A PEG is called ''well-formed''<ref name="For04"/> if it contains no ''[[left recursion|left-recursive]]'' rules, i.e., rules that allow a nonterminal to expand to an expression in which the same nonterminal occurs as the leftmost symbol. For a left-to-right top-down parser, such rules cause infinite regress: parsing will continually expand the same nonterminal without moving forward in the string.
Therefore, to allow packrat parsing, left recursion must be eliminated. For example, in the arithmetic grammar above, it wouldcould beseem tempting to moveexpress someoperator rulesprecedence aroundas soa thatmatter theof precedenceordered orderchoice of— products<code>Value / Product / Sum</code> would mean first try viewing as <code>Value</code>, second try viewing as <code>Product</code>, and sumsonly couldthird betry viewing as <code>Sum</code> — rather than via nesting of definitions. This (non-well-formed) grammar seeks to keep precedence order expressedonly in one line:
<syntaxhighlight lang="peg">
Line 189:
Product ← Expr (('*' / '/') Expr)*
Sum ← Expr (('+' / '-') Expr)*
Expr ← ProductValue / SumProduct / ValueSum
</syntaxhighlight>
In this new grammar,Unfortunately matching an <code>Expr</code> (once it has been found <code>Value</code> did not match) requires testing if a <code>Product</code> matches, while matching a <code>Product</code> requires testing if an <code>Expr</code> matches. Because the term appears in the leftmost position, these rules make up a [[circular definition]] that cannot be resolved. (Circular definitions that can be resolved exist—such as in the original formulation from the first example—but such definitions are required not to exhibit pathological recursion.) However, left-recursive rules can always be rewritten to eliminate left-recursion.<ref name="pegs" /><ref name="AhoSethiUllman 1986">{{cite book |last1=Aho |first1=A.V. |last2=Sethi |first2=R. |last3=Ullman |first3=J.D. |date=1986 |title=Compilers: Principles, Techniques, and Tools |publisher=[[Addison-Wesley Longman]] |place=Boston, MA, USA |url=https://archive.org/details/compilersprincip0000ahoa/ |url-access=registration |isbn=0-201-10088-6}}</ref> For example, the following left-recursive CFG rule:
