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( L ⊢ break 𝐑 [ d , break e ] break ⦃ T ⦄ )"
146 non associative with precedence 45
147 for @{ 'Reducible $L $d $e $T }.
149 notation "hvbox( L ⊢ break 𝐈 [ d , break e ] break ⦃ T ⦄ )"
150 non associative with precedence 45
151 for @{ 'NotReducible $L $d $e $T }.
153 notation "hvbox( L ⊢ break 𝐍 [ d , break e ] break ⦃ T ⦄ )"
154 non associative with precedence 45
155 for @{ 'Normal $L $d $e $T }.
157 notation "hvbox( ⇧ [ d , break e ] break term 46 T1 ≡ break term 46 T2 )"
158 non associative with precedence 45
159 for @{ 'RLift $d $e $T1 $T2 }.
161 notation "hvbox( T1 break ≼ [ d , break e ] break term 46 T2 )"
162 non associative with precedence 45
163 for @{ 'SubEq $T1 $d $e $T2 }.
165 notation "hvbox( ≽ [ d , break e ] break term 46 T2 )"
166 non associative with precedence 45
167 for @{ 'SubEqBottom $d $e $T2 }.
169 notation "hvbox( ⇩ [ e ] break term 46 L1 ≡ break term 46 L2 )"
170 non associative with precedence 45
171 for @{ 'RDrop $e $L1 $L2 }.
173 notation "hvbox( ⇩ [ d , break e ] break term 46 L1 ≡ break term 46 L2 )"
174 non associative with precedence 45
175 for @{ 'RDrop $d $e $L1 $L2 }.
177 notation "hvbox( L ⊢ break ⌘ ⦃ T ⦄ ≡ break term 46 k )"
178 non associative with precedence 45
179 for @{ 'ICM $L $T $k }.
181 notation "hvbox( L ⊢ break term 46 T1 break ▶ [ d , break e ] break term 46 T2 )"
182 non associative with precedence 45
183 for @{ 'PSubst $L $T1 $d $e $T2 }.
185 (* Unfold *******************************************************************)
187 notation "hvbox( @ [ T1 ] break term 46 f ≡ break term 46 T2 )"
188 non associative with precedence 45
189 for @{ 'RAt $T1 $f $T2 }.
191 notation "hvbox( T1 ▭ break term 46 T2 ≡ break term 46 T )"
192 non associative with precedence 45
193 for @{ 'RMinus $T1 $T2 $T }.
195 notation "hvbox( ⇧ * [ e ] break term 46 T1 ≡ break term 46 T2 )"
196 non associative with precedence 45
197 for @{ 'RLiftStar $e $T1 $T2 }.
199 notation "hvbox( ⇩ * [ e ] break term 46 L1 ≡ break term 46 L2 )"
200 non associative with precedence 45
201 for @{ 'RDropStar $e $L1 $L2 }.
203 notation "hvbox( T1 break ▶ * [ d , break e ] break term 46 T2 )"
204 non associative with precedence 45
205 for @{ 'PSubstStar $T1 $d $e $T2 }.
207 notation "hvbox( L ⊢ break term 46 T1 break ▶ * [ d , break e ] break term 46 T2 )"
208 non associative with precedence 45
209 for @{ 'PSubstStar $L $T1 $d $e $T2 }.
211 notation "hvbox( L ⊢ break term 46 T1 break ▶ ▶ * [ d , break e ] break term 46 T2 )"
212 non associative with precedence 45
213 for @{ 'PSubstStarAlt $L $T1 $d $e $T2 }.
215 notation "hvbox( ▼ * [ d , break e ] break term 46 T1 ≡ break term 46 T2 )"
216 non associative with precedence 45
217 for @{ 'TSubst $T1 $d $e $T2 }.
219 notation "hvbox( L ⊢ break ▼ * [ d , break e ] break term 46 T1 ≡ break term 46 T2 )"
220 non associative with precedence 45
221 for @{ 'TSubst $L $T1 $d $e $T2 }.
223 notation "hvbox( ▼ ▼ * [ d , break e ] break term 46 T1 ≡ break term 46 T2 )"
224 non associative with precedence 45
225 for @{ 'TSubstAlt $T1 $d $e $T2 }.
227 notation "hvbox( L ⊢ break ▼ ▼ * [ d , break e ] break term 46 T1 ≡ break term 46 T2 )"
228 non associative with precedence 45
229 for @{ 'TSubstAlt $L $T1 $d $e $T2 }.
231 (* Static typing ************************************************************)
233 notation "hvbox( L ⊢ break term 46 T ⁝ break term 46 A )"
234 non associative with precedence 45
235 for @{ 'AtomicArity $L $T $A }.
237 notation "hvbox( T1 ⁝ ⊑ break term 46 T2 )"
238 non associative with precedence 45
239 for @{ 'CrSubEqA $T1 $T2 }.
241 notation "hvbox( ⦃ h , break L ⦄ ⊢ break term 46 T ÷ break term 46 A )"
242 non associative with precedence 45
243 for @{ 'BinaryArity $h $L $T $A }.
245 notation "hvbox( h ⊢ break term 46 L1 ÷ ⊑ break term 46 L2 )"
246 non associative with precedence 45
247 for @{ 'CrSubEqB $h $L1 $L2 }.
249 notation "hvbox( ⦃ h , break L ⦄ ⊢ break term 46 T1 • break [ g , break l ] break term 46 T2 )"
250 non associative with precedence 45
251 for @{ 'StaticType $h $g $l $L $T1 $T2 }.
253 notation "hvbox( h ⊢ break term 46 L1 • ⊑ [ g ] break term 46 L2 )"
254 non associative with precedence 45
255 for @{ 'CrSubEqS $h $g $L1 $L2 }.
257 (* Unwind *******************************************************************)
259 notation "hvbox( L1 ⊢ ⧫* break term 46 T ≡ break term 46 L2 )"
260 non associative with precedence 45
261 for @{ 'Unwind $L1 $T $L2 }.
263 (* Reducibility *************************************************************)
265 notation "hvbox( 𝐑 ⦃ T ⦄ )"
266 non associative with precedence 45
267 for @{ 'Reducible $T }.
269 notation "hvbox( L ⊢ break 𝐑 ⦃ T ⦄ )"
270 non associative with precedence 45
271 for @{ 'Reducible $L $T }.
273 notation "hvbox( 𝐈 ⦃ T ⦄ )"
274 non associative with precedence 45
275 for @{ 'NotReducible $T }.
277 notation "hvbox( L ⊢ break 𝐈 ⦃ T ⦄ )"
278 non associative with precedence 45
279 for @{ 'NotReducible $L $T }.
281 notation "hvbox( 𝐍 ⦃ T ⦄ )"
282 non associative with precedence 45
285 notation "hvbox( L ⊢ break 𝐍 ⦃ T ⦄ )"
286 non associative with precedence 45
287 for @{ 'Normal $L $T }.
289 notation "hvbox( 𝐖𝐇𝐑 ⦃ T ⦄ )"
290 non associative with precedence 45
291 for @{ 'WHdReducible $T }.
293 notation "hvbox( L ⊢ break 𝐖𝐇𝐑 ⦃ T ⦄ )"
294 non associative with precedence 45
295 for @{ 'WHdReducible $L $T }.
297 notation "hvbox( 𝐖𝐇𝐈 ⦃ T ⦄ )"
298 non associative with precedence 45
299 for @{ 'NotWHdReducible $T }.
301 notation "hvbox( L ⊢ break 𝐖𝐇𝐈 ⦃ T ⦄ )"
302 non associative with precedence 45
303 for @{ 'NotWHdReducible $L $T }.
305 notation "hvbox( 𝐖𝐇𝐍 ⦃ T ⦄ )"
306 non associative with precedence 45
307 for @{ 'WHdNormal $T }.
309 notation "hvbox( L ⊢ break 𝐖𝐇𝐍 ⦃ T ⦄ )"
310 non associative with precedence 45
311 for @{ 'WHdNormal $L $T }.
313 notation "hvbox( T1 ➡ break term 46 T2 )"
314 non associative with precedence 45
315 for @{ 'PRed $T1 $T2 }.
317 notation "hvbox( L ⊢ break term 46 T1 ➡ break term 46 T2 )"
318 non associative with precedence 45
319 for @{ 'PRed $L $T1 $T2 }.
321 notation "hvbox( L1 ⊢ ➡ break term 46 L2 )"
322 non associative with precedence 45
323 for @{ 'CPRed $L1 $L2 }.
325 notation "hvbox( ⦃ L1 ⦄ ➡ break ⦃ L2 ⦄ )"
326 non associative with precedence 45
327 for @{ 'FocalizedPRed $L1 $L2 }.
329 notation "hvbox( ⦃ L1, break T1 ⦄ ➡ break ⦃ L2 , break T2 ⦄ )"
330 non associative with precedence 45
331 for @{ 'FocalizedPRed $L1 $T1 $L2 $T2 }.
333 notation "hvbox( ⦃ h , break L ⦄ ⊢ break term 46 T1 ➸ break [ g ] break term 46 T2 )"
334 non associative with precedence 45
335 for @{ 'XPRed $h $g $L $T1 $T2 }.
337 (* Computation **************************************************************)
339 notation "hvbox( T1 ➡* break term 46 T2 )"
340 non associative with precedence 45
341 for @{ 'PRedStar $T1 $T2 }.
343 notation "hvbox( L ⊢ break term 46 T1 ➡* break term 46 T2 )"
344 non associative with precedence 45
345 for @{ 'PRedStar $L $T1 $T2 }.
347 notation "hvbox( L1 ⊢ ➡* break term 46 L2 )"
348 non associative with precedence 45
349 for @{ 'CPRedStar $L1 $L2 }.
351 notation "hvbox( L ⊢ break term 46 T1 ➡* break 𝐍 ⦃ T2 ⦄ )"
352 non associative with precedence 45
353 for @{ 'PEval $L $T1 $T2 }.
355 notation "hvbox( ⬊ * term 46 T )"
356 non associative with precedence 45
359 notation "hvbox( L ⊢ ⬊ * break term 46 T )"
360 non associative with precedence 45
363 notation "hvbox( L ⊢ ⬊ ⬊ * break term 46 T )"
364 non associative with precedence 45
365 for @{ 'SNAlt $L $T }.
367 notation "hvbox( ⦃ L, break T ⦄ ϵ break [ R ] break 〚 A 〛 )"
368 non associative with precedence 45
369 for @{ 'InEInt $R $L $T $A }.
371 notation "hvbox( T1 ⊑ break [ R ] break term 46 T2 )"
372 non associative with precedence 45
373 for @{ 'CrSubEq $T1 $R $T2 }.
375 notation "hvbox( ⦃ h , break L ⦄ ⊢ break term 46 T1 ➸ * break [ g ] break term 46 T2 )"
376 non associative with precedence 45
377 for @{ 'XPRedStar $h $g $L $T1 $T2 }.
379 notation "hvbox( ⦃ h , break L ⦄ ⊢ ➷ * break [ g ] break term 46 T2 )"
380 non associative with precedence 45
381 for @{ 'XSN $h $g $L $T }.
383 (* Conversion ***************************************************************)
385 notation "hvbox( L ⊢ break term 46 T1 ⬌ break term 46 T2 )"
386 non associative with precedence 45
387 for @{ 'PConv $L $T1 $T2 }.
389 notation "hvbox( T1 ⊢ ⬌ break term 46 T2 )"
390 non associative with precedence 45
391 for @{ 'CPConv $T1 $T2 }.
393 (* Equivalence **************************************************************)
395 notation "hvbox( L ⊢ break term 46 T1 ⬌* break term 46 T2 )"
396 non associative with precedence 45
397 for @{ 'PConvStar $L $T1 $T2 }.
399 notation "hvbox( T1 ⊢ ⬌* break term 46 T2 )"
400 non associative with precedence 45
401 for @{ 'CPConvStar $T1 $T2 }.
403 (* Dynamic typing ***********************************************************)
405 notation "hvbox( ⦃ h , break L ⦄ ⊩ break term 46 T : break [ g ] )"
406 non associative with precedence 45
407 for @{ 'NativeValid $h $g $L $T }.
409 notation "hvbox( ⦃ h , break L ⦄ ⊢ break term 46 T1 : break term 46 T2 )"
410 non associative with precedence 45
411 for @{ 'NativeType $h $L $T1 $T2 }.
413 notation "hvbox( ⦃ h , break L ⦄ ⊢ break term 46 T1 : : break term 46 T2 )"
414 non associative with precedence 45
415 for @{ 'NativeTypeAlt $h $L $T1 $T2 }.
417 (* Higher order dynamic typing **********************************************)
419 notation "hvbox( ⦃ h , break L ⦄ ⊢ break term 46 T1 : * break term 46 T2 )"
420 non associative with precedence 45
421 for @{ 'NativeTypeStar $h $L $T1 $T2 }.