:- prompt(_, '').
:- use_module(library(readutil)).
%%%% IDEONE compatibility for mutually recursive predicates %%%%
eqty/2.
unify_oemap/2.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
kind
(KC
,var(X
), K1
) :- first
(X
:K
,KC
).kind(KC,F $ G, K2) :- K2\==row, kind(KC,F,K1->K2),
K1\==row, kind(KC,G,K1).
kind(KC,A -> B, o) :- kind(KC,A,o), kind(KC,B,o).
kind(KC,{R}, o) :- kind(KC,R,row).
kind(KC,[], row).
kind(KC,[X:T|R], row) :- kind(KC,T,o), kind(KC,R,row).
type
(KC
,C
,var(X
), A
) --> { first
(X
:S
,C
) }, inst_ty
(KC
,S
,A
).type(KC,C,lam(X,E),A->B) --> type(KC,[X:mono(A)|C],E,B),
[ kind(KC,A->B,o) ].
type(KC,C,X $ Y, B) --> type(KC,C,X,A->B), type(KC,C,Y,A1),
!, { eqty(A,A1) }. % note the cut !
type(KC,C,let(X=E0,E),T) --> type(KC,C,E0,A),
type(KC,[X:poly(C,A)|C],E,T).
type(KC,C,{XEs}, {R}) --> { zip_with('=',Xs,Es,XEs) },
type_many(KC,C,Es,Ts),
{ zip_with(':',Xs,Ts,R) }.
type(KC,C,sel(L,X), T) --> { first(X:T,R) }, type(KC,C,L,{R}).
first(K:V,[K1:V1|Xs]) :- K = K1, V=V1.
first(K:V,[K1:V1|Xs]) :- K\==K1, first(K:V, Xs).
inst_ty
(KC
,poly
(C
,T
),T2
) --> { copy_term(t
(C
,T
),t
(C
,T1
)), free_variables(T,Xs),
free_variables(T1,Xs1) },
samekinds(KC,Xs,Xs1), { T1=T2 }.
inst_ty(KC,mono(T), T) --> [].
samekinds(KC,[], [] ) --> [].
samekinds(KC,[X|Xs],[Y|Ys]) --> { X\==Y },
[ kind(KC,X,K), kind(KC,Y,K) ],
samekinds(KC,Xs,Ys).
samekinds(KC,[X|Xs],[X|Ys]) --> [], samekinds(KC,Xs,Ys).
zip_with(F,[], [], [] ).
zip_with(F,[X|Xs],[Y|Ys],[FXY|Ps]) :- FXY=..[F,X,Y],
zip_with(F,Xs,Ys,Ps).
type_many(KC,C,[], [] ) --> [].
type_many(KC,C,[E|Es],[T|Ts]) --> type(KC,C,E,T),
type_many(KC,C,Es,Ts).
variablize
(var(X
)) :- gensym
(t
,X
).
infer_type(KC,C,E,T) :-
phrase( type(KC,C,E,T), Gs0 ),
(bagof(Ty
,X^Y^member
(kind
(X
,Ty
,Y
),Gs
),Tys
); Tys
=[]), free_variables(Tys,Xs),
maplist(variablize,Xs), % replace free tyvar to var(t)
maplist
(call,Gs
). % run all goals in Gs
ctx0([ 'Nat':mono(o)
, 'List':mono(o->o)
, 'Pair':mono(o->o->o)
| _
],
[ 'Zero':mono(Nat)
, 'Succ':mono(Nat -> Nat)
, 'Nil' :poly([], List$A)
, 'Cons':poly([], A->((List$A)->(List$A)))
, 'Pair':poly([], A0->B0->Pair$A0$B0)
])
:- Nat
= var('Nat'), List
= var('List'), Pair
=var('Pair').
run(N,T) :- ctx0(KC,C),
Zero
= var('Zero'), Succ
= var('Succ'), Cons
= var('Cons'), Nil
= var('Nil'), E0
= let
(id
=lam
(x
,var(x
)),var(id
)$var
(id
)), % A->A E1
= lam
(y
,let
(x
=lam
(z
,var(y
)),var(x
)$var
(x
))), % A->A E2
= {[z
=lam
(x
,var(x
))]}, % {[z:A->A]} E3
= lam
(r
,sel
(var(r
),x
)), % {[x:A |R]} -> A %E4: {[y:A,x:B |R]} -> Pair$A$B
E4
= lam
(r
,Pair$sel
(var(r
),y
)$sel
(var(r
),x
)), %E5: {[x:(A->A),y:(B->B)]}
E5
= {[x
=lam
(x
,var(x
)),y
=lam
(x
,var(x
))]}, E6 = E4 $ E5, % Pair $ B->B $ A->A
%E7: {[y:A |R]} -> Pair $ A $ {[y:A| R]}
E7
= lam
(r
,Pair$sel
(var(r
),y
)$var
(r
)), E8
= E7 $
{[y
=lam
(x
,var(x
))]}, % Pair $ B->B $ {[y:(B->B)| R]} E9 = E7 $ {[]},
E10 = {[]},
Es = [E0,E1,E2,E3,E4,E5,E6,E7,E8,E9,E10],
nth0(N,Es,E), infer_type(KC,C,E,T).
% related paper:
%
% Membership-Constraints and Complexity in Logic Programming with Sets,
% Frieder Stolzenburg (1996).
% http://l...content-available-to-author-only...r.com/chapter/10.1007%2F978-94-009-0349-4_15
% http://c...content-available-to-author-only...u.edu/viewdoc/summary?doi=10.1.1.54.8356
% more advanced notion of type equality at work
eqty
(A1
,A2
) :- (var(A1
); var(A2
)), !, A1
=A2
.eqty({R1},{R2}) :- !, unify_oemap(R1,R2). % permutation(R1,R2), !.
eqty(A1->B1,A2->B2) :- !, eqty(A2,A1), !, eqty(B1,B2). % in case of subtyping
eqty(A,A).
% set/map membership with extra-logical builtin \==
% to cut down duplicate answers as sets
memb(X,[X|_]).
memb(X,[Y|L]) :- X \== Y, memb(X,L).
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% once inspired by the idea of the paper,
% finite map unification is just like this
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% unify finite maps
unify_map(A,B) :- submap_of(A,B), submap_of(B,A).
submap_of([], _).
submap_of([X:V|R],M) :- first(X:V1,M), eqty(V,V1), submap_of(R,M).
% finite map minus
mapminus(A,[],A).
mapminus([],_,[]).
mapminus([X:V|Ps],B,C) :- first(X:V1,B), !, eqty(V,V1) -> mapminus(Ps,B,C).
mapminus([X:V|Ps],B,[X:V|C]) :- mapminus(Ps,B,C).
% unify open ended maps with possibly uninstantiated variable tail at the end
unify_oemap
(A
,B
) :- ( var(A
); var(B
) ), !, A
=B
.unify_oemap(A,B) :-
split_heads(A,Xs-T1), make_map(Xs,M1),
split_heads(B,Ys-T2), make_map(Ys,M2),
unify_oe_map(M1-T1, M2-T2).
make_map
(L
,M
) :- setof(X
:V
,first
(X
:V
,L
),M
). % remove duplicatesmake_map([],[]).
split_heads([],[]-[]).
split_heads
([X
:V
|T
],[X
:V
]-T
) :- var(T
), !, true.split_heads([X:V|Ps],[X:V|Hs]-T) :- split_heads(Ps,Hs-T).
% helper function for unify_oemap
unify_oe_map(Xs-T1,Ys-T2) :- T1==[], T2==[], unify_map(Xs,Ys).
unify_oe_map(Xs-T1,Ys-T2) :- T1==[], submap_of(Ys,Xs), mapminus(Xs,Ys,T2).
unify_oe_map(Xs-T1,Ys-T2) :- T2==[], submap_of(Xs,Ys), mapminus(Ys,Xs,T1).
unify_oe_map(Xs-T1,Ys-T2) :-
mapminus(Ys,Xs,L1), append(L1,T,T1),
mapminus(Xs,Ys,L2), append(L2,T,T2).
%% ?- unify_oemap([z:string,y:bool|M1],[y:T,x:int|M2]).
%% M1 = [x:int|_G1426],
%% T = bool,
%% M2 = [z:string|_G1426].
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
main:-
process,
process:-
run
(0,T0
), print
(T0
), nl, run
(1,T1
), print
(T1
), nl, run
(2,T2
), print
(T2
), nl, run
(3,T3
), print
(T3
), nl, run
(4,T4
), print
(T4
), nl, run
(5,T5
), print
(T5
), nl, run
(6,T6
), print
(T6
), nl, run
(7,T7
), print
(T7
), nl, run
(8,T8
), print
(T8
), nl, run
(10,T10
), print
(T10
), nl,
:- main.
:- set_prolog_flag(verbose,silent).
:- set_prolog_flag(occurs_check,true).
:- op(500,yfx,$).
:- prompt(_, '').
:- use_module(library(readutil)).

%%%% IDEONE compatibility for mutually recursive predicates %%%%
eqty/2.
unify_oemap/2.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

kind(KC,var(X),   K1) :- first(X:K,KC).
kind(KC,F $ G,    K2) :- K2\==row, kind(KC,F,K1->K2),
                         K1\==row, kind(KC,G,K1).
kind(KC,A -> B,    o) :- kind(KC,A,o), kind(KC,B,o).
kind(KC,{R},       o) :- kind(KC,R,row).
kind(KC,[],      row).
kind(KC,[X:T|R], row) :- kind(KC,T,o), kind(KC,R,row).

type(KC,C,var(X),     A) --> { first(X:S,C) }, inst_ty(KC,S,A).
type(KC,C,lam(X,E),A->B) --> type(KC,[X:mono(A)|C],E,B),
                             [ kind(KC,A->B,o) ].
type(KC,C,X $ Y,      B) --> type(KC,C,X,A->B), type(KC,C,Y,A1),
                             !, { eqty(A,A1) }. % note the cut !
type(KC,C,let(X=E0,E),T) --> type(KC,C,E0,A),
                             type(KC,[X:poly(C,A)|C],E,T).
type(KC,C,{XEs},    {R}) --> { zip_with('=',Xs,Es,XEs) },
                             type_many(KC,C,Es,Ts),
                             { zip_with(':',Xs,Ts,R) }.
type(KC,C,sel(L,X),   T) --> { first(X:T,R) }, type(KC,C,L,{R}).

first(K:V,[K1:V1|Xs]) :- K = K1, V=V1.
first(K:V,[K1:V1|Xs]) :- K\==K1, first(K:V, Xs).

inst_ty(KC,poly(C,T),T2) --> { copy_term(t(C,T),t(C,T1)), 
                               free_variables(T,Xs),
                               free_variables(T1,Xs1) },
                             samekinds(KC,Xs,Xs1), { T1=T2 }.
inst_ty(KC,mono(T),   T) --> [].

samekinds(KC,[],    []    ) --> [].
samekinds(KC,[X|Xs],[Y|Ys]) --> { X\==Y },
                                [ kind(KC,X,K), kind(KC,Y,K) ],
                                samekinds(KC,Xs,Ys).
samekinds(KC,[X|Xs],[X|Ys]) --> [], samekinds(KC,Xs,Ys).

zip_with(F,[],    [],    []      ).
zip_with(F,[X|Xs],[Y|Ys],[FXY|Ps]) :- FXY=..[F,X,Y],
                                      zip_with(F,Xs,Ys,Ps).

type_many(KC,C,[],    []    ) --> [].
type_many(KC,C,[E|Es],[T|Ts]) --> type(KC,C,E,T),
                                  type_many(KC,C,Es,Ts).

variablize(var(X)) :- gensym(t,X).

infer_type(KC,C,E,T) :-
  phrase( type(KC,C,E,T), Gs0 ),
  copy_term(Gs0,Gs), 
  (bagof(Ty,X^Y^member(kind(X,Ty,Y),Gs),Tys); Tys=[]),
  free_variables(Tys,Xs),
  maplist(variablize,Xs), % replace free tyvar to var(t)
  maplist(call,Gs). % run all goals in Gs

ctx0([ 'Nat':mono(o)
     , 'List':mono(o->o)
     , 'Pair':mono(o->o->o)
     | _
     ],
     [ 'Zero':mono(Nat)
     , 'Succ':mono(Nat -> Nat)
     , 'Nil' :poly([], List$A)
     , 'Cons':poly([], A->((List$A)->(List$A)))
     , 'Pair':poly([], A0->B0->Pair$A0$B0)
     ])
  :- Nat = var('Nat'), List = var('List'), Pair=var('Pair').

run(N,T) :- ctx0(KC,C),
  Zero = var('Zero'), Succ = var('Succ'),
  Cons = var('Cons'), Nil = var('Nil'),
  Pair = var('Pair'),
  E0 = let(id=lam(x,var(x)),var(id)$var(id)),     % A->A
  E1 = lam(y,let(x=lam(z,var(y)),var(x)$var(x))), % A->A
  E2 = {[z=lam(x,var(x))]},   % {[z:A->A]}
  E3 = lam(r,sel(var(r),x)),  % {[x:A |R]} -> A
  %E4: {[y:A,x:B |R]} -> Pair$A$B
  E4 = lam(r,Pair$sel(var(r),y)$sel(var(r),x)),
  %E5: {[x:(A->A),y:(B->B)]}
  E5 = {[x=lam(x,var(x)),y=lam(x,var(x))]},
  E6 = E4 $ E5, % Pair $ B->B $ A->A
  %E7: {[y:A |R]} -> Pair $ A $ {[y:A| R]}
  E7 = lam(r,Pair$sel(var(r),y)$var(r)),
  E8 = E7 $ {[y=lam(x,var(x))]}, % Pair $ B->B $ {[y:(B->B)| R]}
  E9 = E7 $ {[]},
  E10 = {[]},
  Es = [E0,E1,E2,E3,E4,E5,E6,E7,E8,E9,E10],
  nth0(N,Es,E), infer_type(KC,C,E,T).


% related paper:
%
% Membership-Constraints and Complexity in Logic Programming with Sets,
% Frieder Stolzenburg (1996).
% http://l...content-available-to-author-only...r.com/chapter/10.1007%2F978-94-009-0349-4_15
% http://c...content-available-to-author-only...u.edu/viewdoc/summary?doi=10.1.1.54.8356

% more advanced notion of type equality at work
eqty(A1,A2) :- (var(A1); var(A2)), !, A1=A2.
eqty({R1},{R2}) :- !, unify_oemap(R1,R2). % permutation(R1,R2), !.
eqty(A1->B1,A2->B2) :- !, eqty(A2,A1), !, eqty(B1,B2). % in case of subtyping
eqty(A,A).

% set/map membership with extra-logical builtin \==
% to cut down duplicate answers as sets
memb(X,[X|_]).
memb(X,[Y|L]) :- X \== Y, memb(X,L).

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% once inspired by the idea of the paper,
% finite map unification is just like this
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% unify finite maps
unify_map(A,B) :- submap_of(A,B), submap_of(B,A).

submap_of([], _).
submap_of([X:V|R],M) :- first(X:V1,M), eqty(V,V1), submap_of(R,M).


% finite map minus
mapminus(A,[],A).
mapminus([],_,[]).
mapminus([X:V|Ps],B,C) :- first(X:V1,B), !, eqty(V,V1) -> mapminus(Ps,B,C).
mapminus([X:V|Ps],B,[X:V|C]) :- mapminus(Ps,B,C).



% unify open ended maps with possibly uninstantiated variable tail at the end
unify_oemap(A,B) :- ( var(A); var(B) ), !, A=B.
unify_oemap(A,B) :-
        split_heads(A,Xs-T1), make_map(Xs,M1),
        split_heads(B,Ys-T2), make_map(Ys,M2),
        unify_oe_map(M1-T1, M2-T2).

make_map(L,M) :- setof(X:V,first(X:V,L),M). % remove duplicates
make_map([],[]).

split_heads([],[]-[]).
split_heads([X:V|T],[X:V]-T) :- var(T), !, true.
split_heads([X:V|Ps],[X:V|Hs]-T) :- split_heads(Ps,Hs-T).

% helper function for unify_oemap
unify_oe_map(Xs-T1,Ys-T2) :- T1==[], T2==[], unify_map(Xs,Ys).
unify_oe_map(Xs-T1,Ys-T2) :- T1==[], submap_of(Ys,Xs), mapminus(Xs,Ys,T2).
unify_oe_map(Xs-T1,Ys-T2) :- T2==[], submap_of(Xs,Ys), mapminus(Ys,Xs,T1).
unify_oe_map(Xs-T1,Ys-T2) :- 
        mapminus(Ys,Xs,L1), append(L1,T,T1),
        mapminus(Xs,Ys,L2), append(L2,T,T2).

%% ?- unify_oemap([z:string,y:bool|M1],[y:T,x:int|M2]).
%% M1 = [x:int|_G1426],
%% T = bool,
%% M2 = [z:string|_G1426].

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

main:-
	process,
	halt.

process:-
    run(0,T0), print(T0), nl,
    run(1,T1), print(T1), nl,
    run(2,T2), print(T2), nl,
    run(3,T3), print(T3), nl,
    run(4,T4), print(T4), nl,
    run(5,T5), print(T5), nl,
    run(6,T6), print(T6), nl,
    run(7,T7), print(T7), nl,
    run(8,T8), print(T8), nl,
    (run(9,T9) -> write("must fail but "), print(T9); print(fail) ), nl,
    run(10,T10), print(T10), nl,
	true.

:- main.


