Let \(\sysm{G}\) be an abbreviation for \(\sysm{(S\fs(S\bs NP))}\)

\[\begin{align} \textit{donkey} &:=& \sysm{N} &:& \sysm{\lam x.donkey'x} &::& et\\ \textit{student}&:=& \sysm{N} &:& \sysm{\lam x.student'x} &::& et\\ \textit{John} &:=& \sysm{S\fs(S\bs NP)} &:& \sysm{\lam p.p\cnct{}john'} &::& ett\\ \quad \nonumber\\ \textit{sleeps} &:=& \sysm{S\bs NP} &:& \sysm{\lam x.sleeps'x} &::& et\\ \textit{walk(s)} &:=& \sysm{S\bs NP} &:& \sysm{\lam x.walk'x} &::& et\\ \quad \nonumber\\ \textit{lazy} &:=& \sysm{N\fs N} &:& \sysm{\lam p\lam x.p'x \land lazy'x} &::& et(et)\\ \quad \nonumber\\ \textit{slowly} &:=& \sysm{S\bs NP \bs (S\bs NP)} &:& \sysm{\lam p\lam x.slowly'px} &::& et(et)\\ \quad \nonumber\\ \textit{and} &:=& \sysm{G\bs G\fs G} &:& \sysm{\lam p\lam q\lam r.pr \land qr} &::& ett(ett(ett))\\ \quad \nonumber\\ \textit{every} &:=& \sysm{S\fs(S\bs NP)\fs N} &:& \sysm{\lam{p}\lam{q}\forall x.px\to qx} &::& et(ett)\\ \textit{a} &:=& \sysm{S\fs(S\bs NP)\fs N} &:& \sysm{\lam{p}\lam{q}\exists x.px\land qx} &::& et(et t) \end{align}\]