%% predefined universe containing all types,

%% superclass of all other classes

class Type < Type

var s : Type; t : Type

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%% invisible type "Unit" for formulae

type Unit

%% flat cpo with bottom

%% type aliases

pred true, false : Unit

pred __/\__, __\/__, __=>__, __if__, __<=>__ : Unit * Unit

pred not : Unit

pred __=__ : s * s

%% =e=

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%% (builtin) type (constructors)

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

%% nested pairs are different from n-tupels (n > 2)

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

%% ...

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%% "pred p args = e" abbreviates "op p args :? unit = e"

%% CASL requires "<=>" for pred-defn and disallows "()" as result

op def, tt : Pred s

var x : s

program (op def[s] : forall s : Type . Pred s_v-1@(s_v-1 ->? Unit))

= \ (var x : s) : s . ()

%% def is also total (identical to tt)

program (op tt[s] : forall s : Type . Pred s_v-1@(s_v-1 ->? Unit))

= \ (var x : s) : s . ()

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

%% total function type

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

type __->__(s : Type)(t : Type) < s_v1 ->? t_v2

%% total functions

op __res__ : forall s : Type; t : Type . s_v-1 * t_v-2 ->? s_v-1

= \ (var x : s, var y : t) .! (var x : s) as s_v1

op fst : forall s : Type; t : Type . s_v-1 * t_v-2 ->? s_v-1

= \ (var x : s, var y : t) .! (var x : s) as s_v1

%% trivial because its the strict function property

. (fun __=__[_var_33_v33 * _var_35_v35 ->? _var_33_v33]

: forall s : Type . s_v-1 * s_v-1 ->? Unit)

(op fst[_var_33_v33; _var_35_v35]

: forall s : Type; t : Type . s_v-1 * t_v-2 ->? s_v-1,

op __res__[_var_33_v33; _var_35_v35]

: forall s : Type; t : Type . s_v-1 * t_v-2 ->? s_v-1)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%% Internal Logic

pred eq : s * s

. (fun __=__[s ->? Unit]

: forall s : Type . s_v-1 * s_v-1 ->? Unit)

(\ (var x : s) : s

. (pred eq[s] : forall s : Type . s_v-1 * s_v-1)

(var x : s, var x : s),

op tt[s] : forall s : Type . Pred s_v-1@(s_v-1 ->? Unit))

. (fun __=__[s * s ->? s]

: forall s : Type . s_v-1 * s_v-1 ->? Unit)

(\ (var x : s, var y : s)

. (op __res__[s; Unit]

: forall s : Type; t : Type . s_v-1 * t_v-2 ->? s_v-1)

(var x : s,

(pred eq[s] : forall s : Type . s_v-1 * s_v-1)

(var x : s, var y : s)),

\ (var x : s, var y : s)

. (op __res__[s; Unit]

: forall s : Type; t : Type . s_v-1 * t_v-2 ->? s_v-1)

(var y : s,

(pred eq[s] : forall s : Type . s_v-1 * s_v-1)

(var x : s, var y : s)))

%% then %def

%% notation "\ ." abbreviates "\bla:unit."

%% where "bla" is never used, but only "()" instead

%% for type inference

%% an implicit cast from s to ?s of a term "e" yields the term "\ . e"

type s < ? s_v1

%% the cast from ?s to s is still done manually here (for the strict "und")

%% use "And" instead of "und" to avoid cast from "?unit" to "unit"

%% the type instance for the first "eq" should be "?t"

%% this is explicitely enforced by "\ .f(x)"

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%% Recursion (requires "free type nat ::= 0 | Suc(nat)" and "+"

type nat

class Cpo < Type

{var c : Cpo; pred __<<=__ : c * c; ;

pred isChain : forall c : Cpo . nat -> c_v-1;

pred isBound : forall c : Cpo . c_v-1 * (nat -> c_v-1);

op sup : (nat -> c) ->? c;}

class Pcpo < Cpo

{var p : Pcpo; op bottom : p;}

class instance Flatcpo < Cpo

{var f : Flatcpo;}

var c : Cpo; d : Cpo

type instance __*__ : Cpo+ -> Cpo+ -> Cpo

var x1 : c; x2 : c; y1 : d; y2 : d

type instance __*__ : Pcpo+ -> Pcpo+ -> Pcpo

type Unit : Pcpo

%% Pcont

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

type __-->?__(c : Cpo)(d : Cpo) < c_v155 ->? d_v160

%% Tcont

type instance __-->__ : Cpo- -> Cpo+ -> Cpo

type __-->__(c : Cpo)(d : Cpo) < c_v155 -->? d_v160

var f : c --> d; g : c --> d

type instance __-->__ : Cpo- -> Pcpo+ -> Pcpo

op undefined : forall c : Cpo; p : Pcpo . c_v-1 -->? p_v-2

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%% user stuff

free type bool ::= true |

false

type bool : Flatcpo

type nat : Flatcpo

%% Classes ---------------------------------------------------------------

Cpo < Type

Flatcpo < Cpo

Pcpo < Cpo

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

Logical : Type := Unit ->? Unit

Pred : Type -> Type := \ a : Type . a_v-1 ->? Unit

Unit : Pcpo

__*__

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

Type+ -> Type+ -> Type)

__-->__

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

Type- -> Type+ -> Type) < (c_v155 -->? d_v160, __-->?__, __->__)

__-->?__

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

Type- -> Type+ -> Type) < (c_v155 ->? d_v160, __->?__)

__->__ : Type- -> Type+ -> Type < (s_v1 ->? t_v2, __->?__)

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

bool

: Flatcpo

%[free type bool

::= true : bool

false : bool]%

c : Cpo %(var_155)%

d : Cpo %(var_160)%

f : Flatcpo %(var_159)%

nat : Flatcpo

p : Pcpo %(var_158)%

s : Type %(var_1)%

t : Type %(var_2)%

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

__/\__ : Unit * Unit ->? Unit %(fun)%

__<<=__ : forall c : Cpo . c_v-1 * c_v-1 ->? Unit %(pred)%

__<=>__ : Unit * Unit ->? Unit %(fun)%

__=__ : forall s : Type . s_v-1 * s_v-1 ->? Unit %(fun)%

__=>__ : Unit * Unit ->? Unit %(fun)%

__=e=__ : forall a : Type . a_v-1 * a_v-1 ->? Unit %(fun)%

__\/__ : Unit * Unit ->? Unit %(fun)%

__if__ : Unit * Unit ->? Unit %(fun)%

__res__

: forall s : Type; t : Type . s_v-1 * t_v-2 ->? s_v-1

%(op)% = \ (var x : s, var y : t) .! (var x : s) as s_v1

__when__else__

: forall a : Type . a_v-1 * ? Unit * a_v-1 ->? a_v-1 %(fun)%

bottom : forall p : Pcpo . p_v-1 %(fun)%

def : forall s : Type . Pred s_v-1@(s_v-1 ->? Unit) %(op)%

def__ : forall a : Type . a_v-1 ->? Unit %(fun)%

eq : forall s : Type . s_v-1 * s_v-1 ->? Unit %(pred)%

f : c --> d %(var)%

false

: bool %(construct bool)%

: Unit ->? Unit %(pred)%

: Unit %(fun)%

fst

: forall s : Type; t : Type . s_v-1 * t_v-2 ->? s_v-1

%(op)% = \ (var x : s, var y : t) .! (var x : s) as s_v1

g : c --> d %(var)%

isBound : forall c : Cpo . c_v-1 * (nat -> c_v-1) ->? Unit %(pred)%

isChain : forall c : Cpo . (nat -> c_v-1) ->? Unit %(pred)%

not : Unit ->? Unit %(pred)%

not__ : ? Unit ->? Unit %(fun)%

sup : forall c : Cpo . (nat -> c_v-1) ->? c_v-1 %(op)%

true

: bool %(construct bool)%

: Unit ->? Unit %(pred)%

: Unit %(fun)%

tt : forall s : Type . Pred s_v-1@(s_v-1 ->? Unit) %(op)%

undefined : forall c : Cpo; p : Pcpo . c_v-1 -->? p_v-2 %(op)%

x : s %(var)%

x1 : c %(var)%

x2 : c %(var)%

y1 : d %(var)%

y2 : d %(var)%

�__ : ? Unit ->? Unit %(fun)%

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

program (op def[s] : forall s : Type . Pred s_v-1@(s_v-1 ->? Unit))

= \ (var x : s) : s . () %(pe_def)%

program (op tt[s] : forall s : Type . Pred s_v-1@(s_v-1 ->? Unit))

= \ (var x : s) : s . () %(pe_tt)%

forall x : s; y : t

. (fun __=__ : forall a : Type . a_v-1 * a_v-1 ->? Unit)

((op __res__ : forall s : Type; t : Type . s_v-1 * t_v-2 ->? s_v-1)

(var x : s, var y : t),

(var x : s) as s_v1) %(def___res__)%

forall x : s; y : t

. (fun __=__ : forall a : Type . a_v-1 * a_v-1 ->? Unit)

((op fst : forall s : Type; t : Type . s_v-1 * t_v-2 ->? s_v-1)

(var x : s, var y : t),

(var x : s) as s_v1) %(def_fst)%

(fun __=__[_var_33_v33 * _var_35_v35 ->? _var_33_v33]

: forall s : Type . s_v-1 * s_v-1 ->? Unit)

(op fst[_var_33_v33; _var_35_v35]

: forall s : Type; t : Type . s_v-1 * t_v-2 ->? s_v-1,

op __res__[_var_33_v33; _var_35_v35]

: forall s : Type; t : Type . s_v-1 * t_v-2 ->? s_v-1)

(fun __=__[s ->? Unit] : forall s : Type . s_v-1 * s_v-1 ->? Unit)

(\ (var x : s) : s

. (pred eq[s] : forall s : Type . s_v-1 * s_v-1)

(var x : s, var x : s),

op tt[s] : forall s : Type . Pred s_v-1@(s_v-1 ->? Unit))

(fun __=__[s * s ->? s] : forall s : Type . s_v-1 * s_v-1 ->? Unit)

(\ (var x : s, var y : s)

. (op __res__[s; Unit]

: forall s : Type; t : Type . s_v-1 * t_v-2 ->? s_v-1)

(var x : s,

(pred eq[s] : forall s : Type . s_v-1 * s_v-1)

(var x : s, var y : s)),

\ (var x : s, var y : s)

. (op __res__[s; Unit]

: forall s : Type; t : Type . s_v-1 * t_v-2 ->? s_v-1)

(var y : s,

(pred eq[s] : forall s : Type . s_v-1 * s_v-1)

(var x : s, var y : s)))

free type bool

::= true : bool

false : bool %(ga_bool)%

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

*** Error 4.7, illegal universe class declaration 'Type'

*** Hint 6.5, is type variable 's'

*** Hint 6.7, is type variable 't'

*** Hint 11.6, redeclared type 'Unit'

*** Error 14.11, illegal type pattern argument '__'

*** Error 15.8, illegal type pattern argument '__'

*** Error 17.6, illegal overloading of predefined identifier 'true'

*** Error 17.12, illegal overloading of predefined identifier 'false'

*** Error 19.9, illegal overloading of predefined identifier '__/\__'

*** Error 19.17, illegal overloading of predefined identifier '__\/__'

*** Error 19.25, illegal overloading of predefined identifier '__=>__'

*** Error 19.33, illegal overloading of predefined identifier '__if__'

*** Error 19.40, illegal overloading of predefined identifier '__<=>__'

*** Error 22.8, illegal overloading of predefined identifier '__=__'

*** Hint 27.8, redeclared type '__->?__'

*** Hint 30.8, redeclared type '__*__'

*** Error 31.6, illegal type pattern '__ * __ * __'

*** Hint 42.16, variable shadows global name(s) 'x'

*** Hint 44.15, variable shadows global name(s) 'x'

*** Error 46.11, unexpected mixfix token: und

*** Hint 50.8, redeclared type '__->__'

*** Error 52.8, incompatible kind of: __->__

expected: Type- -> Type+ -> Type

found: Type -> Type -> Type

*** Error 54.42, ambiguous mixfix term

def__(f(x))

def(f)(x)

*** Error 54.32, unexpected mixfix token: all

*** Error 54.6, unexpected mixfix token: :

*** Hint 58.13, variable shadows global name(s) 'x'

*** Hint 59.9, variable shadows global name(s) 'x'

*** Hint 60.9, no type match for: snd

with (maximal) type: _var_11_v11 ->? t

known types:

*** Hint 60.9, untypable application (with result type: t)

'snd(x : s, var y : t)'

*** Error 60.30, no typing for 'program snd(x : s, var y : t) : t = y'

*** Error 65.18, ambiguous mixfix term

def(__res__(x, y))

def__(__res__(x, y))

*** Error 65.59, unexpected mixfix token: und

*** Hint 66.3, in type of '(op fst[_var_28_v28; _var_29_v29]

: forall s : Type; t : Type . s_v-1 * t_v-2 ->? s_v-1,

op __res__[_var_30_v30; _var_31_v31]

: forall s : Type; t : Type . s_v-1 * t_v-2 ->? s_v-1)'

type '(_var_28_v28 * _var_29_v29 ->? _var_28_v28) *

(_var_30_v30 * _var_31_v31 ->? _var_30_v30)' (59.12)

is not unifiable with type 'Unit ->? _var_14_v14 * _var_15_v15' (22.14)

*** Hint 74.5, variable shadows global name(s) 'x'

*** Hint 74.14, in type of '(var x : s, var x : s)'

type 's * s' (40.9)

is not unifiable with type 'Unit ->? _var_44_v44 * _var_45_v45' (72.11)

*** Hint 74.5, variable shadows global name(s) 'x'

*** Hint 74.14, in type of '(var x : s, var x : s)'

type 's * s' (40.9)

is not unifiable with type 'Unit ->? _var_55_v55 * _var_56_v56' (72.11)

*** Hint 74.11, in type of '(\ (var x : s) : s

. (pred eq[_var_54_v54] : forall s : Type . s_v-1 * s_v-1)

(var x : s, var x : s),

op tt[_var_57_v57] : forall s : Type . Pred s_v-1@(s_v-1 ->? Unit))'

type '(s ->? Unit) * Pred _var_57_v57@(_var_57_v57 ->? Unit)' (74.8)

is not unifiable with type 'Unit ->? _var_38_v38 * _var_39_v39' (22.14)

*** Hint 75.6, variable shadows global name(s) 'x'

*** Hint 75.24, in type of '(var x : s, var y : s)'

type 's * s' (40.9)

is not unifiable with type 'Unit ->? _var_76_v76 * _var_77_v77' (72.11)

*** Hint 75.24, in type of '(var x : s, var y : s)'

type 's * s' (40.9)

is not unifiable with type 'Unit ->? _var_81_v81 * _var_82_v82' (72.11)

*** Hint 75.15, in type of '(var x : s,

(pred eq[_var_80_v80] : forall s : Type . s_v-1 * s_v-1)

(var x : s, var y : s))'

type 's * Unit' (40.9)

is not unifiable with type 'Unit ->? _var_71_v71 * _var_72_v72' (58.16)

*** Hint 75.35, variable shadows global name(s) 'x'

*** Hint 75.53, in type of '(var x : s, var y : s)'

type 's * s' (40.9)

is not unifiable with type 'Unit ->? _var_95_v95 * _var_96_v96' (72.11)

*** Hint 75.53, in type of '(var x : s, var y : s)'

type 's * s' (40.9)

is not unifiable with type 'Unit ->? _var_100_v100 * _var_101_v101' (72.11)

*** Hint 75.44, in type of '(var y : s,

(pred eq[_var_99_v99] : forall s : Type . s_v-1 * s_v-1)

(var x : s, var y : s))'

type 's * Unit' (75.40)

is not unifiable with type 'Unit ->? _var_90_v90 * _var_91_v91' (58.16)

*** Hint 75.6, variable shadows global name(s) 'x'

*** Hint 75.24, in type of '(var x : s, var y : s)'

type 's * s' (40.9)

is not unifiable with type 'Unit ->? _var_122_v122 * _var_123_v123' (72.11)

*** Hint 75.24, in type of '(var x : s, var y : s)'

type 's * s' (40.9)

is not unifiable with type 'Unit ->? _var_127_v127 * _var_128_v128' (72.11)

*** Hint 75.15, in type of '(var x : s,

(pred eq[_var_126_v126] : forall s : Type . s_v-1 * s_v-1)

(var x : s, var y : s))'

type 's * Unit' (40.9)

is not unifiable with type 'Unit ->? _var_117_v117 * _var_118_v118' (58.16)

*** Hint 75.35, variable shadows global name(s) 'x'

*** Hint 75.53, in type of '(var x : s, var y : s)'

type 's * s' (40.9)

is not unifiable with type 'Unit ->? _var_141_v141 * _var_142_v142' (72.11)

*** Hint 75.53, in type of '(var x : s, var y : s)'

type 's * s' (40.9)

is not unifiable with type 'Unit ->? _var_146_v146 * _var_147_v147' (72.11)

*** Hint 75.44, in type of '(var y : s,

(pred eq[_var_145_v145] : forall s : Type . s_v-1 * s_v-1)

(var x : s, var y : s))'

type 's * Unit' (75.40)

is not unifiable with type 'Unit ->? _var_136_v136 * _var_137_v137' (58.16)

*** Hint 75.17, in type of '(\ (var x : s, var y : s)

. (op __res__[_var_115_v115; _var_116_v116]

: forall s : Type; t : Type . s_v-1 * t_v-2 ->? s_v-1)

(var x : s,

(pred eq[_var_121_v121] : forall s : Type . s_v-1 * s_v-1)

(var x : s, var y : s)),

\ (var x : s, var y : s)

. (op __res__[_var_134_v134; _var_135_v135]

: forall s : Type; t : Type . s_v-1 * t_v-2 ->? s_v-1)

(var y : s,

(pred eq[_var_140_v140] : forall s : Type . s_v-1 * s_v-1)

(var x : s, var y : s)))'

type '(s * s ->? s) * (s * s ->? s)' (40.9)

is not unifiable with type 'Unit ->? _var_62_v62 * _var_63_v63' (22.14)

*** Hint 85.6, redeclared type 's'

*** Error 85.6, merge: TypeVarDefn of 's'

*** Error 85.11, illegal supertype for variable '? s_v1'

*** Hint 87.9, no type match for: all

with (maximal) type: _var_152_v152 ->? Unit ->? Unit

known types:

*** Hint 87.9, untypable application (with result type: Unit ->? Unit)

'all(var p : s ->? Unit)'

*** Error 87.38, no typing for 'program all(var p : s ->? Unit) : Unit ->? Unit = eq(p, tt)'

*** Error 90.45, unexpected mixfix token: t1

*** Error 93.11, unexpected mixfix token: impl

*** Error 93.58, unexpected mixfix token: And

*** Error 95.11, unexpected mixfix token: or

*** Error 96.21, unexpected mixfix token: impl

*** Error 95.48, unexpected mixfix token: all

*** Error 99.32, unexpected mixfix token: impl

*** Error 99.17, unexpected mixfix token: all

*** Error 98.39, unexpected mixfix token: all

*** Error 101.29, unexpected mixfix token: all

*** Error 103.44, unexpected mixfix token: impl

*** Error 108.51, unexpected mixfix token: impl

*** Error 108.22, unexpected mixfix token: all

*** Error 108.3, unexpected mixfix token: all

*** Hint 117.5, is type variable 'c'

*** Error 121.3, unexpected mixfix token: all

*** Error 122.31, unexpected mixfix token: und

*** Error 122.3, unexpected mixfix token: all

*** Error 123.31, unexpected mixfix token: und

*** Error 123.3, unexpected mixfix token: all

*** Error 125.55, unexpected mixfix token: Suc

*** Error 125.32, unexpected mixfix token: all

*** Hint 126.15, variable shadows global name(s) 'x'

*** Error 126.38, unexpected mixfix token: all

*** Error 131.56, unexpected mixfix token: impl

*** Error 130.32, unexpected mixfix token: impl

*** Error 130.3, unexpected mixfix token: all

*** Error 134.31, unexpected mixfix token: impl

*** Error 134.3, unexpected mixfix token: all

*** Hint 139.5, is type variable 'p'

*** Error 141.4, illegal overloading of predefined identifier 'bottom'

*** Error 143.3, unexpected mixfix token: all

*** Hint 148.6, is type variable 'f'

*** Error 150.15, unexpected mixfix token: [

*** Hint 153.5, is type variable 'c'

*** Hint 153.5, redeclared type 'c'

*** Hint 153.8, is type variable 'd'

*** Error 159.45, unexpected mixfix token: und

*** Error 169.9, incompatible kind of: __-->?__

expected: Type- -> Type+ -> Type

found: Type -> Type -> Type

*** Error 171.35, unexpected mixfix token: und

*** Error 174.45, unexpected mixfix token: +

*** Error 173.40, unexpected mixfix token: und

*** Error 172.39, unexpected mixfix token: und

*** Error 171.9, unexpected mixfix token: all

*** Error 170.7, unexpected mixfix token: :

*** Error 176.51, unexpected mixfix token: impl

*** Error 176.31, unexpected mixfix token: all

*** Error 181.9, incompatible kind of: __-->__

expected: Type- -> Type+ -> Type

found: Type -> Type -> Type

*** Error 182.46, ambiguous mixfix term

def__(f(x))

def(f)(x)

*** Error 182.36, unexpected mixfix token: all

*** Error 182.7, unexpected mixfix token: :

*** Error 186.26, unexpected mixfix token: c

*** Error 190.9, incompatible kind of: p_v158 -->? p_v158

expected: Cpo-

found: Type

*** Error 193.32, unexpected mixfix token: impl

*** Error 192.27, unexpected mixfix token: Y

*** Error 192.3, unexpected mixfix token: all

*** Error 195.27, unexpected mixfix token: Y

*** Error 200.20, illegal overloading of predefined identifier 'true'

*** Error 200.27, illegal overloading of predefined identifier 'false'