-
Notifications
You must be signed in to change notification settings - Fork 0
/
fomega.pl
138 lines (113 loc) · 5.33 KB
/
fomega.pl
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
:- style_check(-singleton).
% ------------------------ SYNTAX ------------------------
k(K) :- K = kStar
; K = kArr(K1,K2) , k(K1),k(K2)
.
t(T) :- T = tVar(X) , atom(X)
; T = tArr(T1,T2) , t(T1),t(T2)
; T = tAll(X,K,T1) , atom(X),k(K),t(T1)
; T = tAbs(TX,K,T2) , atom(TX),k(K),t(T2)
; T = tApp(T1,T2) , t(T1),t(T2)
.
m(M) :- 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 = mTAbs(TX,K,M2) , atom(TX),k(K),m(M2)
; M = mTApp(M1,T2) , m(M1),t(T2)
.
% ------------------------ SUBSTITUTION ------------------------
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,tAll(TX,K,T2),tAll(TX,K,T2_)) :- tsubst2(TX,J,S,T2,T2_).
tsubst(J,S,tAbs(TX,K,T2),tAbs(TX,K,T2_)) :- tsubst2(TX,J,S,T2,T2_).
tsubst(J,S,tApp(T1,T2),tApp(T1_,T2_)) :- tsubst(J,S,T1,T1_),tsubst(J,S,T2,T2_).
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,A,B):-writeln(subst(J,M,A,B)),fail.
subst(J,M,mVar(J),M).
subst(J,M,mAbs(X1,T1,M2),mAbs(X1,T1,M2_)) :- subst2(X1,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,mTAbs(TX,K,M2),mTAbs(TX,K,M2_)) :- subst(J,M,M2,M2_).
subst(J,M,mTApp(M1,T2),mTApp(M1_,T2)) :- subst(J,M,M1,M1_).
subst(J,M,M1,M1).
subst(J,M,A,B):-writeln(error:subst(J,M,A,B)),fail.
subst2(X,X,M,T,T).
subst2(X,J,M,T,T_) :- subst(J,M,T,T_).
tmsubst(J,S,mVar(X),mVar(X)).
tmsubst(J,S,mAbs(X,T1,M2),mAbs(X,T1_,M2_)) :- tsubst(J,S,T1,T1_),tmsubst(J,S,M2,M2_).
tmsubst(J,S,mApp(M1,M2),mApp(M1_,M2_)) :- tmsubst(J,S,M1,M1_),tmsubst(J,S,M2,M2_).
tmsubst(J,S,mTAbs(TX,K,M2),mTAbs(TX,K,M2_)) :- tmsubst2(TX,J,S,M2,M2_).
tmsubst(J,S,mTApp(M1,T2),mTApp(M1_,T2_)) :- tmsubst(J,S,M1,M1_),tsubst(J,S,T2,T2_).
tmsubst2(X,X,S,T,T).
tmsubst2(X,J,S,T,T_) :- tmsubst(J,S,T,T_).
getb(G,X,B) :- member(X-B,G).
gett(G,X,T) :- getb(G,X,bVar(T)).
%gett(G,X,_) :- writeln(error:gett(G,X)),fail.
% ------------------------ EVALUATION ------------------------
v(mAbs(_,_,_)).
v(mTAbs(_,_,_)).
%eval1(G,M,_) :- \+var(M),writeln(eval1(M)),fail.
eval1(G,mApp(mAbs(X,T11,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,mTApp(mTAbs(X,_,M11),T2),M11_) :- tmsubst(X,T2,M11,M11_).
eval1(G,mTApp(M1,T2),mTApp(M1_,T2)) :- eval1(G,M1,M1_).
%eval1(G,M,_):-writeln(error:eval1(G,M)),fail.
eval(G,M,M_) :- eval1(G,M,M1),eval(G,M1,M_).
eval(G,M,M).
% ------------------------ KINDING ------------------------
compute(G,tApp(tAbs(X,_,T12),T2), T) :- tsubst(X,T2,T12,T).
simplify(G,tApp(T1,T2),T_) :- simplify(G,T1,T1_),simplify2(G,tApp(T1_,T2),T_).
simplify(G,T,T_) :- simplify2(G,T,T_).
simplify2(G,T,T_) :- compute(G,T,T1),simplify(G,T1,T_).
simplify2(G,T,T).
teq(G,S,T) :- simplify(G,S,S_),simplify(G,T,T_),teq2(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,tAll(TX1,K1,S2),tAll(_,K2,T2)) :- K1=K2,teq([TX1-bName|G],S2,T2).
teq2(G,tAbs(TX1,K1,S2),tAbs(_,K2,T2)) :- K1=K2,teq([TX1-bName|G],S2,T2).
teq2(G,tApp(S1,S2),tApp(T1,T2)) :- teq(G,S1,T1),teq(G,S2,T2).
kindof(G,T,K) :- kindof1(G,T,K),!.
kindof(G,T,K) :- writeln(error:kindof(T,K)),fail.
kindof1(G,tVar(X),kStar) :- \+member(X-_,G).
kindof1(G,tVar(X),K) :- !,getb(G,X,bTVar(K)).
kindof1(G,tArr(T1,T2),kStar) :- !,kindof(G,T1,kStar),kindof(G,T2,kStar).
kindof1(G,tAll(TX,K1,T2),kStar) :- !,kindof([TX-bTVar(K1)|G],T2,kStar).
kindof1(G,tAbs(TX,K1,T2),kArr(K1,K)) :- !,kindof([TX-bTVar(K1)|G],T2,K).
kindof1(G,tApp(T1,T2),K12) :- !,kindof(G,T1,kArr(K11,K12)),kindof(G,T2,K11).
kindof1(G,T,kStar).
% ------------------------ TYPING ------------------------ *)
%typeof(G,M,_) :- writeln(typeof(G,M)),fail.
typeof(G,mVar(X),T) :- !,gett(G,X,T).
typeof(G,mAbs(X,T1,M2),tArr(T1,T2_)) :- kindof(G,T1,kStar),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,mTAbs(TX,K1,M2),tAll(TX,K1,T2)) :- typeof([TX-bTVar(K1)|G],M2,T2).
typeof(G,mTApp(M1,T2),T12_) :- kindof(G,T2,K2),typeof(G,M1,T1),simplify(G,T1,tAll(X,K2,T12)),tsubst(X,T2,T12,T12_).
typeof(G,M,_) :- writeln(error:typeof(M)),!,halt.
show_bind(G,bName,'').
show_bind(G,bVar(T),R) :- swritef(R,' : %w',[T]).
show_bind(G,bTVar(K1),R) :- swritef(R, ' :: %w',[K1]).
run(eval(M),G,G) :- !,m(M),!,typeof(G,M,T),eval(G,M,M_),!, writeln(M_:T),!.
run(bind(X,Bind),G,[X-Bind|G]) :-
show_bind(G,Bind,S),write(X),writeln(S),!.
run(Ls) :- foldl(run,Ls,[],G).
% ------------------------ TEST ------------------------
% lambda X. lambda x:X. x;
:- run([eval(mTAbs('X',kStar,mAbs(x,tVar('X'),mVar(x))))]).
% (lambda X. lambda x:X. x) [All X.X->X];
:- run([eval(mTApp(mTAbs('X',kStar,mAbs(x,tVar('X'),mVar(x))),tAll('X',kStar,tArr(tVar('X'),tVar('X')))))]).
% T :: *;
% k : T;
:- run([bind('T', bTVar(kStar)),bind(k,bVar(tVar('T')))]).
% TT :: * => *;
% kk : TT;
:- run([bind('TT', bTVar(kArr(kStar,kStar))),bind(kk,bVar(tVar('TT')))]).
% T :: *;
% x : (lambda X::*=>*.T) T;
:- run([
bind('T', bTVar(kStar)),
bind('x', bVar(tApp(tAbs('X',kArr(kStar,kStar),tVar('T')),tVar('T') )))
]).
:- halt.