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peano.c File Reference

The implementation for Peano Arithmetic. More...

#include "peano.h"

Include dependency graph for peano.c:

Functions
void	error (const char *s, const int n)
Natnum_t	Natnum_malloc ()
Natnum_t	Z ()
Natnum_t	S (const Natnum_t n)
Natnum_t	recsum (const Natnum_t s0, const Natnum_t s1)
Natnum_t	itsum (const Natnum_t s0, const Natnum_t s1)
Natnum_t	loopsum (Natnum_t s0, Natnum_t s1)
int	Zeq (Natnum_t n)
const Natnum_t	pred (const Natnum_t n)
int	eq (Natnum_t n0, Natnum_t n1)
unsigned	nn2uns (Natnum_t nn)
Natnum_t	uns2nn (unsigned u)

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Detailed Description

The implementation for Peano Arithmetic.

Operations on Natnum_t objects are defined.

struct Natnum is a cell containing just a pointer. A linked list with of those cells, followed by a null pointer represents the integer : iterations of , the sucessor function applied to , the zero constructor.

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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

void error (  const char *    s, const int    n )  [static]

a local error procedure A procedure for producing an error message and aborting the program Parameters: s  pointer to error message n  an interger constant to be returned to the operating system

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.

Natnum_t Natnum_malloc (    )  [static]

An allocator for Natnum It uses malloc to allocate space for Natnum, possibly aborting the program Returns: pointer to newly allocated Natnum

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

Natnum_t Z (    )

int Zeq (  Natnum_t    )

whether a number is zero

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