cu/bool.h: Boolean Functions
[Data Types]

Enumerations
enum	cu_bool1f_t { CU_BOOL1F_FALSE = 0x0, CU_BOOL1F_TRUE = 0x3, CU_BOOL1F_IDENT = 0x2, CU_BOOL1F_NOT = 0x1 }
enum	cu_bool2f_t {   CU_BOOL2F_FALSE = 0x0, CU_BOOL2F_TRUE = 0xf, CU_BOOL2F_LEFT = 0xa, CU_BOOL2F_RIGHT = 0xc,   CU_BOOL2F_NOT_LEFT = 0x5, CU_BOOL2F_NOT_RIGHT = 0x3, CU_BOOL2F_NOR = 0x1, CU_BOOL2F_XOR = 0x6,   CU_BOOL2F_NAND = 0x7, CU_BOOL2F_AND = 0x8, CU_BOOL2F_IFF = 0x9, CU_BOOL2F_OR = 0xe,   CU_BOOL2F_AND_NOT = 0x2, CU_BOOL2F_NOT_AND = 0x4, CU_BOOL2F_OR_NOT = 0xb, CU_BOOL2F_NOT_OR = 0xd }
Functions
int	cu_bool_cmp (cu_bool_t x, cu_bool_t y)
cu_bool1f_t	cu_bool1f_from_func (cu_bool_t(*f)(cu_bool_t))
cu_bool_t	cu_bool1f_apply (cu_bool1f_t f, cu_bool_t x)
cu_bool1f_t	cu_bool1f_konst (cu_bool_t x)
cu_bool1f_t	cu_bool1f_not (cu_bool1f_t f)
cu_bool1f_t	cu_bool1f_compose (cu_bool1f_t f, cu_bool1f_t g)
cu_bool2f_t	cu_bool2f_from_func (cu_bool_t(*f)(cu_bool_t, cu_bool_t))
cu_bool_t	cu_bool2f_apply (cu_bool2f_t f, cu_bool_t x, cu_bool_t y)
cu_bool1f_t	cu_bool2f_apply_left (cu_bool2f_t f, cu_bool_t x)
cu_bool1f_t	cu_bool2f_apply_right (cu_bool2f_t f, cu_bool_t y)
cu_bool2f_t	cu_bool2f_konst (cu_bool_t v)
cu_bool2f_t	cu_bool2f_not (cu_bool2f_t f)
cu_bool2f_t	cu_bool2f_not_left (cu_bool2f_t f)
cu_bool2f_t	cu_bool2f_not_right (cu_bool2f_t f)
cu_bool2f_t	cu_bool2f_swap (cu_bool2f_t f)
cu_bool2f_t	cu_bool2f_compose (cu_bool1f_t f, cu_bool2f_t g)
cu_bool2f_t	cu_bool2f_compose_left (cu_bool2f_t f, cu_bool1f_t g)
cu_bool2f_t	cu_bool2f_compose_right (cu_bool2f_t f, cu_bool1f_t g)
Variables
cu_bool_t(*)(cu_bool_t)	cu_bool1f_to_func (cu_bool1f_t f)
cu_bool_t(*)(cu_bool_t, cu_bool_t)	cu_bool2f_to_func (cu_bool2f_t f)

---

Enumeration Type Documentation

enum cu_bool1f_t

An enumeration of unary boolean functions.

Enumerator:

CU_BOOL1F_FALSE	λx. false
CU_BOOL1F_TRUE	λx. true
CU_BOOL1F_IDENT	λx. x
CU_BOOL1F_NOT	λx. ¬x

enum cu_bool2f_t

An enumeration of binary boolean functions.

Enumerator:

CU_BOOL2F_FALSE	λ(x, y). false
CU_BOOL2F_TRUE	λ(x, y). true
CU_BOOL2F_LEFT	λ(x, y). x
CU_BOOL2F_RIGHT	λ(x, y). y
CU_BOOL2F_NOT_LEFT	λ(x, y). ¬x
CU_BOOL2F_NOT_RIGHT	λ(x, y). ¬y
CU_BOOL2F_NOR	λ(x, y). ¬(x ∨ y)
CU_BOOL2F_XOR	λ(x, y). x ⊻ y
CU_BOOL2F_NAND	λ(x, y). ¬(x ∧ y)
CU_BOOL2F_AND	λ(x, y). x ∧ y
CU_BOOL2F_IFF	λ(x, y). x ⇔ y
CU_BOOL2F_OR	λ(x, y). x ∨ y
CU_BOOL2F_AND_NOT	λ(x, y). x ∧ ¬y
CU_BOOL2F_NOT_AND	λ(x, y). ¬x ∧ y
CU_BOOL2F_OR_NOT	λ(x, y). x ∨ ¬y
CU_BOOL2F_NOT_OR	λ(x, y). ¬x ∨ y

---

Function Documentation

cu_bool_t cu_bool1f_apply	(	cu_bool1f_t	f,
		cu_bool_t	x
	)

Evaluate f(x).

cu_bool1f_t cu_bool1f_compose	(	cu_bool1f_t	f,
		cu_bool1f_t	g
	)

Return the composition f ∘ g.

cu_bool1f_t cu_bool1f_from_func

(

cu_bool_t(*)(cu_bool_t)

f

)

Return the enumerated boolean function corresponding to f. f will be called twice upon construction.

cu_bool1f_t cu_bool1f_konst

(

cu_bool_t

x

)

Return the constant function, λy. x.

cu_bool1f_t cu_bool1f_not

(

cu_bool1f_t

f

)

Return the function λx. ¬f(x).

cu_bool_t cu_bool2f_apply	(	cu_bool2f_t	f,
		cu_bool_t	x,
		cu_bool_t	y
	)

Evaluate f(x, y).

cu_bool1f_t cu_bool2f_apply_left	(	cu_bool2f_t	f,
		cu_bool_t	x
	)

Return the partial evaluation λy. f(x, y).

cu_bool1f_t cu_bool2f_apply_right	(	cu_bool2f_t	f,
		cu_bool_t	y
	)

Return the partial evaluation λx. f(x, y).

cu_bool2f_t cu_bool2f_compose	(	cu_bool1f_t	f,
		cu_bool2f_t	g
	)

Return the composition f ∘ g, i.e. the function λ(x, y). f (g (x, y)).

cu_bool2f_t cu_bool2f_compose_left	(	cu_bool2f_t	f,
		cu_bool1f_t	g
	)

Return the composition of f on the left operand with g, λ(x, y). f (g(x), y).

cu_bool2f_t cu_bool2f_compose_right	(	cu_bool2f_t	f,
		cu_bool1f_t	g
	)

Return the composition of f on the right operand with g, λ(x, y). f (x, g(y)).

cu_bool2f_t cu_bool2f_from_func

(

cu_bool_t(*)(cu_bool_t, cu_bool_t)

f

)

Return the enumerated boolean function which agrees with f on its domain. This samples f 4 times.

cu_bool2f_t cu_bool2f_konst

(

cu_bool_t

v

)

The constant function λ(x, y). v.

cu_bool2f_t cu_bool2f_not

(

cu_bool2f_t

f

)

Return the function λ(x, y). ¬f(x, y).

cu_bool2f_t cu_bool2f_swap

(

cu_bool2f_t

f

)

Swap the arguments, i.e. λ(x, y). f(y, x).

int cu_bool_cmp	(	cu_bool_t	x,
		cu_bool_t	y
	)

Returns -1 if ¬x ∧ y, 0 if x ⇔ y, and 1 if x ∧ ¬y.

---

Variable Documentation

cu_bool_t(*)(cu_bool_t) cu_bool1f_to_func(cu_bool1f_t f)

Return the C function which at x returns cu_bool1f_apply(f, x).

cu_bool_t(*)(cu_bool_t, cu_bool_t) cu_bool2f_to_func(cu_bool2f_t f)

The C function which agrees with f on its domain.