Grammar
S -> NP VP	{DCL(VP.sem(NP.sem))}
S -> VP	{IMP(VP.sem(DummyYou))}
S -> Aux NP VP	{YNQ(VP.sem(NP.sem))}
S -> WhWord NP VP	{WHQ(NP.sem.var,VP.sem(NP.sem))}
S -> WhWord Aux NP VP	{WHQ(WhWord.sem,VP.sem(NP.sem))}
NP -> ProperNoun	{ProperNoun.sem}
NP -> MassNoun	{MassNoun.sem}
NP -> Det Nominal	{}
NP -> ComplexDet Nominal	{<∃x Nominal.sem(x) ⋀ GN(x,ComplexDet.sem)>}
Nominal -> Noun	{λx ISA(x,Noun.sem)}
Nominal -> Adj Nominal	{λx Nominal.sem(x) ⋀ AM(x,Adj.sem)}
Nominal -> Noun Nominal	{λx Nominal.sem(x) ⋀ NN(Noun.sem,x)}
Nominal -> Nominal PP	{λz Nominal.sem(z) ⋀ PP.sem(z)}
ComplexDet -> NP 's	{NP.sem}
VP -> Verb NP	{Verb.sem(NP.sem)}
VP -> Verb NP VPto	{Verb.sem(NP.sem,VPto.sem)}
VP -> VP PP	{λy VP.sem(y) ⋀ PP.sem(VP.sem.variable)}
VPto -> to VP	{VP.sem}
PP -> P NP	{P.sem(NP.sem)}
PP -> P NP	{NP.sem}
Lexicon
Noun -> restaurant	{Restaurant}
ProperNoun -> Sally	{Sally}
MassNoun -> bread	{Bread}
Adj -> green	{Green}
Det -> a	{∃}
P -> on	{λx λy On(x,y)}
Verb -> serves	{λxλy ∃ e, x, y ISA(e,Serving) ⋀ Server(e,y) ⋀ Served(e,x)}
Verb -> tell	{λxλyλz ∃ e, y.variable ISA(e,Telling) ⋀ Teller(e,z) ⋀ Tellee(e,x) ⋀ ToldThing(e,y.variable) ⋀ y(x)}