author | wenzelm |
Sun, 27 Dec 2015 22:07:17 +0100 | |
changeset 61943 | 7fba644ed827 |
parent 61585 | a9599d3d7610 |
child 61952 | 546958347e05 |
permissions | -rw-r--r-- |
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(* Title: HOL/Library/Old_Datatype.thy |
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Author: Lawrence C Paulson, Cambridge University Computer Laboratory |
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Author: Stefan Berghofer and Markus Wenzel, TU Muenchen |
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New theory Datatype. Needed as an ancestor when defining datatypes.
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*) |
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section \<open>Old Datatype package: constructing datatypes from Cartesian Products and Disjoint Sums\<close> |
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theory Old_Datatype |
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imports "../Main" |
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keywords "old_datatype" :: thy_decl |
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begin |
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ML_file "~~/src/HOL/Tools/datatype_realizer.ML" |
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subsection \<open>The datatype universe\<close> |
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definition "Node = {p. EX f x k. p = (f :: nat => 'b + nat, x ::'a + nat) & f k = Inr 0}" |
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typedef ('a, 'b) node = "Node :: ((nat => 'b + nat) * ('a + nat)) set" |
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morphisms Rep_Node Abs_Node |
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unfolding Node_def by auto |
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text\<open>Datatypes will be represented by sets of type \<open>node\<close>\<close> |
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type_synonym 'a item = "('a, unit) node set" |
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type_synonym ('a, 'b) dtree = "('a, 'b) node set" |
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consts |
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Push :: "[('b + nat), nat => ('b + nat)] => (nat => ('b + nat))" |
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Push_Node :: "[('b + nat), ('a, 'b) node] => ('a, 'b) node" |
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ndepth :: "('a, 'b) node => nat" |
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Atom :: "('a + nat) => ('a, 'b) dtree" |
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Leaf :: "'a => ('a, 'b) dtree" |
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Numb :: "nat => ('a, 'b) dtree" |
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Scons :: "[('a, 'b) dtree, ('a, 'b) dtree] => ('a, 'b) dtree" |
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In0 :: "('a, 'b) dtree => ('a, 'b) dtree" |
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In1 :: "('a, 'b) dtree => ('a, 'b) dtree" |
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Lim :: "('b => ('a, 'b) dtree) => ('a, 'b) dtree" |
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ntrunc :: "[nat, ('a, 'b) dtree] => ('a, 'b) dtree" |
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uprod :: "[('a, 'b) dtree set, ('a, 'b) dtree set]=> ('a, 'b) dtree set" |
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usum :: "[('a, 'b) dtree set, ('a, 'b) dtree set]=> ('a, 'b) dtree set" |
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Split :: "[[('a, 'b) dtree, ('a, 'b) dtree]=>'c, ('a, 'b) dtree] => 'c" |
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Case :: "[[('a, 'b) dtree]=>'c, [('a, 'b) dtree]=>'c, ('a, 'b) dtree] => 'c" |
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dprod :: "[(('a, 'b) dtree * ('a, 'b) dtree)set, (('a, 'b) dtree * ('a, 'b) dtree)set] |
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=> (('a, 'b) dtree * ('a, 'b) dtree)set" |
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dsum :: "[(('a, 'b) dtree * ('a, 'b) dtree)set, (('a, 'b) dtree * ('a, 'b) dtree)set] |
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=> (('a, 'b) dtree * ('a, 'b) dtree)set" |
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defs |
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Push_Node_def: "Push_Node == (%n x. Abs_Node (apfst (Push n) (Rep_Node x)))" |
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(*crude "lists" of nats -- needed for the constructions*) |
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Push_def: "Push == (%b h. case_nat b h)" |
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(** operations on S-expressions -- sets of nodes **) |
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(*S-expression constructors*) |
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Atom_def: "Atom == (%x. {Abs_Node((%k. Inr 0, x))})" |
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Scons_def: "Scons M N == (Push_Node (Inr 1) ` M) Un (Push_Node (Inr (Suc 1)) ` N)" |
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(*Leaf nodes, with arbitrary or nat labels*) |
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Leaf_def: "Leaf == Atom o Inl" |
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Numb_def: "Numb == Atom o Inr" |
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(*Injections of the "disjoint sum"*) |
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In0_def: "In0(M) == Scons (Numb 0) M" |
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In1_def: "In1(M) == Scons (Numb 1) M" |
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(*Function spaces*) |
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Lim_def: "Lim f == Union {z. ? x. z = Push_Node (Inl x) ` (f x)}" |
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(*the set of nodes with depth less than k*) |
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ndepth_def: "ndepth(n) == (%(f,x). LEAST k. f k = Inr 0) (Rep_Node n)" |
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ntrunc_def: "ntrunc k N == {n. n:N & ndepth(n)<k}" |
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(*products and sums for the "universe"*) |
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uprod_def: "uprod A B == UN x:A. UN y:B. { Scons x y }" |
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usum_def: "usum A B == In0`A Un In1`B" |
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(*the corresponding eliminators*) |
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Split_def: "Split c M == THE u. EX x y. M = Scons x y & u = c x y" |
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Case_def: "Case c d M == THE u. (EX x . M = In0(x) & u = c(x)) |
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| (EX y . M = In1(y) & u = d(y))" |
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(** equality for the "universe" **) |
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dprod_def: "dprod r s == UN (x,x'):r. UN (y,y'):s. {(Scons x y, Scons x' y')}" |
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dsum_def: "dsum r s == (UN (x,x'):r. {(In0(x),In0(x'))}) Un |
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(UN (y,y'):s. {(In1(y),In1(y'))})" |
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lemma apfst_convE: |
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"[| q = apfst f p; !!x y. [| p = (x,y); q = (f(x),y) |] ==> R |
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|] ==> R" |
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by (force simp add: apfst_def) |
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(** Push -- an injection, analogous to Cons on lists **) |
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lemma Push_inject1: "Push i f = Push j g ==> i=j" |
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apply (simp add: Push_def fun_eq_iff) |
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apply (drule_tac x=0 in spec, simp) |
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done |
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lemma Push_inject2: "Push i f = Push j g ==> f=g" |
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apply (auto simp add: Push_def fun_eq_iff) |
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apply (drule_tac x="Suc x" in spec, simp) |
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done |
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lemma Push_inject: |
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"[| Push i f =Push j g; [| i=j; f=g |] ==> P |] ==> P" |
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by (blast dest: Push_inject1 Push_inject2) |
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lemma Push_neq_K0: "Push (Inr (Suc k)) f = (%z. Inr 0) ==> P" |
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by (auto simp add: Push_def fun_eq_iff split: nat.split_asm) |
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lemmas Abs_Node_inj = Abs_Node_inject [THEN [2] rev_iffD1] |
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(*** Introduction rules for Node ***) |
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lemma Node_K0_I: "(%k. Inr 0, a) : Node" |
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by (simp add: Node_def) |
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lemma Node_Push_I: "p: Node ==> apfst (Push i) p : Node" |
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apply (simp add: Node_def Push_def) |
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apply (fast intro!: apfst_conv nat.case(2)[THEN trans]) |
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done |
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subsection\<open>Freeness: Distinctness of Constructors\<close> |
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(** Scons vs Atom **) |
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lemma Scons_not_Atom [iff]: "Scons M N \<noteq> Atom(a)" |
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unfolding Atom_def Scons_def Push_Node_def One_nat_def |
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by (blast intro: Node_K0_I Rep_Node [THEN Node_Push_I] |
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dest!: Abs_Node_inj |
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elim!: apfst_convE sym [THEN Push_neq_K0]) |
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lemmas Atom_not_Scons [iff] = Scons_not_Atom [THEN not_sym] |
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(*** Injectiveness ***) |
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(** Atomic nodes **) |
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lemma inj_Atom: "inj(Atom)" |
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apply (simp add: Atom_def) |
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apply (blast intro!: inj_onI Node_K0_I dest!: Abs_Node_inj) |
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done |
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lemmas Atom_inject = inj_Atom [THEN injD] |
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lemma Atom_Atom_eq [iff]: "(Atom(a)=Atom(b)) = (a=b)" |
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by (blast dest!: Atom_inject) |
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lemma inj_Leaf: "inj(Leaf)" |
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apply (simp add: Leaf_def o_def) |
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apply (rule inj_onI) |
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apply (erule Atom_inject [THEN Inl_inject]) |
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done |
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lemmas Leaf_inject [dest!] = inj_Leaf [THEN injD] |
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lemma inj_Numb: "inj(Numb)" |
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apply (simp add: Numb_def o_def) |
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apply (rule inj_onI) |
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apply (erule Atom_inject [THEN Inr_inject]) |
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done |
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lemmas Numb_inject [dest!] = inj_Numb [THEN injD] |
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(** Injectiveness of Push_Node **) |
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lemma Push_Node_inject: |
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"[| Push_Node i m =Push_Node j n; [| i=j; m=n |] ==> P |
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|] ==> P" |
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apply (simp add: Push_Node_def) |
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apply (erule Abs_Node_inj [THEN apfst_convE]) |
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apply (rule Rep_Node [THEN Node_Push_I])+ |
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apply (erule sym [THEN apfst_convE]) |
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apply (blast intro: Rep_Node_inject [THEN iffD1] trans sym elim!: Push_inject) |
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done |
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(** Injectiveness of Scons **) |
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lemma Scons_inject_lemma1: "Scons M N <= Scons M' N' ==> M<=M'" |
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unfolding Scons_def One_nat_def |
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by (blast dest!: Push_Node_inject) |
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lemma Scons_inject_lemma2: "Scons M N <= Scons M' N' ==> N<=N'" |
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unfolding Scons_def One_nat_def |
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by (blast dest!: Push_Node_inject) |
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lemma Scons_inject1: "Scons M N = Scons M' N' ==> M=M'" |
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apply (erule equalityE) |
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apply (iprover intro: equalityI Scons_inject_lemma1) |
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done |
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lemma Scons_inject2: "Scons M N = Scons M' N' ==> N=N'" |
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apply (erule equalityE) |
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apply (iprover intro: equalityI Scons_inject_lemma2) |
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done |
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lemma Scons_inject: |
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"[| Scons M N = Scons M' N'; [| M=M'; N=N' |] ==> P |] ==> P" |
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by (iprover dest: Scons_inject1 Scons_inject2) |
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lemma Scons_Scons_eq [iff]: "(Scons M N = Scons M' N') = (M=M' & N=N')" |
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by (blast elim!: Scons_inject) |
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(*** Distinctness involving Leaf and Numb ***) |
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(** Scons vs Leaf **) |
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lemma Scons_not_Leaf [iff]: "Scons M N \<noteq> Leaf(a)" |
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unfolding Leaf_def o_def by (rule Scons_not_Atom) |
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lemmas Leaf_not_Scons [iff] = Scons_not_Leaf [THEN not_sym] |
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(** Scons vs Numb **) |
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lemma Scons_not_Numb [iff]: "Scons M N \<noteq> Numb(k)" |
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unfolding Numb_def o_def by (rule Scons_not_Atom) |
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lemmas Numb_not_Scons [iff] = Scons_not_Numb [THEN not_sym] |
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(** Leaf vs Numb **) |
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lemma Leaf_not_Numb [iff]: "Leaf(a) \<noteq> Numb(k)" |
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by (simp add: Leaf_def Numb_def) |
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lemmas Numb_not_Leaf [iff] = Leaf_not_Numb [THEN not_sym] |
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(*** ndepth -- the depth of a node ***) |
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lemma ndepth_K0: "ndepth (Abs_Node(%k. Inr 0, x)) = 0" |
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by (simp add: ndepth_def Node_K0_I [THEN Abs_Node_inverse] Least_equality) |
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lemma ndepth_Push_Node_aux: |
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"case_nat (Inr (Suc i)) f k = Inr 0 --> Suc(LEAST x. f x = Inr 0) <= k" |
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apply (induct_tac "k", auto) |
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apply (erule Least_le) |
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done |
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lemma ndepth_Push_Node: |
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"ndepth (Push_Node (Inr (Suc i)) n) = Suc(ndepth(n))" |
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apply (insert Rep_Node [of n, unfolded Node_def]) |
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apply (auto simp add: ndepth_def Push_Node_def |
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Rep_Node [THEN Node_Push_I, THEN Abs_Node_inverse]) |
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apply (rule Least_equality) |
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apply (auto simp add: Push_def ndepth_Push_Node_aux) |
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apply (erule LeastI) |
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done |
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(*** ntrunc applied to the various node sets ***) |
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lemma ntrunc_0 [simp]: "ntrunc 0 M = {}" |
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by (simp add: ntrunc_def) |
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lemma ntrunc_Atom [simp]: "ntrunc (Suc k) (Atom a) = Atom(a)" |
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by (auto simp add: Atom_def ntrunc_def ndepth_K0) |
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lemma ntrunc_Leaf [simp]: "ntrunc (Suc k) (Leaf a) = Leaf(a)" |
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unfolding Leaf_def o_def by (rule ntrunc_Atom) |
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lemma ntrunc_Numb [simp]: "ntrunc (Suc k) (Numb i) = Numb(i)" |
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unfolding Numb_def o_def by (rule ntrunc_Atom) |
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lemma ntrunc_Scons [simp]: |
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"ntrunc (Suc k) (Scons M N) = Scons (ntrunc k M) (ntrunc k N)" |
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unfolding Scons_def ntrunc_def One_nat_def |
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by (auto simp add: ndepth_Push_Node) |
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(** Injection nodes **) |
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lemma ntrunc_one_In0 [simp]: "ntrunc (Suc 0) (In0 M) = {}" |
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apply (simp add: In0_def) |
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apply (simp add: Scons_def) |
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done |
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lemma ntrunc_In0 [simp]: "ntrunc (Suc(Suc k)) (In0 M) = In0 (ntrunc (Suc k) M)" |
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by (simp add: In0_def) |
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lemma ntrunc_one_In1 [simp]: "ntrunc (Suc 0) (In1 M) = {}" |
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apply (simp add: In1_def) |
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apply (simp add: Scons_def) |
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done |
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lemma ntrunc_In1 [simp]: "ntrunc (Suc(Suc k)) (In1 M) = In1 (ntrunc (Suc k) M)" |
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by (simp add: In1_def) |
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subsection\<open>Set Constructions\<close> |
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(*** Cartesian Product ***) |
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lemma uprodI [intro!]: "[| M:A; N:B |] ==> Scons M N : uprod A B" |
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by (simp add: uprod_def) |
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(*The general elimination rule*) |
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lemma uprodE [elim!]: |
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"[| c : uprod A B; |
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!!x y. [| x:A; y:B; c = Scons x y |] ==> P |
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|] ==> P" |
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by (auto simp add: uprod_def) |
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(*Elimination of a pair -- introduces no eigenvariables*) |
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lemma uprodE2: "[| Scons M N : uprod A B; [| M:A; N:B |] ==> P |] ==> P" |
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by (auto simp add: uprod_def) |
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(*** Disjoint Sum ***) |
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lemma usum_In0I [intro]: "M:A ==> In0(M) : usum A B" |
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by (simp add: usum_def) |
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||
339 |
lemma usum_In1I [intro]: "N:B ==> In1(N) : usum A B" |
|
340 |
by (simp add: usum_def) |
|
341 |
||
342 |
lemma usumE [elim!]: |
|
343 |
"[| u : usum A B; |
|
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!!x. [| x:A; u=In0(x) |] ==> P; |
|
345 |
!!y. [| y:B; u=In1(y) |] ==> P |
|
346 |
|] ==> P" |
|
347 |
by (auto simp add: usum_def) |
|
348 |
||
349 |
||
350 |
(** Injection **) |
|
351 |
||
352 |
lemma In0_not_In1 [iff]: "In0(M) \<noteq> In1(N)" |
|
35216 | 353 |
unfolding In0_def In1_def One_nat_def by auto |
20819 | 354 |
|
45607 | 355 |
lemmas In1_not_In0 [iff] = In0_not_In1 [THEN not_sym] |
20819 | 356 |
|
357 |
lemma In0_inject: "In0(M) = In0(N) ==> M=N" |
|
358 |
by (simp add: In0_def) |
|
359 |
||
360 |
lemma In1_inject: "In1(M) = In1(N) ==> M=N" |
|
361 |
by (simp add: In1_def) |
|
362 |
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363 |
lemma In0_eq [iff]: "(In0 M = In0 N) = (M=N)" |
|
364 |
by (blast dest!: In0_inject) |
|
365 |
||
366 |
lemma In1_eq [iff]: "(In1 M = In1 N) = (M=N)" |
|
367 |
by (blast dest!: In1_inject) |
|
368 |
||
369 |
lemma inj_In0: "inj In0" |
|
370 |
by (blast intro!: inj_onI) |
|
371 |
||
372 |
lemma inj_In1: "inj In1" |
|
373 |
by (blast intro!: inj_onI) |
|
374 |
||
375 |
||
376 |
(*** Function spaces ***) |
|
377 |
||
378 |
lemma Lim_inject: "Lim f = Lim g ==> f = g" |
|
379 |
apply (simp add: Lim_def) |
|
380 |
apply (rule ext) |
|
381 |
apply (blast elim!: Push_Node_inject) |
|
382 |
done |
|
383 |
||
384 |
||
385 |
(*** proving equality of sets and functions using ntrunc ***) |
|
386 |
||
387 |
lemma ntrunc_subsetI: "ntrunc k M <= M" |
|
388 |
by (auto simp add: ntrunc_def) |
|
389 |
||
390 |
lemma ntrunc_subsetD: "(!!k. ntrunc k M <= N) ==> M<=N" |
|
391 |
by (auto simp add: ntrunc_def) |
|
392 |
||
393 |
(*A generalized form of the take-lemma*) |
|
394 |
lemma ntrunc_equality: "(!!k. ntrunc k M = ntrunc k N) ==> M=N" |
|
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apply (rule equalityI) |
|
396 |
apply (rule_tac [!] ntrunc_subsetD) |
|
397 |
apply (rule_tac [!] ntrunc_subsetI [THEN [2] subset_trans], auto) |
|
398 |
done |
|
399 |
||
400 |
lemma ntrunc_o_equality: |
|
401 |
"[| !!k. (ntrunc(k) o h1) = (ntrunc(k) o h2) |] ==> h1=h2" |
|
402 |
apply (rule ntrunc_equality [THEN ext]) |
|
39302
d7728f65b353
renamed lemmas: ext_iff -> fun_eq_iff, set_ext_iff -> set_eq_iff, set_ext -> set_eqI
nipkow
parents:
39198
diff
changeset
|
403 |
apply (simp add: fun_eq_iff) |
20819 | 404 |
done |
405 |
||
406 |
||
407 |
(*** Monotonicity ***) |
|
408 |
||
409 |
lemma uprod_mono: "[| A<=A'; B<=B' |] ==> uprod A B <= uprod A' B'" |
|
410 |
by (simp add: uprod_def, blast) |
|
411 |
||
412 |
lemma usum_mono: "[| A<=A'; B<=B' |] ==> usum A B <= usum A' B'" |
|
413 |
by (simp add: usum_def, blast) |
|
414 |
||
415 |
lemma Scons_mono: "[| M<=M'; N<=N' |] ==> Scons M N <= Scons M' N'" |
|
416 |
by (simp add: Scons_def, blast) |
|
417 |
||
418 |
lemma In0_mono: "M<=N ==> In0(M) <= In0(N)" |
|
35216 | 419 |
by (simp add: In0_def Scons_mono) |
20819 | 420 |
|
421 |
lemma In1_mono: "M<=N ==> In1(M) <= In1(N)" |
|
35216 | 422 |
by (simp add: In1_def Scons_mono) |
20819 | 423 |
|
424 |
||
425 |
(*** Split and Case ***) |
|
426 |
||
427 |
lemma Split [simp]: "Split c (Scons M N) = c M N" |
|
428 |
by (simp add: Split_def) |
|
429 |
||
430 |
lemma Case_In0 [simp]: "Case c d (In0 M) = c(M)" |
|
431 |
by (simp add: Case_def) |
|
432 |
||
433 |
lemma Case_In1 [simp]: "Case c d (In1 N) = d(N)" |
|
434 |
by (simp add: Case_def) |
|
435 |
||
436 |
||
437 |
||
438 |
(**** UN x. B(x) rules ****) |
|
439 |
||
440 |
lemma ntrunc_UN1: "ntrunc k (UN x. f(x)) = (UN x. ntrunc k (f x))" |
|
441 |
by (simp add: ntrunc_def, blast) |
|
442 |
||
443 |
lemma Scons_UN1_x: "Scons (UN x. f x) M = (UN x. Scons (f x) M)" |
|
444 |
by (simp add: Scons_def, blast) |
|
445 |
||
446 |
lemma Scons_UN1_y: "Scons M (UN x. f x) = (UN x. Scons M (f x))" |
|
447 |
by (simp add: Scons_def, blast) |
|
448 |
||
449 |
lemma In0_UN1: "In0(UN x. f(x)) = (UN x. In0(f(x)))" |
|
450 |
by (simp add: In0_def Scons_UN1_y) |
|
451 |
||
452 |
lemma In1_UN1: "In1(UN x. f(x)) = (UN x. In1(f(x)))" |
|
453 |
by (simp add: In1_def Scons_UN1_y) |
|
454 |
||
455 |
||
456 |
(*** Equality for Cartesian Product ***) |
|
457 |
||
458 |
lemma dprodI [intro!]: |
|
459 |
"[| (M,M'):r; (N,N'):s |] ==> (Scons M N, Scons M' N') : dprod r s" |
|
460 |
by (auto simp add: dprod_def) |
|
461 |
||
462 |
(*The general elimination rule*) |
|
463 |
lemma dprodE [elim!]: |
|
464 |
"[| c : dprod r s; |
|
465 |
!!x y x' y'. [| (x,x') : r; (y,y') : s; |
|
466 |
c = (Scons x y, Scons x' y') |] ==> P |
|
467 |
|] ==> P" |
|
468 |
by (auto simp add: dprod_def) |
|
469 |
||
470 |
||
471 |
(*** Equality for Disjoint Sum ***) |
|
472 |
||
473 |
lemma dsum_In0I [intro]: "(M,M'):r ==> (In0(M), In0(M')) : dsum r s" |
|
474 |
by (auto simp add: dsum_def) |
|
475 |
||
476 |
lemma dsum_In1I [intro]: "(N,N'):s ==> (In1(N), In1(N')) : dsum r s" |
|
477 |
by (auto simp add: dsum_def) |
|
478 |
||
479 |
lemma dsumE [elim!]: |
|
480 |
"[| w : dsum r s; |
|
481 |
!!x x'. [| (x,x') : r; w = (In0(x), In0(x')) |] ==> P; |
|
482 |
!!y y'. [| (y,y') : s; w = (In1(y), In1(y')) |] ==> P |
|
483 |
|] ==> P" |
|
484 |
by (auto simp add: dsum_def) |
|
485 |
||
486 |
||
487 |
(*** Monotonicity ***) |
|
488 |
||
489 |
lemma dprod_mono: "[| r<=r'; s<=s' |] ==> dprod r s <= dprod r' s'" |
|
490 |
by blast |
|
491 |
||
492 |
lemma dsum_mono: "[| r<=r'; s<=s' |] ==> dsum r s <= dsum r' s'" |
|
493 |
by blast |
|
494 |
||
495 |
||
496 |
(*** Bounding theorems ***) |
|
497 |
||
61943 | 498 |
lemma dprod_Sigma: "(dprod (A \<times> B) (C \<times> D)) <= (uprod A C) \<times> (uprod B D)" |
20819 | 499 |
by blast |
500 |
||
45607 | 501 |
lemmas dprod_subset_Sigma = subset_trans [OF dprod_mono dprod_Sigma] |
20819 | 502 |
|
503 |
(*Dependent version*) |
|
504 |
lemma dprod_subset_Sigma2: |
|
58112
8081087096ad
renamed modules defining old datatypes, as a step towards having 'datatype_new' take 'datatype's place
blanchet
parents:
55642
diff
changeset
|
505 |
"(dprod (Sigma A B) (Sigma C D)) <= Sigma (uprod A C) (Split (%x y. uprod (B x) (D y)))" |
20819 | 506 |
by auto |
507 |
||
61943 | 508 |
lemma dsum_Sigma: "(dsum (A \<times> B) (C \<times> D)) <= (usum A C) \<times> (usum B D)" |
20819 | 509 |
by blast |
510 |
||
45607 | 511 |
lemmas dsum_subset_Sigma = subset_trans [OF dsum_mono dsum_Sigma] |
20819 | 512 |
|
513 |
||
58157 | 514 |
(*** Domain theorems ***) |
515 |
||
516 |
lemma Domain_dprod [simp]: "Domain (dprod r s) = uprod (Domain r) (Domain s)" |
|
517 |
by auto |
|
518 |
||
519 |
lemma Domain_dsum [simp]: "Domain (dsum r s) = usum (Domain r) (Domain s)" |
|
520 |
by auto |
|
521 |
||
522 |
||
60500 | 523 |
text \<open>hides popular names\<close> |
36176
3fe7e97ccca8
replaced generic 'hide' command by more conventional 'hide_class', 'hide_type', 'hide_const', 'hide_fact' -- frees some popular keywords;
wenzelm
parents:
35216
diff
changeset
|
524 |
hide_type (open) node item |
3fe7e97ccca8
replaced generic 'hide' command by more conventional 'hide_class', 'hide_type', 'hide_const', 'hide_fact' -- frees some popular keywords;
wenzelm
parents:
35216
diff
changeset
|
525 |
hide_const (open) Push Node Atom Leaf Numb Lim Split Case |
20819 | 526 |
|
58372
bfd497f2f4c2
moved 'old_datatype' out of 'Main' (but put it in 'HOL-Proofs' because of the inductive realizer)
blanchet
parents:
58305
diff
changeset
|
527 |
ML_file "~~/src/HOL/Tools/Old_Datatype/old_datatype.ML" |
bfd497f2f4c2
moved 'old_datatype' out of 'Main' (but put it in 'HOL-Proofs' because of the inductive realizer)
blanchet
parents:
58305
diff
changeset
|
528 |
ML_file "~~/src/HOL/Tools/inductive_realizer.ML" |
13635
c41e88151b54
Added functions Suml and Sumr which are useful for constructing
berghofe
parents:
12918
diff
changeset
|
529 |
|
5181
4ba3787d9709
New theory Datatype. Needed as an ancestor when defining datatypes.
berghofe
parents:
diff
changeset
|
530 |
end |