hl, nr_hl);
diff --git a/mie/parse/parser.c b/mie/parse/parser.c
index 9713327..c787fb8 100644
--- a/mie/parse/parser.c
+++ b/mie/parse/parser.c
@@ -543,6 +543,8 @@ bool mie_parser_parse_operand(struct mie_parser *ctx, struct mie_op_arg *out)
 		result = true;
 	}
 
+	out->arg_span = loc;
+
 	return result;
 }
 
@@ -611,6 +613,8 @@ bool mie_parser_parse_parameter(struct mie_parser *ctx, struct mie_op_arg *out)
 		return false;
 	}
 
+	out->arg_span = loc;
+
 	if (!mie_parser_parse_symbol(ctx, MIE_SYM_COLON)) {
 		return false;
 	}
@@ -710,6 +714,7 @@ bool mie_parser_parse_register(
 		break;
 	}
 
+	out->reg_span = tok->tok_location;
 	mie_parser_advance(ctx);
 
 	return name != NULL;
@@ -927,6 +932,8 @@ bool mie_parser_parse_block(
 		return false;
 	}
 
+	memcpy(&block->b_name.n_span, &span, sizeof span);
+
 	if (mie_parser_peek_symbol(ctx) == MIE_SYM_LEFT_PAREN
 	    && !parse_block_parameters(ctx, names, block)) {
 		return false;
@@ -964,9 +971,8 @@ bool mie_parser_parse_successor(struct mie_parser *ctx, struct mie_op_successor
 	memset(out, 0x0, sizeof *out);
 	b_string *str = get_temp_string(ctx);
 	bool result = false;
-	struct mie_file_span span;
 
-	if (!mie_parser_parse_blockname(ctx, str, &span)) {
+	if (!mie_parser_parse_blockname(ctx, str, &out->s_name_span)) {
 		return false;
 	}
 
@@ -1159,6 +1165,15 @@ bool mie_parser_parse_op(
 		}
 	}
 
+	for (size_t i = 0; i < MIE_VECTOR_COUNT(dest->op_result); i++) {
+		struct mie_register *reg = &dest->op_result.items[i];
+		reg->reg_flags |= MIE_REGISTER_F_OP_RESULT;
+		reg->reg_op = dest;
+		reg->reg_block = dest->op_container;
+	}
+
+	dest->op_src = mie_lex_get_line_source(ctx->p_lex);
+
 	if (mie_parser_check_type(ctx, MIE_TOK_NAME)) {
 		/* custom-format operation */
 		return parse_custom_op(ctx, names, dest);
diff --git a/mie/print/op.c b/mie/print/op.c
index f4b19b2..5977684 100644
--- a/mie/print/op.c
+++ b/mie/print/op.c
@@ -11,9 +11,13 @@ void mie_printer_print_op_arg(
 	enum mie_register_flags arg_flags = 0;
 	const char *arg_name = NULL;
 	const struct mie_type *arg_type = NULL;
+	bool resolved = false;
 
 	if (MIE_TEST_FLAGS(arg->arg_flags, MIE_OP_F_ARG_RESOLVED)) {
+		resolved = true;
+
 		if (!arg->arg_value.u_reg) {
+			/* this should only be caused by an internal parser/rewriter bug */
 			arg_flags = 0;
 			arg_name = "<NULL>";
 			arg_type = NULL;
@@ -36,6 +40,12 @@ void mie_printer_print_op_arg(
 
 	b_stream_write_string(printer->p_stream, arg_name, NULL);
 
+	if (!resolved
+	    && MIE_TEST_FLAGS(
+		    printer->p_flags, MIE_PRINT_F_MARK_UNRESOLVED_ELEMENTS)) {
+		b_stream_write_char(printer->p_stream, '?');
+	}
+
 	if (!include_type || !arg_type) {
 		return;
 	}
@@ -50,14 +60,23 @@ void mie_printer_print_op_successor(
 	bool compact)
 {
 	b_stream_write_char(printer->p_stream, '^');
+	bool resolved = false;
+
 	if (successor->s_flags & MIE_OP_F_SUCCESSOR_RESOLVED) {
 		b_stream_write_string(
 			printer->p_stream, successor->s_block->b_name.n_str, NULL);
+		resolved = true;
 	} else {
 		b_stream_write_string(
 			printer->p_stream, successor->s_block_name, NULL);
 	}
 
+	if (!resolved
+	    && MIE_TEST_FLAGS(
+		    printer->p_flags, MIE_PRINT_F_MARK_UNRESOLVED_ELEMENTS)) {
+		b_stream_write_char(printer->p_stream, '?');
+	}
+
 	if (MIE_VECTOR_COUNT(successor->s_args) == 0) {
 		return;
 	}
@@ -210,6 +229,11 @@ static void print_generic_op(struct mie_printer *printer, const struct mie_op *o
 			op->op_info->op_parent->d_name, op->op_info->op_name);
 	} else {
 		b_stream_write_string(printer->p_stream, op->op_name, NULL);
+
+		if (MIE_TEST_FLAGS(
+			    printer->p_flags, MIE_PRINT_F_MARK_UNRESOLVED_ELEMENTS)) {
+			b_stream_write_char(printer->p_stream, '?');
+		}
 	}
 
 	b_stream_write_char(printer->p_stream, '(');