atom : type.  %name atom P.
a : atom.
b : atom.
c : atom.
d : atom.
e : atom.

prop : type.  %name prop A.
=> : prop -> prop -> prop.  %infix right 10 =>.
\/ : prop -> prop -> prop.  %infix right 11 \/.
/\ : prop -> prop -> prop.  %infix right 12 /\.
?  : atom -> prop.          %prefix 14 ?.
ff : prop.
tt : prop.

% just as M $ A represented the on-paper judgement M : A,
% true A represents the on-paper judgement A true.

true : prop -> type.    %name true D.

/\I : true (A /\ B)
    <- true A
    <- true B.

/\EL : true A
     <- true (A /\ B).

/\ER : true B
     <- true (A /\ B).

=>I : true (A => B)
    <- (true A -> true B).

=>E : true B
    <- true (A => B)
    <- true A.