var b : Type

var a : +Type

type List a

free type List a ::= Nil | Cons (head : a; tail : List a)

free type

free type

free type

free type Tree a ::= Leaf | Branch (head : Tree a; tail : Tree a)

generated type Tree1 a

::= Leaf | Branch (head : Tree a; tail : Tree1 a)

type Tree2 a ::= Leaf | Branch (head : Tree a; tail : Tree2 a)

free types

even a ::= rek (odd a);

odd a ::= rek (even a)

free type odd2 a ::= rek (even2 a)

types

List : +Type -> Type;

Tree : +Type -> Type;

Tree1 : +Type -> Type;

Tree2 : +Type -> Type;

even : +Type -> Type;

even2 : +Type -> Type;

odd : +Type -> Type;

odd2 : +Type -> Type

types

List

%[free type List(a : +Type) ::=

Cons (head : a; tail : List a) | Nil]%;

Tree

%[free type Tree(a : +Type) ::=

Branch (head : Tree a; tail : Tree a) | Leaf]%;

Tree1

%[generated type Tree1(a : +Type) ::=

Branch (head : Tree a; tail : Tree1 a) | Leaf]%;

Tree2

%[type Tree2(a : +Type) ::=

Branch (head : Tree a; tail : Tree2 a) | Leaf]%;

even %[free type even(a : +Type) ::= rek (odd a)]%;

even2 %(data type)%;

odd %[free type odd(a : +Type) ::= rek (even a)]%;

odd2 %[free type odd2(a : +Type) ::= rek (even2 a)]%

vars

a : +Type %(var_2)%;

b : Type %(var_1)%

op Branch : forall a : Type . Tree a * Tree a -> Tree a

%(constructor)%

op Branch : forall a : Type . Tree a * Tree1 a -> Tree1 a

%(constructor)%

op Branch : forall a : Type . Tree a * Tree2 a -> Tree2 a

%(constructor)%

op Cons : forall a : Type . a * List a -> List a %(constructor)%

op Leaf : forall a : Type . Tree a %(constructor)%

op Leaf : forall a : Type . Tree1 a %(constructor)%

op Leaf : forall a : Type . Tree2 a %(constructor)%

op Nil : forall a : Type . List a %(constructor)%

op head : forall a : Type . List a -> a

%(selector of constructor(s)

Cons : forall a : Type . a * List a -> List a)%

op head : forall a : Type . Tree a -> Tree a

%(selector of constructor(s)

Branch : forall a : Type . Tree a * Tree a -> Tree a)%

op head : forall a : Type . Tree1 a -> Tree a

%(selector of constructor(s)

Branch : forall a : Type . Tree a * Tree1 a -> Tree1 a)%

op head : forall a : Type . Tree2 a -> Tree a

%(selector of constructor(s)

Branch : forall a : Type . Tree a * Tree2 a -> Tree2 a)%

op rek : forall a : Type . even a -> odd a %(constructor)%

op rek : forall a : Type . even2 a -> odd2 a %(constructor)%

op rek : forall a : Type . odd a -> even a %(constructor)%

op tail : forall a : Type . List a -> List a

%(selector of constructor(s)

Cons : forall a : Type . a * List a -> List a)%

op tail : forall a : Type . Tree a -> Tree a

%(selector of constructor(s)

Branch : forall a : Type . Tree a * Tree a -> Tree a)%

op tail : forall a : Type . Tree1 a -> Tree1 a

%(selector of constructor(s)

Branch : forall a : Type . Tree a * Tree1 a -> Tree1 a)%

op tail : forall a : Type . Tree2 a -> Tree2 a

%(selector of constructor(s)

Branch : forall a : Type . Tree a * Tree2 a -> Tree2 a)%

forall a : +Type; x_1_1 : a; x_1_2 : List a

. (op head : forall a : Type . List a -> a) (Cons (x_1_1, x_1_2))

= x_1_1 %(ga_select_head)%

forall a : +Type; x_1_1 : a; x_1_2 : List a

. (op tail : forall a : Type . List a -> List a)

(Cons (x_1_1, x_1_2))

= x_1_2 %(ga_select_tail)%

free type List(a : +Type) ::= Cons (head : a; tail : List a) | Nil

%(ga_List)%

free type List(a : +Type) ::= Cons (head : a; tail : List a) | Nil

%(ga_List)%

free type List(a : +Type) ::= Cons (head : a; tail : List a) | Nil

%(ga_List)%

free type List(a : +Type) ::= Cons (head : a; tail : List a) | Nil

%(ga_List)%

forall a : +Type; x_1_1 : Tree a; x_1_2 : Tree a

. (op head : forall a : Type . Tree a -> Tree a)

((op Branch : forall a : Type . Tree a * Tree a -> Tree a)

(x_1_1, x_1_2))

= x_1_1 %(ga_select_head)%

forall a : +Type; x_1_1 : Tree a; x_1_2 : Tree a

. (op tail : forall a : Type . Tree a -> Tree a)

((op Branch : forall a : Type . Tree a * Tree a -> Tree a)

(x_1_1, x_1_2))

= x_1_2 %(ga_select_tail)%

free type Tree(a : +Type) ::=

Branch (head : Tree a; tail : Tree a) | Leaf %(ga_Tree)%

forall a : +Type; x_1_1 : Tree a; x_1_2 : Tree1 a

. (op head : forall a : Type . Tree1 a -> Tree a)

((op Branch : forall a : Type . Tree a * Tree1 a -> Tree1 a)

(x_1_1, x_1_2))

= x_1_1 %(ga_select_head)%

forall a : +Type; x_1_1 : Tree a; x_1_2 : Tree1 a

. (op tail : forall a : Type . Tree1 a -> Tree1 a)

((op Branch : forall a : Type . Tree a * Tree1 a -> Tree1 a)

(x_1_1, x_1_2))

= x_1_2 %(ga_select_tail)%

generated type Tree1(a : +Type) ::=

Branch (head : Tree a; tail : Tree1 a) | Leaf

%(ga_Tree1)%

forall a : +Type; x_1_1 : Tree a; x_1_2 : Tree2 a

. (op head : forall a : Type . Tree2 a -> Tree a)

((op Branch : forall a : Type . Tree a * Tree2 a -> Tree2 a)

(x_1_1, x_1_2))

= x_1_1 %(ga_select_head)%

forall a : +Type; x_1_1 : Tree a; x_1_2 : Tree2 a

. (op tail : forall a : Type . Tree2 a -> Tree2 a)

((op Branch : forall a : Type . Tree a * Tree2 a -> Tree2 a)

(x_1_1, x_1_2))

= x_1_2 %(ga_select_tail)%

type Tree2(a : +Type) ::=

Branch (head : Tree a; tail : Tree2 a) | Leaf %(ga_Tree2)%

free type even(a : +Type) ::= rek (odd a)

free type odd(a : +Type) ::= rek (even a) %(ga_even_odd)%

free type odd2(a : +Type) ::= rek (even2 a) %(ga_even2_odd2)%

### Hint 1.5, is type variable 'b'

### Hint 2.5, is type variable 'a'

### Hint 4.11, redeclared type 'List'

*** Error 5.50-5.55, unbound type variable(s)

b in 'List b'

*** Error 6.50-6.57, unexpected type argument 'b'

*** Error 7.50-7.61, illegal polymorphic recursion

expected: List a

found: List (List a)

*** Error 14.27-14.38, illegal polymorphic recursion

expected: odd2 a

found: odd2 (odd2 a)