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( ⓑ { a , I } break term 55 T1 . break term 55 T )"
52 non associative with precedence 55
53 for @{ 'SnBind2 $a $I $T1 $T }.
55 notation "hvbox( + ⓑ { I } break term 55 T1 . break term 55 T )"
56 non associative with precedence 55
57 for @{ 'SnBind2Pos $I $T1 $T }.
59 notation "hvbox( - ⓑ { I } break term 55 T1 . break term 55 T )"
60 non associative with precedence 55
61 for @{ 'SnBind2Neg $I $T1 $T }.
63 notation "hvbox( ⓕ { I } break term 55 T1 . break term 55 T )"
64 non associative with precedence 55
65 for @{ 'SnFlat2 $I $T1 $T }.
67 notation "hvbox( ⓓ { a } term 55 T1 . break term 55 T2 )"
68 non associative with precedence 55
69 for @{ 'SnAbbr $a $T1 $T2 }.
71 notation "hvbox( + ⓓ term 55 T1 . break term 55 T2 )"
72 non associative with precedence 55
73 for @{ 'SnAbbrPos $T1 $T2 }.
75 notation "hvbox( - ⓓ term 55 T1 . break term 55 T2 )"
76 non associative with precedence 55
77 for @{ 'SnAbbrNeg $T1 $T2 }.
79 notation "hvbox( ⓛ { a } term 55 T1 . break term 55 T2 )"
80 non associative with precedence 55
81 for @{ 'SnAbst $a $T1 $T2 }.
83 notation "hvbox( + ⓛ term 55 T1 . break term 55 T2 )"
84 non associative with precedence 55
85 for @{ 'SnAbstPos $T1 $T2 }.
87 notation "hvbox( - ⓛ term 55 T1 . break term 55 T2 )"
88 non associative with precedence 55
89 for @{ 'SnAbstNeg $T1 $T2 }.
91 notation "hvbox( ⓐ term 55 T1 . break term 55 T2 )"
92 non associative with precedence 55
93 for @{ 'SnAppl $T1 $T2 }.
95 notation "hvbox( ⓝ term 55 T1 . break term 55 T2 )"
96 non associative with precedence 55
97 for @{ 'SnCast $T1 $T2 }.
99 notation "hvbox( Ⓐ term 55 T1 . break term 55 T )"
100 non associative with precedence 55
101 for @{ 'SnApplV $T1 $T }.
103 notation > "hvbox( T . break ②{ I } break term 47 T1 )"
104 non associative with precedence 46
105 for @{ 'DxBind2 $T $I $T1 }.
107 notation "hvbox( T . break ⓑ { I } break term 48 T1 )"
108 non associative with precedence 47
109 for @{ 'DxBind2 $T $I $T1 }.
111 notation "hvbox( T1 . break ⓓ T2 )"
112 left associative with precedence 48
113 for @{ 'DxAbbr $T1 $T2 }.
115 notation "hvbox( T1 . break ⓛ T2 )"
116 left associative with precedence 49
117 for @{ 'DxAbst $T1 $T2 }.
119 notation "hvbox( T . break ④ { I } break { T1 , break T2 , break T3 } )"
120 non associative with precedence 50
121 for @{ 'DxItem4 $T $I $T1 $T2 $T3 }.
123 notation "hvbox( # { x } )"
124 non associative with precedence 90
127 notation "hvbox( # { x , break y } )"
128 non associative with precedence 90
129 for @{ 'Weight $x $y }.
131 notation "hvbox( 𝐒 ⦃ T ⦄ )"
132 non associative with precedence 45
135 notation "hvbox( L ⊢ break term 46 T1 ≈ break term 46 T2 )"
136 non associative with precedence 45
137 for @{ 'Hom $L $T1 $T2 }.
139 notation "hvbox( T1 ≃ break term 46 T2 )"
140 non associative with precedence 45
141 for @{ 'Iso $T1 $T2 }.
143 (* Substitution *************************************************************)
145 notation "hvbox( ⇧ [ d , break e ] break term 46 T1 ≡ break term 46 T2 )"
146 non associative with precedence 45
147 for @{ 'RLift $d $e $T1 $T2 }.
149 notation "hvbox( T1 break ≼ [ d , break e ] break term 46 T2 )"
150 non associative with precedence 45
151 for @{ 'SubEq $T1 $d $e $T2 }.
153 notation "hvbox( ≽ [ d , break e ] break term 46 T2 )"
154 non associative with precedence 45
155 for @{ 'SubEqBottom $d $e $T2 }.
157 notation "hvbox( ⇩ [ e ] break term 46 L1 ≡ break term 46 L2 )"
158 non associative with precedence 45
159 for @{ 'RDrop $e $L1 $L2 }.
161 notation "hvbox( ⇩ [ d , break e ] break term 46 L1 ≡ break term 46 L2 )"
162 non associative with precedence 45
163 for @{ 'RDrop $d $e $L1 $L2 }.
165 notation "hvbox( L ⊢ break ⌘ ⦃ T ⦄ ≡ break term 46 k )"
166 non associative with precedence 45
167 for @{ 'ICM $L $T $k }.
169 notation "hvbox( L ⊢ break term 46 T1 break ▶ [ d , break e ] break term 46 T2 )"
170 non associative with precedence 45
171 for @{ 'PSubst $L $T1 $d $e $T2 }.
173 (* Unfold *******************************************************************)
175 notation "hvbox( @ ⦃ T1 , break f ⦄ ≡ break term 46 T2 )"
176 non associative with precedence 45
177 for @{ 'RAt $T1 $f $T2 }.
179 notation "hvbox( T1 ▭ break term 46 T2 ≡ break term 46 T )"
180 non associative with precedence 45
181 for @{ 'RMinus $T1 $T2 $T }.
183 notation "hvbox( ⇧ * [ e ] break term 46 T1 ≡ break term 46 T2 )"
184 non associative with precedence 45
185 for @{ 'RLiftStar $e $T1 $T2 }.
187 notation "hvbox( ⇩ * [ e ] break term 46 L1 ≡ break term 46 L2 )"
188 non associative with precedence 45
189 for @{ 'RDropStar $e $L1 $L2 }.
191 notation "hvbox( T1 break ▶ * [ d , break e ] break term 46 T2 )"
192 non associative with precedence 45
193 for @{ 'PSubstStar $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 @{ 'PSubstStar $L $T1 $d $e $T2 }.
199 notation "hvbox( L ⊢ break term 46 T1 break ▶ ▶ * [ d , break e ] break term 46 T2 )"
200 non associative with precedence 45
201 for @{ 'PSubstStarAlt $L $T1 $d $e $T2 }.
203 notation "hvbox( T1 break ⊢ ▶ * [ d , break e ] break term 46 T2 )"
204 non associative with precedence 45
205 for @{ 'PSubstStarSn $T1 $d $e $T2 }.
207 notation "hvbox( T1 break ⊢ ▶ ▶ * [ d , break e ] break term 46 T2 )"
208 non associative with precedence 45
209 for @{ 'PSubstStarSnAlt $T1 $d $e $T2 }.
211 notation "hvbox( ▼ * [ d , break e ] break term 46 T1 ≡ break term 46 T2 )"
212 non associative with precedence 45
213 for @{ 'TSubst $T1 $d $e $T2 }.
215 notation "hvbox( L ⊢ break ▼ * [ d , break e ] break term 46 T1 ≡ break term 46 T2 )"
216 non associative with precedence 45
217 for @{ 'TSubst $L $T1 $d $e $T2 }.
219 notation "hvbox( ▼ ▼ * [ d , break e ] break term 46 T1 ≡ break term 46 T2 )"
220 non associative with precedence 45
221 for @{ 'TSubstAlt $T1 $d $e $T2 }.
223 notation "hvbox( L ⊢ break ▼ ▼ * [ d , break e ] break term 46 T1 ≡ break term 46 T2 )"
224 non associative with precedence 45
225 for @{ 'TSubstAlt $L $T1 $d $e $T2 }.
227 (* Static typing ************************************************************)
229 notation "hvbox( L ⊢ break term 46 T ⁝ break term 46 A )"
230 non associative with precedence 45
231 for @{ 'AtomicArity $L $T $A }.
233 notation "hvbox( T1 ⁝ ⊑ break term 46 T2 )"
234 non associative with precedence 45
235 for @{ 'CrSubEqA $T1 $T2 }.
237 notation "hvbox( ⦃ h , break L ⦄ ⊢ break term 46 T ÷ break term 46 A )"
238 non associative with precedence 45
239 for @{ 'BinaryArity $h $L $T $A }.
241 notation "hvbox( h ⊢ break term 46 L1 ÷ ⊑ break term 46 L2 )"
242 non associative with precedence 45
243 for @{ 'CrSubEqB $h $L1 $L2 }.
245 notation "hvbox( ⦃ h , break L ⦄ ⊢ break term 46 T1 • break [ g , break l ] break term 46 T2 )"
246 non associative with precedence 45
247 for @{ 'StaticType $h $g $l $L $T1 $T2 }.
249 notation "hvbox( h ⊢ break term 46 L1 • ⊑ [ g ] break term 46 L2 )"
250 non associative with precedence 45
251 for @{ 'CrSubEqS $h $g $L1 $L2 }.
253 (* Unwind *******************************************************************)
255 notation "hvbox( L1 ⊢ ⧫ * break term 46 T ≡ break term 46 L2 )"
256 non associative with precedence 45
257 for @{ 'Unwind $L1 $T $L2 }.
259 (* Reducibility *************************************************************)
261 notation "hvbox( L ⊢ break 𝐑 ⦃ T ⦄ )"
262 non associative with precedence 45
263 for @{ 'Reducible $L $T }.
265 notation "hvbox( L ⊢ break 𝐈 ⦃ T ⦄ )"
266 non associative with precedence 45
267 for @{ 'NotReducible $L $T }.
269 notation "hvbox( L ⊢ break 𝐍 ⦃ T ⦄ )"
270 non associative with precedence 45
271 for @{ 'Normal $L $T }.
273 (* this might be removed *)
274 notation "hvbox( 𝐇𝐑 ⦃ T ⦄ )"
275 non associative with precedence 45
276 for @{ 'HdReducible $T }.
278 (* this might be removed *)
279 notation "hvbox( L ⊢ break 𝐇𝐑 ⦃ T ⦄ )"
280 non associative with precedence 45
281 for @{ 'HdReducible $L $T }.
283 (* this might be removed *)
284 notation "hvbox( 𝐇𝐈 ⦃ T ⦄ )"
285 non associative with precedence 45
286 for @{ 'NotHdReducible $T }.
288 (* this might be removed *)
289 notation "hvbox( L ⊢ break 𝐇𝐈 ⦃ T ⦄ )"
290 non associative with precedence 45
291 for @{ 'NotHdReducible $L $T }.
293 (* this might be removed *)
294 notation "hvbox( 𝐇𝐍 ⦃ T ⦄ )"
295 non associative with precedence 45
296 for @{ 'HdNormal $T }.
298 (* this might be removed *)
299 notation "hvbox( L ⊢ break 𝐇𝐍 ⦃ T ⦄ )"
300 non associative with precedence 45
301 for @{ 'HdNormal $L $T }.
303 notation "hvbox( T1 ➡ break term 46 T2 )"
304 non associative with precedence 45
305 for @{ 'PRed $T1 $T2 }.
307 notation "hvbox( L ⊢ break term 46 T1 ➡ break term 46 T2 )"
308 non associative with precedence 45
309 for @{ 'PRed $L $T1 $T2 }.
311 notation "hvbox( L1 ⊢ ➡ break term 46 L2 )"
312 non associative with precedence 45
313 for @{ 'CPRed $L1 $L2 }.
315 notation "hvbox( ⦃ L1 ⦄ ➡ break ⦃ L2 ⦄ )"
316 non associative with precedence 45
317 for @{ 'FocalizedPRed $L1 $L2 }.
319 notation "hvbox( ⦃ L1, break T1 ⦄ ➡ break ⦃ L2 , break T2 ⦄ )"
320 non associative with precedence 45
321 for @{ 'FocalizedPRed $L1 $T1 $L2 $T2 }.
323 notation "hvbox( ⦃ L1 ⦄ ➡ ➡ break ⦃ L2 ⦄ )"
324 non associative with precedence 45
325 for @{ 'FocalizedPRedAlt $L1 $L2 }.
327 notation "hvbox( ⦃ h , break L ⦄ ⊢ break term 46 T1 ➸ break [ g ] break term 46 T2 )"
328 non associative with precedence 45
329 for @{ 'XPRed $h $g $L $T1 $T2 }.
331 (* Computation **************************************************************)
333 notation "hvbox( T1 ➡* break term 46 T2 )"
334 non associative with precedence 45
335 for @{ 'PRedStar $T1 $T2 }.
337 notation "hvbox( L ⊢ break term 46 T1 ➡* break term 46 T2 )"
338 non associative with precedence 45
339 for @{ 'PRedStar $L $T1 $T2 }.
341 notation "hvbox( T1 ➡➡* break term 46 T2 )"
342 non associative with precedence 45
343 for @{ 'PRedStarAlt $T1 $T2 }.
345 notation "hvbox( L1 ⊢ ➡* break term 46 L2 )"
346 non associative with precedence 45
347 for @{ 'CPRedStar $L1 $L2 }.
349 notation "hvbox( L ⊢ break term 46 T1 ➡* break 𝐍 ⦃ T2 ⦄ )"
350 non associative with precedence 45
351 for @{ 'PEval $L $T1 $T2 }.
353 notation "hvbox( ⬊ * term 46 T )"
354 non associative with precedence 45
357 notation "hvbox( L ⊢ ⬊ * break term 46 T )"
358 non associative with precedence 45
361 notation "hvbox( L ⊢ ⬊ ⬊ * break term 46 T )"
362 non associative with precedence 45
363 for @{ 'SNAlt $L $T }.
365 notation "hvbox( ⦃ L, break T ⦄ ϵ break [ R ] break 〚 A 〛 )"
366 non associative with precedence 45
367 for @{ 'InEInt $R $L $T $A }.
369 notation "hvbox( T1 ⊑ break [ R ] break term 46 T2 )"
370 non associative with precedence 45
371 for @{ 'CrSubEq $T1 $R $T2 }.
373 notation "hvbox( ⦃ h , break L ⦄ ⊢ break term 46 T1 ➸ * break [ g ] break term 46 T2 )"
374 non associative with precedence 45
375 for @{ 'XPRedStar $h $g $L $T1 $T2 }.
377 notation "hvbox( ⦃ h , break L ⦄ ⊢ ➷ * break [ g ] break term 46 T2 )"
378 non associative with precedence 45
379 for @{ 'XSN $h $g $L $T }.
381 (* Conversion ***************************************************************)
383 notation "hvbox( L ⊢ break term 46 T1 ⬌ break term 46 T2 )"
384 non associative with precedence 45
385 for @{ 'PConv $L $T1 $T2 }.
387 notation "hvbox( T1 ⊢ ⬌ break term 46 T2 )"
388 non associative with precedence 45
389 for @{ 'CPConv $T1 $T2 }.
391 (* Equivalence **************************************************************)
393 notation "hvbox( L ⊢ break term 46 T1 ⬌* break term 46 T2 )"
394 non associative with precedence 45
395 for @{ 'PConvStar $L $T1 $T2 }.
397 notation "hvbox( T1 ⊢ ⬌* break term 46 T2 )"
398 non associative with precedence 45
399 for @{ 'CPConvStar $T1 $T2 }.
401 (* Dynamic typing ***********************************************************)
403 notation "hvbox( ⦃ h , break L ⦄ ⊩ break term 46 T : break [ g ] )"
404 non associative with precedence 45
405 for @{ 'NativeValid $h $g $L $T }.
407 notation "hvbox( ⦃ h , break L ⦄ ⊢ break term 46 T1 : break term 46 T2 )"
408 non associative with precedence 45
409 for @{ 'NativeType $h $L $T1 $T2 }.
411 notation "hvbox( ⦃ h , break L ⦄ ⊢ break term 46 T1 : : break term 46 T2 )"
412 non associative with precedence 45
413 for @{ 'NativeTypeAlt $h $L $T1 $T2 }.
415 (* Higher order dynamic typing **********************************************)
417 notation "hvbox( ⦃ h , break L ⦄ ⊢ break term 46 T1 : * break term 46 T2 )"
418 non associative with precedence 45
419 for @{ 'NativeTypeStar $h $L $T1 $T2 }.