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2

Given two functions:

f :: EvenInteger -> 0
g :: OddInteger -> 1

consider the function

h = (x :: Integer) => 
 if(x is even)return f(x);
 return g(x);

What the smallest type T such that

h :: T

I was thinking that it is simply

h :: (typeof f) & (typeof g)

But then I would also think that a function call distributes over conjunction i.e., that

x :: EvenInteger
h(x) :: (typeof f(x)) & (typeof g(x))

which begs another question:

What is

(OddInteger -> 1)(EvenInteger)

type-theory

share|improve this question

edited Mar 23 at 21:44

Ray Toal

68k11128185

asked Mar 23 at 21:39

AdamAdam

1,067314

add a comment | 

2

Given two functions:

f :: EvenInteger -> 0
g :: OddInteger -> 1

consider the function

h = (x :: Integer) => 
 if(x is even)return f(x);
 return g(x);

What the smallest type T such that

h :: T

I was thinking that it is simply

h :: (typeof f) & (typeof g)

But then I would also think that a function call distributes over conjunction i.e., that

x :: EvenInteger
h(x) :: (typeof f(x)) & (typeof g(x))

which begs another question:

What is

(OddInteger -> 1)(EvenInteger)

type-theory

share|improve this question

edited Mar 23 at 21:44

Ray Toal

68k11128185

asked Mar 23 at 21:39

AdamAdam

1,067314

add a comment | 

Given two functions:

f :: EvenInteger -> 0
g :: OddInteger -> 1

consider the function

h = (x :: Integer) => 
 if(x is even)return f(x);
 return g(x);

What the smallest type T such that

h :: T

I was thinking that it is simply

h :: (typeof f) & (typeof g)

But then I would also think that a function call distributes over conjunction i.e., that

x :: EvenInteger
h(x) :: (typeof f(x)) & (typeof g(x))

which begs another question:

What is

(OddInteger -> 1)(EvenInteger)

type-theory

share|improve this question

edited Mar 23 at 21:44

Ray Toal

68k11128185

asked Mar 23 at 21:39

AdamAdam

1,067314

f :: EvenInteger -> 0
g :: OddInteger -> 1

h = (x :: Integer) => 
 if(x is even)return f(x);
 return g(x);

h :: T

h :: (typeof f) & (typeof g)

x :: EvenInteger
h(x) :: (typeof f(x)) & (typeof g(x))

(OddInteger -> 1)(EvenInteger)

share|improve this question

edited Mar 23 at 21:44

Ray Toal

68k11128185

asked Mar 23 at 21:39

AdamAdam

1,067314

share|improve this question

edited Mar 23 at 21:44

Ray Toal

68k11128185

asked Mar 23 at 21:39

AdamAdam

1,067314

edited Mar 23 at 21:44

Ray Toal

68k11128185

edited Mar 23 at 21:44

Ray Toal

68k11128185

asked Mar 23 at 21:39

AdamAdam

1,067314

asked Mar 23 at 21:39

AdamAdam

1,067314