-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathMarking.agda
153 lines (126 loc) · 6.67 KB
/
Marking.agda
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
open import Data.List using (List; []; _∷_)
open import Data.List.Relation.Unary.All using (All)
open import Data.Product using (_×_; _,_; ∃-syntax; Σ-syntax)
open import Grove.Ident
open import Grove.Marking.STyp
open import Grove.Marking.Typ
open import Grove.Marking.Ctx
open import Grove.Marking.UExp
open import Grove.Marking.MExp
module Grove.Marking.Marking where
infix 4 _⊢_↬⇒_
infix 4 _⊢_↬⇐_
infix 4 _⊢s_↬⇒_
infix 4 _⊢s_↬⇐_
-- mark insertion
mutual
-- synthesis
data _⊢_↬⇒_ : {τ : STyp} (Γ : Ctx) → (e : UExp) → (Γ ⊢⇒ τ) → Set where
MKSVar : ∀ {Γ x τ u}
→ (∋x : Γ ∋ x ∶ τ)
→ Γ ⊢ - x ^ u ↬⇒ ⊢ ∋x ^ u
MKSFree : ∀ {Γ y u}
→ (∌y : Γ ∌ y)
→ Γ ⊢ - y ^ u ↬⇒ ⊢⟦ ∌y ⟧^ u
MKSLam : ∀ {Γ x τ e τ₁ u}
→ {ě : Γ , x ∶ (τ △s) ⊢⇒s τ₁}
→ (e↬⇒ě : Γ , x ∶ (τ △s) ⊢s e ↬⇒ ě)
→ Γ ⊢ -λ x ∶ τ ∙ e ^ u ↬⇒ ⊢λ x ∶ τ ∙ ě ^ u
MKSAp1 : ∀ {Γ e₁ e₂ τ τ₁ τ₂ u}
→ {ě₁ : Γ ⊢⇒s τ}
→ {ě₂ : Γ ⊢⇐s τ₁}
→ (e₁↬⇒ě₁ : Γ ⊢s e₁ ↬⇒ ě₁)
→ (τ▸ : τ ▸ τ₁ -→ τ₂)
→ (e₂↬⇐ě₂ : Γ ⊢s e₂ ↬⇐ ě₂)
→ Γ ⊢ - e₁ ∙ e₂ ^ u ↬⇒ ⊢ ě₁ ∙ ě₂ [ τ▸ ]^ u
MKSAp2 : ∀ {Γ e₁ e₂ τ u}
→ {ě₁ : Γ ⊢⇒s τ}
→ {ě₂ : Γ ⊢⇐s unknown}
→ (e₁↬⇒ě₁ : Γ ⊢s e₁ ↬⇒ ě₁)
→ (τ!▸ : τ !▸-→)
→ (e₂↬⇐ě₂ : Γ ⊢s e₂ ↬⇐ ě₂)
→ Γ ⊢ - e₁ ∙ e₂ ^ u ↬⇒ ⊢⸨ ě₁ ⸩∙ ě₂ [ τ!▸ ]^ u
MKSNum : ∀ {Γ n u}
→ Γ ⊢ -ℕ n ^ u ↬⇒ ⊢ℕ n ^ u
MKSPlus : ∀ {Γ e₁ e₂ u}
→ {ě₁ : Γ ⊢⇐s num}
→ {ě₂ : Γ ⊢⇐s num}
→ (e₁↬⇐ě₁ : Γ ⊢s e₁ ↬⇐ ě₁)
→ (e₂↬⇐ě₂ : Γ ⊢s e₂ ↬⇐ ě₂)
→ Γ ⊢ - e₁ + e₂ ^ u ↬⇒ ⊢ ě₁ + ě₂ ^ u
MKSMultiLocationConflict : ∀ {Γ w v}
→ Γ ⊢ -⋎^ w ^ v ↬⇒ ⊢⋎^ w ^ v
MKSCycleLocationConflict : ∀ {Γ w v}
→ Γ ⊢ -↻^ w ^ v ↬⇒ ⊢↻^ w ^ v
MKSLocalConflictChildren : ∀ {Γ} {ė* : List UChildExp'}
→ (ė↬⇒ě* : All (λ (_ , e) → ∃[ τ ] Σ[ ě ∈ Γ ⊢⇒ τ ] Γ ⊢ e ↬⇒ ě) ė*)
→ List (EdgeId × ∃[ τ ] Γ ⊢⇒ τ)
MKSLocalConflictChildren All.[] = []
MKSLocalConflictChildren (All._∷_ {w , _} (τ , ě , _) ė↬⇒ě*) = (w , τ , ě) ∷ (MKSLocalConflictChildren ė↬⇒ě*)
data _⊢s_↬⇒_ : {τ : STyp} (Γ : Ctx) → (e : UChildExp) → (Γ ⊢⇒s τ) → Set where
MKSHole : ∀ {Γ s}
→ Γ ⊢s -□ s ↬⇒ ⊢□ s
MKSOnly : ∀ {Γ w e τ}
→ {ě : Γ ⊢⇒ τ}
→ (e↬⇒ě : Γ ⊢ e ↬⇒ ě)
→ Γ ⊢s -∶ (w , e) ↬⇒ ⊢∶ (w , ě)
MKSLocalConflict : ∀ {Γ s ė*}
→ (ė↬⇒ě* : All (λ (_ , e) → ∃[ τ ] Σ[ ě ∈ Γ ⊢⇒ τ ] Γ ⊢ e ↬⇒ ě) ė*)
→ Γ ⊢s -⋏ s ė* ↬⇒ ⊢⋏ s (MKSLocalConflictChildren ė↬⇒ě*)
USu→MSu : ∀ {e : UExp} {Γ : Ctx} {τ : STyp} {ě : Γ ⊢⇒ τ} → USubsumable e → Γ ⊢ e ↬⇒ ě → MSubsumable ě
USu→MSu {ě = ⊢_^_ {x = x} ∋x u} USuVar _ = MSuVar
USu→MSu {ě = ⊢⟦ x ⟧^ u} USuVar _ = MSuFree
USu→MSu {ě = ⊢ ě₁ ∙ ě₂ [ τ▸ ]^ u} USuAp _ = MSuAp1
USu→MSu {ě = ⊢⸨ ě₁ ⸩∙ ě₂ [ τ!▸ ]^ u} USuAp _ = MSuAp2
USu→MSu {ě = ⊢ℕ n ^ u} USuNum _ = MSuNum
USu→MSu {ě = ⊢ ě₁ + ě₂ ^ u} USuPlus _ = MSuPlus
-- analysis
data _⊢_↬⇐_ : {τ : STyp} (Γ : Ctx) → (e : UExp) → (Γ ⊢⇐ τ) → Set where
MKALam1 : ∀ {Γ x τ e τ₁ τ₂ τ₃ u}
→ {ě : Γ , x ∶ (τ △s) ⊢⇐s τ₂}
→ (τ₃▸ : τ₃ ▸ τ₁ -→ τ₂)
→ (τ~τ₁ : (τ △s) ~ τ₁)
→ Γ , x ∶ (τ △s) ⊢s e ↬⇐ ě
→ Γ ⊢ (-λ x ∶ τ ∙ e ^ u) ↬⇐ (⊢λ x ∶ τ ∙ ě [ τ₃▸ ∙ τ~τ₁ ]^ u)
MKALam2 : ∀ {Γ x τ e τ' u}
→ {ě : Γ , x ∶ (τ △s) ⊢⇐s unknown}
→ (τ'!▸ : τ' !▸-→)
→ Γ , x ∶ (τ △s) ⊢s e ↬⇐ ě
→ Γ ⊢ (-λ x ∶ τ ∙ e ^ u) ↬⇐ (⊢⸨λ x ∶ τ ∙ ě ⸩[ τ'!▸ ]^ u)
MKALam3 : ∀ {Γ x τ e τ₁ τ₂ τ₃ u}
→ {ě : Γ , x ∶ (τ △s) ⊢⇐s τ₂}
→ (τ₃▸ : τ₃ ▸ τ₁ -→ τ₂)
→ (τ~̸τ₁ : (τ △s) ~̸ τ₁)
→ Γ , x ∶ (τ △s) ⊢s e ↬⇐ ě
→ Γ ⊢ (-λ x ∶ τ ∙ e ^ u) ↬⇐ (⊢λ x ∶⸨ τ ⸩∙ ě [ τ₃▸ ∙ τ~̸τ₁ ]^ u)
MKAMultiLocationConflict : ∀ {Γ w v τ}
→ Γ ⊢ -⋎^ w ^ v ↬⇐ ⊢⋎^_^_ {τ = τ} w v
MKACycleLocationConflict : ∀ {Γ w v τ}
→ Γ ⊢ -↻^ w ^ v ↬⇐ ⊢↻^_^_ {τ = τ} w v
MKASubsume : ∀ {Γ e τ τ'}
→ {ě : Γ ⊢⇒ τ'}
→ (e↬⇒ě : Γ ⊢ e ↬⇒ ě)
→ (τ~τ' : τ ~ τ')
→ (s : USubsumable e)
→ Γ ⊢ e ↬⇐ ⊢∙ ě [ τ~τ' ∙ USu→MSu s e↬⇒ě ]
MKAInconsistentSTypes : ∀ {Γ e τ τ'}
→ {ě : Γ ⊢⇒ τ'}
→ (e↬⇒ě : Γ ⊢ e ↬⇒ ě)
→ (τ~̸τ' : τ ~̸ τ')
→ (s : USubsumable e)
→ Γ ⊢ e ↬⇐ ⊢⸨ ě ⸩[ τ~̸τ' ∙ USu→MSu s e↬⇒ě ]
MKALocalConflictChildren : ∀ {Γ τ} {ė* : List UChildExp'}
→ (ė↬⇐ě* : All (λ (_ , e) → Σ[ ě ∈ Γ ⊢⇐ τ ] Γ ⊢ e ↬⇐ ě) ė*)
→ List (EdgeId × Γ ⊢⇐ τ)
MKALocalConflictChildren All.[] = []
MKALocalConflictChildren (All._∷_ {w , _} (ě , _) ė↬⇐ě*) = (w , ě) ∷ (MKALocalConflictChildren ė↬⇐ě*)
data _⊢s_↬⇐_ : {τ : STyp} (Γ : Ctx) → (e : UChildExp) → (Γ ⊢⇐s τ) → Set where
MKAHole : ∀ {Γ s τ}
→ Γ ⊢s -□ s ↬⇐ ⊢□ {τ = τ} s
MKAOnly : ∀ {Γ w e τ}
→ {ě : Γ ⊢⇐ τ}
→ (e↬⇐ě : Γ ⊢ e ↬⇐ ě)
→ Γ ⊢s -∶ (w , e) ↬⇐ ⊢∶ (w , ě)
MKALocalConflict : ∀ {Γ s ė* τ}
→ (ė↬⇐ě* : All (λ (_ , e) → Σ[ ě ∈ Γ ⊢⇐ τ ] Γ ⊢ e ↬⇐ ě) ė*)
→ Γ ⊢s -⋏ s ė* ↬⇐ ⊢⋏ s (MKALocalConflictChildren ė↬⇐ě*)