vars a, b, c : Type; x : a; f : a -> b; g : b -> c

ops __comp__ : (b -> c) * (a -> b) -> a -> c;

id : a -> a

. id x = x

. (g comp f) x = g (f x);

class Functor < Type -> Type

{vars a, b, c : Type; F : Functor; f : a -> b; g : b -> c

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

. map id = (id : F a -> F a)

. (map (g comp f) : F a -> F c) = map g comp map f;

}

class PolyFunctor < Functor

class PolyBifunctor < Type -> PolyFunctor

vars F : Functor; a, b : Type

type Alg F a := F a -> a

op __::__->__ : Pred ((a -> b) * (Alg F a) * (Alg F b))

class DTFunctor < Functor

{vars F : DTFunctor; a : Type

type InitialCarrier F

ops initialAlg : Alg F (InitialCarrier F);

fold : Alg F a -> InitialCarrier F -> a

vars alpha : Alg F a; g : InitialCarrier F -> a

. g :: initialAlg -> alpha <=> g = fold alpha;

}

class PolyFunctor < DTFunctor

var G : PolyBifunctor

type ParamDT G a := InitialCarrier (G a)

type ParamDT G : DTFunctor

vars l : ParamDT G a; f : a -> a

. map f l = fold initialAlg l;

classes

DTFunctor : Type -> Type;

Functor : Type -> Type;

PolyBifunctor : Type -> Type -> Type;

PolyFunctor : Type -> Type

classes

DTFunctor < Functor;

PolyBifunctor < Type -> PolyFunctor;

PolyFunctor < DTFunctor

types

Alg : Functor -> Type -> Type;

InitialCarrier : DTFunctor -> Type;

ParamDT : PolyBifunctor -> DTFunctor;

gn_t183 : Type -> Type;

gn_t254 : DTFunctor

types

Alg := \ F : Functor . gn_t183;

ParamDT := \ G : PolyBifunctor . gn_t254;

gn_t183 := \ a : Type . F a -> a;

gn_t254 := \ a : Type . InitialCarrier (G a)

vars

F : DTFunctor %(var_184)%;

G : PolyBifunctor %(var_251)%;

a : Type %(var_185)%;

b : Type %(var_180)%;

c : Type %(var_42)%

op __::__->__ : forall F : Functor; a : Type; b : Type

. Pred ((a -> b) * Alg F a * Alg F b)

%(op)%

op __comp__ : forall a : Type; b : Type; c : Type

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

%(op)%

op fold : forall F : DTFunctor; a : Type

. Alg F a -> InitialCarrier F -> a

%(op)%

op id : forall a : Type . a -> a %(op)%

op initialAlg : forall F : DTFunctor . Alg F (InitialCarrier F)

%(op)%

op map : forall a : Type; b : Type; F : Functor

. (a -> b) -> F a -> F b

%(op)%

vars

alpha : Alg F a;

f : a -> a;

g : InitialCarrier F -> a;

l : ParamDT G a;

x : a

forall a : Type; x : a . id x = x

forall a : Type; b : Type; c : Type; f : a -> b; g : b -> c; x : a

. (g comp f) x = g (f x)

forall F : Functor; a : Type . map id = (id : F a -> F a)

forall

F : Functor; a : Type; b : Type; c : Type; f : a -> b; g : b -> c

. map (g comp f) = map g comp map f

forall

F : DTFunctor; a : Type; alpha : Alg F a; g : InitialCarrier F -> a

. g :: initialAlg -> alpha <=> g = fold alpha

forall G : PolyBifunctor; a : Type; f : a -> a; l : ParamDT G a

. map f l = fold initialAlg l

### Hint 1.6, is type variable 'a'

### Hint 1.8, is type variable 'b'

### Hint 1.10, is type variable 'c'

### Hint 1.20, not a class 'a'

### Hint 1.26, not a class 'a'

### Hint 1.26, not a class 'b'

### Hint 1.37, not a class 'b'

### Hint 1.37, not a class 'c'

### Hint 8.7, is type variable 'a'

### Hint 8.7, rebound type variable 'a'

### Hint 8.9, is type variable 'b'

### Hint 8.9, rebound type variable 'b'

### Hint 8.11, is type variable 'c'

### Hint 8.11, rebound type variable 'c'

### Hint 8.20, is type variable 'F'

### Hint 8.33, not a class 'a'

### Hint 8.33, not a class 'b'

### Hint 8.32, rebound variable 'f'

### Hint 8.44, not a class 'b'

### Hint 8.44, not a class 'c'

### Hint 8.43, rebound variable 'g'

### Hint 16.5, is type variable 'F'

### Hint 16.5, rebound type variable 'F'

### Hint 16.17, is type variable 'a'

### Hint 16.17, rebound type variable 'a'

### Hint 16.19, is type variable 'b'

### Hint 16.19, rebound type variable 'b'

### Hint 21.5, is type variable 'F'

### Hint 21.5, rebound type variable 'F'

### Hint 21.19, is type variable 'a'

### Hint 21.19, rebound type variable 'a'

### Hint 25.10, not a kind 'Alg F a'

### Hint 25.22, not a kind 'InitialCarrier F -> a'

### Hint 25.21, rebound variable 'g'

### Hint 28.7, refined class 'PolyFunctor'

### Hint 29.5, is type variable 'G'

### Hint 33.7, not a kind 'ParamDT G a'

### Hint 33.23, not a class 'a'

### Hint 33.23, not a class 'a'

### Hint 33.22, rebound variable 'f'