1 (**************************************************************************)
4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
13 (**************************************************************************)
15 (* NOTATION FOR THE FORMAL SYSTEM λδ ****************************************)
17 (* Grammar ******************************************************************)
20 non associative with precedence 90
23 notation "hvbox( ⋆ term 90 k )"
24 non associative with precedence 90
27 notation "hvbox( # term 90 i )"
28 non associative with precedence 90
31 notation "hvbox( § term 90 p )"
32 non associative with precedence 90
36 non associative with precedence 90
39 notation "hvbox( 𝕒 { I } )"
40 non associative with precedence 90
43 notation "hvbox( 𝕔 term 90 T1 . break term 90 T )"
44 non associative with precedence 90
45 for @{ 'SItem $T1 $T }.
47 notation "hvbox( 𝕔 { I } break term 90 T1 . break term 90 T )"
48 non associative with precedence 90
49 for @{ 'SItem $I $T1 $T }.
51 notation "hvbox( 𝕓 { I } break term 90 T1 . break term 90 T )"
52 non associative with precedence 90
53 for @{ 'SBind $I $T1 $T }.
55 notation "hvbox( 𝕗 { I } break term 90 T1 . break term 90 T )"
56 non associative with precedence 90
57 for @{ 'SFlat $I $T1 $T }.
59 notation "hvbox( Ⓐ term 90 T1 . break term 90 T )"
60 non associative with precedence 90
61 for @{ 'ApplV $T1 $T }.
63 notation "hvbox( T . break 𝕓 { I } break term 90 T1 )"
64 non associative with precedence 89
65 for @{ 'DBind $T $I $T1 }.
67 notation > "hvbox( T . break 𝕔 { I } break term 90 T1 )"
68 non associative with precedence 89
69 for @{ 'DBind $T $I $T1 }.
70 *) (**) (* this breaks all parsing *)
71 notation "hvbox( T . break ④ { I } break { T1 , break T2 , break T3 } )"
72 non associative with precedence 47
73 for @{ 'DBind $T $I $T1 $T2 $T3 }.
75 notation "hvbox( # [ x ] )"
76 non associative with precedence 90
79 notation "hvbox( # [ x , break y ] )"
80 non associative with precedence 90
81 for @{ 'Weight $x $y }.
83 notation "hvbox( 𝕊 [ T ] )"
84 non associative with precedence 45
87 notation "hvbox( T1 break [ d , break e ] ≼ break T2 )"
88 non associative with precedence 45
89 for @{ 'SubEq $T1 $d $e $T2 }.
91 (* Substitution *************************************************************)
93 notation "hvbox( ⇧ [ d , break e ] break T1 ≡ break T2 )"
94 non associative with precedence 45
95 for @{ 'RLift $d $e $T1 $T2 }.
97 notation "hvbox( ⇩ [ e ] break L1 ≡ break L2 )"
98 non associative with precedence 45
99 for @{ 'RDrop $e $L1 $L2 }.
101 notation "hvbox( ⇩ [ d , break e ] break L1 ≡ break L2 )"
102 non associative with precedence 45
103 for @{ 'RDrop $d $e $L1 $L2 }.
105 notation "hvbox( T1 break [ d , break e ] ▶ break T2 )"
106 non associative with precedence 45
107 for @{ 'PSubst $T1 $d $e $T2 }.
109 notation "hvbox( L ⊢ break term 90 T1 break [ d , break e ] ▶ break T2 )"
110 non associative with precedence 45
111 for @{ 'PSubst $L $T1 $d $e $T2 }.
113 (* Unfold *******************************************************************)
115 notation "hvbox( @ [ T1 ] break f ≡ break T2 )"
116 non associative with precedence 45
117 for @{ 'RAt $T1 $f $T2 }.
119 notation "hvbox( T1 ▭ break T2 ≡ break T )"
120 non associative with precedence 45
121 for @{ 'RMinus $T1 $T2 $T }.
123 notation "hvbox( ⇧ * [ e ] break T1 ≡ break T2 )"
124 non associative with precedence 45
125 for @{ 'RLiftStar $e $T1 $T2 }.
127 notation "hvbox( ⇩ * [ e ] break L1 ≡ break L2 )"
128 non associative with precedence 45
129 for @{ 'RDropStar $e $L1 $L2 }.
131 notation "hvbox( T1 break [ d , break e ] ▶* break T2 )"
132 non associative with precedence 45
133 for @{ 'PSubstStar $T1 $d $e $T2 }.
135 notation "hvbox( L ⊢ break term 90 T1 break [ d , break e ] ▶* break T2 )"
136 non associative with precedence 45
137 for @{ 'PSubstStar $L $T1 $d $e $T2 }.
139 notation "hvbox( T1 break [ d , break e ] ≡ break T2 )"
140 non associative with precedence 45
141 for @{ 'TSubst $T1 $d $e $T2 }.
143 notation "hvbox( L ⊢ break term 90 T1 break [ d , break e ] ≡ break T2 )"
144 non associative with precedence 45
145 for @{ 'TSubst $L $T1 $d $e $T2 }.
147 (* Static Typing ************************************************************)
149 notation "hvbox( L ⊢ break term 90 T ÷ break A )"
150 non associative with precedence 45
151 for @{ 'AtomicArity $L $T $A }.
153 (* Reducibility *************************************************************)
155 notation "hvbox( ℝ [ T ] )"
156 non associative with precedence 45
157 for @{ 'Reducible $T }.
159 notation "hvbox( L ⊢ ℝ [ T ] )"
160 non associative with precedence 45
161 for @{ 'Reducible $L $T }.
163 notation "hvbox( 𝕀 [ T ] )"
164 non associative with precedence 45
165 for @{ 'NotReducible $T }.
167 notation "hvbox( L ⊢ 𝕀 [ T ] )"
168 non associative with precedence 45
169 for @{ 'NotReducible $L $T }.
171 notation "hvbox( ℕ [ T ] )"
172 non associative with precedence 45
175 notation "hvbox( L ⊢ ℕ [ T ] )"
176 non associative with precedence 45
177 for @{ 'Normal $L $T }.
179 notation "hvbox( 𝕎ℍℝ [ T ] )"
180 non associative with precedence 45
181 for @{ 'WHdReducible $T }.
183 notation "hvbox( L ⊢ 𝕎ℍℝ [ T ] )"
184 non associative with precedence 45
185 for @{ 'WHdReducible $L $T }.
187 notation "hvbox( 𝕎ℍ𝕀 [ T ] )"
188 non associative with precedence 45
189 for @{ 'NotWHdReducible $T }.
191 notation "hvbox( L ⊢ 𝕎ℍ𝕀 [ T ] )"
192 non associative with precedence 45
193 for @{ 'NotWHdReducible $L $T }.
195 notation "hvbox( 𝕎ℍℕ [ T ] )"
196 non associative with precedence 45
197 for @{ 'WHdNormal $T }.
199 notation "hvbox( L ⊢ 𝕎ℍℕ [ T ] )"
200 non associative with precedence 45
201 for @{ 'WHdNormal $L $T }.
203 notation "hvbox( T1 ➡ break T2 )"
204 non associative with precedence 45
205 for @{ 'PRed $T1 $T2 }.
207 notation "hvbox( L ⊢ break term 90 T1 ➡ break T2 )"
208 non associative with precedence 45
209 for @{ 'PRed $L $T1 $T2 }.
211 notation "hvbox( L1 ⊢ ➡ break L2 )"
212 non associative with precedence 45
213 for @{ 'CPRed $L1 $L2 }.
215 (* Computation **************************************************************)
217 notation "hvbox( T1 ➡* break T2 )"
218 non associative with precedence 45
219 for @{ 'PRedStar $T1 $T2 }.
221 notation "hvbox( L ⊢ break term 90 T1 ➡* break T2 )"
222 non associative with precedence 45
223 for @{ 'PRedStar $L $T1 $T2 }.
225 notation "hvbox( L1 ⊢ ➡* break L2 )"
226 non associative with precedence 45
227 for @{ 'CPRedStar $L1 $L2 }.
229 notation "hvbox( ⬇ * T )"
230 non associative with precedence 45
233 notation "hvbox( L ⊢ ⬇ * T )"
234 non associative with precedence 45
237 notation "hvbox( ⦃ L, break T ⦄ break [ R ] ϵ break 〚 A 〛 )"
238 non associative with precedence 45
239 for @{ 'InEInt $R $L $T $A }.
241 notation "hvbox( T1 break [ R ] ⊑ break T2 )"
242 non associative with precedence 45
243 for @{ 'CrSubEq $T1 $R $T2 }.
245 (* Functional ***************************************************************)
247 notation "hvbox( ↑ [ d , break e ] break T )"
248 non associative with precedence 55
249 for @{ 'Lift $d $e $T }.
251 notation "hvbox( [ d ← break V ] break T )"
252 non associative with precedence 55
253 for @{ 'Subst $V $d $T }.
255 notation "hvbox( T1 ⇨ break T2 )"
256 non associative with precedence 45
257 for @{ 'SRed $T1 $T2 }.