25 where |
25 where |
26 "bv1 (BUnit) = {}" |
26 "bv1 (BUnit) = {}" |
27 | "bv1 (BVr x) = {atom x}" |
27 | "bv1 (BVr x) = {atom x}" |
28 | "bv1 (BPr bp1 bp2) = (bv1 bp1) \<union> (bv1 bp2)" |
28 | "bv1 (BPr bp1 bp2) = (bv1 bp1) \<union> (bv1 bp2)" |
29 |
29 |
30 local_setup {* define_raw_fv "Terms.rtrm1" |
30 setup {* snd o define_raw_perms ["rtrm1", "bp"] ["Terms.rtrm1", "Terms.bp"] *} |
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31 |
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32 local_setup {* snd o define_fv_alpha "Terms.rtrm1" |
31 [[[[]], [[], []], [[(NONE, 0)], [(NONE, 0)]], [[(SOME @{term bv1}, 0)], [], [(SOME @{term bv1}, 0)]]], |
33 [[[[]], [[], []], [[(NONE, 0)], [(NONE, 0)]], [[(SOME @{term bv1}, 0)], [], [(SOME @{term bv1}, 0)]]], |
32 [[], [[]], [[], []]]] *} |
34 [[], [[]], [[], []]]] *} |
33 print_theorems |
35 print_theorems |
34 |
36 notation |
35 setup {* snd o define_raw_perms ["rtrm1", "bp"] ["Terms.rtrm1", "Terms.bp"] *} |
37 alpha_rtrm1 ("_ \<approx>1 _" [100, 100] 100) and |
36 |
38 alpha_bp ("_ \<approx>1b _" [100, 100] 100) |
37 inductive |
39 thm alpha_rtrm1_alpha_bp.intros |
38 alpha1 :: "rtrm1 \<Rightarrow> rtrm1 \<Rightarrow> bool" ("_ \<approx>1 _" [100, 100] 100) |
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39 where |
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40 a1: "a = b \<Longrightarrow> (rVr1 a) \<approx>1 (rVr1 b)" |
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41 | a2: "\<lbrakk>t1 \<approx>1 t2; s1 \<approx>1 s2\<rbrakk> \<Longrightarrow> rAp1 t1 s1 \<approx>1 rAp1 t2 s2" |
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42 | a3: "(\<exists>pi. (({atom aa}, t) \<approx>gen alpha1 fv_rtrm1 pi ({atom ab}, s))) \<Longrightarrow> rLm1 aa t \<approx>1 rLm1 ab s" |
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43 | a4: "t1 \<approx>1 t2 \<Longrightarrow> (\<exists>pi. (((bv1 b1), s1) \<approx>gen alpha1 fv_rtrm1 pi ((bv1 b2), s2))) \<Longrightarrow> rLt1 b1 t1 s1 \<approx>1 rLt1 b2 t2 s2" |
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44 |
40 |
45 lemma alpha1_inj: |
41 lemma alpha1_inj: |
46 "(rVr1 a \<approx>1 rVr1 b) = (a = b)" |
42 "(rVr1 a \<approx>1 rVr1 b) = (a = b)" |
47 "(rAp1 t1 s1 \<approx>1 rAp1 t2 s2) = (t1 \<approx>1 t2 \<and> s1 \<approx>1 s2)" |
43 "(rAp1 t1 s1 \<approx>1 rAp1 t2 s2) = (t1 \<approx>1 t2 \<and> s1 \<approx>1 s2)" |
48 "(rLm1 aa t \<approx>1 rLm1 ab s) = (\<exists>pi. (({atom aa}, t) \<approx>gen alpha1 fv_rtrm1 pi ({atom ab}, s)))" |
44 "(rLm1 aa t \<approx>1 rLm1 ab s) = (\<exists>pi. (({atom aa}, t) \<approx>gen alpha_rtrm1 fv_rtrm1 pi ({atom ab}, s)))" |
49 "(rLt1 b1 t1 s1 \<approx>1 rLt1 b2 t2 s2) = (t1 \<approx>1 t2 \<and> (\<exists>pi. (((bv1 b1), s1) \<approx>gen alpha1 fv_rtrm1 pi ((bv1 b2), s2))))" |
45 "(rLt1 bp rtrm11 rtrm12 \<approx>1 rLt1 bpa rtrm11a rtrm12a) = |
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46 ((\<exists>pi. (bv1 bp, bp) \<approx>gen alpha_bp fv_bp pi (bv1 bpa, bpa)) \<and> rtrm11 \<approx>1 rtrm11a \<and> |
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47 (\<exists>pi. (bv1 bp, rtrm12) \<approx>gen alpha_rtrm1 fv_rtrm1 pi (bv1 bpa, rtrm12a)))" |
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48 "alpha_bp BUnit BUnit" |
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49 "(alpha_bp (BVr name) (BVr namea)) = (name = namea)" |
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50 "(alpha_bp (BPr bp1 bp2) (BPr bp1a bp2a)) = (alpha_bp bp1 bp1a \<and> alpha_bp bp2 bp2a)" |
50 apply - |
51 apply - |
51 apply rule apply (erule alpha1.cases) apply (simp_all add: alpha1.intros) |
52 apply rule apply (erule alpha_rtrm1.cases) apply (simp_all add: alpha_rtrm1_alpha_bp.intros) |
52 apply rule apply (erule alpha1.cases) apply (simp_all add: alpha1.intros) |
53 apply rule apply (erule alpha_rtrm1.cases) apply (simp_all add: alpha_rtrm1_alpha_bp.intros) |
53 apply rule apply (erule alpha1.cases) apply (simp_all add: alpha1.intros) |
54 apply rule apply (erule alpha_rtrm1.cases) apply (simp_all add: alpha_rtrm1_alpha_bp.intros) |
54 apply rule apply (erule alpha1.cases) apply (simp_all add: alpha1.intros) |
55 apply rule apply (erule alpha_rtrm1.cases) apply (simp_all add: alpha_rtrm1_alpha_bp.intros) |
55 done |
56 apply rule apply (erule alpha_bp.cases) apply (simp_all add: alpha_rtrm1_alpha_bp.intros) |
56 |
57 apply rule apply (erule alpha_bp.cases) apply (simp_all add: alpha_rtrm1_alpha_bp.intros) |
57 (* Shouyld we derive it? But bv is given by the user? *) |
58 done |
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59 |
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60 lemma alpha_bp_refl: "alpha_bp a a" |
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61 apply induct |
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62 apply (simp_all add: alpha1_inj) |
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63 done |
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64 |
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65 lemma alpha_bp_eq_eq: "alpha_bp a b = (a = b)" |
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66 apply rule |
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67 apply (induct a b rule: alpha_rtrm1_alpha_bp.inducts(2)) |
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68 apply (simp_all add: alpha_bp_refl) |
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69 done |
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70 |
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71 lemma alpha_bp_eq: "alpha_bp = (op =)" |
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72 apply (rule ext)+ |
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73 apply (rule alpha_bp_eq_eq) |
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74 done |
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75 |
58 lemma bv1_eqvt[eqvt]: |
76 lemma bv1_eqvt[eqvt]: |
59 shows "(pi \<bullet> bv1 x) = bv1 (pi \<bullet> x)" |
77 shows "(pi \<bullet> bv1 x) = bv1 (pi \<bullet> x)" |
60 apply (induct x) |
78 apply (induct x) |
61 apply (simp_all add: empty_eqvt insert_eqvt atom_eqvt eqvts) |
79 apply (simp_all add: empty_eqvt insert_eqvt atom_eqvt eqvts) |
62 done |
80 done |
83 apply(rule conjI) |
101 apply(rule conjI) |
84 apply(rule_tac ?p1="- pi" in fresh_star_permute_iff[THEN iffD1]) |
102 apply(rule_tac ?p1="- pi" in fresh_star_permute_iff[THEN iffD1]) |
85 apply(simp add: atom_eqvt Diff_eqvt fv_rtrm1_eqvt insert_eqvt empty_eqvt) |
103 apply(simp add: atom_eqvt Diff_eqvt fv_rtrm1_eqvt insert_eqvt empty_eqvt) |
86 apply(simp add: permute_eqvt[symmetric]) |
104 apply(simp add: permute_eqvt[symmetric]) |
87 apply (erule exE) |
105 apply (erule exE) |
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106 apply (erule exE) |
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107 apply (rule conjI) |
88 apply (rule_tac x="pi \<bullet> pia" in exI) |
108 apply (rule_tac x="pi \<bullet> pia" in exI) |
89 apply (simp add: alpha_gen) |
109 apply (simp add: alpha_gen) |
90 apply(erule conjE)+ |
110 apply(erule conjE)+ |
91 apply(rule conjI) |
111 apply(rule conjI) |
92 apply(rule_tac ?p1="- pi" in permute_eq_iff[THEN iffD1]) |
112 apply(rule_tac ?p1="- pi" in permute_eq_iff[THEN iffD1]) |
93 apply(simp add: fv_rtrm1_eqvt Diff_eqvt bv1_eqvt) |
113 apply(simp add: fv_rtrm1_eqvt Diff_eqvt bv1_eqvt) |
94 apply(rule conjI) |
114 apply(rule conjI) |
95 apply(rule_tac ?p1="- pi" in fresh_star_permute_iff[THEN iffD1]) |
115 apply(rule_tac ?p1="- pi" in fresh_star_permute_iff[THEN iffD1]) |
96 apply(simp add: atom_eqvt fv_rtrm1_eqvt Diff_eqvt bv1_eqvt) |
116 apply(simp add: atom_eqvt fv_rtrm1_eqvt Diff_eqvt bv1_eqvt) |
97 apply(simp add: permute_eqvt[symmetric]) |
117 apply(simp add: permute_eqvt[symmetric]) |
98 done |
118 apply (rule_tac x="pi \<bullet> piaa" in exI) |
99 |
119 apply (simp add: alpha_gen) |
100 lemma alpha1_equivp: "equivp alpha1" |
120 apply(erule conjE)+ |
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121 apply(rule conjI) |
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122 apply(rule_tac ?p1="- pi" in permute_eq_iff[THEN iffD1]) |
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123 apply(simp add: fv_rtrm1_eqvt Diff_eqvt bv1_eqvt) |
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124 apply(rule conjI) |
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125 apply(rule_tac ?p1="- pi" in fresh_star_permute_iff[THEN iffD1]) |
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126 apply(simp add: atom_eqvt fv_rtrm1_eqvt Diff_eqvt bv1_eqvt) |
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127 apply(simp add: permute_eqvt[symmetric]) |
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128 done |
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129 |
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130 lemma alpha1_equivp: "equivp alpha_rtrm1" |
101 sorry |
131 sorry |
102 |
132 |
103 quotient_type trm1 = rtrm1 / alpha1 |
133 quotient_type trm1 = rtrm1 / alpha_rtrm1 |
104 by (rule alpha1_equivp) |
134 by (rule alpha1_equivp) |
105 |
135 |
106 local_setup {* |
136 local_setup {* |
107 (fn ctxt => ctxt |
137 (fn ctxt => ctxt |
108 |> snd o (Quotient_Def.quotient_lift_const ("Vr1", @{term rVr1})) |
138 |> snd o (Quotient_Def.quotient_lift_const ("Vr1", @{term rVr1})) |
113 *} |
143 *} |
114 print_theorems |
144 print_theorems |
115 |
145 |
116 lemma alpha_rfv1: |
146 lemma alpha_rfv1: |
117 shows "t \<approx>1 s \<Longrightarrow> fv_rtrm1 t = fv_rtrm1 s" |
147 shows "t \<approx>1 s \<Longrightarrow> fv_rtrm1 t = fv_rtrm1 s" |
118 apply(induct rule: alpha1.induct) |
148 apply(induct rule: alpha_rtrm1_alpha_bp.inducts(1)) |
119 apply(simp_all add: alpha_gen.simps) |
149 apply(simp_all add: alpha_gen.simps) |
120 sorry |
150 done |
121 |
151 |
122 lemma [quot_respect]: |
152 lemma [quot_respect]: |
123 "(op = ===> alpha1) rVr1 rVr1" |
153 "(op = ===> alpha_rtrm1) rVr1 rVr1" |
124 "(alpha1 ===> alpha1 ===> alpha1) rAp1 rAp1" |
154 "(alpha_rtrm1 ===> alpha_rtrm1 ===> alpha_rtrm1) rAp1 rAp1" |
125 "(op = ===> alpha1 ===> alpha1) rLm1 rLm1" |
155 "(op = ===> alpha_rtrm1 ===> alpha_rtrm1) rLm1 rLm1" |
126 "(op = ===> alpha1 ===> alpha1 ===> alpha1) rLt1 rLt1" |
156 "(op = ===> alpha_rtrm1 ===> alpha_rtrm1 ===> alpha_rtrm1) rLt1 rLt1" |
127 apply (auto simp add: alpha1_inj) |
157 apply (auto simp add: alpha1_inj) |
128 apply (rule_tac x="0" in exI) |
158 apply (rule_tac x="0" in exI) |
129 apply (simp add: fresh_star_def fresh_zero_perm alpha_rfv1 alpha_gen) |
159 apply (simp add: fresh_star_def fresh_zero_perm alpha_rfv1 alpha_gen) |
130 apply (rule_tac x="0" in exI) |
160 apply (rule_tac x="0" in exI) |
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161 apply (simp add: alpha_gen fresh_star_def fresh_zero_perm alpha_rfv1 alpha_bp_eq) |
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162 apply (rule_tac x="0" in exI) |
131 apply (simp add: alpha_gen fresh_star_def fresh_zero_perm alpha_rfv1) |
163 apply (simp add: alpha_gen fresh_star_def fresh_zero_perm alpha_rfv1) |
132 done |
164 done |
133 |
165 |
134 lemma [quot_respect]: |
166 lemma [quot_respect]: |
135 "(op = ===> alpha1 ===> alpha1) permute permute" |
167 "(op = ===> alpha_rtrm1 ===> alpha_rtrm1) permute permute" |
136 by (simp add: alpha1_eqvt) |
168 by (simp add: alpha1_eqvt) |
137 |
169 |
138 lemma [quot_respect]: |
170 lemma [quot_respect]: |
139 "(alpha1 ===> op =) fv_rtrm1 fv_rtrm1" |
171 "(alpha_rtrm1 ===> op =) fv_rtrm1 fv_rtrm1" |
140 by (simp add: alpha_rfv1) |
172 by (simp add: alpha_rfv1) |
141 |
173 |
142 lemmas trm1_bp_induct = rtrm1_bp.induct[quot_lifted] |
174 lemmas trm1_bp_induct = rtrm1_bp.induct[quot_lifted] |
143 lemmas trm1_bp_inducts = rtrm1_bp.inducts[quot_lifted] |
175 lemmas trm1_bp_inducts = rtrm1_bp.inducts[quot_lifted] |
144 |
176 |
231 apply(simp add: alpha_gen.simps) |
269 apply(simp add: alpha_gen.simps) |
232 apply(simp add: supp_eqvt[symmetric] fv_trm1_eqvt[symmetric]) |
270 apply(simp add: supp_eqvt[symmetric] fv_trm1_eqvt[symmetric]) |
233 apply(subgoal_tac "supp (Lt1 bp rtrm11 rtrm12) = supp(rtrm11) \<union> supp (Abs (bv1 bp) rtrm12)") |
271 apply(subgoal_tac "supp (Lt1 bp rtrm11 rtrm12) = supp(rtrm11) \<union> supp (Abs (bv1 bp) rtrm12)") |
234 apply(simp add: supp_Abs fv_trm1 fv_eq_bv) |
272 apply(simp add: supp_Abs fv_trm1 fv_eq_bv) |
235 apply(simp (no_asm) add: supp_def) |
273 apply(simp (no_asm) add: supp_def) |
236 apply(simp add: alpha1_INJ) |
274 apply(simp add: alpha1_INJ alpha_bp_eq) |
237 apply(simp add: Abs_eq_iff) |
275 apply(simp add: Abs_eq_iff) |
238 apply(simp add: alpha_gen) |
276 apply(simp add: alpha_gen) |
239 apply(simp add: supp_eqvt[symmetric] fv_trm1_eqvt[symmetric] bv1_eqvt) |
277 apply(simp add: supp_eqvt[symmetric] fv_trm1_eqvt[symmetric] bv1_eqvt fv_eq_bv) |
240 apply(simp add: Collect_imp_eq Collect_neg_eq) |
278 apply(simp add: Collect_imp_eq Collect_neg_eq fresh_star_def helper) |
241 done |
279 done |
242 |
280 |
243 lemma trm1_supp: |
281 lemma trm1_supp: |
244 "supp (Vr1 x) = {atom x}" |
282 "supp (Vr1 x) = {atom x}" |
245 "supp (Ap1 t1 t2) = supp t1 \<union> supp t2" |
283 "supp (Ap1 t1 t2) = supp t1 \<union> supp t2" |
269 primrec |
307 primrec |
270 rbv2 |
308 rbv2 |
271 where |
309 where |
272 "rbv2 (rAs x t) = {atom x}" |
310 "rbv2 (rAs x t) = {atom x}" |
273 |
311 |
274 local_setup {* define_raw_fv "Terms.rtrm2" |
312 setup {* snd o define_raw_perms ["rtrm2", "rassign"] ["Terms.rtrm2", "Terms.rassign"] *} |
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313 |
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314 local_setup {* snd o define_fv_alpha "Terms.rtrm2" |
275 [[[[]], [[], []], [[(NONE, 0)], [(NONE, 0)]], [[(SOME @{term rbv2}, 0)], [(SOME @{term rbv2}, 0)]]], |
315 [[[[]], [[], []], [[(NONE, 0)], [(NONE, 0)]], [[(SOME @{term rbv2}, 0)], [(SOME @{term rbv2}, 0)]]], |
276 [[[], []]]] *} |
316 [[[], []]]] *} |
277 print_theorems |
317 print_theorems |
278 |
318 |
279 setup {* snd o define_raw_perms ["rtrm2", "rassign"] ["Terms.rtrm2", "Terms.rassign"] *} |
319 notation |
280 |
320 alpha_rtrm2 ("_ \<approx>2 _" [100, 100] 100) and |
281 inductive |
321 alpha_rassign ("_ \<approx>2b _" [100, 100] 100) |
282 alpha2 :: "rtrm2 \<Rightarrow> rtrm2 \<Rightarrow> bool" ("_ \<approx>2 _" [100, 100] 100) |
322 thm alpha_rtrm2_alpha_rassign.intros |
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323 |
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324 lemma alpha2_equivp: |
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325 "equivp alpha_rtrm2" |
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326 "equivp alpha_rassign" |
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327 sorry |
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328 |
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329 quotient_type |
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330 trm2 = rtrm2 / alpha_rtrm2 |
283 and |
331 and |
284 alpha2a :: "rassign \<Rightarrow> rassign \<Rightarrow> bool" ("_ \<approx>2a _" [100, 100] 100) |
332 assign = rassign / alpha_rassign |
285 where |
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286 a1: "a = b \<Longrightarrow> (rVr2 a) \<approx>2 (rVr2 b)" |
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287 | a2: "\<lbrakk>t1 \<approx>2 t2; s1 \<approx>2 s2\<rbrakk> \<Longrightarrow> rAp2 t1 s1 \<approx>2 rAp2 t2 s2" |
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288 | a3: "(\<exists>pi. (({atom a}, t) \<approx>gen alpha2 fv_rtrm2 pi ({atom b}, s))) \<Longrightarrow> rLm2 a t \<approx>2 rLm2 b s" |
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289 | a4: "\<lbrakk>\<exists>pi. ((rbv2 bt, t) \<approx>gen alpha2 fv_rtrm2 pi ((rbv2 bs), s)); |
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290 \<exists>pi. ((rbv2 bt, bt) \<approx>gen alpha2a fv_rassign pi (rbv2 bs, bs))\<rbrakk> |
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291 \<Longrightarrow> rLt2 bt t \<approx>2 rLt2 bs s" |
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292 | a5: "\<lbrakk>a = b; t \<approx>2 s\<rbrakk> \<Longrightarrow> rAs a t \<approx>2a rAs b s" (* This way rbv2 can be lifted *) |
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293 |
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294 lemma alpha2_equivp: |
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295 "equivp alpha2" |
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296 "equivp alpha2a" |
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297 sorry |
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298 |
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299 quotient_type |
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300 trm2 = rtrm2 / alpha2 |
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301 and |
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302 assign = rassign / alpha2a |
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303 by (auto intro: alpha2_equivp) |
333 by (auto intro: alpha2_equivp) |
304 |
334 |
305 local_setup {* |
335 local_setup {* |
306 (fn ctxt => ctxt |
336 (fn ctxt => ctxt |
307 |> snd o (Quotient_Def.quotient_lift_const ("Vr2", @{term rVr2})) |
337 |> snd o (Quotient_Def.quotient_lift_const ("Vr2", @{term rVr2})) |
331 bv3 |
361 bv3 |
332 where |
362 where |
333 "bv3 ANil = {}" |
363 "bv3 ANil = {}" |
334 | "bv3 (ACons x t as) = {atom x} \<union> (bv3 as)" |
364 | "bv3 (ACons x t as) = {atom x} \<union> (bv3 as)" |
335 |
365 |
336 local_setup {* define_raw_fv "Terms.trm3" |
366 setup {* snd o define_raw_perms ["rtrm3", "assigns"] ["Terms.trm3", "Terms.assigns"] *} |
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367 |
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368 local_setup {* snd o define_fv_alpha "Terms.trm3" |
337 [[[[]], [[], []], [[(NONE, 0)], [(NONE, 0)]], [[(SOME @{term bv3}, 0)], [(SOME @{term bv3}, 0)]]], |
369 [[[[]], [[], []], [[(NONE, 0)], [(NONE, 0)]], [[(SOME @{term bv3}, 0)], [(SOME @{term bv3}, 0)]]], |
338 [[], [[], [], []]]] *} |
370 [[], [[], [], []]]] *} |
339 print_theorems |
371 print_theorems |
340 |
372 |
341 setup {* snd o define_raw_perms ["rtrm3", "assigns"] ["Terms.trm3", "Terms.assigns"] *} |
373 notation |
342 |
374 alpha_trm3 ("_ \<approx>3 _" [100, 100] 100) and |
343 inductive |
375 alpha_assigns ("_ \<approx>3a _" [100, 100] 100) |
344 alpha3 :: "trm3 \<Rightarrow> trm3 \<Rightarrow> bool" ("_ \<approx>3 _" [100, 100] 100) |
376 thm alpha_trm3_alpha_assigns.intros |
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377 |
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378 lemma alpha3_equivp: |
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379 "equivp alpha_trm3" |
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380 "equivp alpha_assigns" |
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381 sorry |
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382 |
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383 quotient_type |
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384 qtrm3 = trm3 / alpha_trm3 |
345 and |
385 and |
346 alpha3a :: "assigns \<Rightarrow> assigns \<Rightarrow> bool" ("_ \<approx>3a _" [100, 100] 100) |
386 qassigns = assigns / alpha_assigns |
347 where |
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348 a1: "a = b \<Longrightarrow> (Vr3 a) \<approx>3 (Vr3 b)" |
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349 | a2: "\<lbrakk>t1 \<approx>3 t2; s1 \<approx>3 s2\<rbrakk> \<Longrightarrow> Ap3 t1 s1 \<approx>3 Ap3 t2 s2" |
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350 | a3: "(\<exists>pi. (({atom a}, t) \<approx>gen alpha3 fv_rtrm3 pi ({atom b}, s))) \<Longrightarrow> Lm3 a t \<approx>3 Lm3 b s" |
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351 | a4: "\<lbrakk>\<exists>pi. ((bv3 bt, t) \<approx>gen alpha3 fv_trm3 pi ((bv3 bs), s)); |
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352 \<exists>pi. ((bv3 bt, bt) \<approx>gen alpha3a fv_assign pi (bv3 bs, bs))\<rbrakk> |
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353 \<Longrightarrow> Lt3 bt t \<approx>3 Lt3 bs s" |
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354 | a5: "ANil \<approx>3a ANil" |
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355 | a6: "\<lbrakk>a = b; t \<approx>3 s; tt \<approx>3a st\<rbrakk> \<Longrightarrow> ACons a t tt \<approx>3a ACons b s st" |
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356 |
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357 lemma alpha3_equivp: |
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358 "equivp alpha3" |
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359 "equivp alpha3a" |
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360 sorry |
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361 |
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362 quotient_type |
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363 qtrm3 = trm3 / alpha3 |
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364 and |
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365 qassigns = assigns / alpha3a |
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366 by (auto intro: alpha3_equivp) |
387 by (auto intro: alpha3_equivp) |
367 |
388 |
368 |
389 |
369 section {*** lam with indirect list recursion ***} |
390 section {*** lam with indirect list recursion ***} |
370 |
391 |
393 done |
410 done |
394 |
411 |
395 thm permute_trm4_permute_trm4_list.simps |
412 thm permute_trm4_permute_trm4_list.simps |
396 thm permute_trm4_permute_trm4_list.simps[simplified repaired] |
413 thm permute_trm4_permute_trm4_list.simps[simplified repaired] |
397 |
414 |
398 inductive |
415 local_setup {* snd o define_fv_alpha "Terms.trm4" [ |
399 alpha4 :: "trm4 \<Rightarrow> trm4 \<Rightarrow> bool" ("_ \<approx>4 _" [100, 100] 100) |
416 [[[]], [[], []], [[(NONE, 0)], [(NONE, 0)]]], [[], [[], []]] ] *} |
400 and alpha4list :: "trm4 list \<Rightarrow> trm4 list \<Rightarrow> bool" ("_ \<approx>4list _" [100, 100] 100) |
417 print_theorems |
401 where |
418 |
402 a1: "a = b \<Longrightarrow> (Vr4 a) \<approx>4 (Vr4 b)" |
419 notation |
403 | a2: "\<lbrakk>t1 \<approx>4 t2; s1 \<approx>4list s2\<rbrakk> \<Longrightarrow> Ap4 t1 s1 \<approx>4 Ap4 t2 s2" |
420 alpha_trm4 ("_ \<approx>4 _" [100, 100] 100) and |
404 | a3: "(\<exists>pi. (({atom a}, t) \<approx>gen alpha4 fv_rtrm4 pi ({atom b}, s))) \<Longrightarrow> Lm4 a t \<approx>4 Lm4 b s" |
421 alpha_trm4_list ("_ \<approx>4l _" [100, 100] 100) |
405 | a5: "[] \<approx>4list []" |
422 thm alpha_trm4_alpha_trm4_list.intros |
406 | a6: "\<lbrakk>t \<approx>4 s; ts \<approx>4list ss\<rbrakk> \<Longrightarrow> (t#ts) \<approx>4list (s#ss)" |
423 |
407 |
424 lemma alpha4_equivp: "equivp alpha_trm4" sorry |
408 lemma alpha4_equivp: "equivp alpha4" sorry |
425 lemma alpha4list_equivp: "equivp alpha_trm4_list" sorry |
409 lemma alpha4list_equivp: "equivp alpha4list" sorry |
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410 |
426 |
411 quotient_type |
427 quotient_type |
412 qtrm4 = trm4 / alpha4 and |
428 qtrm4 = trm4 / alpha_trm4 and |
413 qtrm4list = "trm4 list" / alpha4list |
429 qtrm4list = "trm4 list" / alpha_trm4_list |
414 by (simp_all add: alpha4_equivp alpha4list_equivp) |
430 by (simp_all add: alpha4_equivp alpha4list_equivp) |
415 |
431 |
416 |
432 |
417 datatype rtrm5 = |
433 datatype rtrm5 = |
418 rVr5 "name" |
434 rVr5 "name" |
427 where |
443 where |
428 "rbv5 rLnil = {}" |
444 "rbv5 rLnil = {}" |
429 | "rbv5 (rLcons n t ltl) = {atom n} \<union> (rbv5 ltl)" |
445 | "rbv5 (rLcons n t ltl) = {atom n} \<union> (rbv5 ltl)" |
430 |
446 |
431 |
447 |
432 local_setup {* define_raw_fv "Terms.rtrm5" [ |
448 setup {* snd o define_raw_perms ["rtrm5", "rlts"] ["Terms.rtrm5", "Terms.rlts"] *} |
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449 print_theorems |
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450 |
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451 local_setup {* snd o define_fv_alpha "Terms.rtrm5" [ |
433 [[[]], [[], []], [[(SOME @{term rbv5}, 0)], [(SOME @{term rbv5}, 0)]]], [[], [[], [], []]] ] *} |
452 [[[]], [[], []], [[(SOME @{term rbv5}, 0)], [(SOME @{term rbv5}, 0)]]], [[], [[], [], []]] ] *} |
434 print_theorems |
453 print_theorems |
435 |
454 |
436 (* Alternate version with additional binding of name in rlts in rLcons *) |
455 (* Alternate version with additional binding of name in rlts in rLcons *) |
437 (*local_setup {* define_raw_fv "Terms.rtrm5" [ |
456 (*local_setup {* snd o define_fv_alpha "Terms.rtrm5" [ |
438 [[[]], [[], []], [[(SOME @{term rbv5}, 0)], [(SOME @{term rbv5}, 0)]]], [[], [[(NONE,0)], [], [(NONE,0)]]] ] *} |
457 [[[]], [[], []], [[(SOME @{term rbv5}, 0)], [(SOME @{term rbv5}, 0)]]], [[], [[(NONE,0)], [], [(NONE,0)]]] ] *} |
439 print_theorems*) |
458 print_theorems*) |
440 |
459 |
441 |
460 notation |
442 setup {* snd o define_raw_perms ["rtrm5", "rlts"] ["Terms.rtrm5", "Terms.rlts"] *} |
461 alpha_rtrm5 ("_ \<approx>5 _" [100, 100] 100) and |
443 print_theorems |
462 alpha_rlts ("_ \<approx>l _" [100, 100] 100) |
444 |
463 thm alpha_rtrm5_alpha_rlts.intros |
445 inductive |
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446 alpha5 :: "rtrm5 \<Rightarrow> rtrm5 \<Rightarrow> bool" ("_ \<approx>5 _" [100, 100] 100) |
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447 and |
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448 alphalts :: "rlts \<Rightarrow> rlts \<Rightarrow> bool" ("_ \<approx>l _" [100, 100] 100) |
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449 where |
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450 a1: "a = b \<Longrightarrow> (rVr5 a) \<approx>5 (rVr5 b)" |
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451 | a2: "\<lbrakk>t1 \<approx>5 t2; s1 \<approx>5 s2\<rbrakk> \<Longrightarrow> rAp5 t1 s1 \<approx>5 rAp5 t2 s2" |
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452 | a3: "\<lbrakk>\<exists>pi. ((rbv5 l1, t1) \<approx>gen alpha5 fv_rtrm5 pi (rbv5 l2, t2)); |
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453 \<exists>pi. ((rbv5 l1, l1) \<approx>gen alphalts fv_rlts pi (rbv5 l2, l2))\<rbrakk> |
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454 \<Longrightarrow> rLt5 l1 t1 \<approx>5 rLt5 l2 t2" |
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455 | a4: "rLnil \<approx>l rLnil" |
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456 | a5: "ls1 \<approx>l ls2 \<Longrightarrow> t1 \<approx>5 t2 \<Longrightarrow> n1 = n2 \<Longrightarrow> rLcons n1 t1 ls1 \<approx>l rLcons n2 t2 ls2" |
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457 |
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458 print_theorems |
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459 |
464 |
460 lemma alpha5_inj: |
465 lemma alpha5_inj: |
461 "((rVr5 a) \<approx>5 (rVr5 b)) = (a = b)" |
466 "((rVr5 a) \<approx>5 (rVr5 b)) = (a = b)" |
462 "(rAp5 t1 s1 \<approx>5 rAp5 t2 s2) = (t1 \<approx>5 t2 \<and> s1 \<approx>5 s2)" |
467 "(rAp5 t1 s1 \<approx>5 rAp5 t2 s2) = (t1 \<approx>5 t2 \<and> s1 \<approx>5 s2)" |
463 "(rLt5 l1 t1 \<approx>5 rLt5 l2 t2) = ((\<exists>pi. ((rbv5 l1, t1) \<approx>gen alpha5 fv_rtrm5 pi (rbv5 l2, t2))) \<and> |
468 "(rLt5 l1 t1 \<approx>5 rLt5 l2 t2) = ((\<exists>pi. ((rbv5 l1, t1) \<approx>gen alpha_rtrm5 fv_rtrm5 pi (rbv5 l2, t2))) \<and> |
464 (\<exists>pi. ((rbv5 l1, l1) \<approx>gen alphalts fv_rlts pi (rbv5 l2, l2))))" |
469 (\<exists>pi. ((rbv5 l1, l1) \<approx>gen alpha_rlts fv_rlts pi (rbv5 l2, l2))))" |
465 "rLnil \<approx>l rLnil" |
470 "rLnil \<approx>l rLnil" |
466 "(rLcons n1 t1 ls1 \<approx>l rLcons n2 t2 ls2) = (n1 = n2 \<and> ls1 \<approx>l ls2 \<and> t1 \<approx>5 t2)" |
471 "(rLcons n1 t1 ls1 \<approx>l rLcons n2 t2 ls2) = (n1 = n2 \<and> ls1 \<approx>l ls2 \<and> t1 \<approx>5 t2)" |
467 apply - |
472 apply - |
468 apply (simp_all add: alpha5_alphalts.intros) |
473 apply (simp_all add: alpha_rtrm5_alpha_rlts.intros) |
469 apply rule |
474 apply rule |
470 apply (erule alpha5.cases) |
475 apply (erule alpha_rtrm5.cases) |
471 apply (simp_all add: alpha5_alphalts.intros) |
476 apply (simp_all add: alpha_rtrm5_alpha_rlts.intros) |
472 apply rule |
477 apply rule |
473 apply (erule alpha5.cases) |
478 apply (erule alpha_rtrm5.cases) |
474 apply (simp_all add: alpha5_alphalts.intros) |
479 apply (simp_all add: alpha_rtrm5_alpha_rlts.intros) |
475 apply rule |
480 apply rule |
476 apply (erule alpha5.cases) |
481 apply (erule alpha_rtrm5.cases) |
477 apply (simp_all add: alpha5_alphalts.intros) |
482 apply (simp_all add: alpha_rtrm5_alpha_rlts.intros) |
478 apply rule |
483 apply rule |
479 apply (erule alphalts.cases) |
484 apply (erule alpha_rlts.cases) |
480 apply (simp_all add: alpha5_alphalts.intros) |
485 apply (simp_all add: alpha_rtrm5_alpha_rlts.intros) |
481 done |
486 done |
482 |
487 |
483 lemma alpha5_equivps: |
488 lemma alpha5_equivps: |
484 shows "equivp alpha5" |
489 shows "equivp alpha_rtrm5" |
485 and "equivp alphalts" |
490 and "equivp alpha_rlts" |
486 sorry |
491 sorry |
487 |
492 |
488 quotient_type |
493 quotient_type |
489 trm5 = rtrm5 / alpha5 |
494 trm5 = rtrm5 / alpha_rtrm5 |
490 and |
495 and |
491 lts = rlts / alphalts |
496 lts = rlts / alpha_rlts |
492 by (auto intro: alpha5_equivps) |
497 by (auto intro: alpha5_equivps) |
493 |
498 |
494 local_setup {* |
499 local_setup {* |
495 (fn ctxt => ctxt |
500 (fn ctxt => ctxt |
496 |> snd o (Quotient_Def.quotient_lift_const ("Vr5", @{term rVr5})) |
501 |> snd o (Quotient_Def.quotient_lift_const ("Vr5", @{term rVr5})) |
517 sorry |
522 sorry |
518 |
523 |
519 lemma alpha5_eqvt: |
524 lemma alpha5_eqvt: |
520 "xa \<approx>5 y \<Longrightarrow> (x \<bullet> xa) \<approx>5 (x \<bullet> y)" |
525 "xa \<approx>5 y \<Longrightarrow> (x \<bullet> xa) \<approx>5 (x \<bullet> y)" |
521 "xb \<approx>l ya \<Longrightarrow> (x \<bullet> xb) \<approx>l (x \<bullet> ya)" |
526 "xb \<approx>l ya \<Longrightarrow> (x \<bullet> xb) \<approx>l (x \<bullet> ya)" |
522 apply(induct rule: alpha5_alphalts.inducts) |
527 apply(induct rule: alpha_rtrm5_alpha_rlts.inducts) |
523 apply (simp_all add: alpha5_inj) |
528 apply (simp_all add: alpha5_inj) |
524 apply (erule exE)+ |
529 apply (erule exE)+ |
525 apply(unfold alpha_gen) |
530 apply(unfold alpha_gen) |
526 apply (erule conjE)+ |
531 apply (erule conjE)+ |
527 apply (rule conjI) |
532 apply (rule conjI) |
528 apply (rule_tac x="x \<bullet> pi" in exI) |
533 apply (rule_tac x="x \<bullet> pia" in exI) |
529 apply (rule conjI) |
534 apply (rule conjI) |
530 apply(rule_tac ?p1="- x" in permute_eq_iff[THEN iffD1]) |
535 apply(rule_tac ?p1="- x" in permute_eq_iff[THEN iffD1]) |
531 apply(simp add: atom_eqvt Diff_eqvt insert_eqvt set_eqvt empty_eqvt rbv5_eqvt fv_rtrm5_eqvt) |
536 apply(simp add: atom_eqvt Diff_eqvt insert_eqvt set_eqvt empty_eqvt rbv5_eqvt fv_rtrm5_eqvt) |
532 apply(rule conjI) |
537 apply(rule conjI) |
533 apply(rule_tac ?p1="- x" in fresh_star_permute_iff[THEN iffD1]) |
538 apply(rule_tac ?p1="- x" in fresh_star_permute_iff[THEN iffD1]) |
534 apply(simp add: atom_eqvt Diff_eqvt insert_eqvt set_eqvt empty_eqvt rbv5_eqvt fv_rtrm5_eqvt) |
539 apply(simp add: atom_eqvt Diff_eqvt insert_eqvt set_eqvt empty_eqvt rbv5_eqvt fv_rtrm5_eqvt) |
535 apply (subst permute_eqvt[symmetric]) |
540 apply (subst permute_eqvt[symmetric]) |
536 apply (simp) |
541 apply (simp) |
537 apply (rule_tac x="x \<bullet> pia" in exI) |
542 apply (rule_tac x="x \<bullet> pi" in exI) |
538 apply (rule conjI) |
543 apply (rule conjI) |
539 apply(rule_tac ?p1="- x" in permute_eq_iff[THEN iffD1]) |
544 apply(rule_tac ?p1="- x" in permute_eq_iff[THEN iffD1]) |
540 apply(simp add: atom_eqvt Diff_eqvt insert_eqvt set_eqvt empty_eqvt rbv5_eqvt fv_rlts_eqvt) |
545 apply(simp add: atom_eqvt Diff_eqvt insert_eqvt set_eqvt empty_eqvt rbv5_eqvt fv_rlts_eqvt) |
541 apply(rule conjI) |
546 apply(rule conjI) |
542 apply(rule_tac ?p1="- x" in fresh_star_permute_iff[THEN iffD1]) |
547 apply(rule_tac ?p1="- x" in fresh_star_permute_iff[THEN iffD1]) |
546 done |
551 done |
547 |
552 |
548 lemma alpha5_rfv: |
553 lemma alpha5_rfv: |
549 "(t \<approx>5 s \<Longrightarrow> fv_rtrm5 t = fv_rtrm5 s)" |
554 "(t \<approx>5 s \<Longrightarrow> fv_rtrm5 t = fv_rtrm5 s)" |
550 "(l \<approx>l m \<Longrightarrow> fv_rlts l = fv_rlts m)" |
555 "(l \<approx>l m \<Longrightarrow> fv_rlts l = fv_rlts m)" |
551 apply(induct rule: alpha5_alphalts.inducts) |
556 apply(induct rule: alpha_rtrm5_alpha_rlts.inducts) |
552 apply(simp_all add: alpha_gen) |
557 apply(simp_all add: alpha_gen) |
553 done |
558 done |
554 |
559 |
555 lemma bv_list_rsp: |
560 lemma bv_list_rsp: |
556 shows "x \<approx>l y \<Longrightarrow> rbv5 x = rbv5 y" |
561 shows "x \<approx>l y \<Longrightarrow> rbv5 x = rbv5 y" |
557 apply(induct rule: alpha5_alphalts.inducts(2)) |
562 apply(induct rule: alpha_rtrm5_alpha_rlts.inducts(2)) |
558 apply(simp_all) |
563 apply(simp_all) |
559 done |
564 done |
560 |
565 |
561 lemma [quot_respect]: |
566 lemma [quot_respect]: |
562 "(alphalts ===> op =) fv_rlts fv_rlts" |
567 "(alpha_rlts ===> op =) fv_rlts fv_rlts" |
563 "(alpha5 ===> op =) fv_rtrm5 fv_rtrm5" |
568 "(alpha_rtrm5 ===> op =) fv_rtrm5 fv_rtrm5" |
564 "(alphalts ===> op =) rbv5 rbv5" |
569 "(alpha_rlts ===> op =) rbv5 rbv5" |
565 "(op = ===> alpha5) rVr5 rVr5" |
570 "(op = ===> alpha_rtrm5) rVr5 rVr5" |
566 "(alpha5 ===> alpha5 ===> alpha5) rAp5 rAp5" |
571 "(alpha_rtrm5 ===> alpha_rtrm5 ===> alpha_rtrm5) rAp5 rAp5" |
567 "(alphalts ===> alpha5 ===> alpha5) rLt5 rLt5" |
572 "(alpha_rlts ===> alpha_rtrm5 ===> alpha_rtrm5) rLt5 rLt5" |
568 "(alphalts ===> alpha5 ===> alpha5) rLt5 rLt5" |
573 "(alpha_rlts ===> alpha_rtrm5 ===> alpha_rtrm5) rLt5 rLt5" |
569 "(op = ===> alpha5 ===> alphalts ===> alphalts) rLcons rLcons" |
574 "(op = ===> alpha_rtrm5 ===> alpha_rlts ===> alpha_rlts) rLcons rLcons" |
570 "(op = ===> alpha5 ===> alpha5) permute permute" |
575 "(op = ===> alpha_rtrm5 ===> alpha_rtrm5) permute permute" |
571 "(op = ===> alphalts ===> alphalts) permute permute" |
576 "(op = ===> alpha_rlts ===> alpha_rlts) permute permute" |
572 apply (simp_all add: alpha5_inj alpha5_rfv alpha5_eqvt bv_list_rsp) |
577 apply (simp_all add: alpha5_inj alpha5_rfv alpha5_eqvt bv_list_rsp) |
573 apply (clarify) apply (rule conjI) |
578 apply (clarify) apply (rule conjI) |
574 apply (rule_tac x="0" in exI) apply (simp add: fresh_star_def fresh_zero_perm alpha_gen alpha5_rfv) |
579 apply (rule_tac x="0" in exI) apply (simp add: fresh_star_def fresh_zero_perm alpha_gen alpha5_rfv) |
575 apply (rule_tac x="0" in exI) apply (simp add: fresh_star_def fresh_zero_perm alpha_gen alpha5_rfv) |
580 apply (rule_tac x="0" in exI) apply (simp add: fresh_star_def fresh_zero_perm alpha_gen alpha5_rfv) |
576 apply (clarify) apply (rule conjI) |
581 apply (clarify) apply (rule conjI) |
577 apply (rule_tac x="0" in exI) apply (simp add: fresh_star_def fresh_zero_perm alpha_gen alpha5_rfv) |
582 apply (rule_tac x="0" in exI) apply (simp add: fresh_star_def fresh_zero_perm alpha_gen alpha5_rfv) |
578 apply (rule_tac x="0" in exI) apply (simp add: fresh_star_def fresh_zero_perm alpha_gen alpha5_rfv) |
583 apply (rule_tac x="0" in exI) apply (simp add: fresh_star_def fresh_zero_perm alpha_gen alpha5_rfv) |
579 done |
584 done |
580 |
585 |
581 lemma |
586 lemma |
582 shows "(alphalts ===> op =) rbv5 rbv5" |
587 shows "(alpha_rlts ===> op =) rbv5 rbv5" |
583 by (simp add: bv_list_rsp) |
588 by (simp add: bv_list_rsp) |
584 |
589 |
585 lemmas trm5_lts_inducts = rtrm5_rlts.inducts[quot_lifted] |
590 lemmas trm5_lts_inducts = rtrm5_rlts.inducts[quot_lifted] |
586 |
591 |
587 instantiation trm5 and lts :: pt |
592 instantiation trm5 and lts :: pt |
699 where |
704 where |
700 "rbv6 (rVr6 n) = {}" |
705 "rbv6 (rVr6 n) = {}" |
701 | "rbv6 (rLm6 n t) = {atom n} \<union> rbv6 t" |
706 | "rbv6 (rLm6 n t) = {atom n} \<union> rbv6 t" |
702 | "rbv6 (rLt6 l r) = rbv6 l \<union> rbv6 r" |
707 | "rbv6 (rLt6 l r) = rbv6 l \<union> rbv6 r" |
703 |
708 |
704 local_setup {* define_raw_fv "Terms.rtrm6" [ |
709 setup {* snd o define_raw_perms ["rtrm6"] ["Terms.rtrm6"] *} |
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710 print_theorems |
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711 |
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712 local_setup {* snd o define_fv_alpha "Terms.rtrm6" [ |
705 [[[]], [[(NONE, 0)], [(NONE, 0)]], [[(SOME @{term rbv6}, 0)], [(SOME @{term rbv6}, 0)]]]] *} |
713 [[[]], [[(NONE, 0)], [(NONE, 0)]], [[(SOME @{term rbv6}, 0)], [(SOME @{term rbv6}, 0)]]]] *} |
706 print_theorems |
714 notation alpha_rtrm6 ("_ \<approx>6a _" [100, 100] 100) |
707 |
715 (* HERE THE RULES DIFFER *) |
708 setup {* snd o define_raw_perms ["rtrm6"] ["Terms.rtrm6"] *} |
716 thm alpha_rtrm6.intros |
709 print_theorems |
|
710 |
717 |
711 inductive |
718 inductive |
712 alpha6 :: "rtrm6 \<Rightarrow> rtrm6 \<Rightarrow> bool" ("_ \<approx>6 _" [100, 100] 100) |
719 alpha6 :: "rtrm6 \<Rightarrow> rtrm6 \<Rightarrow> bool" ("_ \<approx>6 _" [100, 100] 100) |
713 where |
720 where |
714 a1: "a = b \<Longrightarrow> (rVr6 a) \<approx>6 (rVr6 b)" |
721 a1: "a = b \<Longrightarrow> (rVr6 a) \<approx>6 (rVr6 b)" |
839 where |
846 where |
840 "rbv7 (rVr7 n) = {atom n}" |
847 "rbv7 (rVr7 n) = {atom n}" |
841 | "rbv7 (rLm7 n t) = rbv7 t - {atom n}" |
848 | "rbv7 (rLm7 n t) = rbv7 t - {atom n}" |
842 | "rbv7 (rLt7 l r) = rbv7 l \<union> rbv7 r" |
849 | "rbv7 (rLt7 l r) = rbv7 l \<union> rbv7 r" |
843 |
850 |
844 local_setup {* define_raw_fv "Terms.rtrm7" [ |
851 setup {* snd o define_raw_perms ["rtrm7"] ["Terms.rtrm7"] *} |
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852 print_theorems |
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853 |
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854 local_setup {* snd o define_fv_alpha "Terms.rtrm7" [ |
845 [[[]], [[(NONE, 0)], [(NONE, 0)]], [[(SOME @{term rbv7}, 0)], [(SOME @{term rbv7}, 0)]]]] *} |
855 [[[]], [[(NONE, 0)], [(NONE, 0)]], [[(SOME @{term rbv7}, 0)], [(SOME @{term rbv7}, 0)]]]] *} |
846 print_theorems |
856 notation |
847 |
857 alpha_rtrm7 ("_ \<approx>7a _" [100, 100] 100) |
848 setup {* snd o define_raw_perms ["rtrm7"] ["Terms.rtrm7"] *} |
858 (* HERE THE RULES DIFFER *) |
849 print_theorems |
859 thm alpha_rtrm7.intros |
850 |
860 |
851 inductive |
861 inductive |
852 alpha7 :: "rtrm7 \<Rightarrow> rtrm7 \<Rightarrow> bool" ("_ \<approx>7 _" [100, 100] 100) |
862 alpha7 :: "rtrm7 \<Rightarrow> rtrm7 \<Rightarrow> bool" ("_ \<approx>7 _" [100, 100] 100) |
853 where |
863 where |
854 a1: "a = b \<Longrightarrow> (rVr7 a) \<approx>7 (rVr7 b)" |
864 a1: "a = b \<Longrightarrow> (rVr7 a) \<approx>7 (rVr7 b)" |
882 rbv8 |
892 rbv8 |
883 where |
893 where |
884 "rbv8 (Bar0 x) = {}" |
894 "rbv8 (Bar0 x) = {}" |
885 | "rbv8 (Bar1 v x b) = {atom v}" |
895 | "rbv8 (Bar1 v x b) = {atom v}" |
886 |
896 |
887 local_setup {* define_raw_fv "Terms.rfoo8" [ |
897 setup {* snd o define_raw_perms ["rfoo8", "rbar8"] ["Terms.rfoo8", "Terms.rbar8"] *} |
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898 print_theorems |
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899 |
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900 local_setup {* snd o define_fv_alpha "Terms.rfoo8" [ |
888 [[[]], [[(SOME @{term rbv8}, 0)], [(SOME @{term rbv8}, 0)]]], [[[]], [[], [(NONE, 1)], [(NONE, 1)]]]] *} |
901 [[[]], [[(SOME @{term rbv8}, 0)], [(SOME @{term rbv8}, 0)]]], [[[]], [[], [(NONE, 1)], [(NONE, 1)]]]] *} |
889 print_theorems |
902 notation |
890 |
903 alpha_rfoo8 ("_ \<approx>f' _" [100, 100] 100) and |
891 setup {* snd o define_raw_perms ["rfoo8", "rbar8"] ["Terms.rfoo8", "Terms.rbar8"] *} |
904 alpha_rbar8 ("_ \<approx>b' _" [100, 100] 100) |
892 print_theorems |
905 (* HERE THE RULE DIFFERS *) |
|
906 thm alpha_rfoo8_alpha_rbar8.intros |
|
907 |
893 |
908 |
894 inductive |
909 inductive |
895 alpha8f :: "rfoo8 \<Rightarrow> rfoo8 \<Rightarrow> bool" ("_ \<approx>f _" [100, 100] 100) |
910 alpha8f :: "rfoo8 \<Rightarrow> rfoo8 \<Rightarrow> bool" ("_ \<approx>f _" [100, 100] 100) |
896 and |
911 and |
897 alpha8b :: "rbar8 \<Rightarrow> rbar8 \<Rightarrow> bool" ("_ \<approx>b _" [100, 100] 100) |
912 alpha8b :: "rbar8 \<Rightarrow> rbar8 \<Rightarrow> bool" ("_ \<approx>b _" [100, 100] 100) |
939 rbv9 |
954 rbv9 |
940 where |
955 where |
941 "rbv9 (Var9 x) = {}" |
956 "rbv9 (Var9 x) = {}" |
942 | "rbv9 (Lam9 x b) = {atom x}" |
957 | "rbv9 (Lam9 x b) = {atom x}" |
943 |
958 |
944 local_setup {* define_raw_fv "Terms.rlam9" [ |
959 setup {* snd o define_raw_perms ["rlam9", "rbla9"] ["Terms.rlam9", "Terms.rbla9"] *} |
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960 print_theorems |
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961 |
|
962 local_setup {* snd o define_fv_alpha "Terms.rlam9" [ |
945 [[[]], [[(NONE, 0)], [(NONE, 0)]]], [[[(SOME @{term rbv9}, 0)], [(SOME @{term rbv9}, 0)]]]] *} |
963 [[[]], [[(NONE, 0)], [(NONE, 0)]]], [[[(SOME @{term rbv9}, 0)], [(SOME @{term rbv9}, 0)]]]] *} |
946 print_theorems |
964 notation |
947 |
965 alpha_rlam9 ("_ \<approx>9l' _" [100, 100] 100) and |
948 setup {* snd o define_raw_perms ["rlam9", "rbla9"] ["Terms.rlam9", "Terms.rbla9"] *} |
966 alpha_rbla9 ("_ \<approx>9b' _" [100, 100] 100) |
949 print_theorems |
967 (* HERE THE RULES DIFFER *) |
|
968 thm alpha_rlam9_alpha_rbla9.intros |
|
969 |
950 |
970 |
951 inductive |
971 inductive |
952 alpha9l :: "rlam9 \<Rightarrow> rlam9 \<Rightarrow> bool" ("_ \<approx>9l _" [100, 100] 100) |
972 alpha9l :: "rlam9 \<Rightarrow> rlam9 \<Rightarrow> bool" ("_ \<approx>9l _" [100, 100] 100) |
953 and |
973 and |
954 alpha9b :: "rbla9 \<Rightarrow> rbla9 \<Rightarrow> bool" ("_ \<approx>9b _" [100, 100] 100) |
974 alpha9b :: "rbla9 \<Rightarrow> rbla9 \<Rightarrow> bool" ("_ \<approx>9b _" [100, 100] 100) |