3 begin |
3 begin |
4 |
4 |
5 (* Type Schemes *) |
5 (* Type Schemes *) |
6 atom_decl name |
6 atom_decl name |
7 |
7 |
8 (*ML {* val _ = alpha_type := AlphaRes *}*) |
8 ML {* val _ = alpha_type := AlphaRes *} |
9 nominal_datatype t = |
9 nominal_datatype t = |
10 Var "name" |
10 Var "name" |
11 | Fun "t" "t" |
11 | Fun "t" "t" |
12 and tyS = |
12 and tyS = |
13 All xs::"name fset" ty::"t" bind xs in ty |
13 All xs::"name fset" ty::"t" bind xs in ty |
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14 |
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15 lemmas t_tyS_supp = t_tyS.fv[simplified t_tyS.supp] |
14 |
16 |
15 lemma size_eqvt_raw: |
17 lemma size_eqvt_raw: |
16 "size (pi \<bullet> t :: t_raw) = size t" |
18 "size (pi \<bullet> t :: t_raw) = size t" |
17 "size (pi \<bullet> ts :: tyS_raw) = size ts" |
19 "size (pi \<bullet> ts :: tyS_raw) = size ts" |
18 apply (induct rule: t_raw_tyS_raw.inducts) |
20 apply (induct rule: t_raw_tyS_raw.inducts) |
67 thm t_tyS.perm |
69 thm t_tyS.perm |
68 thm t_tyS.inducts |
70 thm t_tyS.inducts |
69 thm t_tyS.distinct |
71 thm t_tyS.distinct |
70 ML {* Sign.of_sort @{theory} (@{typ t}, @{sort fs}) *} |
72 ML {* Sign.of_sort @{theory} (@{typ t}, @{sort fs}) *} |
71 |
73 |
72 lemmas t_tyS_supp = t_tyS.fv[simplified t_tyS.supp] |
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73 |
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74 lemma induct: |
74 lemma induct: |
75 assumes a1: "\<And>name b. P b (Var name)" |
75 assumes a1: "\<And>name b. P b (Var name)" |
76 and a2: "\<And>t1 t2 b. \<lbrakk>\<And>c. P c t1; \<And>c. P c t2\<rbrakk> \<Longrightarrow> P b (Fun t1 t2)" |
76 and a2: "\<And>t1 t2 b. \<lbrakk>\<And>c. P c t1; \<And>c. P c t2\<rbrakk> \<Longrightarrow> P b (Fun t1 t2)" |
77 and a3: "\<And>fset t b. \<lbrakk>\<And>c. P c t; fset_to_set (fmap atom fset) \<sharp>* b\<rbrakk> \<Longrightarrow> P' b (All fset t)" |
77 and a3: "\<And>fset t b. \<lbrakk>\<And>c. P c t; fset_to_set (fmap atom fset) \<sharp>* b\<rbrakk> \<Longrightarrow> P' b (All fset t)" |
78 shows "P (a :: 'a :: pt) t \<and> P' (d :: 'b :: {fs}) ts " |
78 shows "P (a :: 'a :: pt) t \<and> P' (d :: 'b :: {fs}) ts " |
118 lemma |
118 lemma |
119 shows "All {|a, b|} (Fun (Var a) (Var b)) = All {|b, a|} (Fun (Var a) (Var b))" |
119 shows "All {|a, b|} (Fun (Var a) (Var b)) = All {|b, a|} (Fun (Var a) (Var b))" |
120 apply(simp add: t_tyS.eq_iff) |
120 apply(simp add: t_tyS.eq_iff) |
121 apply(rule_tac x="0::perm" in exI) |
121 apply(rule_tac x="0::perm" in exI) |
122 apply(simp add: alphas) |
122 apply(simp add: alphas) |
123 apply(auto) |
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124 apply(simp add: fresh_star_def fresh_zero_perm) |
123 apply(simp add: fresh_star_def fresh_zero_perm) |
125 done |
124 done |
126 |
125 |
127 lemma |
126 lemma |
128 shows "All {|a, b|} (Fun (Var a) (Var b)) = All {|a, b|} (Fun (Var b) (Var a))" |
127 shows "All {|a, b|} (Fun (Var a) (Var b)) = All {|a, b|} (Fun (Var b) (Var a))" |
129 apply(simp add: t_tyS.eq_iff) |
128 apply(simp add: t_tyS.eq_iff) |
130 apply(rule_tac x="(atom a \<rightleftharpoons> atom b)" in exI) |
129 apply(rule_tac x="(atom a \<rightleftharpoons> atom b)" in exI) |
131 apply(simp add: alpha_gen fresh_star_def eqvts) |
130 apply(simp add: alphas fresh_star_def eqvts) |
132 apply auto |
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133 done |
131 done |
134 |
132 |
135 lemma |
133 lemma |
136 shows "All {|a, b, c|} (Fun (Var a) (Var b)) = All {|a, b|} (Fun (Var a) (Var b))" |
134 shows "All {|a, b, c|} (Fun (Var a) (Var b)) = All {|a, b|} (Fun (Var a) (Var b))" |
137 apply(simp add: t_tyS.eq_iff) |
135 apply(simp add: t_tyS.eq_iff) |
138 apply(rule_tac x="0::perm" in exI) |
136 apply(rule_tac x="0::perm" in exI) |
139 apply(simp add: alpha_gen fresh_star_def eqvts t_tyS.eq_iff) |
137 apply(simp add: alphas fresh_star_def eqvts t_tyS.eq_iff) |
140 oops |
138 done |
141 |
139 |
142 lemma |
140 lemma |
143 assumes a: "a \<noteq> b" |
141 assumes a: "a \<noteq> b" |
144 shows "\<not>(All {|a, b|} (Fun (Var a) (Var b)) = All {|c|} (Fun (Var c) (Var c)))" |
142 shows "\<not>(All {|a, b|} (Fun (Var a) (Var b)) = All {|c|} (Fun (Var c) (Var c)))" |
145 using a |
143 using a |
146 apply(simp add: t_tyS.eq_iff) |
144 apply(simp add: t_tyS.eq_iff) |
147 apply(clarify) |
145 apply(clarify) |
148 apply(simp add: alpha_gen fresh_star_def eqvts t_tyS.eq_iff) |
146 apply(simp add: alphas fresh_star_def eqvts t_tyS.eq_iff) |
149 apply auto |
147 apply auto |
150 done |
148 done |
151 |
149 |
152 (* PROBLEM: |
150 (* PROBLEM: |
153 Type schemes with separate datatypes |
151 Type schemes with separate datatypes |