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fullsimple.pl
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fullsimple.pl
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:- style_check(-singleton).
% ------------------------ SYNTAX ------------------------
l(L) :- atom(L) ; integer(L).
t(T) :- T = tBool
; T = tNat
; T = tUnit
; T = tFloat
; T = tString
; T = tVar(X) , atom(X)
; T = tArr(T1,T2) , t(T1),t(T2)
; T = tRecord(Tf) , maplist([X:T1]>>(l(X),t(T1)),Tf)
; T = tVariant(Tf) , maplist([X:T1]>>(atom(X),t(T1)),Tf)
.
m(M) :- M = mTrue
; M = mFalse
; M = mIf(M1,M2,M3) , m(M1),m(M2),m(M3)
; M = mZero
; M = mSucc(M1) , m(M1)
; M = mPred(M1) , m(M1)
; M = mIsZero(M1) , m(M1)
; M = mUnit
; M = mFloat(F) , float(F)
; M = mTimesfloat(M1,M2), m(M1),m(M2)
; M = mString(X) , atom(X)
; M = mVar(X) , atom(X)
; M = mAbs(X,T1,M1) , atom(X),t(T1),m(M1)
; M = mApp(M1,M2) , m(M1),m(M2)
; M = mLet(X,M1,M2) , atom(X),m(M1),m(M2)
; M = mFix(M1) , m(M1)
; M = mInert(T1) , t(T1)
; M = mAscribe(M1,T1) , m(M1),t(T1)
; M = mRecord(Tf) , maplist([X=M1]>>(l(X),m(M1)), Mf)
; M = mProj(M1,L) , m(M1),l(L)
; M = mCase(M1,Cases) , m(M1), maplist([X=(X1,M2)]>>(atom(X),atom(X1),m(M2)), Cases)
; M = mTag(X,M1,T1) , atom(X),m(M1),t(T1)
.
% ------------------------ SUBSTITUTION ------------------------
maplist2(_,[],[]).
maplist2(F,[X|Xs],[Y|Ys]) :- call(F,X,Y), maplist2(F,Xs,Ys).
tsubst(J,S,tBool,tBool).
tsubst(J,S,tNat,tNat).
tsubst(J,S,tUnit,tUnit).
tsubst(J,S,tFloat,tFloat).
tsubst(J,S,tString,tString).
tsubst(J,S,tVar(J),S).
tsubst(J,S,tVar(X),tVar(X)).
tsubst(J,S,tArr(T1,T2),tArr(T1_,T2_)) :- tsubst(J,S,T1,T1_),tsubst(J,S,T2,T2_).
tsubst(J,S,tRecord(Mf),tRecord(Mf_)) :- maplist([L:T,L:T_]>>tsubst(J,S,T,T_),Mf,Mf_).
tsubst(J,S,tVariant(Mf),tVariant(Mf_)) :- maplist([L:T,L:T_]>>tsubst(J,S,T,T_),Mf,Mf_).
tsubst(J,S,T,T_) :- writeln(error:tsubst(J,S,T,T_)),halt.
tsubst2(X,X,S,T,T).
tsubst2(X,J,S,T,T_) :- tsubst(J,S,T,T_).
subst(J,M,mTrue,mTrue).
subst(J,M,mFalse,mFalse).
subst(J,M,mIf(M1,M2,M3),mIf(M1_,M2_,M3_)) :- subst(J,M,M1,M1_),subst(J,M,M2,M2_),subst(J,M,M3,M3_).
subst(J,M,mZero,mZero).
subst(J,M,mSucc(M1),mSucc(M1_)) :- subst(J,M,M1,M1_).
subst(J,M,mPred(M1),mPred(M1_)) :- subst(J,M,M1,M1_).
subst(J,M,mIsZero(M1),mIsZero(M1_)) :- subst(J,M,M1,M1_).
subst(J,M,mUnit,mUnit).
subst(J,M,mFloat(F1),mFloat(F1)).
subst(J,M,mTimesfloat(M1,M2), mTimesfloat(M1_,M2_)) :- subst(J,M,M1,M1_), subst(J,M,M2,M2_).
subst(J,M,mString(X),mString(X)).
subst(J,M,mVar(J), M).
subst(J,M,mVar(X), mVar(X)).
subst(J,M,mAbs(X,T1,M2),mAbs(X,T1,M2_)) :- subst2(X,J,M,M2,M2_).
subst(J,M,mApp(M1,M2), mApp(M1_,M2_)) :- subst(J,M,M1,M1_), subst(J,M,M2,M2_).
subst(J,M,mLet(X,M1,M2),mLet(X,M1_,M2_)) :- subst(J,M,M1,M1_),subst2(X,J,M,M2,M2_).
subst(J,M,mFix(M1), mFix(M1_)) :- subst(J,M,M1,M1_).
subst(J,M,mInert(T1), mInert(T1)).
subst(J,M,mAscribe(M1,T1), mAscribe(M1_,T1)) :- subst(J,M,M1,M1_).
subst(J,M,mRecord(Mf),mRecord(Mf_)) :- maplist([L=Mi,L=Mi_]>>subst(J,M,Mi,Mi_),Mf,Mf_).
subst(J,M,mProj(M1,L),mProj(M1_,L)) :- subst(J,M,M1,M1_).
subst(J,M,mTag(L,M1,T1), mTag(L,M1_,T1)) :- subst(J,M,M1,M1_).
subst(J,M,mCase(M1,Cases), mCase(M1_,Cases_)) :- subst(J,M,M1,M1_),maplist([L=(X,M2),L=(X,M2_)]>>subst(J,M,M2,M2_), Cases,Cases_).
subst(J,M,S,_) :- writeln(error:subst(J,M,S)),fail.
subst2(J,J,M,S,S).
subst2(X,J,M,S,M_) :- subst(J,M,S,M_).
getb(G,X,B) :- member(X-B,G).
gett(G,X,X) :- getb(G,X,bName).
gett(G,X,T) :- getb(G,X,bVar(T)).
gett(G,X,T) :- getb(G,X,bMAbb(_,some(T))).
%gett(G,X,_) :- writeln(error:gett(G,X)),fail.
% ------------------------ EVALUATION ------------------------
n(mZero).
n(mSucc(M1)) :- n(M1).
v(mTrue).
v(mFalse).
v(M) :- n(M).
v(mUnit).
v(mFloat(_)).
v(mString(_)).
v(mAbs(_,_,_)).
v(mRecord(Mf)) :- maplist([L=M]>>v(M),Mf).
v(mTag(_,M1,_)) :- v(M1).
e([L=M|Mf],M,[L=M_|Mf],M_) :- \+v(M).
e([L=M|Mf],M1,[L=M|Mf_],M_) :- v(M), e(Mf,M1,Mf_,M_).
%eval1(_,M,_) :- writeln(eval1:M),fail.
eval1(G,mIf(mTrue,M2,_),M2).
eval1(G,mIf(mFalse,_,M3),M3).
eval1(G,mIf(M1,M2,M3),mIf(M1_,M2,M3)) :- eval1(G,M1,M1_).
eval1(G,mSucc(M1),mSucc(M1_)) :- eval1(G,M1,M1_).
eval1(G,mPred(mZero),mZero).
eval1(G,mPred(mSucc(N1)),N1) :- n(N1).
eval1(G,mPred(M1),mPred(M1_)) :- eval1(G,M1,M1_).
eval1(G,mIsZero(mZero),mTrue).
eval1(G,mIsZero(mSucc(N1)),mFalse) :- n(N1).
eval1(G,mIsZero(M1),mIsZero(M1_)) :- eval1(G,M1,M1_).
eval1(G,mTimesfloat(mFloat(F1),mFloat(F2)),mFloat(F3)) :- F3 is F1 * F2.
eval1(G,mTimesfloat(V1,M2),mTimesfloat(V1, M2_)) :- v(V1), eval1(G,M2,M2_).
eval1(G,mTimesfloat(M1,M2),mTimesfloat(M1_, M2)) :- eval1(G,M1,M1_).
eval1(G,mVar(X),M) :- getb(G,X,bMAbb(M,_)).
eval1(G,mApp(mAbs(X,_,M12),V2),R) :- v(V2), subst(X, V2, M12, R).
eval1(G,mApp(V1,M2),mApp(V1, M2_)) :- v(V1), eval1(G,M2,M2_).
eval1(G,mApp(M1,M2),mApp(M1_, M2)) :- eval1(G,M1,M1_).
eval1(G,mLet(X,V1,M2),M2_) :- v(V1),subst(X,V1,M2,M2_).
eval1(G,mLet(X,M1,M2),mLet(X,M1_,M2)) :- eval1(G,M1,M1_).
eval1(G,mFix(mAbs(X,T,M12)),M12_) :- subst(X,mFix(mAbs(X,T,M12)),M12,M12_).
eval1(G,mFix(M1),mFix(M1_)) :- eval1(G,M1,M1_).
eval1(G,mAscribe(V1,_), V1) :- v(V1).
eval1(G,mAscribe(M1,T), mAscribe(M1_,T)) :- eval1(G,M1,M1_).
eval1(G,mRecord(Mf),mRecord(Mf_)) :- e(Mf,M,Mf_,M_),eval1(G,M,M_).
eval1(G,mProj(mRecord(Mf),L),M) :- member(L=M,Mf).
eval1(G,mProj(M1,L),mProj(M1_, L)) :- eval1(G,M1,M1_).
eval1(G,mTag(L,M1,T),mTag(L,M1_,T)) :- eval1(G,M1,M1_).
eval1(G,mCase(mTag(L,V11,_),Bs),M_) :- v(V11),member((L=(X,M)),Bs),subst(X,V11,M,M_).
eval1(G,mCase(M1,Bs),mCase(M1_, Bs)) :- eval1(G,M1,M1_).
eval(G,M,M_) :- eval1(G,M,M1), eval(G,M1,M_).
eval(G,M,M).
evalbinding(G,bMAbb(M,T),bMAbb(M_,T)) :- eval(G,M,M_).
evalbinding(G,Bind,Bind).
gettabb(G,X,T) :- getb(G,X,bTAbb(T)).
compute(G,tVar(X),T) :- gettabb(G,X,T).
simplify(G,T,T_) :- compute(G,T,T1),simplify(G,T1,T_).
simplify(G,T,T).
teq(G,S,T) :- simplify(G,S,S_),simplify(G,T,T_),teq2(G,S_,T_).
teq2(G,tBool,tBool).
teq2(G,tNat,tNat).
teq2(G,tUnit,tUnit).
teq2(G,tFloat,tFloat).
teq2(G,tString,tString).
teq2(G,tVar(X),T) :- gettabb(G,X,S),teq(G,S,T).
teq2(G,S,tVar(X)) :- gettabb(G,X,T),teq(G,S,T).
teq2(G,tVar(X),tVar(X)).
teq2(G,tArr(S1,S2),tArr(T1,T2)) :- teq(G,S1,T1),teq(G,S2,T2).
teq2(G,tRecord(Sf),tRecord(Tf)) :- length(Sf,Len),length(Tf,Len),maplist([L:T]>>(member(L:S,Sf),teq(G,S,T)), Tf).
teq2(G,tVariant(Sf),tVariant(Tf)) :- length(Sf,Len),length(Tf,Len),maplist2([L:S,L:T]>>teq(G,S,T),Sf,Tf).
% ------------------------ TYPING ------------------------
%typeof(G,M,_) :- writeln(typeof(G,M)),fail.
typeof(G,mTrue,tBool).
typeof(G,mFalse,tBool).
typeof(G,mIf(M1,M2,M3),T2) :- typeof(G,M1,T1),teq(G,T1,tBool),typeof(G,M2,T2),typeof(G,M3,T3), teq(G,T2,T3).
typeof(G,mZero,tNat).
typeof(G,mSucc(M1),tNat) :- typeof(G,M1,T1),teq(G,T1,tNat),!.
typeof(G,mPred(M1),tNat) :- typeof(G,M1,T1),teq(G,T1,tNat),!.
typeof(G,mIsZero(M1),tBool) :- typeof(G,M1,T1),teq(G,T1,tNat),!.
typeof(G,mUnit,tUnit).
typeof(G,mFloat(_),tFloat).
typeof(G,mTimesfloat(M1,M2),tFloat) :- typeof(G,M1,T1),teq(G,T1,tFloat),typeof(G,M2,T2),teq(G,T2,tFloat).
typeof(G,mString(_),tString).
typeof(G,mVar(X),T) :- gett(G,X,T).
typeof(G,mAbs(X,T1,M2),tArr(T1,T2_)) :- typeof([X-bVar(T1)|G],M2,T2_).
typeof(G,mApp(M1,M2),T12) :- typeof(G,M1,T1),simplify(G,T1,tArr(T11,T12)),typeof(G,M2,T2), teq(G,T11,T2).
typeof(G,mLet(X,M1,M2),T) :- typeof(G,M1,T1),typeof([X-bVar(T1)|G],M2,T).
typeof(G,mFix(M1),T12) :- typeof(G,M1,T1),simplify(G,T1,tArr(T11,T12)),teq(G,T12,T11).
typeof(G,mInert(T),T).
typeof(G,mAscribe(M1,T),T) :- typeof(G,M1,T1),teq(G,T1,T).
typeof(G,mRecord(Mf),tRecord(Tf)) :- maplist([(L=M),(L:T)]>>typeof(G,M,T),Mf,Tf).
typeof(G,mProj(M1,L),T) :- typeof(G,M1,T1),simplify(G,T1,tRecord(Tf)),member(L:T,Tf).
typeof(G,mTag(Li, Mi, T), T) :- simplify(G,T,tVariant(Tf)),member(Li:Te,Tf),typeof(G,Mi, T_),teq(G,T_,Te).
typeof(G,mCase(M, Cases), T1) :-
typeof(G,M,T),simplify(G,T,tVariant(Tf)),
maplist([L=_]>>member(L:_,Tf),Cases),
maplist([Li=(Xi,Mi),Ti_]>>(member(Li:Ti,Tf),typeof([Xi-bVar(Ti)|G],Mi,Ti_)),Cases,[T1|RestT]),
maplist([Tt]>>teq(G,Tt,T1), RestT).
typeof(G,M,_) :- writeln(error:typeof(G,M)),fail.
% ------------------------ MAIN ------------------------
show_bind(G,bName,'').
show_bind(G,bVar(T),R) :- swritef(R,' : %w',[T]).
show_bind(G,bTVar,'').
show_bind(G,bMAbb(M,none),R) :- typeof(G,M,T),swritef(R,' : %w',[T]).
show_bind(G,bMAbb(M,some(T)),R) :- swritef(R,' : %w',[T]).
show_bind(G,bTAbb(T),' :: *').
run(eval(M),G,G) :- !,m(M),!,typeof(G,M,T),!,eval(G,M,M_),!,writeln(M_:T).
run(bind(X,bMAbb(M,none)),G,[X-Bind|G]) :-
typeof(G,M,T),evalbinding(G,bMAbb(M,some(T)),Bind),write(X),show_bind(G,Bind,S),writeln(S).
run(bind(X,bMAbb(M,some(T))),G,[X-Bind|G]) :-
typeof(G,M,T_),teq(G,T_,T),evalbinding(G,bMAbb(M,some(T)),Bind),show_bind(G,Bind,S),write(X),writeln(S).
run(bind(X,Bind),G,[X-Bind_|G]) :-
evalbinding(G,Bind,Bind_),show_bind(G,Bind_,S),write(X),writeln(S).
run(Ls) :- foldl(run,Ls,[],_).
% ------------------------ TEST ------------------------
% lambda x:<a:Bool,b:Bool>. x;
:- run([eval(mAbs(x,tVariant([a:tBool,b:tBool]),mVar(x)))]).
% "hello";
:- run([eval(mString(hello))]).
% unit;
:- run([eval(mUnit)]).
% lambda x:A. x;
:- run([eval(mAbs(x,tVar('A'),mVar(x)))]).
% let x=true in x;
:- run([eval(mLet(x,mTrue,mVar(x)))]).
% timesfloat 2.0 3.14159;
:- run([eval(mTimesfloat(mFloat(2.0),mFloat(3.14159))) ]).
% {x=true, y=false};
:- run([eval(mRecord([x=mTrue,y=mFalse])) ]).
% {x=true, y=false}.x;
:- run([eval(mProj(mRecord([x=mTrue,y=mFalse]),x)) ]).
% {true, false};
:- run([eval(mRecord([1=mTrue,2=mFalse])) ]).
% {true, false}.1;
:- run([eval(mProj(mRecord([1=mTrue,2=mFalse]),1)) ]).
% lambda x:Bool. x;
:- run([eval(mAbs(x,tBool,mVar(x)))]).
% (lambda x:Bool->Bool. if x false then true else false)
% (lambda x:Bool. if x then false else true);
:- run([eval(mApp(mAbs(x,tArr(tBool,tBool), mIf(mApp(mVar(x), mFalse), mTrue, mFalse)),
mAbs(x,tBool, mIf(mVar(x), mFalse, mTrue)))) ]).
% lambda x:Nat. succ x;
:- run([eval(mAbs(x,tNat, mSucc(mVar(x))))]).
% (lambda x:Nat. succ (succ x)) (succ 0);
:- run([eval(mApp(mAbs(x,tNat, mSucc(mSucc(mVar(x)))),mSucc(mZero) )) ]).
% T = Nat->Nat;
% lambda f:T. lambda x:Nat. f (f x);
:- run([bind('T',bTAbb(tArr(tNat,tNat))),
eval(mAbs(f,tVar('T'),mAbs(x,tNat,mApp(mVar(f),mApp(mVar(f),mVar(x))))))]).
% a = let x = succ 2 in succ x;
% a;
:- run([bind(a,bMAbb(mLet(x,mSucc(mSucc(mSucc(mZero))),mSucc(mVar(x))),none)),
eval(mVar(a))]).
% <a=0> as <a:nat,b:bool>
:- run([eval(mTag(a,mPred(mSucc(mZero)),tVariant([a:tNat,b:tBool]))) ]).
% case <a=0> as <a:nat,b:bool> of
% <a=n> ==> isZero(n)
% | <b=b> ==> b;
:- run([eval(mCase(mTag(a,mPred(mSucc(mZero)),tVariant([a:tNat,b:tBool])),[a=(n,mIsZero(mVar(n))),b=(b,mVar(b))] ))]).
:- halt.