--- a/Univ.thy Fri Nov 25 20:07:22 1994 +0100
+++ b/Univ.thy Mon Nov 28 14:42:42 1994 +0100
@@ -1,9 +1,9 @@
-(* Title: HOL/univ.thy
+(* Title: HOL/Univ.thy
ID: $Id$
- Author: Lawrence C Paulson, Cambridge University Computer Laboratory
+ 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?
+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)
@@ -11,31 +11,29 @@
Could <*> be generalized to a general summation (Sigma)?
*)
-Univ = Arith + Sum +
+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 node
'a item = "'a node set"
-arities
- node :: (term)term
-
consts
Least :: "(nat=>bool) => nat" (binder "LEAST " 10)
apfst :: "['a=>'c, 'a*'b] => 'c*'b"
Push :: "[nat, nat=>nat] => (nat=>nat)"
- Node :: "((nat=>nat) * ('a+nat)) set"
- Rep_Node :: "'a node => (nat=>nat) * ('a+nat)"
- Abs_Node :: "(nat=>nat) * ('a+nat) => 'a node"
Push_Node :: "[nat, 'a node] => 'a node"
ndepth :: "'a node => nat"
Atom :: "('a+nat) => 'a item"
Leaf :: "'a => 'a item"
Numb :: "nat => 'a item"
- "$" :: "['a item, 'a item]=> 'a item" (infixr 60)
+ "$" :: "['a item, 'a item]=> 'a item" (infixr 60)
In0,In1 :: "'a item => 'a item"
ntrunc :: "[nat, 'a item] => 'a item"
@@ -43,7 +41,7 @@
"<*>" :: "['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"
+ 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"
@@ -52,17 +50,11 @@
"<++>" :: "[('a item * 'a item)set, ('a item * 'a item)set] \
\ => ('a item * 'a item)set" (infixr 70)
-rules
+defs
(*least number operator*)
Least_def "Least(P) == @k. P(k) & (ALL j. j<k --> ~P(j))"
- (** lists, trees will be sets of nodes **)
- Node_def "Node == {p. EX f x k. p = <f,x> & f(k)=0}"
- (*faking the type definition 'a node == (nat=>nat) * ('a+nat) *)
- Rep_Node "Rep_Node(n): Node"
- Rep_Node_inverse "Abs_Node(Rep_Node(n)) = n"
- Abs_Node_inverse "p: Node ==> Rep_Node(Abs_Node(p)) = p"
Push_Node_def "Push_Node == (%n x. Abs_Node (apfst(Push(n),Rep_Node(x))))"
(*crude "lists" of nats -- needed for the constructions*)
@@ -94,8 +86,8 @@
(*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))"
+ 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" **)