
diff -r f04b33ce250f -r a4dc62a46ee4 Univ.thy
--- a/Univ.thy	Tue Oct 24 14:59:17 1995 +0100
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,103 +0,0 @@
-(*  Title:      HOL/Univ.thy
-    ID:         $Id$
-    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
-    Copyright   1993  University of Cambridge
-
-Move LEAST to Nat.thy???  Could it be defined for all types 'a::ord?
-
-Declares the type 'a node, a subtype of (nat=>nat) * ('a+nat)
-
-Defines "Cartesian Product" and "Disjoint Sum" as set operations.
-Could <*> be generalized to a general summation (Sigma)?
-*)
-
-Univ = Arith + Sum +
-
-(** lists, trees will be sets of nodes **)
-
-subtype (Node)
-  'a node = "{p. EX f x k. p = <f::nat=>nat, x::'a+nat> & f(k)=0}"
-
-types
-  'a item = "'a node set"
-
-consts
-  Least     :: "(nat=>bool) => nat"    (binder "LEAST " 10)
-
-  apfst     :: "['a=>'c, 'a*'b] => 'c*'b"
-  Push      :: "[nat, nat=>nat] => (nat=>nat)"
-
-  Push_Node :: "[nat, 'a node] => 'a node"
-  ndepth    :: "'a node => nat"
-
-  Atom      :: "('a+nat) => 'a item"
-  Leaf      :: "'a => 'a item"
-  Numb      :: "nat => 'a item"
-  "$"       :: "['a item, 'a item]=> 'a item"   (infixr 60)
-  In0,In1   :: "'a item => 'a item"
-
-  ntrunc    :: "[nat, 'a item] => 'a item"
-
-  "<*>"  :: "['a item set, 'a item set]=> 'a item set" (infixr 80)
-  "<+>"  :: "['a item set, 'a item set]=> 'a item set" (infixr 70)
-
-  Split  :: "[['a item, 'a item]=>'b, 'a item] => 'b"
-  Case   :: "[['a item]=>'b, ['a item]=>'b, 'a item] => 'b"
-
-  diag   :: "'a set => ('a * 'a)set"
-  "<**>" :: "[('a item * 'a item)set, ('a item * 'a item)set] 
-           => ('a item * 'a item)set" (infixr 80)
-  "<++>" :: "[('a item * 'a item)set, ('a item * 'a item)set] 
-           => ('a item * 'a item)set" (infixr 70)
-
-defs
-
-  (*least number operator*)
-  Least_def        "Least(P) == @k. P(k) & (ALL j. j<k --> ~P(j))"
-
-  Push_Node_def    "Push_Node == (%n x. Abs_Node (apfst(Push(n),Rep_Node(x))))"
-
-  (*crude "lists" of nats -- needed for the constructions*)
-  apfst_def  "apfst == (%f. split(%x y. <f(x),y>))"
-  Push_def   "Push == (%b h. nat_case(Suc(b),h))"
-
-  (** operations on S-expressions -- sets of nodes **)
-
-  (*S-expression constructors*)
-  Atom_def   "Atom == (%x. {Abs_Node(<%k.0, x>)})"
-  Scons_def  "M$N == (Push_Node(0) `` M) Un (Push_Node(Suc(0)) `` N)"
-
-  (*Leaf nodes, with arbitrary or nat labels*)
-  Leaf_def   "Leaf == Atom o Inl"
-  Numb_def   "Numb == Atom o Inr"
-
-  (*Injections of the "disjoint sum"*)
-  In0_def    "In0(M) == Numb(0) $ M"
-  In1_def    "In1(M) == Numb(Suc(0)) $ M"
-
-  (*the set of nodes with depth less than k*)
-  ndepth_def "ndepth(n) == split(%f x. LEAST k. f(k)=0, Rep_Node(n))"
-  ntrunc_def "ntrunc(k,N) == {n. n:N & ndepth(n)<k}"
-
-  (*products and sums for the "universe"*)
-  uprod_def  "A<*>B == UN x:A. UN y:B. { (x$y) }"
-  usum_def   "A<+>B == In0``A Un In1``B"
-
-  (*the corresponding eliminators*)
-  Split_def  "Split(c,M) == @u. ? x y. M = x$y & u = c(x,y)"
-
-  Case_def   "Case(c,d,M) == @u.  (? x . M = In0(x) & u = c(x)) 
-                               | (? y . M = In1(y) & u = d(y))"
-
-
-  (** diagonal sets and equality for the "universe" **)
-
-  diag_def   "diag(A) == UN x:A. {<x,x>}"
-
-  dprod_def  "r<**>s == UN u:r. split(%x x'. 
-                       UN v:s. split(%y y'. {<x$y,x'$y'>}, v), u)"
-
-  dsum_def   "r<++>s == (UN u:r. split(%x x'. {<In0(x),In0(x')>}, u)) Un 
-                       (UN v:s. split(%y y'. {<In1(y),In1(y')>}, v))"
-
-end




