Attempt at an X-Bar syntax for FOPL.

_ → CP₁
CP₁ → C₁″ (LBracketP | ArrowCooP)?
C₁″ → C₁ CP₂
LBracketP → LBracket RBracketP
RBracketP → CP₁ RBracket
CP₂ → PeriodP? C₂″ | C₂ (CP₃ | LBracketP)
C₂″ → C₂ (CP₂ | CP₃ | LBracketP)
CP₃ → C₃″ AndOrCooP | C₃ (CP₄ | LBracketP)
C₃″ → C₃ CP₃
CP₄ → NegP C₄″ | C₄ (CP₅ | LBracketP)
C₄″ → C₄ CP₄
CP₅ → C₅ (VP | EqP)
VP → V LParenP

PeriodP → PeriodP Period′ | QP Period′
QP → NegP QP | Q NP
EqP → (NP | FuncP) Eq″
Eq″ → Eq (NP | FuncP)
NP → N | FuncP
FuncP → Func LParenP
LParenP → LParen RParenP
RParenP → NP RParen″
RParen″ → CommaP? RParen
CommaP → Comma′ CommaP | Comma (NP | FuncP)
NegP → Neg

ArrowCooP → (CP₂ | LBracketP) ArrowCoo″
ArrowCoo″ → ArrowCoo (CP₂ | LBracketP)
AndOrCooP → (CP₃ | LBracketP) AndOrCoo″
AndOrCoo″ → AndOrCoo (CP₂ | LBracketP)

C₁ → ⟪⟫
C₂ → ⟪⟫
C₃ → ⟪⟫
C₄ → ⟪⟫
C₅ → ⟪⟫
ArrowCoo → ⟪→⟫ | ⟪←⟫ | ⟪↔⟫ | ⟪⇒⟫ | ⟪⇐⟫ | ⟪⇔⟫
AndOrCoo → ⟪∧⟫ | ⟪∨⟫ | ⟪⊻⟫
Neg → ⟪¬⟫
Q → ⟪𝜆⟫ | ⟪∀⟫ | ⟪∃⟫ | ⟪∄⟫
Eq → ⟪=⟫ | ⟪≠⟫
LBracket → ⟪[⟫
RBracket → ⟪]⟫
LParen → ⟪(⟫
RParen → ⟪)⟫
Comma → ⟪,⟫
Period → ⟪.⟫
V → ❰[A-Z]+❱
Func → ❰[a-z]+❱
N → ❰[a-z]+❱