godel
Class Godel3

java.lang.Object
  java.awt.Component
      java.awt.Container
          java.awt.Panel
              java.applet.Applet
                  godel.Godel3

All Implemented Interfaces:

java.awt.event.ActionListener, java.awt.image.ImageObserver, java.awt.MenuContainer, java.io.Serializable, java.util.EventListener, javax.accessibility.Accessible, javax.swing.event.CaretListener

public class Godel3
extends java.applet.Applet
implements java.awt.event.ActionListener, javax.swing.event.CaretListener

This applet implements the conversion of a function (expressed as a computer program) into an arithmetical formula. This is the program which carries out the most important part of this Gödel's incompleteness theorem project. It works very much like a compiler, you input a program written in a programming language, and it tranforms this program into another form. In this case, rather than producing executable output, it expresses the program in terms of the Gödel number of an arithmetical formula.

Author:

Stephen Lee

See Also:

Serialized Form

Nested Class Summary

(package private) class	Godel3.Funinfo Holds information about Haskell function
(package private) class	Godel3.IdList List of identifiers
(package private) class	Godel3.TExpr Holds an encoded representation of an expression

Nested classes/interfaces inherited from class java.applet.Applet

java.applet.Applet.AccessibleApplet

Nested classes/interfaces inherited from class java.awt.Panel

java.awt.Panel.AccessibleAWTPanel

Nested classes/interfaces inherited from class java.awt.Container

java.awt.Container.AccessibleAWTContainer

Nested classes/interfaces inherited from class java.awt.Component

java.awt.Component.AccessibleAWTComponent, java.awt.Component.BaselineResizeBehavior, java.awt.Component.BltBufferStrategy, java.awt.Component.FlipBufferStrategy

Field Summary

(package private) javax.swing.JButton	but3 Press to encode statement of the form y=f(x) for a function f
(package private) javax.swing.JButton	but4 Press to encode statement of the form σ1
(package private) javax.swing.JButton	but5 Press to encode statement of the form σ2
(package private) java.math.BigInteger	c0 Coded form of zero
(package private) int	Csp Stack pointer for CStore
(package private) java.math.BigInteger[]	Cstore Store for coded conditions
(package private) char	curch current character
(package private) java.math.BigInteger	curnum current item if it is an integer
(package private) int	curtok current item if it is a token
(package private) java.lang.String	curword current item if it is an identifier
(package private) java.util.BitSet	dep1 Set of function nos.
(package private) java.util.BitSet	dep2 Set of function nos.
(package private) int[]	deplist list of numbers of functions used in code
(package private) int	Esp Stack pointer for EStore
(package private) int[]	Estore Store for variables which need ∃ condition before current piece of code
(package private) int	fdct Counter for deplist
(package private) javax.swing.JTextField	fedit Edit area for name of function for y=f(x) encoding
(package private) Godel3.Funinfo	finf info for function currently being compiled
(package private) Godel3.Funinfo[]	finfo Store for information about functions
(package private) java.math.BigInteger	FOUR
(package private) java.math.BigInteger[]	Fstore Store for code of functions
(package private) Godel3.IdList	FunList Function names
(package private) java.lang.Error	InvInp General compilation error
(package private) int	itype Type of current item
(package private) java.lang.String	lfile Haskell file loaded automatically
(package private) int	locv
(package private) int	nonf number of functions without a name 2 i.e.
(package private) java.math.BigInteger[]	numc Bitstream forms of 0-3 (0,0',0'',0''')
(package private) javax.swing.JTextArea	plines Text area for input of Haskell code
(package private) int	pos Current position in strin
(package private) java.math.BigInteger	predefs Encoded form of predefined functions
(package private) javax.swing.JTextArea	prnum Text area for output of Gödel number of Gödel statement
(package private) java.util.List	ResList Reserved words in List form
(package private) java.lang.String[]	reswords Reserved words
private static long	serialVersionUID
(package private) java.lang.String	strin Holds the Haskell code
(package private) java.math.BigInteger	THREE
(package private) char[][]	tokens 2 character tokens
(package private) java.lang.Error	TypeErr More specific type Error
(package private) Godel3.IdList	VarList Haskell variable names
(package private) int[]	Varstore Store for info about Haskell variables Match position in VarList.
(package private) int	vbase counter for int form of variables
(package private) java.math.BigInteger	Vloc coded form of variable x1 (locv)
(package private) int	z0 int form of first variable (x)
(package private) java.math.BigInteger	Z0 coded form of first variable (x)
(package private) java.math.BigInteger	ZERO

Fields inherited from class java.awt.Component

BOTTOM_ALIGNMENT, CENTER_ALIGNMENT, LEFT_ALIGNMENT, RIGHT_ALIGNMENT, TOP_ALIGNMENT

Fields inherited from interface java.awt.image.ImageObserver

ABORT, ALLBITS, ERROR, FRAMEBITS, HEIGHT, PROPERTIES, SOMEBITS, WIDTH

Constructor Summary

Godel3()

Method Summary

void	actionPerformed(java.awt.event.ActionEvent e) responds to button press
(package private) void	addcond(java.math.BigInteger A) Add a condition to the list
(package private) java.math.BigInteger	binop(java.math.BigInteger x1, int op, java.math.BigInteger x2) Encodes the result of a binary operator
(package private) void	calcdep(int f) Recursively calculates which functions a function depends upon f may be recursively defined, but mutual recursion is not allowed
(package private) void	calcdeps(int f) Calculates which functions a function depends upon, using calcdep
void	caretUpdate(javax.swing.event.CaretEvent e) Reset caret colour after it's turned red to show an error
(package private) boolean	chkch(char c) Checks whether the current item is a single character matching c
(package private) int	chkchS(java.lang.String S) Checks whether the current item is a single character in S.
(package private) void	chkchv(char c) requires the current item to be a single character matching c
(package private) void	chkIntv() Requires current item to be 'Integer' reserved word
(package private) void	chkResv(int i) Ensures that current word is a given reserved word
(package private) void	chktokv(int t) Checks whether the current item is a 2 character token number t
(package private) void	DefFn(java.lang.String name) Deals with the definition part of a function (which must be present)
(package private) java.math.BigInteger	diag(java.math.BigInteger n) ¬(∀z (z=num(n)⇒¬#n)
(package private) java.math.BigInteger	DoFun(int id) Processes body of a function
(package private) java.math.BigInteger	exists(int v, java.math.BigInteger T) ∃ #v #T
(package private) Godel3.TExpr	expr10() Function calls, variables, numbers,[], (expr),duples
(package private) Godel3.TExpr	expr2(int vareq) if, case and let and || operator
(package private) Godel3.TExpr	expr3() && operator
(package private) Godel3.TExpr	expr4() relational operators
(package private) Godel3.TExpr	expr5()
(package private) Godel3.TExpr	expr6() + and -
(package private) Godel3.TExpr	expr7() , `div`, `mod`
(package private) Godel3.TExpr	expr9() !! operator
(package private) java.math.BigInteger	falll(int v, java.math.BigInteger t1) ∀ #v #t1
(package private) void	fcompile() compiles the functions defined in the plines edit,
(package private) java.math.BigInteger	funcround(java.math.BigInteger fcode)
(package private) void	getitem() Gets item from input text.
(package private) int	getType() Gets type descriptor.
(package private) void	getword() Requires a word, that is an identifier or reserved word
(package private) java.math.BigInteger	impp(java.math.BigInteger A, java.math.BigInteger B) #A ⇒ #B
void	init() Initalise applet
(package private) java.math.BigInteger	iseq(java.math.BigInteger t1, java.math.BigInteger t2) Code for #t1=#t2
(package private) java.math.BigInteger	J(java.math.BigInteger t1, java.math.BigInteger t2) J is a 1 to 1 functio combining two integers into one
(package private) java.math.BigInteger	Jn(int[] vs, int n) Combines n integer variables into one integer
(package private) java.math.BigInteger	lessthan(java.math.BigInteger t1, java.math.BigInteger t2) #t1<#t2
(package private) int	makesym(int type) Defines the current identifier to be a variable of a given type
(package private) int	mulop() #0, `div` #1, `mod` #2
(package private) int	newV() new arithmetic variable
(package private) java.math.BigInteger	nott(java.math.BigInteger A) Encode ¬#A
(package private) java.math.BigInteger	num(java.math.BigInteger x) Encodes a number as an arithmetic expression
(package private) void	paramcond(int v, int fno) #v<Nf
(package private) void	parse1() Parses program in strin
(package private) void	predefines() produces the code for predefined list operators (:),(!!) and functions length and tail
(package private) java.math.BigInteger	resconds(int csb, int esb, int vsb) ∃ variables (∧ Conditions)
(package private) java.math.BigInteger	sigma(java.math.BigInteger phi) σφ
(package private) void	skipsps() moves pos to the first non-whitespace character
(package private) java.math.BigInteger	unop(int op, java.math.BigInteger x1) Encodes the result of the unary operator
(package private) java.math.BigInteger	varb(int n)
(package private) java.math.BigInteger	varb0(int n)
(package private) java.math.BigInteger	vform(java.math.BigInteger Term) Creates (if needed) a variable equal to a given term
(package private) java.math.BigInteger	yisfx(java.lang.String fname)

Methods inherited from class java.applet.Applet

destroy, getAccessibleContext, getAppletContext, getAppletInfo, getAudioClip, getAudioClip, getCodeBase, getDocumentBase, getImage, getImage, getLocale, getParameter, getParameterInfo, isActive, newAudioClip, play, play, resize, resize, setStub, showStatus, start, stop

Methods inherited from class java.awt.Panel

addNotify

Methods inherited from class java.awt.Container

add, add, add, add, add, addContainerListener, addImpl, addPropertyChangeListener, addPropertyChangeListener, applyComponentOrientation, areFocusTraversalKeysSet, countComponents, deliverEvent, doLayout, findComponentAt, findComponentAt, getAlignmentX, getAlignmentY, getComponent, getComponentAt, getComponentAt, getComponentCount, getComponents, getComponentZOrder, getContainerListeners, getFocusTraversalKeys, getFocusTraversalPolicy, getInsets, getLayout, getListeners, getMaximumSize, getMinimumSize, getMousePosition, getPreferredSize, insets, invalidate, isAncestorOf, isFocusCycleRoot, isFocusCycleRoot, isFocusTraversalPolicyProvider, isFocusTraversalPolicySet, layout, list, list, locate, minimumSize, paint, paintComponents, paramString, preferredSize, print, printComponents, processContainerEvent, processEvent, remove, remove, removeAll, removeContainerListener, removeNotify, setComponentZOrder, setFocusCycleRoot, setFocusTraversalKeys, setFocusTraversalPolicy, setFocusTraversalPolicyProvider, setFont, setLayout, transferFocusBackward, transferFocusDownCycle, update, validate, validateTree

Methods inherited from class java.awt.Component

action, add, addComponentListener, addFocusListener, addHierarchyBoundsListener, addHierarchyListener, addInputMethodListener, addKeyListener, addMouseListener, addMouseMotionListener, addMouseWheelListener, bounds, checkImage, checkImage, coalesceEvents, contains, contains, createImage, createImage, createVolatileImage, createVolatileImage, disable, disableEvents, dispatchEvent, enable, enable, enableEvents, enableInputMethods, firePropertyChange, firePropertyChange, firePropertyChange, firePropertyChange, firePropertyChange, firePropertyChange, firePropertyChange, firePropertyChange, firePropertyChange, getBackground, getBaseline, getBaselineResizeBehavior, getBounds, getBounds, getColorModel, getComponentListeners, getComponentOrientation, getCursor, getDropTarget, getFocusCycleRootAncestor, getFocusListeners, getFocusTraversalKeysEnabled, getFont, getFontMetrics, getForeground, getGraphics, getGraphicsConfiguration, getHeight, getHierarchyBoundsListeners, getHierarchyListeners, getIgnoreRepaint, getInputContext, getInputMethodListeners, getInputMethodRequests, getKeyListeners, getLocation, getLocation, getLocationOnScreen, getMouseListeners, getMouseMotionListeners, getMousePosition, getMouseWheelListeners, getName, getParent, getPeer, getPropertyChangeListeners, getPropertyChangeListeners, getSize, getSize, getToolkit, getTreeLock, getWidth, getX, getY, gotFocus, handleEvent, hasFocus, hide, imageUpdate, inside, isBackgroundSet, isCursorSet, isDisplayable, isDoubleBuffered, isEnabled, isFocusable, isFocusOwner, isFocusTraversable, isFontSet, isForegroundSet, isLightweight, isMaximumSizeSet, isMinimumSizeSet, isOpaque, isPreferredSizeSet, isShowing, isValid, isVisible, keyDown, keyUp, list, list, list, location, lostFocus, mouseDown, mouseDrag, mouseEnter, mouseExit, mouseMove, mouseUp, move, nextFocus, paintAll, postEvent, prepareImage, prepareImage, printAll, processComponentEvent, processFocusEvent, processHierarchyBoundsEvent, processHierarchyEvent, processInputMethodEvent, processKeyEvent, processMouseEvent, processMouseMotionEvent, processMouseWheelEvent, remove, removeComponentListener, removeFocusListener, removeHierarchyBoundsListener, removeHierarchyListener, removeInputMethodListener, removeKeyListener, removeMouseListener, removeMouseMotionListener, removeMouseWheelListener, removePropertyChangeListener, removePropertyChangeListener, repaint, repaint, repaint, repaint, requestFocus, requestFocus, requestFocusInWindow, requestFocusInWindow, reshape, setBackground, setBounds, setBounds, setComponentOrientation, setCursor, setDropTarget, setEnabled, setFocusable, setFocusTraversalKeysEnabled, setForeground, setIgnoreRepaint, setLocale, setLocation, setLocation, setMaximumSize, setMinimumSize, setName, setPreferredSize, setSize, setSize, setVisible, show, show, size, toString, transferFocus, transferFocusUpCycle

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

Field Detail

serialVersionUID

private static final long serialVersionUID

See Also:

Constant Field Values

lfile

java.lang.String lfile

Haskell file loaded automatically

vbase

int vbase

counter for int form of variables

finfo

Godel3.Funinfo[] finfo

Store for information about functions

nonf

int nonf

number of functions without a name 2 i.e. !! and (:)

locv

final int locv

See Also:

Constant Field Values

deplist

int[] deplist

list of numbers of functions used in code

reswords

java.lang.String[] reswords

Reserved words

tokens

char[][] tokens

2 character tokens

FunList

Godel3.IdList FunList

Function names

VarList

Godel3.IdList VarList

Haskell variable names

ResList

java.util.List ResList

Reserved words in List form

Fstore

java.math.BigInteger[] Fstore

Store for code of functions

Cstore

java.math.BigInteger[] Cstore

Store for coded conditions

Estore

int[] Estore

Store for variables which need ∃ condition before current piece of code

Varstore

int[] Varstore

Store for info about Haskell variables Match position in VarList. Stores (int form)*8)+type

but3

javax.swing.JButton but3

Press to encode statement of the form y=f(x) for a function f

but4

javax.swing.JButton but4

Press to encode statement of the form σ₁

but5

javax.swing.JButton but5

Press to encode statement of the form σ₂

fedit

javax.swing.JTextField fedit

Edit area for name of function for y=f(x) encoding

prnum

javax.swing.JTextArea prnum

Text area for output of Gödel number of Gödel statement

plines

javax.swing.JTextArea plines

Text area for input of Haskell code

strin

java.lang.String strin

Holds the Haskell code

pos

int pos

Current position in strin

fdct

int fdct

Counter for deplist

Csp

int Csp

Stack pointer for CStore

Esp

int Esp

Stack pointer for EStore

InvInp

java.lang.Error InvInp

General compilation error

TypeErr

java.lang.Error TypeErr

More specific type Error

THREE

final java.math.BigInteger THREE

FOUR

final java.math.BigInteger FOUR

ZERO

final java.math.BigInteger ZERO

predefs

java.math.BigInteger predefs

Encoded form of predefined functions

c0

final java.math.BigInteger c0

Coded form of zero

Vloc

final java.math.BigInteger Vloc

coded form of variable x1 (locv)

Z0

final java.math.BigInteger Z0

coded form of first variable (x)

z0

final int z0

int form of first variable (x)

See Also:

Constant Field Values

finf

Godel3.Funinfo finf

info for function currently being compiled

dep1

java.util.BitSet dep1

Set of function nos. for which dependency calculation has started

dep2

java.util.BitSet dep2

Set of function nos. for which dependency calculation has finished

numc

java.math.BigInteger[] numc

Bitstream forms of 0-3 (0,0',0'',0''')

itype

int itype

Type of current item

curch

char curch

current character

curnum

java.math.BigInteger curnum

current item if it is an integer

curword

java.lang.String curword

current item if it is an identifier

curtok

int curtok

current item if it is a token

Constructor Detail

Godel3

public Godel3()

Method Detail

newV

int newV()

new arithmetic variable

Returns:

int form of new variable

init

public void init()

Initalise applet

Overrides:

init in class java.applet.Applet

caretUpdate

public void caretUpdate(javax.swing.event.CaretEvent e)

Reset caret colour after it's turned red to show an error

Specified by:

caretUpdate in interface javax.swing.event.CaretListener

iseq

java.math.BigInteger iseq(java.math.BigInteger t1,
                          java.math.BigInteger t2)

Code for #t1=#t2

falll

java.math.BigInteger falll(int v,
                           java.math.BigInteger t1)

∀ #v #t1

paramcond

void paramcond(int v,
               int fno)

#v<N_f

lessthan

java.math.BigInteger lessthan(java.math.BigInteger t1,
                              java.math.BigInteger t2)

#t1<#t2

diag

java.math.BigInteger diag(java.math.BigInteger n)

¬(∀z (z=num(n)⇒¬#n)

exists

java.math.BigInteger exists(int v,
                            java.math.BigInteger T)

∃ #v #T

sigma

java.math.BigInteger sigma(java.math.BigInteger phi)

σ_φ

predefines

void predefines()

produces the code for predefined list operators (:),(!!) and functions length and tail

calcdep

void calcdep(int f)

Recursively calculates which functions a function depends upon f may be recursively defined, but mutual recursion is not allowed

Parameters:

f - index of function

calcdeps

void calcdeps(int f)

Calculates which functions a function depends upon, using calcdep

Parameters:

f - index of function

fcompile

void fcompile()

compiles the functions defined in the plines edit,

funcround

java.math.BigInteger funcround(java.math.BigInteger fcode)

yisfx

java.math.BigInteger yisfx(java.lang.String fname)

actionPerformed

public void actionPerformed(java.awt.event.ActionEvent e)

responds to button press

Specified by:

actionPerformed in interface java.awt.event.ActionListener

num

java.math.BigInteger num(java.math.BigInteger x)

Encodes a number as an arithmetic expression

skipsps

void skipsps()

moves pos to the first non-whitespace character

getitem

void getitem()

Gets item from input text.

getword

void getword()

Requires a word, that is an identifier or reserved word

chkch

boolean chkch(char c)

Checks whether the current item is a single character matching c

chkchS

int chkchS(java.lang.String S)

Checks whether the current item is a single character in S.

Parameters:

S - characters considered

Returns:

The index of the character in S if found, otherwise -1

chkchv

void chkchv(char c)

requires the current item to be a single character matching c

Parameters:

c - the character to match

chktokv

void chktokv(int t)

Checks whether the current item is a 2 character token number t

unop

java.math.BigInteger unop(int op,
                          java.math.BigInteger x1)

Encodes the result of the unary operator

binop

java.math.BigInteger binop(java.math.BigInteger x1,
                           int op,
                           java.math.BigInteger x2)

Encodes the result of a binary operator

impp

java.math.BigInteger impp(java.math.BigInteger A,
                          java.math.BigInteger B)

#A ⇒ #B

expr10

Godel3.TExpr expr10()

Function calls, variables, numbers,[], (expr),duples

expr9

Godel3.TExpr expr9()

!! operator

mulop

int mulop()

#0, `div` #1, `mod` #2

expr7

Godel3.TExpr expr7()

, `div`, `mod`

expr6

Godel3.TExpr expr6()

+ and -

expr5

Godel3.TExpr expr5()

nott

java.math.BigInteger nott(java.math.BigInteger A)

Encode ¬#A

addcond

void addcond(java.math.BigInteger A)

Add a condition to the list

resconds

java.math.BigInteger resconds(int csb,
                              int esb,
                              int vsb)

∃ variables (∧ Conditions)

expr4

Godel3.TExpr expr4()

relational operators

expr3

Godel3.TExpr expr3()

&& operator

expr2

Godel3.TExpr expr2(int vareq)

if, case and let and || operator

chkIntv

void chkIntv()

Requires current item to be 'Integer' reserved word

getType

int getType()

Gets type descriptor. Type will be based on Integer

DefFn

void DefFn(java.lang.String name)

Deals with the definition part of a function (which must be present)

makesym

int makesym(int type)

Defines the current identifier to be a variable of a given type

Parameters:

type -

Returns:

int representation of variable

varb0

java.math.BigInteger varb0(int n)

Parameters:

n - - an int representation of an arithmetic variable

Returns:

the bitstream representation of the variable

varb

java.math.BigInteger varb(int n)

Parameters:

n - - an int representation of an arithmetic variable

Returns:

the bitstream representation of the variable with last bit 0 (signifying a variable)

J

java.math.BigInteger J(java.math.BigInteger t1,
                       java.math.BigInteger t2)

J is a 1 to 1 functio combining two integers into one

Parameters:

t1 - 1st term

t2 - 2nd term

Returns:

representation of (t1+t2)^2+t1+1

Jn

java.math.BigInteger Jn(int[] vs,
                        int n)

Combines n integer variables into one integer

Parameters:

vs - int representation of variables

n - number of variables

Returns:

values combined using J function

vform

java.math.BigInteger vform(java.math.BigInteger Term)

Creates (if needed) a variable equal to a given term

Parameters:

Term -

Returns:

int form of variable equal to Term

DoFun

java.math.BigInteger DoFun(int id)

Processes body of a function

Parameters:

id - function identifier

Returns:

code for function

chkResv

void chkResv(int i)

Ensures that current word is a given reserved word

Parameters:

i - Number of reserved word required

parse1

void parse1()

Parses program in strin