class Functor < Type -> Type;

class Monad < Functor;

type List : Monad

var a : Type; b : Type

var m : Monad

op fail : m a

op return : a -> m a

var f : Functor

op fmap : (a -> b) -> f a -> f b

op empty : List a

type Set : Functor

op emptySet : Set a

. fail = emptySet

. fail = "";

op map : (a -> b) -> List a -> List b

op __bind__ : m a * (a -> m b) -> m b

var g : a -> b

var x : m a

. fmap g = map g

. fmap g x = (x bind (\ y : a .! return (g y)));

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

Functor < Type -> Type

Monad < Functor

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

List : Monad

Set : Functor

%% Type Variables --------------------------------------------------------

a : Type %(var_1)%

b : Type %(var_2)%

f : Functor %(var_4)%

m : Monad %(var_3)%

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

__bind__

: forall a : Type; b : Type; m : Monad . m a * (a -> m b) -> m b

%(op)%

empty : forall a : Type . List a %(op)%

emptySet : forall a : Type . Set a %(op)%

fail : forall a : Type; m : Monad . m a %(op)%

fmap

: forall a : Type; b : Type; f : Functor . (a -> b) -> f a -> f b

%(op)%

map

: forall a : Type; b : Type . (a -> b) -> List a -> List b %(op)%

return : forall a : Type; m : Monad . a -> m a %(op)%

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

g : a -> b

x : m a

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

fail = emptySet

fail = ""

fmap g = map g

fmap g x = (x bind (\ y : a .! return (g y)))

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

### Hint 7.5, is type variable 'a'

### Hint 7.8, is type variable 'b'

### Hint 9.5, is type variable 'm'

### Hint 15.5, is type variable 'f'

### Hint 25.8, constrain 'Set : Monad' is unprovable

known kinds are: Functor

*** Error 25.8, in term '(op fail[_v12; Set] : forall a : Type; m : Monad . m a) =

(op emptySet[_v12] : forall a : Type . Set a)' of type 'Unit'

unresolved constraints '{Set : Monad}'

### Hint 33.7, not a class 'a'

### Hint 33.7, not a class 'b'

### Hint 33.23, not a kind 'm a'