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peano.h File Reference

An interface (header file) for Peano Arithmetic. More...

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Compounds
struct	Natnum
	A structure for representing Natural Numbers from the Peano Arithmetic. More...
Typedefs
typedef Natnum *	Natnum_t
	Natnum_t : the object that will be operated on. More...
Functions
Natnum_t	Z ()
Natnum_t	S (const Natnum_t n)
Natnum_t	itsum (const Natnum_t, const Natnum_t)
Natnum_t	recsum (const Natnum_t, const Natnum_t)
Natnum_t	loopsum (const Natnum_t, const Natnum_t)
const Natnum_t	pred (const Natnum_t)
int	Zeq (Natnum_t)
int	eq (Natnum_t, Natnum_t)
unsigned	nn2uns (Natnum_t)
Natnum_t	uns2nn (unsigned)

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Detailed Description

An interface (header file) for Peano Arithmetic.

It defines the representation for Peano numbers and the interface to operations on them.

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Typedef Documentation

Natnum_t

Natnum_t : the object that will be operated on. A Peano number will always be a pointer to a Natnum, i.e., a Natnum_t

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Function Documentation

int eq (  Natnum_t    n0, Natnum_t    n1 )

equlity test Notice that equality is defined with respect to the intended representation

Natnum_t itsum (  const Natnum_t    s0, const Natnum_t    s1 )

tail recursive function for computing sum over Natnum

Natnum_t loopsum (  Natnum_t    s0, Natnum_t    s1 )

The sum of two Natnum object, using iteration It implements invariant assertion.

unsigned nn2uns (  Natnum_t    )

Converting a Natnum_t to binary representation

const Natnum_t pred (  const    Natnum_t )

the predecessor of a given number

Natnum_t recsum (  const Natnum_t    s0, const Natnum_t    s1 )

recursive function for computing sum over Natnum it computes sum of two Natnum objects, using recursion with suspended computation (computation with draft on stack)

Natnum_t S (  const Natnum_t    n )

A constructor for an object representing the successor of a given number Parameters: n  a number Returns: the successor of n

Natnum_t uns2nn (  unsigned    )

From binary to Natnum_t

Z (    )

A constructor for an object representing the number zero

int Zeq (  Natnum_t    )

whether a number is zero

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