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 55 T1 . break term 55 T )"
44 non associative with precedence 55
45 for @{ 'SnItem2 $T1 $T }.
47 notation "hvbox( ② { I } break term 55 T1 . break term 55 T )"
48 non associative with precedence 55
49 for @{ 'SnItem2 $I $T1 $T }.
51 notation "hvbox( ⓑ { I } break term 55 T1 . break term 55 T )"
52 non associative with precedence 55
53 for @{ 'SnBind2 $I $T1 $T }.
55 notation "hvbox( ⓕ { I } break term 55 T1 . break term 55 T )"
56 non associative with precedence 55
57 for @{ 'SnFlat2 $I $T1 $T }.
59 notation "hvbox( ⓓ term 55 T1 . break term 55 T2 )"
60 non associative with precedence 55
61 for @{ 'SnAbbr $T1 $T2 }.
63 notation "hvbox( ⓛ term 55 T1 . break term 55 T2 )"
64 non associative with precedence 55
65 for @{ 'SnAbst $T1 $T2 }.
67 notation "hvbox( ⓐ term 55 T1 . break term 55 T2 )"
68 non associative with precedence 55
69 for @{ 'SnAppl $T1 $T2 }.
71 notation "hvbox( ⓣ term 55 T1 . break term 55 T2 )"
72 non associative with precedence 55
73 for @{ 'SnCast $T1 $T2 }.
75 notation "hvbox( Ⓐ term 55 T1 . break term 55 T )"
76 non associative with precedence 55
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 48 T1 )"
84 non associative with precedence 47
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 50
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( L ⊢ break term 46 T1 ≈ break term 46 T2 )"
112 non associative with precedence 45
113 for @{ 'Hom $L $T1 $T2 }.
115 notation "hvbox( T1 ≃ break term 46 T2 )"
116 non associative with precedence 45
117 for @{ 'Iso $T1 $T2 }.
119 (* Substitution *************************************************************)
121 notation "hvbox( L ⊢ break 𝐑 [ d , break e ] break ⦃ T ⦄ )"
122 non associative with precedence 45
123 for @{ 'Reducible $L $d $e $T }.
125 notation "hvbox( L ⊢ break 𝐈 [ d , break e ] break ⦃ T ⦄ )"
126 non associative with precedence 45
127 for @{ 'NotReducible $L $d $e $T }.
129 notation "hvbox( L ⊢ break 𝐍 [ d , break e ] break ⦃ T ⦄ )"
130 non associative with precedence 45
131 for @{ 'Normal $L $d $e $T }.
133 notation "hvbox( ⇧ [ d , break e ] break term 46 T1 ≡ break term 46 T2 )"
134 non associative with precedence 45
135 for @{ 'RLift $d $e $T1 $T2 }.
137 notation "hvbox( T1 break ≼ [ d , break e ] break term 46 T2 )"
138 non associative with precedence 45
139 for @{ 'SubEq $T1 $d $e $T2 }.
141 notation "hvbox( ≼ [ d , break e ] break term 46 T2 )"
142 non associative with precedence 45
143 for @{ 'SubEqTop $d $e $T2 }.
145 notation "hvbox( ⇩ [ e ] break term 46 L1 ≡ break term 46 L2 )"
146 non associative with precedence 45
147 for @{ 'RDrop $e $L1 $L2 }.
149 notation "hvbox( ⇩ [ d , break e ] break term 46 L1 ≡ break term 46 L2 )"
150 non associative with precedence 45
151 for @{ 'RDrop $d $e $L1 $L2 }.
153 notation "hvbox( L ⊢ break ⌘ ⦃ T ⦄ ≡ break term 46 k )"
154 non associative with precedence 45
155 for @{ 'ICM $L $T $k }.
157 notation "hvbox( L ⊢ break term 46 T1 break ▶ [ d , break e ] break term 46 T2 )"
158 non associative with precedence 45
159 for @{ 'PSubst $L $T1 $d $e $T2 }.
161 (* Unfold *******************************************************************)
163 notation "hvbox( @ [ T1 ] break term 46 f ≡ break term 46 T2 )"
164 non associative with precedence 45
165 for @{ 'RAt $T1 $f $T2 }.
167 notation "hvbox( T1 ▭ break term 46 T2 ≡ break term 46 T )"
168 non associative with precedence 45
169 for @{ 'RMinus $T1 $T2 $T }.
171 notation "hvbox( ⇧ * [ e ] break term 46 T1 ≡ break term 46 T2 )"
172 non associative with precedence 45
173 for @{ 'RLiftStar $e $T1 $T2 }.
175 notation "hvbox( ⇩ * [ e ] break term 46 L1 ≡ break term 46 L2 )"
176 non associative with precedence 45
177 for @{ 'RDropStar $e $L1 $L2 }.
179 notation "hvbox( T1 break ▶* [ d , break e ] break term 46 T2 )"
180 non associative with precedence 45
181 for @{ 'PSubstStar $T1 $d $e $T2 }.
183 notation "hvbox( L ⊢ break term 46 T1 break ▶* [ d , break e ] break term 46 T2 )"
184 non associative with precedence 45
185 for @{ 'PSubstStar $L $T1 $d $e $T2 }.
187 notation "hvbox( L ⊢ break term 46 T1 break ▶▶* [ d , break e ] break term 46 T2 )"
188 non associative with precedence 45
189 for @{ 'PSubstStarAlt $L $T1 $d $e $T2 }.
191 notation "hvbox( T1 break [ d , break e ] ≡ break term 46 T2 )"
192 non associative with precedence 45
193 for @{ 'TSubst $T1 $d $e $T2 }.
195 notation "hvbox( L ⊢ break term 46 T1 break [ d , break e ] ≡ break term 46 T2 )"
196 non associative with precedence 45
197 for @{ 'TSubst $L $T1 $d $e $T2 }.
199 notation "hvbox( T1 break [ d , break e ] ≡ ≡ break term 46 T2 )"
200 non associative with precedence 45
201 for @{ 'TSubstAlt $T1 $d $e $T2 }.
203 notation "hvbox( L ⊢ break term 46 T1 break [ d , break e ] ≡ ≡ break term 46 T2 )"
204 non associative with precedence 45
205 for @{ 'TSubstAlt $L $T1 $d $e $T2 }.
207 (* Static typing ************************************************************)
209 notation "hvbox( L ⊢ break term 46 T ⁝ break term 46 A )"
210 non associative with precedence 45
211 for @{ 'AtomicArity $L $T $A }.
213 notation "hvbox( T1 ⁝ ⊑ break term 46 T2 )"
214 non associative with precedence 45
215 for @{ 'CrSubEqA $T1 $T2 }.
217 notation "hvbox( L ⊢ break term 46 T ÷ break term 46 A )"
218 non associative with precedence 45
219 for @{ 'BinaryArity $L $T $A }.
221 notation "hvbox( T1 ÷ ⊑ break term 46 T2 )"
222 non associative with precedence 45
223 for @{ 'CrSubEqB $T1 $T2 }.
225 notation "hvbox( ⦃ h , break L ⦄ ⊢ break term 46 T1 • break term 46 T2 )"
226 non associative with precedence 45
227 for @{ 'StaticType $h $L $T1 $T2 }.
229 (* Unwind *******************************************************************)
231 notation "hvbox( ⦃ h , break L ⦄ ⊢ break term 46 T1 •* break term 46 T2 )"
232 non associative with precedence 45
233 for @{ 'StaticTypeStar $h $L $T1 $T2 }.
235 (* Reducibility *************************************************************)
237 notation "hvbox( 𝐑 [ T ] )"
238 non associative with precedence 45
239 for @{ 'Reducible $T }.
241 notation "hvbox( L ⊢ break 𝐑 [ T ] )"
242 non associative with precedence 45
243 for @{ 'Reducible $L $T }.
245 notation "hvbox( 𝐈 [ T ] )"
246 non associative with precedence 45
247 for @{ 'NotReducible $T }.
249 notation "hvbox( L ⊢ break 𝐈 [ T ] )"
250 non associative with precedence 45
251 for @{ 'NotReducible $L $T }.
253 notation "hvbox( 𝐍 [ T ] )"
254 non associative with precedence 45
257 notation "hvbox( L ⊢ break 𝐍 [ T ] )"
258 non associative with precedence 45
259 for @{ 'Normal $L $T }.
261 notation "hvbox( 𝐖𝐇𝐑 [ T ] )"
262 non associative with precedence 45
263 for @{ 'WHdReducible $T }.
265 notation "hvbox( L ⊢ break 𝐖𝐇𝐑 [ T ] )"
266 non associative with precedence 45
267 for @{ 'WHdReducible $L $T }.
269 notation "hvbox( 𝐖𝐇𝐈 [ T ] )"
270 non associative with precedence 45
271 for @{ 'NotWHdReducible $T }.
273 notation "hvbox( L ⊢ break 𝐖𝐇𝐈 [ T ] )"
274 non associative with precedence 45
275 for @{ 'NotWHdReducible $L $T }.
277 notation "hvbox( 𝐖𝐇𝐍 [ T ] )"
278 non associative with precedence 45
279 for @{ 'WHdNormal $T }.
281 notation "hvbox( L ⊢ break 𝐖𝐇𝐍 [ T ] )"
282 non associative with precedence 45
283 for @{ 'WHdNormal $L $T }.
285 notation "hvbox( T1 ➡ break term 46 T2 )"
286 non associative with precedence 45
287 for @{ 'PRed $T1 $T2 }.
289 notation "hvbox( L ⊢ break term 46 T1 ➡ break term 46 T2 )"
290 non associative with precedence 45
291 for @{ 'PRed $L $T1 $T2 }.
293 notation "hvbox( L1 ⊢ ➡ break term 46 L2 )"
294 non associative with precedence 45
295 for @{ 'CPRed $L1 $L2 }.
297 (* Computation **************************************************************)
299 notation "hvbox( T1 ➡* break term 46 T2 )"
300 non associative with precedence 45
301 for @{ 'PRedStar $T1 $T2 }.
303 notation "hvbox( L ⊢ break term 46 T1 ➡* break term 46 T2 )"
304 non associative with precedence 45
305 for @{ 'PRedStar $L $T1 $T2 }.
307 notation "hvbox( L1 ⊢ ➡* break term 46 L2 )"
308 non associative with precedence 45
309 for @{ 'CPRedStar $L1 $L2 }.
311 notation "hvbox( L ⊢ break term 46 T1 ➡* break 𝐍 [ T2 ] )"
312 non associative with precedence 45
313 for @{ 'PEval $L $T1 $T2 }.
315 notation "hvbox( ⬇ * term 46 T )"
316 non associative with precedence 45
319 notation "hvbox( L ⊢ break ⬇ * term 46 T )"
320 non associative with precedence 45
323 notation "hvbox( L ⊢ break ⬇ ⬇ * term 46 T )"
324 non associative with precedence 45
325 for @{ 'SNAlt $L $T }.
327 notation "hvbox( ⦃ L, break T ⦄ ϵ break [ R ] break 〚 A 〛 )"
328 non associative with precedence 45
329 for @{ 'InEInt $R $L $T $A }.
331 notation "hvbox( T1 ⊑ break [ R ] break term 46 T2 )"
332 non associative with precedence 45
333 for @{ 'CrSubEq $T1 $R $T2 }.
335 (* Conversion ***************************************************************)
337 notation "hvbox( L ⊢ break term 46 T1 ⬌ break term 46 T2 )"
338 non associative with precedence 45
339 for @{ 'PConv $L $T1 $T2 }.
341 notation "hvbox( T1 ⊢ ⬌ break term 46 T2 )"
342 non associative with precedence 45
343 for @{ 'CPConv $T1 $T2 }.
345 (* Equivalence **************************************************************)
347 notation "hvbox( L ⊢ break term 46 T1 ⬌* break term 46 T2 )"
348 non associative with precedence 45
349 for @{ 'PConvStar $L $T1 $T2 }.
351 notation "hvbox( T1 ⊢ ⬌* break term 46 T2 )"
352 non associative with precedence 45
353 for @{ 'CPConvStar $T1 $T2 }.
355 (* Dynamic typing ***********************************************************)
357 notation "hvbox( ⦃ h , break L ⦄ ⊢ break term 46 T1 : break term 46 T2 )"
358 non associative with precedence 45
359 for @{ 'NativeType $h $L $T1 $T2 }.
361 notation "hvbox( ⦃ h , break L ⦄ ⊢ break term 46 T1 :: break term 46 T2 )"
362 non associative with precedence 45
363 for @{ 'NativeTypeAlt $h $L $T1 $T2 }.
365 notation "hvbox( h ⊢ break term 46 L1 : ⊑ break term 46 L2 )"
366 non associative with precedence 45
367 for @{ 'CrSubEqN $h $L1 $L2 }.