1 files changed, 198 insertions, 0 deletions
diff --git a/grammar/item.go b/grammar/item.go
new file mode 100644
index 0000000..153aea4
--- /dev/null
+++ b/grammar/item.go
@@ -0,0 +1,198 @@
+package grammar
+
+import (
+	"crypto/sha256"
+	"encoding/binary"
+	"fmt"
+	"sort"
+	"strconv"
+)
+
+type lrItemID [32]byte
+
+func (id lrItemID) String() string {
+	return fmt.Sprintf("%x", id.num())
+}
+
+func (id lrItemID) num() uint32 {
+	return binary.LittleEndian.Uint32(id[:])
+}
+
+type lookAhead struct {
+	symbols map[symbol]struct{}
+
+	// When propagation is true, an item propagates look-ahead symbols to other items.
+	propagation bool
+}
+
+type lrItem struct {
+	id   lrItemID
+	prod productionID
+
+	// E → E + T
+	//
+	// Dot | Dotted Symbol | Item
+	// ----+---------------+------------
+	// 0   | E             | E →・E + T
+	// 1   | +             | E → E・+ T
+	// 2   | T             | E → E +・T
+	// 3   | Nil           | E → E + T・
+	dot          int
+	dottedSymbol symbol
+
+	// When initial is true, the LHS of the production is the augmented start symbol and dot is 0.
+	// It looks like S' →・S.
+	initial bool
+
+	// When reducible is true, the item looks like E → E + T・.
+	reducible bool
+
+	// When kernel is true, the item is kernel item.
+	kernel bool
+
+	// lookAhead stores look-ahead symbols, and they are terminal symbols.
+	// The item is reducible only when the look-ahead symbols appear as the next input symbol.
+	lookAhead lookAhead
+}
+
+func newLR0Item(prod *production, dot int) (*lrItem, error) {
+	if prod == nil {
+		return nil, fmt.Errorf("production must be non-nil")
+	}
+
+	if dot < 0 || dot > prod.rhsLen {
+		return nil, fmt.Errorf("dot must be between 0 and %v", prod.rhsLen)
+	}
+
+	var id lrItemID
+	{
+		b := []byte{}
+		b = append(b, prod.id[:]...)
+		bDot := make([]byte, 8)
+		binary.LittleEndian.PutUint64(bDot, uint64(dot))
+		b = append(b, bDot...)
+		id = sha256.Sum256(b)
+	}
+
+	dottedSymbol := symbolNil
+	if dot < prod.rhsLen {
+		dottedSymbol = prod.rhs[dot]
+	}
+
+	initial := false
+	if prod.lhs.isStart() && dot == 0 {
+		initial = true
+	}
+
+	reducible := false
+	if dot == prod.rhsLen {
+		reducible = true
+	}
+
+	kernel := false
+	if initial || dot > 0 {
+		kernel = true
+	}
+
+	item := &lrItem{
+		id:           id,
+		prod:         prod.id,
+		dot:          dot,
+		dottedSymbol: dottedSymbol,
+		initial:      initial,
+		reducible:    reducible,
+		kernel:       kernel,
+	}
+
+	return item, nil
+}
+
+type kernelID [32]byte
+
+func (id kernelID) String() string {
+	return fmt.Sprintf("%x", binary.LittleEndian.Uint32(id[:]))
+}
+
+type kernel struct {
+	id    kernelID
+	items []*lrItem
+}
+
+func newKernel(items []*lrItem) (*kernel, error) {
+	if len(items) == 0 {
+		return nil, fmt.Errorf("a kernel need at least one item")
+	}
+
+	// Remove duplicates from items.
+	var sortedItems []*lrItem
+	{
+		m := map[lrItemID]*lrItem{}
+		for _, item := range items {
+			if !item.kernel {
+				return nil, fmt.Errorf("not a kernel item: %v", item)
+			}
+			m[item.id] = item
+		}
+		sortedItems = []*lrItem{}
+		for _, item := range m {
+			sortedItems = append(sortedItems, item)
+		}
+		sort.Slice(sortedItems, func(i, j int) bool {
+			return sortedItems[i].id.num() < sortedItems[j].id.num()
+		})
+	}
+
+	var id kernelID
+	{
+		b := []byte{}
+		for _, item := range sortedItems {
+			b = append(b, item.id[:]...)
+		}
+		id = sha256.Sum256(b)
+	}
+
+	return &kernel{
+		id:    id,
+		items: sortedItems,
+	}, nil
+}
+
+type stateNum int
+
+const stateNumInitial = stateNum(0)
+
+func (n stateNum) Int() int {
+	return int(n)
+}
+
+func (n stateNum) String() string {
+	return strconv.Itoa(int(n))
+}
+
+func (n stateNum) next() stateNum {
+	return stateNum(n + 1)
+}
+
+type lrState struct {
+	*kernel
+	num       stateNum
+	next      map[symbol]kernelID
+	reducible map[productionID]struct{}
+
+	// emptyProdItems stores items that have an empty production like `p → ε` and is reducible.
+	// Thus the items emptyProdItems stores are like `p → ・ε`. emptyProdItems is needed to store
+	// look-ahead symbols because the kernel items don't include these items.
+	//
+	// For instance, we have the following productions, and A is a terminal symbol.
+	//
+	// s' → s
+	// s → A | ε
+	//
+	// CLOSURE({s' → ・s}) generates the following closure, but the kernel of this closure doesn't
+	// include `s → ・ε`.
+	//
+	// s' → ・s
+	// s → ・A
+	// s → ・ε
+	emptyProdItems []*lrItem
+}