private static NonTerminal GetAliasedSymbol(NonTerminal symbol, IReadOnlyDictionary <NonTerminal, ImmutableList <Rule> > rules)
{
var referencingRules = rules.SelectMany(kvp => kvp.Value)
.Where(r => r.Symbols.Contains(symbol))
.ToArray();
return(referencingRules.Length == 1 && referencingRules.Single().Symbols.Count == 1
? referencingRules.Single().Produced
: null);
}
private LeftRecursionRewriter RewriteOne()
{
if (this.aliases.Count != 0)
{
throw new InvalidOperationException("sanity check");
}
// Example with all right associative (left-associative just replaces (+ E)? with (+ EX)*)
//
// START
// E = -E | E * E | E + E | ID
//
// ONE REWRITE
// E = E0 (* E)? | E + E
// E0 = -E0 | ID
//
// TWO REWRITES
// E = E1 (+ E)?
// E1 = E0 (* E)?
// E0 = -E0 | ID
// pick the highest precedence left-recursive rule we can find
var leftRecursiveRule = this.rulesByProduced.SelectMany(kvp => kvp.Value)
.FirstOrDefault(IsSimpleLeftRecursive);
if (leftRecursiveRule == null)
{
return(this);
}
var isBinary = IsSimpleRightRecursive(leftRecursiveRule);
var replacements = new List <RuleReplacement>();
var newSymbol = new NonTerminal($"{leftRecursiveRule.Produced}_{this.rulesByProduced.Count(kvp => kvp.Key.Name.StartsWith(leftRecursiveRule.Produced.Name + "_"))}");
// determine which rules get pushed to the new symbol. These will be any rules that are neither left or simple right recursive
// as well as any simple right-recursive rules that are higher precedence than the current rule. Note: we don't use ToDictionary
// here because we want to preserve order
var leftRecursiveRuleIndex = this.rulesByProduced[leftRecursiveRule.Produced].IndexOf(leftRecursiveRule);
replacements.AddRange(
this.rulesByProduced[leftRecursiveRule.Produced]
.Select(
// this check is simpler than the requirement stated above, because we leverage the fact that we know the current
// rule is the highest-precedence left-recursive rule for the symbol
(r, index) => index < leftRecursiveRuleIndex || (!IsSimpleLeftRecursive(r) && !IsSimpleRightRecursive(r))
// note that right-recursive rules have their last symbol replaced by the new symbol as well. This is to indicate the fact
// that E => -E can't parse as -(1 + 1) because unary minus binds tighter
? new RuleReplacement(r, new Rule(newSymbol, r.Symbols.Select((s, i) => i == r.Symbols.Count - 1 && s == leftRecursiveRule.Produced ? newSymbol : s)))
: null
)
.Where(t => t != null)
);
// associativity is only a binary concept
var isLeftAssociative = isBinary && !this.rightAssociativeRules.Contains(leftRecursiveRule);
if (!isLeftAssociative)
{
// for E ? E : E, we have E = T | T ? E : E
// the former is a no-op
replacements.AddRange(
new[]
{
new RuleReplacement(null, new Rule(leftRecursiveRule.Produced, newSymbol)),
new RuleReplacement(leftRecursiveRule, new Rule(leftRecursiveRule.Produced, leftRecursiveRule.Symbols.Select((s, i) => i == 0 ? newSymbol : s))),
}
);
}
else
{
// for left associativity, we do:
// E = E + E
// E = T List<+T>
// every parse of "+ T" maps to E + E rule
var suffixSymbol = new NonTerminal($"'{string.Join(" ", leftRecursiveRule.Symbols.Skip(1).Take(leftRecursiveRule.Symbols.Count - 2).Append(newSymbol))}'");
var suffixListSymbol = new NonTerminal($"List<{suffixSymbol}>");
replacements.AddRange(
new[]
{
// E = T List<+T>
new RuleReplacement(null, new Rule(leftRecursiveRule.Produced, newSymbol, suffixListSymbol)),
// List<+T> = +T List<+T> | empty
new RuleReplacement(null, new Rule(suffixListSymbol, suffixSymbol, suffixListSymbol)),
new RuleReplacement(null, new Rule(suffixListSymbol)),
// +T = + T
new RuleReplacement(leftRecursiveRule, new Rule(suffixSymbol, leftRecursiveRule.Symbols.Select((s, i) => i == leftRecursiveRule.Symbols.Count - 1 ? newSymbol : s).Skip(1)))
}
);
}
return(this.Replace(replacements));
}
private bool IsAliasOf(Symbol a, NonTerminal b) => a != b && Traverse.Along(a as NonTerminal, s => this.aliases.GetValueOrDefault(s)).Contains(b);
