de.cm.frw.core.fun.impl
Class FP

java.lang.Object
  de.cm.frw.core.fun.impl.FP

public class FP
extends java.lang.Object

Implementation of the FP system described in section 11 of "Can Programming be liberated from the Von Neumann Style" http://www.stanford.edu/class/cs242/readings/backus.pdf Definitions for functions and functional forms are quoted from there using the papers notation as far as possible ... Conventions:

• we use null for bottom
• we use Collection when accessing sequences
• we use Bag when creating new sequences ...
• as a rule FP functions don't throw InvalidArgumentsException, but rather return bottom (i.e. null) to indicate arguments for which a function result would be undefined (all FP functions are bottom preserving)

Author:

cm

sel

public static final Function sel

sel creates a numeric selector function (counting from one)

For any positive integer s the function created is:

   (sel:s):x = x == <x1, ..., xn> && n >= s --> xs ; 
               null
 

rsel

public static final Function rsel

rsel creates a numeric selector function (counting from one)

For any positive integer s the function created is:

   (sel:s):x = x == <x1, ..., xn> && n >= s --> xn-s ; 
               null
 

tail

public static final Function tail

tail produces the tail of a sequence x, i.e. the sequence x without its first element:

 tail:x = x == <x1> --> <>;
          x == <x1 ... xn> & n >= 2 --> <x2 ... xn>;
          null
 

rtail

public static final Function rtail

rtail produces the tail of a sequence x, i.e. the sequence x without its last element:

 rtail:x = x == <x1> --> <>;
           x == <x1 ... xn> & n >= 2 --> <x1 ... xn-1>;
           null
 

id

public static final Function id

Identity:

 id x = x
 

atom

public static final Function atom

atom tests if the given argument is an atom (i.e. not a sequence)

 atom:x = x == <x1 ... xn> --> F; 
          x == <> --> F; 
          x == null --> null;    // bottom preserving 
          T
 

eq

public static final Function eq

Equals:

 eq:x = x == <y,z> && y == z --> T;
        x == <y,z> && y != z --> F;
        null
 

nul

public static final Function nul

Null: function to test if a given object is the empty sequence

 Def nul : x = x == <> --> T;
               x != null --> F;
               null
 

reverse

public static final Function reverse

Reverse

 reverse:x = x == <> --> <>
             x == <x1 .. xn> --> <xn ... x1>
             null
 

distl

public static final Function distl

Distribute left

 distl:x = x == <y, <>> --> <>
           x == <y, <x1 .. xn>> --> <<y,x1> ..  <y,xn>>
           null
 

distr

public static final Function distr

Distribute right

 distl:x = x == <<>, z> --> <>
           x == <<x1 .. xn>, z> --> <<x1,z> ..  <xn,z>>
           null
 

length

public static final Function length

Length

 length:x = x == <x1 ... xn> -->n
            x == <> --> 0
            null
 

add

public static final Function add

substract

public static final Function substract

multiply

public static final Function multiply

divide

public static final Function divide

and

public static final Function and

or

public static final Function or

not

public static final Function not

rotl

public static final Function rotl

rotr

public static final Function rotr

constant

public static final Function constant

Returns a constant function with given value:

 const(x):y = y == null --> null; 
              otherwise --> x
 

compose

public static final Function compose

Returns the composition of functions f and g:

 (f.g):x = f : ( g : x )
 

construct

public static final Function construct

Combines functions in given collection into a function producing a sequence of results f_i(x).

 [f1 ... fn]:x = <f1 :x ... fn:x>
 

cond

public static final Function cond

conditional function application

 (p --> f, g):x = (p:x) --> f:x; 
                  !(p:x) --> g:x; 
                  null
 

insert

public static final Function insert

Insert a binary function into a sequence.

 /f:x = x == <x1> --> x1;
        x == <x1 .. xn> & n>=2 --> f:< x1, /f<x2 .. xn> >;
        null 
 

alpha

public static final Function alpha

Apply to all elements of a sequence.

 alpha f:x = x == <> --> <>;
             x == <x1 .. xn> --> x == <f:x1 .. f:xn>
             null
 

transpose

public static final Function transpose

apndl

public static final Function apndl

Append left

 appendl:x = x == <y, <>> --> <y>
             x == <y, <x1 .. xn>> --> <y, x1 ... xn>
             null
 

apndr

public static final Function apndr

Append left

 appendl:x = x == <<>, z> --> <z>
             x == <<x1 .. xn>, z> --> <x1 ... xn, z>
             null
 

bu

public static final Function bu

Binary to unary

 (bu f x):x = f:<x, y>
 

whyle

public static final Function whyle

Build a while loop from a given predicate p and a function f:

 (while p f):x = p:x == T --> (while p f):(f:x);
                 p:x == F --> x;
                 null
 

Note:Cannot have the name while in JAVA ; while the definition is recursive the implementation uses a while loop to avoid stack build up.

FP

public FP()

sel

public static Function sel(int s)
                    throws Function.InvalidArguments

Method to simplify using sel

Parameters:

s - a positive integer (> 0)

Returns:

the selector function for s

Throws:

Function.InvalidArguments

rsel

public static Function rsel(int s)
                     throws Function.InvalidArguments

Method to simplify using rsel

Parameters:

s - a positive integer (> 0)

Returns:

the right selector function for s

Throws:

Function.InvalidArguments

tail

public static java.util.Collection tail(java.lang.Object x)
                                 throws Function.InvalidArguments

Method to simplify using tail

Parameters:

x - an object

Returns:

a collection containing all but the 1st element of x, if x is a non-empty collection, otherwise null

Throws:

Function.InvalidArguments

rtail

public static java.util.Collection rtail(java.lang.Object x)
                                  throws Function.InvalidArguments

Method to simplify using rtail

Parameters:

x - an object

Returns:

a collection containing all but the last element of x, if x is a non-empty collection, otherwise null

Throws:

Function.InvalidArguments

atom

public static boolean atom(java.lang.Object x)
                    throws Function.InvalidArguments

Method to simplify the use of atom

Parameters:

x - object to test

Returns:

true if x is an atom and not null; false otherwise

Throws:

Function.InvalidArguments

equals

public static boolean equals(java.lang.Object y,
                             java.lang.Object z)
                      throws Function.InvalidArguments

Method to simplify the use of eq

Parameters:

y - object to test for equality with z

z - object to test for equality with y

Returns:

true, if y == z, false otherwise

Throws:

Function.InvalidArguments

nul

public static boolean nul(java.lang.Object x)
                   throws Function.InvalidArguments

Method to simplify the use of nul

Parameters:

x - object to test

Returns:

true, if x is an empty sequence, false otherwise

Throws:

Function.InvalidArguments

compose

public static Function compose(Function f,
                               Function g)
                        throws Function.InvalidArguments

Throws:

Function.InvalidArguments

whyle

public static Function whyle(Predicate p,
                             Function f)
                      throws Function.InvalidArguments

Throws:

Function.InvalidArguments