src/HOL/Univ.thy
changeset 5191 8ceaa19f7717
parent 3947 eb707467f8c5
child 5978 fa2c2dd74f8c
     1.1 --- a/src/HOL/Univ.thy	Fri Jul 24 13:36:49 1998 +0200
     1.2 +++ b/src/HOL/Univ.thy	Fri Jul 24 13:39:47 1998 +0200
     1.3 @@ -31,7 +31,7 @@
     1.4    Atom      :: "('a+nat) => 'a item"
     1.5    Leaf      :: 'a => 'a item
     1.6    Numb      :: nat => 'a item
     1.7 -  "$"       :: ['a item, 'a item]=> 'a item   (infixr 60)
     1.8 +  Scons     :: ['a item, 'a item]=> 'a item
     1.9    In0,In1   :: 'a item => 'a item
    1.10  
    1.11    ntrunc    :: [nat, 'a item] => 'a item
    1.12 @@ -63,26 +63,26 @@
    1.13  
    1.14    (*S-expression constructors*)
    1.15    Atom_def   "Atom == (%x. {Abs_Node((%k.0, x))})"
    1.16 -  Scons_def  "M$N == (Push_Node(0) `` M) Un (Push_Node(Suc(0)) `` N)"
    1.17 +  Scons_def  "Scons M N == (Push_Node(0) `` M) Un (Push_Node(Suc(0)) `` N)"
    1.18  
    1.19    (*Leaf nodes, with arbitrary or nat labels*)
    1.20    Leaf_def   "Leaf == Atom o Inl"
    1.21    Numb_def   "Numb == Atom o Inr"
    1.22  
    1.23    (*Injections of the "disjoint sum"*)
    1.24 -  In0_def    "In0(M) == Numb(0) $ M"
    1.25 -  In1_def    "In1(M) == Numb(Suc(0)) $ M"
    1.26 +  In0_def    "In0(M) == Scons (Numb 0) M"
    1.27 +  In1_def    "In1(M) == Scons (Numb 1) M"
    1.28  
    1.29    (*the set of nodes with depth less than k*)
    1.30    ndepth_def "ndepth(n) == (%(f,x). LEAST k. f(k)=0) (Rep_Node n)"
    1.31    ntrunc_def "ntrunc k N == {n. n:N & ndepth(n)<k}"
    1.32  
    1.33    (*products and sums for the "universe"*)
    1.34 -  uprod_def  "A<*>B == UN x:A. UN y:B. { (x$y) }"
    1.35 +  uprod_def  "A<*>B == UN x:A. UN y:B. { Scons x y }"
    1.36    usum_def   "A<+>B == In0``A Un In1``B"
    1.37  
    1.38    (*the corresponding eliminators*)
    1.39 -  Split_def  "Split c M == @u. ? x y. M = x$y & u = c x y"
    1.40 +  Split_def  "Split c M == @u. ? x y. M = Scons x y & u = c x y"
    1.41  
    1.42    Case_def   "Case c d M == @u.  (? x . M = In0(x) & u = c(x)) 
    1.43                                | (? y . M = In1(y) & u = d(y))"
    1.44 @@ -92,7 +92,7 @@
    1.45  
    1.46    diag_def   "diag(A) == UN x:A. {(x,x)}"
    1.47  
    1.48 -  dprod_def  "r<**>s == UN (x,x'):r. UN (y,y'):s. {(x$y,x'$y')}"
    1.49 +  dprod_def  "r<**>s == UN (x,x'):r. UN (y,y'):s. {(Scons x y, Scons x' y')}"
    1.50  
    1.51    dsum_def   "r<++>s == (UN (x,x'):r. {(In0(x),In0(x'))}) Un 
    1.52                         (UN (y,y'):s. {(In1(y),In1(y'))})"