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
|
program lam; // -*-C-*-ish
/* [Unfinished] evaluator for the untyped lambda calculus with integers */
// Raw values
data Expr = Var(Int x) // de Bruijn indexed variable
| Lam(Expr scope) // Binding
| App(Expr f, Expr s) // Function application
| Const(Int val)
| Inc(Expr ni)
| Dec(Expr nd)
| PrimRec(Expr target,Expr mzero,Expr msuc)
| If(Expr i, Expr t, Expr e);
// Semantic representation of values
data Sem = SemLam(Sem(Sem) scope)
| SemConst(Int val)
| SemPrimRec(Sem target, Sem mzero, Sem msuc)
| SemInc(Sem ni)
| SemDec(Sem nd)
| Blocked(Blocked f, [Sem] args);
// Irreducible terms
data Blocked = BVar(Int x);
data Spine<a> = Lin | Snoc(Spine<a> init, a last);
type Ctxt = Spine<Sem>;
Exception FellOffEndOfContext;
Sem lookup(Int v, Ctxt ctxt)
{
if (v==0) {
return ctxt.last;
} else if (v>0) {
return lookup(v-1,ctxt.init);
} else {
throw(FellOffEndOfContext);
}
}
Sem eval(Ctxt ctxt, Expr e)
{
case e of {
Var(v) -> return lookup(v,ctxt);
| Lam(sc) -> return SemLam(lambda(arg) -> { eval(Snoc(ctxt,arg),sc) });
| App(f,a) -> return lam::apply(ctxt,eval(ctxt,f),eval(ctxt,a));
| Const(c) -> return SemConst(c);
| Inc(n) -> return increment(eval(ctxt,n));
| Dec(n) -> return decrement(eval(ctxt,n));
| PrimRec(t,z,s) ->
return primrec(ctxt, eval(ctxt,t),eval(ctxt,z),eval(ctxt,s));
| If(i,t,e) ->
return runIf(ctxt, eval(ctxt,i),eval(ctxt,t),eval(ctxt,e));
}
}
Sem apply(Ctxt ctxt, Sem f, Sem a)
{
case f of {
SemLam(scfun) -> return scfun(a);
}
}
Sem increment(Sem n)
{
case n of {
SemConst(c) -> return (SemConst(c+1));
}
}
Sem decrement(Sem n)
{
case n of {
SemConst(c) -> return (SemConst(c-1));
}
}
Sem primrec(Ctxt ctxt, Sem t, Sem z, Sem s)
{
case t of {
SemConst(x) ->
if (x==0) {
return z;
}
else
{
dec = SemConst(x-1);
rec = primrec(ctxt,dec,z,s);
return lam::apply(ctxt,lam::apply(ctxt,s,dec),rec);
}
}
}
Sem runIf(Ctxt ctxt, Sem i, Sem t, Sem e)
{
case i of {
SemConst(x) -> if (x!=0) { return t; } else { return e; }
}
}
Void showSem(Sem v)
{
case v of {
SemConst(x) -> putStrLn(String(x));
}
}
Void main()
{
// plus = \m n. primrec n m (\k ih. inc(ih))
plus = Lam(Lam(PrimRec(Var(0),Var(1),
Lam(Lam(Inc(Var(0)))))));
// mult = \m n. primrec n 0 (\k ih. plus m ih)
mult = Lam(Lam(PrimRec(Var(0),Const(0),
Lam(Lam(App(App(plus,Var(3)),Var(0)))))));
// This'll never work because we don't evaluate lazily...
// y = \f . (\x. f (x x)) (\x. f (x x))
y = Lam(App(Lam(App(Var(1),App(Var(0),Var(0)))),
Lam(App(Var(1),App(Var(0),Var(0))))));
// add4 = \x. y (\add4 x. if x==0 then 4 else 1+(add4 (x-1))) x
addbody = Lam(Lam(If(Var(0),Inc(App(Var(1),(Dec(Var(0))))),Const(4))));
add4 = Lam(App(App(y,addbody),Var(0)));
showSem(eval(Lin,App(App(mult, Const(6)),Const(7))));
//showSem(eval(Lin,App(add4,Const(3))));
}
|
