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
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
|
module Term.Syntax
import public Data.SnocList
import public Term
%prefix_record_projections off
-- Combinators
export
Id : Term (ty ~> ty) ctx
Id = Abs (Var Here)
export
Arb : {ty : Ty} -> Term ty ctx
Arb {ty = N} = Zero
Arb {ty = ty ~> ty'} = Const Arb
export
Lit : Nat -> Term N ctx
Lit 0 = Zero
Lit (S k) = Suc (Lit k)
-- HOAS
infix 4 ~>*
public export
(~>*) : SnocList Ty -> Ty -> Ty
sty ~>* ty = foldr (~>) ty sty
export
Abs' : (Term ty (ctx :< ty) -> Term ty' (ctx :< ty)) -> Term (ty ~> ty') ctx
Abs' f = Abs (f $ Var Here)
export
App : {sty : SnocList Ty} -> Term (sty ~>* ty) ctx -> All (flip Term ctx) sty -> Term ty ctx
App t [<] = t
App t (us :< u) = App (App t us) u
export
(.) : {ty, ty' : Ty} -> Term (ty' ~> ty'') ctx -> Term (ty ~> ty') ctx -> Term (ty ~> ty'') ctx
t . u = Abs (App (shift t) [<App (shift u) [<Var Here]])
-- Incomplete Evaluation
data IsFunc : FullTerm (ty ~> ty') ctx -> Type where
ConstFunc : (t : FullTerm ty' ctx) -> IsFunc (Const t)
AbsFunc : (t : FullTerm ty' (ctx :< ty)) -> IsFunc (Abs t)
isFunc : (t : FullTerm (ty ~> ty') ctx) -> Maybe (IsFunc t)
isFunc Var = Nothing
isFunc (Const t) = Just (ConstFunc t)
isFunc (Abs t) = Just (AbsFunc t)
isFunc (App x) = Nothing
isFunc (Rec x) = Nothing
app :
(ratio : Double) ->
{ty : Ty} ->
(t : Term (ty ~> ty') ctx) ->
{auto 0 ok : IsFunc t.value} ->
Term ty ctx ->
Maybe (Term ty' ctx)
app ratio (Const t `Over` thin) u = Just (t `Over` thin)
app ratio (Abs t `Over` thin) u =
let uses = countUses (t `Over` Id) Here in
let sizeU = size u in
if cast (sizeU * uses) <= cast (S (sizeU + uses)) * ratio
then
Just (subst (t `Over` Keep thin) (Base Id :< u))
else
Nothing
App' :
{ty : Ty} ->
(ratio : Double) ->
Term (ty ~> ty') ctx ->
Term ty ctx ->
Maybe (Term ty' ctx)
App' ratio
(Rec (MakePair
t
(MakePair (u `Over` thin2) (Const v `Over` thin3) _ `Over` thin')
_) `Over` thin)
arg =
case (isFunc u, isFunc v) of
(Just ok1, Just ok2) =>
let thinA = thin . thin' . thin2 in
let thinB = thin . thin' . thin3 in
case (app ratio (u `Over` thinA) arg , app ratio (v `Over` thinB) arg)
of
(Just u, Just v) => Just (Rec (wkn t thin) u (Const v))
(Just u, Nothing) => Just (Rec (wkn t thin) u (Const $ App (v `Over` thinB) arg))
(Nothing, Just v) => Just (Rec (wkn t thin) (App (u `Over` thinA) arg) (Const v))
(Nothing, Nothing) =>
Just (Rec (wkn t thin) (App (u `Over` thinA) arg) (Const $ App (v `Over` thinB) arg))
_ => Nothing
App' ratio t arg =
case isFunc t.value of
Just _ => app ratio t arg
Nothing => Nothing
Rec' :
{ty : Ty} ->
FullTerm N ctx' ->
ctx' `Thins` ctx ->
Term ty ctx ->
Term (ty ~> ty) ctx ->
Maybe (Term ty ctx)
Rec' Zero thin u v = Just u
Rec' (Suc t) thin u v =
let rec = maybe (Rec (t `Over` thin) u v) id (Rec' t thin u v) in
Just $ maybe (App v rec) id $ (App' 1 v rec)
Rec' t thin u v = Nothing
eval' : {ty : Ty} -> (fuel : Nat) -> (ratio : Double) -> Term ty ctx -> (Nat, Term ty ctx)
fullEval' : {ty : Ty} -> (fuel : Nat) -> (ratio : Double) -> FullTerm ty ctx -> (Nat, Term ty ctx)
eval' fuel r (t `Over` thin) = mapSnd (flip wkn thin) (fullEval' fuel r t)
fullEval' 0 r t = (0, t `Over` Id)
fullEval' fuel@(S f) r Var = (fuel, Var `Over` Id)
fullEval' fuel@(S f) r (Const t) = mapSnd Const (fullEval' fuel r t)
fullEval' fuel@(S f) r (Abs t) = mapSnd Abs (fullEval' fuel r t)
fullEval' fuel@(S f) r (App (MakePair t u _)) =
case App' r t u of
Just t => (f, t)
Nothing =>
let (fuel', t) = eval' f r t in
let (fuel', u) = eval' (assert_smaller fuel fuel') r u in
(fuel', App t u)
fullEval' fuel@(S f) r Zero = (fuel, Zero `Over` Id)
fullEval' fuel@(S f) r (Suc t) = mapSnd Suc (fullEval' fuel r t)
fullEval' fuel@(S f) r (Rec (MakePair t (MakePair u v _ `Over` thin) _)) =
case Rec' t.value t.thin (wkn u thin) (wkn v thin) of
Just t => (f, t)
Nothing =>
let (fuel', t) = eval' f r t in
let (fuel', u) = eval' (assert_smaller fuel fuel') r u in
let (fuel', v) = eval' (assert_smaller fuel fuel') r v in
(fuel', Rec t (wkn u thin) (wkn v thin))
export
eval :
{ty : Ty} ->
{default 1.5 ratio : Double} ->
{default 20000 fuel : Nat} ->
Term ty ctx ->
Term ty ctx
eval t = loop fuel t
where
loop : Nat -> Term ty ctx -> Term ty ctx
loop fuel t =
case eval' fuel ratio t of
(0, t) => t
(S f, t) => loop (assert_smaller fuel f) t
|
