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theory LetRec
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imports "../Nominal2"
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begin
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atom_decl name
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nominal_datatype let_rec:
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2438
abafea9b39bb
corrected bug with fv-function generation (that was the problem with recursive binders)
Christian Urban <urbanc@in.tum.de>
diff
changeset
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trm =
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2056
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Var "name"
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2438
abafea9b39bb
corrected bug with fv-function generation (that was the problem with recursive binders)
Christian Urban <urbanc@in.tum.de>
diff
changeset
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| App "trm" "trm"
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2950
0911cb7bf696
changed bind to binds in specifications; bind will cause trouble with Monad_Syntax
Christian Urban <urbanc@in.tum.de>
diff
changeset
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| Lam x::"name" t::"trm" binds (set) x in t
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0911cb7bf696
changed bind to binds in specifications; bind will cause trouble with Monad_Syntax
Christian Urban <urbanc@in.tum.de>
diff
changeset
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| Let_Rec bp::"bp" t::"trm" binds (set) "bn bp" in bp t
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1946
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and bp =
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2438
abafea9b39bb
corrected bug with fv-function generation (that was the problem with recursive binders)
Christian Urban <urbanc@in.tum.de>
diff
changeset
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Bp "name" "trm"
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binder
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2438
abafea9b39bb
corrected bug with fv-function generation (that was the problem with recursive binders)
Christian Urban <urbanc@in.tum.de>
diff
changeset
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bn::"bp \<Rightarrow> atom set"
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where
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2438
abafea9b39bb
corrected bug with fv-function generation (that was the problem with recursive binders)
Christian Urban <urbanc@in.tum.de>
diff
changeset
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"bn (Bp x t) = {atom x}"
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thm let_rec.distinct
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thm let_rec.induct
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thm let_rec.exhaust
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thm let_rec.fv_defs
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thm let_rec.bn_defs
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thm let_rec.perm_simps
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thm let_rec.eq_iff
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thm let_rec.fv_bn_eqvt
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thm let_rec.size_eqvt
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2082
0854af516f14
cleaned up a bit the examples; added equivariance to all examples
Christian Urban <urbanc@in.tum.de>
diff
changeset
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nominal_primrec
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height_trm :: "trm \<Rightarrow> nat"
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and height_bp :: "bp \<Rightarrow> nat"
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where
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"height_trm (Var x) = 1"
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| "height_trm (App l r) = max (height_trm l) (height_trm r)"
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| "height_trm (Lam v b) = 1 + (height_trm b)"
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| "height_trm (Let_Rec bp b) = max (height_bp bp) (height_trm b)"
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| "height_bp (Bp v t) = height_trm t"
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3197
25d11b449e92
definition of an auxiliary graph in nominal-primrec definitions
Christian Urban <urbanc@in.tum.de>
diff
changeset
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apply (simp add: eqvt_def height_trm_height_bp_graph_aux_def)
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25d11b449e92
definition of an auxiliary graph in nominal-primrec definitions
Christian Urban <urbanc@in.tum.de>
diff
changeset
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apply(rule TrueI)
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using [[simproc del: alpha_set]]
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apply auto
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apply (case_tac x)
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apply (case_tac a rule: let_rec.exhaust(1))
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using [[simproc del: alpha_set]]
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apply auto
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apply (case_tac b rule: let_rec.exhaust(2))
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apply blast
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apply (erule Abs_set_fcb)
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3183
313e6f2cdd89
added permutation simplification to the simplifier; this makes the simplifier more powerful, but it potentially loops more often
Christian Urban <urbanc@in.tum.de>
diff
changeset
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apply (simp_all add: pure_fresh)[2]
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313e6f2cdd89
added permutation simplification to the simplifier; this makes the simplifier more powerful, but it potentially loops more often
Christian Urban <urbanc@in.tum.de>
diff
changeset
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apply (simp only: eqvt_at_def)
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313e6f2cdd89
added permutation simplification to the simplifier; this makes the simplifier more powerful, but it potentially loops more often
Christian Urban <urbanc@in.tum.de>
diff
changeset
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apply(perm_simp)
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313e6f2cdd89
added permutation simplification to the simplifier; this makes the simplifier more powerful, but it potentially loops more often
Christian Urban <urbanc@in.tum.de>
diff
changeset
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apply(simp)
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apply (simp add: Abs_eq_iff2)
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apply (simp add: alphas)
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apply clarify
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apply (rule trans)
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apply(rule_tac p="p" in supp_perm_eq[symmetric])
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apply (simp add: pure_supp fresh_star_def)
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apply(simp add: eqvt_at_def)
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done
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2975
c62e26830420
preliminary version of automatically generation the eqvt-lemmas for functions defined with nominal_primrec
Christian Urban <urbanc@in.tum.de>
diff
changeset
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termination (eqvt) by lexicographic_order
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2974
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2975
c62e26830420
preliminary version of automatically generation the eqvt-lemmas for functions defined with nominal_primrec
Christian Urban <urbanc@in.tum.de>
diff
changeset
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thm height_trm_height_bp.eqvt
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2974
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end
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