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
35 notation "hvbox( 𝕒 { I } )"
36 non associative with precedence 90
39 notation "hvbox( 𝕔 { I } break term 90 T1 . break term 90 T )"
40 non associative with precedence 90
41 for @{ 'SItem $I $T1 $T }.
43 notation "hvbox( 𝕓 { I } break term 90 T1 . break term 90 T )"
44 non associative with precedence 90
45 for @{ 'SBind $I $T1 $T }.
47 notation "hvbox( 𝕗 { I } break term 90 T1 . break term 90 T )"
48 non associative with precedence 90
49 for @{ 'SFlat $I $T1 $T }.
51 notation "hvbox( T . break 𝕓 { I } break term 90 T1 )"
52 non associative with precedence 89
53 for @{ 'DBind $T $I $T1 }.
55 notation > "hvbox( T . break 𝕔 { I } break term 90 T1 )"
56 non associative with precedence 89
57 for @{ 'DBind $T $I $T1 }.
58 *) (**) (* this breaks all parsing *)
59 notation "hvbox( # [ x ] )"
60 non associative with precedence 90
63 notation "hvbox( # [ x , break y ] )"
64 non associative with precedence 90
65 for @{ 'Weight $x $y }.
67 notation "hvbox( 𝕊 [ T ] )"
68 non associative with precedence 45
71 notation "hvbox( T1 break [ d , break e ] ≼ break T2 )"
72 non associative with precedence 45
73 for @{ 'SubEq $T1 $d $e $T2 }.
75 (* Substitution *************************************************************)
77 notation "hvbox( ↑ [ d , break e ] break T1 ≡ break T2 )"
78 non associative with precedence 45
79 for @{ 'RLift $d $e $T1 $T2 }.
81 notation "hvbox( ↓ [ d , break e ] break L1 ≡ break L2 )"
82 non associative with precedence 45
83 for @{ 'RDrop $d $e $L1 $L2 }.
85 notation "hvbox( T1 break [ d , break e ] ≫ break T2 )"
86 non associative with precedence 45
87 for @{ 'PSubst $T1 $d $e $T2 }.
89 notation "hvbox( L ⊢ break term 90 T1 break [ d , break e ] ≫ break T2 )"
90 non associative with precedence 45
91 for @{ 'PSubst $L $T1 $d $e $T2 }.
93 (* Unfold *******************************************************************)
95 notation "hvbox( T1 break [ d , break e ] ≫* break T2 )"
96 non associative with precedence 45
97 for @{ 'PSubstStar $T1 $d $e $T2 }.
99 notation "hvbox( L ⊢ break term 90 T1 break [ d , break e ] ≫* break T2 )"
100 non associative with precedence 45
101 for @{ 'PSubstStar $L $T1 $d $e $T2 }.
103 notation "hvbox( T1 break [ d , break e ] ≡ break T2 )"
104 non associative with precedence 45
105 for @{ 'TSubst $T1 $d $e $T2 }.
107 notation "hvbox( L ⊢ break term 90 T1 break [ d , break e ] ≡ break T2 )"
108 non associative with precedence 45
109 for @{ 'TSubst $L $T1 $d $e $T2 }.
111 (* Reducibility *************************************************************)
113 notation "hvbox( ℝ [ T ] )"
114 non associative with precedence 45
115 for @{ 'Reducible $T }.
117 notation "hvbox( L ⊢ ℝ [ T ] )"
118 non associative with precedence 45
119 for @{ 'Reducible $L $T }.
121 notation "hvbox( 𝕀 [ T ] )"
122 non associative with precedence 45
123 for @{ 'NotReducible $T }.
125 notation "hvbox( L ⊢ 𝕀 [ T ] )"
126 non associative with precedence 45
127 for @{ 'NotReducible $L $T }.
129 notation "hvbox( ℕ [ T ] )"
130 non associative with precedence 45
133 notation "hvbox( L ⊢ ℕ [ T ] )"
134 non associative with precedence 45
135 for @{ 'Normal $L $T }.
137 notation "hvbox( 𝕎ℍℝ [ T ] )"
138 non associative with precedence 45
139 for @{ 'WHdReducible $T }.
141 notation "hvbox( L ⊢ 𝕎ℍℝ [ T ] )"
142 non associative with precedence 45
143 for @{ 'WHdReducible $L $T }.
145 notation "hvbox( 𝕎ℍ𝕀 [ T ] )"
146 non associative with precedence 45
147 for @{ 'NotWHdReducible $T }.
149 notation "hvbox( L ⊢ 𝕎ℍ𝕀 [ T ] )"
150 non associative with precedence 45
151 for @{ 'NotWHdReducible $L $T }.
153 notation "hvbox( 𝕎ℍℕ [ T ] )"
154 non associative with precedence 45
155 for @{ 'WHdNormal $T }.
157 notation "hvbox( L ⊢ 𝕎ℍℕ [ T ] )"
158 non associative with precedence 45
159 for @{ 'WHdNormal $L $T }.
161 notation "hvbox( T1 ⇒ break T2 )"
162 non associative with precedence 45
163 for @{ 'PRed $T1 $T2 }.
165 notation "hvbox( L ⊢ break term 90 T1 ⇒ break T2 )"
166 non associative with precedence 45
167 for @{ 'PRed $L $T1 $T2 }.
169 notation "hvbox( L1 ⊢ ⇒ break L2 )"
170 non associative with precedence 45
171 for @{ 'CPRed $L1 $L2 }.
173 (* Computation **************************************************************)
175 notation "hvbox( T1 ⇒* break T2 )"
176 non associative with precedence 45
177 for @{ 'PRedStar $T1 $T2 }.
179 notation "hvbox( L ⊢ break term 90 T1 ⇒* break T2 )"
180 non associative with precedence 45
181 for @{ 'PRedStar $L $T1 $T2 }.
183 notation "hvbox( L1 ⊢ ⇒* break L2 )"
184 non associative with precedence 45
185 for @{ 'CPRedStar $L1 $L2 }.
187 notation "hvbox( ⇓ T )"
188 non associative with precedence 45
191 notation "hvbox( L ⊢ ⇓ T )"
192 non associative with precedence 45