class Functor < Type -> Type

class Monad < Functor

type List : Monad

vars a, 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 : Type -> Type

class

Monad < Functor

types

List : Monad;

Set : Functor

vars

a : Type %(var_1)%;

b : Type %(var_2)%;

f : Functor %(var_4)%;

m : Monad %(var_3)%

op __bind__ : forall a : Type; b : Type; m : Monad

. m a * (a -> m b) -> m b

%(op)%

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

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

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

op fmap : forall a : Type; b : Type; f : Functor

. (a -> b) -> f a -> f b

%(op)%

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

%(op)%

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

vars

g : a -> b;

x : m a

. fail = emptySet

. fail = ""

forall a : Type; b : Type; g : a -> b . fmap g = map g

forall a : Type; b : Type; m : Monad; g : a -> b; x : m a

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

### 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 : forall a : Type; m : Monad . m a)

= (op emptySet : forall a : Type . Set a)' of type 'Unit'

unresolved constraints

'{Set : Monad}'

*** Error 25.8,

in term '(op fail : forall a : Type; m : Monad . m a)

= (op emptySet : forall a : Type . Set a)'

are uninstantiated type variables

'[_v12_a]'

*** Error 27.8,

in term '(op fail : forall a : Type; m : Monad . m a)

= (op empty : forall a : Type . List a)'

are uninstantiated type variables

'[_v23_a]'

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

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

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