Cpo

Flatcpo < Cpo

Pcpo < Cpo

Type Constructors

?__ :Type ->Type := \ t:Type . Unit ->? t

Pred__ :Type- ->Type := \ t:Type- . t ->? Unit

Unit :(Type,Pcpo)

__*__ :(Type+ ->Type+ ->Type,Pcpo+ ->Pcpo+ ->Pcpo,

Cpo+ ->Cpo+ ->Cpo)

__*__*__ :Type+ ->Type+ ->Type+ ->Type

__-->__ :(Cpo- ->Cpo+ ->Cpo,Cpo- ->Pcpo+ ->Pcpo)

__-->?__ :Cpo- ->Cpo+ ->Pcpo

__->__ :Type- ->Type+ ->Type

__->?__ :Type- ->Type+ ->Type

bool :(Type,Flatcpo) %% free type definition omitted

c :Cpo %(var)%

c-->d :Type< c -->? d

c-->?d :Type< c ->? d

d :Cpo %(var)%

logical :Type %% free type definition omitted

nat :Flatcpo

s :Type< ? s %(var)%

s->t :Type< s ->? t

t :Type %(var)%

Assumptions

f : c --> d

g : c --> d

x : s

x1 : c

x2 : c

y1 : d

y2 : d

Error (4,7) illegal universe class declaration

Warning (27,11) redeclared type 'Unit'

FatalError (29,1) no analysis yet for: . 1 = ()

Warning (39,16) redeclared type 't'

Error (45,14) undeclared type 'Pred'

Error (45,14) undeclared type 'Pred'

Hint (46,9) not a class 's'

FatalError (48,1) no analysis yet for: program def = \ x : s . ()

%% def is also total (identical to tt)

FatalError (50,1) no analysis yet for: program tt = \ x : s . ()

%% tt is total "op tt(x: s): unit = ()"

FatalError (52,1) no analysis yet for: program __ und __ (x,y : Unit) : Unit = ()

FatalError (60,1) no analysis yet for: . __ in s -> t = \ f : s ->? t . all (\ x : s . def f (x))

FatalError (64,1) no analysis yet for: program __ res __ (x : s,y : t) : s = x

FatalError (65,1) no analysis yet for: program fst (x : s,y : t) : s = x

FatalError (66,1) no analysis yet for: program snd (x : s,y : t) : t = y

FatalError (71,1) no analysis yet for: . (\ x : s; y : t . def (x res y)) =

(\ x : s; y : t . (def y) und (def x))

. fst = (__ res __)

FatalError (78,1) no analysis yet for: pred eq : s � s

FatalError (80,1) no analysis yet for: . (\ x : s . eq (x,x)) = tt

. (\ x : s; y : s . x res eq (x,y)) =

(\ x : s; y : s . y res eq (x,y))

Warning (91,6) redeclared type 's'

FatalError (93,1) no analysis yet for: program all (p : Pred (s)) : Pred Unit = eq (p,tt)

FatalError (96,1) no analysis yet for: program And (x,y : Pred Unit) : Pred Unit = t1 () und t2 ()

FatalError (99,1) no analysis yet for: program __ impl __ (x,y : Pred Unit) : Pred Unit = eq (x,x And y)

FatalError (101,1) no analysis yet for: program __ or __ (x,y : Pred Unit) : Pred Unit =

all (\ r : Pred Unit . ((x impl r) und (y impl r)) impl r)

FatalError (104,1) no analysis yet for: program ex (p : Pred (s)) : Pred Unit =

all (\ r : Pred Unit . all (\ x : s . p (x) impl r) impl r)

FatalError (107,1) no analysis yet for: program ff () : Pred Unit = all (\ r : Pred Unit . r ())

FatalError (109,1) no analysis yet for: program neg (r : Pred Unit) : Pred Unit = r impl ff

FatalError (114,1) no analysis yet for: . all

(\ f : s ->? t; g : s ->? t . all

(\ x : s . eq (\ . f (x),g (x)) impl eq (f,g)))

Warning (119,13) redundant universe class

FatalError (123,1) no analysis yet for: pred __<<=__ : c � c

FatalError (125,1) no analysis yet for: . all (\ x : c . x <<= x) %(reflexive)%

. all

(\ x : c; y : c; z : c . ((x <<= y) und (y <<= z)) impl x <<= z)

%(transitive)%

. all

(\ x : c; y : c; z : c . ((x <<= y) und (y <<= x)) impl eq (x,y))

%(antisymmetric)%

FatalError (129,1) no analysis yet for: pred isChain(s : nat -> c) <=> all

(\ n : nat . s (n) <<= s (Suc (n)))

FatalError (130,1) no analysis yet for: pred isBound(x : c,s : nat -> c) <=> all (\ n : nat . s (n) <<= x)

Error (132,11) undeclared type 'nat'

Error (132,18) undeclared type 'c'

Error (132,25) undeclared type 'c'

FatalError (134,1) no analysis yet for: . all

(\ s : nat -> c . def (sup s) impl

(isBound (sup s,s) und all

(\ x : c . isBound (x,s) impl sup (s) <<= x)))

%(sup is minimally bound)%

. all (\ s : nat -> c . isChain (s) impl def (sup (s)))

%(sup exists)%

Error (145,13) undeclared type 'p'

FatalError (147,1) no analysis yet for: . all (\ x : p . bottom <<= x)

FatalError (154,2) no analysis yet for: program __ <<= [f] __ = eq

Hint (161,13) not a class 'c'

Hint (161,13) not a class 'c'

Hint (161,25) not a class 'd'

Hint (161,25) not a class 'd'

FatalError (163,1) no analysis yet for: program (x1,y1) <<= (x2,y2) = (x1 <<= x2) und (y1 <<= y2)

FatalError (174,2) no analysis yet for: . __ in c -->? d

=

\ f : c ->? d . all

(\ x : c; y : c . (def (f x) und x <<= y) impl def (f y)) und all

(\ s : nat -> c . (isChain (s) und def f (sup (s))) impl ex

(\ m : nat . def f (s (m)) und eq

(sup (\ n : nat .! f (s (n + m))),f (sup (s)))))

FatalError (180,3) no analysis yet for: program f <<= [c -->? d] g =

all (\ x : c . def (f x) impl f (x) <<= g (x))

FatalError (186,2) no analysis yet for: . __ in c --> d = \ f : c -->? d . all (\ x : c . def f (x))

Hint (188,15) not a class 'c --> d'

Hint (188,15) not a class 'c --> d'

FatalError (190,2) no analysis yet for: program f <<= g = f <<= [c -->? d] g

Error (194,9) undeclared type 'p'

Error (194,16) undeclared type 'p'

Error (194,23) undeclared type 'p'

FatalError (196,1) no analysis yet for: . all

(\ f : p -->? p . eq (f (Y (f)),Y (f)) und all

(\ x : p . eq (f (x),x) impl Y (f) <<= x))

FatalError (199,4) no analysis yet for: undefined