letexercise.pl

:- style_check(-singleton).

% ------------------------   SYNTAX  ------------------------

t(T) :- T = bool
      ; T = top
      ; T = arr(T1,T2)       , t(T1),t(T2)
      .
m(M) :- M = true
      ; M = false
      ; M = if(M1,M2,M3)     , m(M1),m(M2),m(M3)
      ; M = var(X)           , atom(X)
      ; M = fn(X,T1,M1)     , atom(X),t(T1),m(M1)
      ; M = app(M1,M2)       , m(M1),m(M2)
      ; M = let(X,M1,M2)     , atom(X),m(M1),m(M2)
      .

% ------------------------   SUBSTITUTION  ------------------------

subst(J,M,true,true).
subst(J,M,false,false).
subst(J,M,if(M1,M2,M3),if(M1_,M2_,M3_)):- subst(J,M,M1,M1_),subst(J,M,M2,M2_),subst(J,M,M3,M3_).
subst(J,M,var(J), M).
subst(J,M,var(X), var(X)).
subst(J,M,fn(X,T1,M2),fn(X,T1,M2_)):-   subst2(X,J,M,M2,M2_).
subst(J,M,app(M1,M2), app(M1_,M2_)):-     subst(J,M,M1,M1_), subst(J,M,M2,M2_).
subst(J,M,let(X,M1,M2),let(X,M1_,M2_)):-  subst(J,M,M1,M1_),subst2(X,J,M,M2,M2_).
subst2(J,J,M,S,S).
subst2(X,J,M,S,M_) :- subst(J,M,S,M_).

getb(Γ,X,B) :- member(X-B,Γ).
gett(Γ,X,T) :- getb(Γ,X,bVar(T)).
%gett(Γ,X,_) :- writeln(error:gett(Γ,X)),fail.

% ------------------------   EVALUATION  ------------------------

v(true).
v(false).
v(fn(_,_,_)).

%eval1(_,M,_) :- writeln(eval1:M),fail.
eval1(Γ,if(true,M2,_),M2).
eval1(Γ,if(false,_,M3),M3).
eval1(Γ,if(M1,M2,M3),if(M1_,M2,M3)) :- eval1(Γ,M1,M1_).
eval1(Γ,app(fn(X,_,M12),V2),R)     :- v(V2), subst(X, V2, M12, R).
eval1(Γ,app(V1,M2),app(V1, M2_))    :- v(V1), eval1(Γ,M2,M2_).
eval1(Γ,app(M1,M2),app(M1_, M2))    :- eval1(Γ,M1,M1_).
/* Insert case(s) for MLet here */

eval(Γ,M,M_)                          :- eval1(Γ,M,M1), eval(Γ,M1,M_).
eval(Γ,M,M).

% ------------------------   TYPING  ------------------------

%typeof(Γ,M,_)                       :- writeln(typeof(Γ,M)),fail.
typeof(Γ,true,bool).
typeof(Γ,false,bool).
typeof(Γ,if(M1,M2,M3),T2)           :- typeof(Γ,M1,bool),typeof(Γ,M2,T2),typeof(Γ,M3,T2).
typeof(Γ,var(X),T)                  :- gett(Γ,X,T).
typeof(Γ,fn(X,T1,M2),arr(T1,T2_)) :- typeof([X-bVar(T1)|Γ],M2,T2_).
typeof(Γ,app(M1,M2),T12)            :- typeof(Γ,M1,arr(T11,T12)),typeof(Γ,M2,T11).
/* Insert case(s) for MLet here */

% ------------------------   MAIN  ------------------------

show_bind(Γ,bName,'').
show_bind(Γ,bVar(T),R)         :- swritef(R,' : %w',[T]). 

run(eval(M),Γ,Γ)               :- !,m(M),!,typeof(Γ,M,T),!,eval(Γ,M,M_),!,writeln(M_:T).
run(bind(X,Bind),Γ,[X-Bind|Γ]) :- show_bind(Γ,Bind,S),write(X),writeln(S).

run(Ls)                        :- foldl(run,Ls,[],_).

% ------------------------   TEST  ------------------------

% lambda x:Bool. x;
:- run([eval(fn(x,bool,var(x)))]).
% (lambda x:Bool->Bool. if x false then true else false)
%   (lambda x:Bool. if x then false else true); 
:- run([eval(app(fn(x,arr(bool,bool), if(app(var(x), false), true, false)),
                  fn(x,bool, if(var(x), false, true)))) ]). 

:- halt.