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( ⓪ { I } )"
24 non associative with precedence 90
28 non associative with precedence 90
31 notation "hvbox( ⋆ term 90 k )"
32 non associative with precedence 90
35 notation "hvbox( # term 90 i )"
36 non associative with precedence 90
39 notation "hvbox( § term 90 p )"
40 non associative with precedence 90
43 notation "hvbox( ② term 90 T1 . break term 90 T )"
44 non associative with precedence 90
45 for @{ 'SnItem2 $T1 $T }.
47 notation "hvbox( ② { I } break term 90 T1 . break term 90 T )"
48 non associative with precedence 90
49 for @{ 'SnItem2 $I $T1 $T }.
51 notation "hvbox( ⓑ { I } break term 90 T1 . break term 90 T )"
52 non associative with precedence 90
53 for @{ 'SnBind2 $I $T1 $T }.
55 notation "hvbox( ⓕ { I } break term 90 T1 . break term 90 T )"
56 non associative with precedence 90
57 for @{ 'SnFlat2 $I $T1 $T }.
59 notation "hvbox( ⓓ term 90 T1 . break term 90 T2 )"
60 non associative with precedence 90
61 for @{ 'SnAbbr $T1 $T2 }.
63 notation "hvbox( ⓛ term 90 T1 . break term 90 T2 )"
64 non associative with precedence 90
65 for @{ 'SnAbst $T1 $T2 }.
67 notation "hvbox( ⓐ term 90 T1 . break term 90 T2 )"
68 non associative with precedence 90
69 for @{ 'SnAppl $T1 $T2 }.
71 notation "hvbox( ⓣ term 90 T1 . break term 90 T2 )"
72 non associative with precedence 90
73 for @{ 'SnCast $T1 $T2 }.
75 notation "hvbox( Ⓐ term 90 T1 . break term 90 T )"
76 non associative with precedence 90
77 for @{ 'SnApplV $T1 $T }.
79 notation > "hvbox( T . break ②{ I } break term 47 T1 )"
80 non associative with precedence 46
81 for @{ 'DxBind2 $T $I $T1 }.
83 notation "hvbox( T . break ⓑ { I } break term 90 T1 )"
84 non associative with precedence 89
85 for @{ 'DxBind2 $T $I $T1 }.
87 notation "hvbox( T1 . break ⓓ T2 )"
88 left associative with precedence 48
89 for @{ 'DxAbbr $T1 $T2 }.
91 notation "hvbox( T1 . break ⓛ T2 )"
92 left associative with precedence 49
93 for @{ 'DxAbst $T1 $T2 }.
95 notation "hvbox( T . break ④ { I } break { T1 , break T2 , break T3 } )"
96 non associative with precedence 47
97 for @{ 'DxItem4 $T $I $T1 $T2 $T3 }.
99 notation "hvbox( # [ x ] )"
100 non associative with precedence 90
103 notation "hvbox( # [ x , break y ] )"
104 non associative with precedence 90
105 for @{ 'Weight $x $y }.
107 notation "hvbox( 𝕊 [ T ] )"
108 non associative with precedence 45
111 notation "hvbox( T1 break [ d , break e ] ≼ break T2 )"
112 non associative with precedence 45
113 for @{ 'SubEq $T1 $d $e $T2 }.
115 (* Substitution *************************************************************)
117 notation "hvbox( ⇧ [ d , break e ] break T1 ≡ break T2 )"
118 non associative with precedence 45
119 for @{ 'RLift $d $e $T1 $T2 }.
121 notation "hvbox( ⇩ [ e ] break L1 ≡ break L2 )"
122 non associative with precedence 45
123 for @{ 'RDrop $e $L1 $L2 }.
125 notation "hvbox( ⇩ [ d , break e ] break L1 ≡ break L2 )"
126 non associative with precedence 45
127 for @{ 'RDrop $d $e $L1 $L2 }.
129 notation "hvbox( T1 break [ d , break e ] ▶ break T2 )"
130 non associative with precedence 45
131 for @{ 'PSubst $T1 $d $e $T2 }.
133 notation "hvbox( L ⊢ break term 90 T1 break [ d , break e ] ▶ break T2 )"
134 non associative with precedence 45
135 for @{ 'PSubst $L $T1 $d $e $T2 }.
137 (* Unfold *******************************************************************)
139 notation "hvbox( @ [ T1 ] break f ≡ break T2 )"
140 non associative with precedence 45
141 for @{ 'RAt $T1 $f $T2 }.
143 notation "hvbox( T1 ▭ break T2 ≡ break T )"
144 non associative with precedence 45
145 for @{ 'RMinus $T1 $T2 $T }.
147 notation "hvbox( ⇧ * [ e ] break T1 ≡ break T2 )"
148 non associative with precedence 45
149 for @{ 'RLiftStar $e $T1 $T2 }.
151 notation "hvbox( ⇩ * [ e ] break L1 ≡ break L2 )"
152 non associative with precedence 45
153 for @{ 'RDropStar $e $L1 $L2 }.
155 notation "hvbox( T1 break [ d , break e ] ▶* break T2 )"
156 non associative with precedence 45
157 for @{ 'PSubstStar $T1 $d $e $T2 }.
159 notation "hvbox( L ⊢ break term 90 T1 break [ d , break e ] ▶* break T2 )"
160 non associative with precedence 45
161 for @{ 'PSubstStar $L $T1 $d $e $T2 }.
163 notation "hvbox( T1 break [ d , break e ] ≡ break T2 )"
164 non associative with precedence 45
165 for @{ 'TSubst $T1 $d $e $T2 }.
167 notation "hvbox( L ⊢ break term 90 T1 break [ d , break e ] ≡ break T2 )"
168 non associative with precedence 45
169 for @{ 'TSubst $L $T1 $d $e $T2 }.
171 (* Static Typing ************************************************************)
173 notation "hvbox( L ⊢ break term 90 T ÷ break A )"
174 non associative with precedence 45
175 for @{ 'AtomicArity $L $T $A }.
177 notation "hvbox( T1 ÷ ⊑ break T2 )"
178 non associative with precedence 45
179 for @{ 'CrSubEqA $T1 $T2 }.
181 (* Reducibility *************************************************************)
183 notation "hvbox( ℝ [ T ] )"
184 non associative with precedence 45
185 for @{ 'Reducible $T }.
187 notation "hvbox( L ⊢ ℝ [ T ] )"
188 non associative with precedence 45
189 for @{ 'Reducible $L $T }.
191 notation "hvbox( 𝕀 [ T ] )"
192 non associative with precedence 45
193 for @{ 'NotReducible $T }.
195 notation "hvbox( L ⊢ 𝕀 [ T ] )"
196 non associative with precedence 45
197 for @{ 'NotReducible $L $T }.
199 notation "hvbox( ℕ [ T ] )"
200 non associative with precedence 45
203 notation "hvbox( L ⊢ ℕ [ T ] )"
204 non associative with precedence 45
205 for @{ 'Normal $L $T }.
207 notation "hvbox( 𝕎ℍℝ [ T ] )"
208 non associative with precedence 45
209 for @{ 'WHdReducible $T }.
211 notation "hvbox( L ⊢ 𝕎ℍℝ [ T ] )"
212 non associative with precedence 45
213 for @{ 'WHdReducible $L $T }.
215 notation "hvbox( 𝕎ℍ𝕀 [ T ] )"
216 non associative with precedence 45
217 for @{ 'NotWHdReducible $T }.
219 notation "hvbox( L ⊢ 𝕎ℍ𝕀 [ T ] )"
220 non associative with precedence 45
221 for @{ 'NotWHdReducible $L $T }.
223 notation "hvbox( 𝕎ℍℕ [ T ] )"
224 non associative with precedence 45
225 for @{ 'WHdNormal $T }.
227 notation "hvbox( L ⊢ 𝕎ℍℕ [ T ] )"
228 non associative with precedence 45
229 for @{ 'WHdNormal $L $T }.
231 notation "hvbox( T1 ➡ break T2 )"
232 non associative with precedence 45
233 for @{ 'PRed $T1 $T2 }.
235 notation "hvbox( L ⊢ break term 90 T1 ➡ break T2 )"
236 non associative with precedence 45
237 for @{ 'PRed $L $T1 $T2 }.
239 notation "hvbox( L1 ⊢ ➡ break L2 )"
240 non associative with precedence 45
241 for @{ 'CPRed $L1 $L2 }.
243 (* Computation **************************************************************)
245 notation "hvbox( T1 ➡* break T2 )"
246 non associative with precedence 45
247 for @{ 'PRedStar $T1 $T2 }.
249 notation "hvbox( L ⊢ break term 90 T1 ➡* break T2 )"
250 non associative with precedence 45
251 for @{ 'PRedStar $L $T1 $T2 }.
253 notation "hvbox( L1 ⊢ ➡* break L2 )"
254 non associative with precedence 45
255 for @{ 'CPRedStar $L1 $L2 }.
257 notation "hvbox( ⬇ * T )"
258 non associative with precedence 45
261 notation "hvbox( L ⊢ ⬇ * T )"
262 non associative with precedence 45
265 notation "hvbox( ⦃ L, break T ⦄ break [ R ] ϵ break 〚 A 〛 )"
266 non associative with precedence 45
267 for @{ 'InEInt $R $L $T $A }.
269 notation "hvbox( T1 break [ R ] ⊑ break T2 )"
270 non associative with precedence 45
271 for @{ 'CrSubEq $T1 $R $T2 }.
273 (* Functional ***************************************************************)
275 notation "hvbox( ↑ [ d , break e ] break T )"
276 non associative with precedence 55
277 for @{ 'Lift $d $e $T }.
279 notation "hvbox( [ d ← break V ] break T )"
280 non associative with precedence 55
281 for @{ 'Subst $V $d $T }.
283 notation "hvbox( T1 ⇨ break T2 )"
284 non associative with precedence 45
285 for @{ 'SRed $T1 $T2 }.