3 begin |
3 begin |
4 |
4 |
5 atom_decl name |
5 atom_decl name |
6 |
6 |
7 nominal_datatype trm = |
7 nominal_datatype trm = |
8 Var "name" |
8 Vr "name" |
9 | App "trm" "trm" |
9 | Ap "trm" "trm" |
10 | Lam x::"name" t::"trm" binds x in t |
10 | Lm x::"name" t::"trm" binds (set) x in t |
11 | Let as::"assn" t::"trm" binds "bn as" in t |
11 | Lt a::"lts" t::"trm" binds "bn a" in a t |
12 | Let_rec as::"assn" t::"trm" binds "bn as" in as t |
12 and lts = |
13 and assn = |
13 Lnil |
14 ANil |
14 | Lcons "name" "trm" "lts" |
15 | ACons "name" "trm" "assn" |
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16 binder |
15 binder |
17 bn |
16 bn |
18 where |
17 where |
19 "bn (ANil) = []" |
18 "bn Lnil = []" |
20 | "bn (ACons x t as) = (atom x) # (bn as)" |
19 | "bn (Lcons x t l) = (atom x) # (bn l)" |
21 |
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22 thm trm_assn.eq_iff |
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23 thm trm_assn.supp |
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24 |
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25 thm trm_assn.fv_defs |
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26 thm trm_assn.eq_iff |
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27 thm trm_assn.bn_defs |
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28 thm trm_assn.perm_simps |
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29 thm trm_assn.induct |
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30 thm trm_assn.distinct |
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31 |
20 |
32 |
21 |
33 |
22 thm trm_lts.fv_defs |
34 section {* Tests *} |
23 thm trm_lts.eq_iff |
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24 thm trm_lts.bn_defs |
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25 thm trm_lts.perm_simps |
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26 thm trm_lts.induct |
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27 thm trm_lts.distinct |
35 |
28 |
36 |
29 |
37 (* why is this not in HOL simpset? *) |
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38 (* |
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39 lemma set_sub: "{a, b} - {b} = {a} - {b}" |
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40 by auto |
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41 |
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42 lemma lets_bla: |
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43 "x \<noteq> z \<Longrightarrow> y \<noteq> z \<Longrightarrow> x \<noteq> y \<Longrightarrow>(Lt (Lcons x (Vr y) Lnil) (Vr x)) \<noteq> (Lt (Lcons x (Vr z) Lnil) (Vr x))" |
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44 apply (auto simp add: trm_lts.eq_iff alphas set_sub supp_at_base) |
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45 done |
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46 |
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47 lemma lets_ok: |
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48 "(Lt (Lcons x (Vr x) Lnil) (Vr x)) = (Lt (Lcons y (Vr y) Lnil) (Vr y))" |
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49 apply (simp add: trm_lts.eq_iff) |
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50 apply (rule_tac x="(x \<leftrightarrow> y)" in exI) |
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51 apply (simp_all add: alphas fresh_star_def eqvts supp_at_base) |
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52 done |
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53 |
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54 lemma lets_ok3: |
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55 "x \<noteq> y \<Longrightarrow> |
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56 (Lt (Lcons x (Ap (Vr y) (Vr x)) (Lcons y (Vr y) Lnil)) (Ap (Vr x) (Vr y))) \<noteq> |
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57 (Lt (Lcons y (Ap (Vr x) (Vr y)) (Lcons x (Vr x) Lnil)) (Ap (Vr x) (Vr y)))" |
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58 apply (simp add: alphas trm_lts.eq_iff) |
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59 done |
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60 |
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61 |
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62 lemma lets_not_ok1: |
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63 "x \<noteq> y \<Longrightarrow> |
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64 (Lt (Lcons x (Vr x) (Lcons y (Vr y) Lnil)) (Ap (Vr x) (Vr y))) \<noteq> |
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65 (Lt (Lcons y (Vr x) (Lcons x (Vr y) Lnil)) (Ap (Vr x) (Vr y)))" |
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66 apply (simp add: alphas trm_lts.eq_iff) |
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67 done |
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68 |
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69 lemma lets_nok: |
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70 "x \<noteq> y \<Longrightarrow> x \<noteq> z \<Longrightarrow> z \<noteq> y \<Longrightarrow> |
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71 (Lt (Lcons x (Ap (Vr z) (Vr z)) (Lcons y (Vr z) Lnil)) (Ap (Vr x) (Vr y))) \<noteq> |
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72 (Lt (Lcons y (Vr z) (Lcons x (Ap (Vr z) (Vr z)) Lnil)) (Ap (Vr x) (Vr y)))" |
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73 apply (simp add: alphas trm_lts.eq_iff fresh_star_def) |
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74 done |
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75 |
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76 lemma lets_ok4: |
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77 "(Lt (Lcons x (Ap (Vr y) (Vr x)) (Lcons y (Vr y) Lnil)) (Ap (Vr x) (Vr y))) = |
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78 (Lt (Lcons y (Ap (Vr x) (Vr y)) (Lcons x (Vr x) Lnil)) (Ap (Vr y) (Vr x)))" |
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79 apply (simp add: alphas trm_lts.eq_iff supp_at_base) |
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80 apply (rule_tac x="(x \<leftrightarrow> y)" in exI) |
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81 apply (simp add: atom_eqvt fresh_star_def) |
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82 done |
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83 *) |
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84 end |
30 end |
85 |
31 |
86 |
32 |
87 |
33 |