6a4fa2d53294f484fa8788a75656eff4ad1fd703Daniel Hausmannfree type Tree(a : Type) ::= Leaf (a) |

6a4fa2d53294f484fa8788a75656eff4ad1fd703Daniel Hausmann Node (Tree a) (a) |

6a4fa2d53294f484fa8788a75656eff4ad1fd703Daniel Hausmann EmptyLeaf

6a4fa2d53294f484fa8788a75656eff4ad1fd703Daniel Hausmannfree type Nat ::= Zero |

6a4fa2d53294f484fa8788a75656eff4ad1fd703Daniel Hausmann Suc (Nat)

6a4fa2d53294f484fa8788a75656eff4ad1fd703Daniel Hausmannop caseTree : forall a . Tree Nat -> Tree Nat

6a4fa2d53294f484fa8788a75656eff4ad1fd703Daniel Hausmannforall h : Tree Nat; n : Nat; t : Tree Nat

6a4fa2d53294f484fa8788a75656eff4ad1fd703Daniel Hausmann. ((fun __=__[Tree Nat]

6a4fa2d53294f484fa8788a75656eff4ad1fd703Daniel Hausmann : forall a : Type . a_v-1 * a_v-1 ->? Unit) :

6a4fa2d53294f484fa8788a75656eff4ad1fd703Daniel Hausmann Tree Nat * Tree Nat ->? Unit)

6a4fa2d53294f484fa8788a75656eff4ad1fd703Daniel Hausmann ((op caseTree : Tree Nat -> Tree Nat)(var t : Tree Nat) : Tree Nat,

6a4fa2d53294f484fa8788a75656eff4ad1fd703Daniel Hausmann (case (var t : Tree Nat) of

6a4fa2d53294f484fa8788a75656eff4ad1fd703Daniel Hausmann (op EmptyLeaf[Nat] : forall a : Type . Tree a_v-1) : Tree Nat ->

6a4fa2d53294f484fa8788a75656eff4ad1fd703Daniel Hausmann (op EmptyLeaf[_var_13_v13] : forall a : Type . Tree a_v-1) :

6a4fa2d53294f484fa8788a75656eff4ad1fd703Daniel Hausmann Tree _var_13_v13 |

6a4fa2d53294f484fa8788a75656eff4ad1fd703Daniel Hausmann ((op Leaf[Nat] : forall a : Type . a_v-1 -> Tree a_v-1) :

6a4fa2d53294f484fa8788a75656eff4ad1fd703Daniel Hausmann Nat -> Tree Nat)

6a4fa2d53294f484fa8788a75656eff4ad1fd703Daniel Hausmann (var n : Nat) :

6a4fa2d53294f484fa8788a75656eff4ad1fd703Daniel Hausmann Tree Nat

6a4fa2d53294f484fa8788a75656eff4ad1fd703Daniel Hausmann ->

6a4fa2d53294f484fa8788a75656eff4ad1fd703Daniel Hausmann (op EmptyLeaf[_var_13_v13] : forall a : Type . Tree a_v-1) :

6a4fa2d53294f484fa8788a75656eff4ad1fd703Daniel Hausmann Tree _var_13_v13 |

6a4fa2d53294f484fa8788a75656eff4ad1fd703Daniel Hausmann (((op Node[Nat]

6a4fa2d53294f484fa8788a75656eff4ad1fd703Daniel Hausmann : forall a : Type . Tree a_v-1 -> a_v-1 -> Tree a_v-1) :

6a4fa2d53294f484fa8788a75656eff4ad1fd703Daniel Hausmann Tree Nat -> Nat -> Tree Nat)

6a4fa2d53294f484fa8788a75656eff4ad1fd703Daniel Hausmann ((op EmptyLeaf[Nat] : forall a : Type . Tree a_v-1) : Tree Nat) :

6a4fa2d53294f484fa8788a75656eff4ad1fd703Daniel Hausmann Nat -> Tree Nat)

6a4fa2d53294f484fa8788a75656eff4ad1fd703Daniel Hausmann (var n : Nat) :

6a4fa2d53294f484fa8788a75656eff4ad1fd703Daniel Hausmann Tree Nat

6a4fa2d53294f484fa8788a75656eff4ad1fd703Daniel Hausmann ->

6a4fa2d53294f484fa8788a75656eff4ad1fd703Daniel Hausmann (op EmptyLeaf[_var_13_v13] : forall a : Type . Tree a_v-1) :

6a4fa2d53294f484fa8788a75656eff4ad1fd703Daniel Hausmann Tree _var_13_v13 |

6a4fa2d53294f484fa8788a75656eff4ad1fd703Daniel Hausmann (((op Node[Nat]

6a4fa2d53294f484fa8788a75656eff4ad1fd703Daniel Hausmann : forall a : Type . Tree a_v-1 -> a_v-1 -> Tree a_v-1) :

6a4fa2d53294f484fa8788a75656eff4ad1fd703Daniel Hausmann Tree Nat -> Nat -> Tree Nat)

6a4fa2d53294f484fa8788a75656eff4ad1fd703Daniel Hausmann ((((op Node[Nat]

6a4fa2d53294f484fa8788a75656eff4ad1fd703Daniel Hausmann : forall a : Type . Tree a_v-1 -> a_v-1 -> Tree a_v-1) :

6a4fa2d53294f484fa8788a75656eff4ad1fd703Daniel Hausmann Tree Nat -> Nat -> Tree Nat)

6a4fa2d53294f484fa8788a75656eff4ad1fd703Daniel Hausmann (var h : Tree Nat) :

6a4fa2d53294f484fa8788a75656eff4ad1fd703Daniel Hausmann Nat -> Tree Nat)

(var n : Nat) :

Tree Nat) :

Nat -> Tree Nat)

(var n : Nat) :

Tree Nat

->

(var h : Tree Nat) |

(((op Node[Nat]

: forall a : Type . Tree a_v-1 -> a_v-1 -> Tree a_v-1) :

Tree Nat -> Nat -> Tree Nat)

(((op Leaf[Nat] : forall a : Type . a_v-1 -> Tree a_v-1) :

Nat -> Tree Nat)

(var n : Nat) :

Tree Nat) :

Nat -> Tree Nat)

(var n : Nat) :

Tree Nat

->

((op Leaf[Nat] : forall a : Type . a_v-1 -> Tree a_v-1) :

Nat -> Tree Nat)

(var n : Nat) :

Tree Nat) :

Tree Nat) :

Unit

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

Logical : Type := Unit ->? Unit

Nat

: Type

%[free type Nat

::= Zero : Nat

Suc : Nat -> Nat (Nat)]%

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

Tree

: Type -> Type

%[free type Tree(a : Type)

::= Leaf : a_v-1 -> Tree a_v-1 (a_v-1)

Node : Tree a_v-1 -> a_v-1 -> Tree a_v-1 (Tree a_v-1)(a_v-1)

EmptyLeaf : Tree a_v-1]%

Unit : Type

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

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

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

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

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

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

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

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

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

EmptyLeaf : forall a : Type . Tree a_v-1 %(construct Tree)%

Leaf : forall a : Type . a_v-1 -> Tree a_v-1 %(construct Tree)%

Node

: forall a : Type . Tree a_v-1 -> a_v-1 -> Tree a_v-1

%(construct Tree)%

Suc : Nat -> Nat %(construct Nat)%

Zero : Nat %(construct Nat)%

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

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

__=__ : forall a : Type . a_v-1 * a_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)%

__when__else__

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

bottom : forall a : Type . a_v-1 %(fun)%

caseTree : Tree Nat -> Tree Nat %(op)%

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

false : Unit %(fun)%

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

true : Unit %(fun)%

�__ : ? Unit ->? Unit %(fun)%

%% Variables -------------------------------------------------------------

h : Tree Nat

n : Nat

t : Tree Nat

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

free type Tree(a : Type)

::= Leaf : a_v-1 -> Tree a_v-1 (a_v-1)

Node : Tree a_v-1 -> a_v-1 -> Tree a_v-1 (Tree a_v-1)(a_v-1)

EmptyLeaf : Tree a_v-1 %(ga_Tree)%

free type Nat

::= Zero : Nat

Suc : Nat -> Nat (Nat) %(ga_Nat)%

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

Tree Nat * Tree Nat ->? Unit)

((op caseTree : Tree Nat -> Tree Nat)(var t : Tree Nat) : Tree Nat,

(case (var t : Tree Nat) of

(op EmptyLeaf[Nat] : forall a : Type . Tree a_v-1) : Tree Nat ->

(op EmptyLeaf[_var_13_v13] : forall a : Type . Tree a_v-1) :

Tree _var_13_v13 |

((op Leaf[Nat] : forall a : Type . a_v-1 -> Tree a_v-1) :

Nat -> Tree Nat)

(var n : Nat) :

Tree Nat

->

(op EmptyLeaf[_var_13_v13] : forall a : Type . Tree a_v-1) :

Tree _var_13_v13 |

(((op Node[Nat]

: forall a : Type . Tree a_v-1 -> a_v-1 -> Tree a_v-1) :

Tree Nat -> Nat -> Tree Nat)

((op EmptyLeaf[Nat] : forall a : Type . Tree a_v-1) : Tree Nat) :

Nat -> Tree Nat)

(var n : Nat) :

Tree Nat

->

(op EmptyLeaf[_var_13_v13] : forall a : Type . Tree a_v-1) :

Tree _var_13_v13 |

(((op Node[Nat]

: forall a : Type . Tree a_v-1 -> a_v-1 -> Tree a_v-1) :

Tree Nat -> Nat -> Tree Nat)

((((op Node[Nat]

: forall a : Type . Tree a_v-1 -> a_v-1 -> Tree a_v-1) :

Tree Nat -> Nat -> Tree Nat)

(var h : Tree Nat) :

Nat -> Tree Nat)

(var n : Nat) :

Tree Nat) :

Nat -> Tree Nat)

(var n : Nat) :

Tree Nat

->

(var h : Tree Nat) |

(((op Node[Nat]

: forall a : Type . Tree a_v-1 -> a_v-1 -> Tree a_v-1) :

Tree Nat -> Nat -> Tree Nat)

(((op Leaf[Nat] : forall a : Type . a_v-1 -> Tree a_v-1) :

Nat -> Tree Nat)

(var n : Nat) :

Tree Nat) :

Nat -> Tree Nat)

(var n : Nat) :

Tree Nat

->

((op Leaf[Nat] : forall a : Type . a_v-1 -> Tree a_v-1) :

Nat -> Tree Nat)

(var n : Nat) :

Tree Nat) :

Tree Nat) :

Unit

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

*** Warning 1.18, missing kind for type variable 'a'

*** Warning 4.23, missing kind for type variable 'a'

*** Warning 4.36, ignoring unused variable(s)

a in 'Tree Nat -> Tree Nat'

*** Hint 6.9, not a kind 'Tree Nat'

*** Hint 7.9, not a class 'Nat'

*** Hint 7.16, not a kind 'Tree Nat'

*** Hint 10.27, rebound variable 'n'

*** Hint 11.37, rebound variable 'n'

*** Hint 12.33, rebound variable 'h'

*** Hint 12.35, rebound variable 'n'

*** Hint 12.37, rebound variable 'n'

*** Hint 13.33, rebound variable 'n'

*** Hint 13.36, rebound variable 'n'