types s, t < t

ops a, b : s

%% op __ + __ : s -> s -> s, idem, assoc, comm;

op __+__ : s * s -> s

op __+__ : t * t -> t

ops a, b : t

op c : s = a + b;

op d : s = a + a;

op e : s * s -> s = __+__;

op f : s * s -> s = __+__;

op g : s * s = (a, b);

op h : s = a + b;

op i : s = (a : s) + (b : s);

op incr : s -> s

op i1 : s = incr a;

op i2 : s = incr a;

op i3 : s = incr a;

op __<=__<=__ : s * s * s -> s

op l1 : s = a <= b <= c;

op l2 : s * s * s -> s = __<=__<=__;

op l3 : s = a <= b <= c;

op l4 : s = a <= b <= c;

op l5 : s * s * s = (a, b, c);

op x : s

op y : s = (op a : s) <= (var x : s) <= (a : s);

op z : s = (x as s) + (x as t as s);

. x in s %(bla_label)%

. x in t;

%% Type Constructors -----------------------------------------------------

s : Type < t

t : Type

%% Assumptions -----------------------------------------------------------

__+__

: t * t -> t %(op)%

: s * s -> s %(op)%

__<=__<=__ : s * s * s -> s %(op)%

a

: t %(op)%

: s %(op)%

b

: t %(op)%

: s %(op)%

c

: s %(op)% = (op __+__ : s * s -> s) ((op a : s), (op b : s)) as s

d

: s %(op)% = (op __+__ : s * s -> s) ((op a : s), (op a : s)) as s

e : s * s -> s %(op)% = (op __+__ : s * s -> s) as s * s -> s

f : s * s -> s %(op)% = (op __+__ : s * s -> s) as s * s -> s

g : s * s %(op)% = ((op a : s), (op b : s)) as s * s

h

: s %(op)% = (op __+__ : s * s -> s) ((op a : s), (op b : s)) as s

i

: s %(op)% = (op __+__ : s * s -> s) ((op a : s), (op b : s)) as s

i1 : s %(op)% = (op incr : s -> s) (op a : s) as s

i2 : s %(op)% = (op incr : s -> s) (op a : s) as s

i3 : s %(op)% = (op incr : s -> s) (op a : s) as s

incr : s -> s %(op)%

l1

: s

%(op)% =

(op __<=__<=__ : s * s * s -> s)

((op a : s), (op b : s), (op c : s))

as s

l2

: s * s * s -> s

%(op)% = (op __<=__<=__ : s * s * s -> s) as s * s * s -> s

l3

: s

%(op)% =

(op __<=__<=__ : s * s * s -> s)

((op a : s), (op b : s), (op c : s))

as s

l4

: s

%(op)% =

(op __<=__<=__ : s * s * s -> s)

((op a : s), (op b : s), (op c : s))

as s

l5

: s * s * s

%(op)% = ((op a : s), (op b : s), (op c : s)) as s * s * s

x : s %(op)%

y

: s

%(op)% =

(op __<=__<=__ : s * s * s -> s)

((op a : s), (var x : s), (op a : s))

as s

z

: s

%(op)% =

(op __+__ : s * s -> s) ((op x : s) as s, (op x : s) as t as s) as

s

%% Sentences -------------------------------------------------------------

c = ((op __+__ : s * s -> s) ((op a : s), (op b : s)) as s)

%(def_c)%

d = ((op __+__ : s * s -> s) ((op a : s), (op a : s)) as s)

%(def_d)%

e = ((op __+__ : s * s -> s) as s * s -> s) %(def_e)%

f = ((op __+__ : s * s -> s) as s * s -> s) %(def_f)%

g = (((op a : s), (op b : s)) as s * s) %(def_g)%

h = ((op __+__ : s * s -> s) ((op a : s), (op b : s)) as s)

%(def_h)%

i = ((op __+__ : s * s -> s) ((op a : s), (op b : s)) as s)

%(def_i)%

i1 = (incr (op a : s) as s) %(def_i1)%

i2 = (incr (op a : s) as s) %(def_i2)%

i3 = (incr (op a : s) as s) %(def_i3)%

l1 = ((op a : s) <= (op b : s) <= c as s) %(def_l1)%

l2 = (__<=__<=__ as s * s * s -> s) %(def_l2)%

l3 = ((op a : s) <= (op b : s) <= c as s) %(def_l3)%

l4 = ((op a : s) <= (op b : s) <= c as s) %(def_l4)%

l5 = (((op a : s), (op b : s), c) as s * s * s) %(def_l5)%

y = ((a : s) <= (var x : s) <= (op a : s) as s) %(def_y)%

z = ((op __+__ : s * s -> s) (x as s, x as t as s) as s) %(def_z)%

x in s %(bla_label)%

x in t

%% Diagnostics -----------------------------------------------------------

*** Error 9.7, expected tuple argument for '__+__'