.BEGIN VERBATIM
.GROUP SKIP 20
				LEAP TUTORIAL


				 By Jim Low
.END
.EVERY HEADING(DRAFT,LEAP TUTORIAL,{DATE⎇)
.EVERY FOOTING(,{PAGE⎇,)
.PREFACE 0

.MACRO BEGSEC(CNT) ⊂ BEGIN
.SKIP 1
.VARIABLE TCNT
.TCNT←CNT
.NARROW CNT ⊃

.MACRO ENDSEC ⊂
.WIDEN TCNT
.INDENT1←INDENT2←0
.END⊃

.MACRO SAMESEC ⊂
.SKIP 1
.IF LINES < 10 THEN NEXT PAGE
.INDENT1←0⊃

.MACRO EXAMPLE ⊂SKIP 1
.ONCE CENTER⊃

.NEXT PAGE
I. INTRODUCTION
.SKIP 3
SAIL contains an associative data system called LEAP. It is
patterned after the LEAP system implemented at LINCOLN LABORATORY
by ROVNER and FELDMAN. Features contained in our LEAP but not in
the Lincoln LEAP include a data-type  called list, and "matching"
procedures to be described below.
.SKIP 1
This document is intended to serve as a companion volume to the
SAIL manual and hopefully will be easier to understand than the
manual as here we can afford expound more on the various
constructs and we also have the space to include more examples.
.SKIP 1
Other documents which may be of interest to the LEAP user include
LEAP.WRU[DOC,AIL], which is a general guide to the leap runtime
environment; LEAP.TXT[DOC,AIL], which is a detailed guide to the
LEAP parts of the SAIL compiler and the SAIL runtime system; and
of course the SAIL manual.
.NEXT PAGE
II. ITEMS
.SKIP 3
The basic entities which LEAP manipulates are called
"items". An item is similar in many respects to a LISP atom.
It optionally has a printname and a datum. A datum is a scalar
or an array of any SAIL data-type other than types "item" and
"itemvar". An itemvar is simply a variable whose values are
items.
.SKIP 1
As an example of an item we may consider the following
declaration.

.EXAMPLE
REAL ITEM RITEM;
.SKIP 1
This declares an item named RITEM whose datum is a
scalar real variable.
.SKIP 1
In addition to declarations of items at compile-time, we
may dynamically create new items by calling the function NEW.
This function may either have no arguments, (in which case the created
item has no datum); or it may have a single argument which is either
an expression or an array. This argument is copied and the copy
becomes the value of the datum of the new item. We may of course later
change the value of the datum or an element of the datum (if the
datum is an array) by using standard algolic assignments. The data-type
of the datum of the new item is the data-type of the argument to NEW. Thus 
NEW(1) would create a new integer item whose datum was initially
given the value 1.
.SKIP 1
Items may be assigned to itemvars by standard SAIL assignment
statements and assignment expressions.
.EXAMPLE
itmvr← itmexpr;
.SKIP 1
Items themselves are considered to be constants and thus may not appear
on the left hand side of an assignment statement or expression.

.NEXT PAGE
III. DATUMS
.SKIP 3
Associated with most items are datums which may be treated
as standard SAIL variables. To refer to the datum of an item we use
the operator DATUM.
.SKIP 1
.GROUP
.BEGIN
.NARROW 15
.VERBATIM
	Example:

		INTEGER ITEM II;
		INTEGER I;
	    L1: DATUM(II)←5;
	    L2:	I ← DATUM(II)+1;
.FILL ADJUST
.WIDEN 15 
.END
.APART
.SKIP 1
At L1 the datum of the item II is given the value "5". At L2, the
value of the datum of II is used in an arithmetic assignment statement
which would cause the variable I to receive the value 6.
.SKIP 1
Datum takes as its argument a typed item expression: Typed
item expressions include:
.BEGSEC(6)
.INDENT2← 3
1. Typed items and itemvars (declared with their type followed by
ITEM or ITEMVAR) as in:
.INDENT1←3
.BEGSEC(4)
.CRBREAK
INTEGER ITEM JJ;
INTEGER ARRAY ITEM X[1:5];
INTEGER ITEMVAR ARRAY Y[1:5];
INTEGER ARRAY ITEMVAR ARRAY Z[1:5];
INTEGER ARRAY ITEMVAR Q;
.CRSPACE
.ENDSEC
.SKIP 1
Note the distinctions between the later four declarations.
X is declared to be a single item whose datum is an integer
array containing five elements. Y is declared to be an array
of five itemvars, each of which is claimed to contain
an item whose datum is a scalar integer. Z is declared to be
an array of five itemvars whose values are claimed to be
items with datums which are integer arrays. Q is an itemvar which
supposedly contains an item whose datum in an integer array.
As is shown above, we do not specify the dimensions of the
the array which is the datum of an array itemvar. Thus for
example, each element of Z could contain items whose datums
were arrays of different dimensions. With declared array items
we must declare the dimension,  otherwise the
compiler would not know how much space to allocate for the array.
We place the dimensions of the array following the item name.
This is somewhat confusing as it appear that we have an
array of items rather than a single item whose datum is an array.
SAIL has solved this problem in a very arbitrary way by outlawing
declarations of arrays of items. One can get the effect of arrays
of items by declaring itemvar arrays and then assigning "NEW"
items to the individual elements.

.SAMESEC
2. Typed itemvar function calls:
.INDENT1←3
.EXAMPLE
	STRING ITEMVAR PROCEDURE SNEW(STRING X);
.EXAMPLE
	     RETURN(NEW(X));
.SKIP 1
Thus we may talk of DATUM(SNEW("anystring"))
.SAMESEC
3. Assignment expressions whose left hand side is a typed itemvar.
.INDENT2←0
.ENDSEC
.SKIP 3
The type of the datum variable is the type of its item expression.
Thus, the datum of an integer item expression is treated as an integer variable,
the datum of a real array item expression is treated as a real array and so forth.
.SKIP 1
NOTE: no check is actually made that the item is of the claimed type. Thus,
for  example, disastrous things may happen if one uses DATUM on a string itemvar
in which an integer item has been stored. The user should be careful
about storing typed items into different type itemvars. When in doubt about
the actual type of an item expression he should use the function TYPEIT to
verify that the item is of the required type. TYPEIT is a predeclared integer
function.
.NEXT PAGE
.EXAMPLE
INTEGER PROCEDURE TYPEIT(ITEMVAR X);
.SKIP 1
.GROUP
The values returned by TYPEIT are:
.SKIP 1
.BEGIN VERBATIM
 0 - deleted or never allocated     1 - item has no datum.
 2 - bracketed triple(no datum)     3 - string item
 4 - real item			    5 - integer item
 6 - set item			    7 - list item
 8 - procedure item		    9 - process item
10 - event-type item		   11 - context item
12 - refitm item		   13 - record!pointer item
23 - string array item             24 - real array item
25 - integer array item            26 - set array item
27 - list array item               31 - context array item
33 - record!pointer array item     37 - invalid type(error in LEAP)

.END
Those codes not mentioned (14-22,28-30,32,34-36) are also invalid and should be
considered erroneous.
.APART
.NEXT PAGE

IV. SETS
.SKIP 3
A set is an unordered collection of unique items. All set 
variables are initialized to PHI, the empty set consisting of no items.
Set variables receive values by assignment or by placing individual
items in them by PUT statements.
.SKIP 2
SET EXPRESSIONS:
.BEGSEC(5)
.INDENT2←3
1. Explicit Set -  A sequence of item expressions which make up
.INDENT1←3
the set surrounded by set brackets.

E. G.

a)  {item1,item2,item3⎇

b)  {item2,item1,item3⎇

c)  {item2,item2,item2,item3⎇
.SKIP 1
Note: Since sets are unordered and a given item may appear at most
once within a set, set expressions a,b,and c above all represent the
same set.
.SAMESEC 
2. PHI - the empty set.
.INDENT1←3
The set consisting of no elements at all is the empty set which may
be written as either

{⎇ or PHI
.SAMESEC
3. Set Union - written SET1 UNION SET2.
.INDENT1←3

The resultant set contains all items which are elements of either SET1
or SET2 or both. 

E.G.

{item1,item2⎇ UNION {item2,item3⎇ = {item1,item2,item3⎇

.SAMESEC
4. Set Intersection - written SET1 INTER SET2
.INDENT1←3

The resultant set contains all items which are elements of both SET1 and SET2.

E. G.

{item1,item2,item3⎇ INTER {item1,item2,item4⎇ = {item1,item2⎇
.SAMESEC
5. Set Subtraction - written SET1 - SET2
.INDENT1←3

The resultant set contains all items which are elements of SET1 but not
elements of SET2.

E. G.

{item1,item2,item3⎇ - {item2,item4,item5⎇ = {item1,item3⎇
.ENDSEC
.SKIP 2
.IF LINES < 10 THEN NEXT PAGE
PUT and REMOVE
.SKIP 2
.BEGSEC(5)
.INDENT2←3
1. To place a single item into a set variable we may use the PUT statement:
.INDENT1←3
.EXAMPLE
PUT itemexpr IN setvar;
.SKIP 1
This has the identical effect as:
.EXAMPLE
setvar ← setvar UNION {itemexpr⎇;
.SKIP 1
However, as the assignment causes the set to be copied, and the PUT doesn,'t
the PUT statement will take less time and space to execute.
.SAMESEC
2. To remove a single item from a set variable we may use the REMOVE statement
.INDENT1←3
.EXAMPLE
REMOVE itemexpr FROM setvar;
.SKIP 1
This has the same effect as:
.EXAMPLE
setvar ← setvar - {itemexpr⎇;
.SKIP 1
Again, as the REMOVE statement avoids copying the set, it is more efficient
than the equivalent assignment statement.
.ENDSEC
.SKIP 3
.NEXT PAGE
SET BOOLEANS
.SKIP 2
.BEGSEC(5)
.INDENT2←3
1. Set membership 
.INDENT1←3
.EXAMPLE
itemexpr IN setexpr
.SKIP 1
TRUE only if the item is an element of the set.
.SAMESEC
2. Set equality
.INDENT1←3
.EXAMPLE
setexpr1 = setexpr2
.SKIP 1
TRUE only if each item in setexpr1 is in setexpr2 and vice versa.
.SAMESEC
3. Set inequality
.INDENT1←3
.EXAMPLE
setexpr1 NEQ setexpr2
.SKIP 1
TRUE if setexpr1 or setexpr2 contains an item not found in the other.

Equivalent to
.EXAMPLE
NOT (setexpr1=setexpr2)
.SAMESEC
4. Proper containment
.INDENT1←3
.EXAMPLE
setexpr1 < setexpr2    or   setexpr2 > setexpr1
.SKIP 1
TRUE if every item in setexpr1 is also in setexpr2, but setexpr1 NEQ setexpr2
Equivalent to:
((setexpr1 INTER setexpr2) = setexpr1) AND (setexpr1 NEQ setexpr2)
.SAMESEC
5. Containment
.INDENT1←3
.EXAMPLE
setexpr1 LEQ setexpr2    or setexpr2 GEQ setexpr1
.SKIP 1
TRUE if every item in setexpr1 in also in setexpr2.
.BREAK
Equivalent to 
.EXAMPLE
(setexpr1 = setexpr2) OR (setexpr1 < setexpr2)
.ENDSEC
.NEXT PAGE
COP, LOP and LENGTH
.SKIP 2
.BEGSEC(5)
.INDENT2←3

1. COP (setexpr) - returns an item which is an element of the set. As sets
.INDENT1←3
are unordered you do not know which element of the set will be returned
It is useful most often when we know the set has but a single element
in which case it will return that item.
.SAMESEC

2. LOP (setvar) - same as COP except argument must be a set variable and
.INDENT1←3
the item returned is also removed from that set.
It is logically equivalent to the  following procedure:
.BEGIN VERBATIM

	ITEMVAR PROCEDURE LOP(REFERENCE SET Y);
	BEGIN ITEMVAR Q;
		Q ← COP(Y);
		REMOVE Q FROM Y;
		RETURN(Q)
	END;

.END
LOP is often valuable if we wish some operation to be performed on each
item of a set. Consider the example below where we wish the datums
of all integer items contained in a set SETI to be incremented by one.
Assume that we have declared IITMVR to be an integer itemvar and TSET
to be a set variable which we will use as temporaries.
.BEGIN VERBATIM

	TSET ← SETI; "Copy set of interest into temporary"
	WHILE (TSET NEQ PHI) DO "loop while TSET has elements"
	BEGIN IITMVR ← LOP(TSET); "remove an element from TSET"
	   IF TYPEIT(IITMVR) = 5 THEN "check if really integer"
		 DATUM(IITMVR) ← DATUM(IITMVR) + 1;
        END;

.END
NOTE: LOP is compiled into code other than a straightforward procedure
call and thus like many other functionals cannot appear as a statement
but only as part of an expression. Thus if we just wanted to remove
an arbitrary set element and throw if away we would have to say:
.EXAMPLE
DMY ← LOP(SETVAR);
.SKIP 1
where DMY is an itemvar whose contents we do not care about, rather than the simpler:
.EXAMPLE
LOP(SETVAR);
.SAMESEC
3. LENGTH(setexpr) - returns the number of items within a set.
.INDENT1←3
Logically equivalent to following procedure:
.BEGIN VERBATIM

	INTEGER PROCEDURE LENGTH(SET Y);
	BEGIN "LENGTH"
	   INTEGER COUNT; ITEMVAR DUMMY;
	   COUNT ← 0;
	   WHILE (Y NEQ PHI) DO
	      BEGIN 
		 DUMMY ← LOP(Y);"remove an element from the set"
		 COUNT ← COUNT +1; "step count of elements"
	      END;
	   RETURN(COUNT);
	END "LENGTH";

.END

The actual implementation of LENGTH is much more efficient than the above
procedure (usually taking only two machine instructions). The most efficient
way of determining if a
given set is empty is to see if the LENGTH of that set is zero. This
is much faster that comparing the set and PHI for equality.
.ENDSEC
.NEXT PAGE

V. LISTS
.SKIP 2
A list is an ordered sequence of items (not necessarily distinct).
List variables are initialized to NIL the empty list containing
no items. List variables receive values by assignment or by
placing individual items in them by PUT statements.
.SKIP 2
LIST Expressions
.SKIP 1
.BEGSEC(5)
.INDENT2←3
1. Explicit List - written as the sequence of items (separated by commas)
.INDENT1←3
all surrounded by list brackets "{{ ⎇⎇".
.SKIP 1 
a. {{ item1, item2, item3⎇⎇

b. {{ item2, item1, item3⎇⎇

c. {{ item2, item2, item1, item 3⎇⎇
.SKIP 1
Note that since the order and number of times each item appears is
important with lists, the expressions a, b, and c above all
represent different list expressions.
.SKIP 1
NOTE: we may represent NIL, the empty list, by {{ ⎇⎇

.SAMESEC
2. Concatenation - written  list1 & list2.
.INDENT1←3
This forms a new list containing all the items in list1 followed by
all the items in list2.

E. G.

.BEGIN CENTER
.SKIP 1
{{item1, item2, item3,⎇⎇ & {{item3, item4, item5 ⎇⎇
=
{{item1, item2, item3, item3, item4, item5⎇⎇
.SKIP 2
{{item1, item2⎇⎇ & {{item 4, item4, item5⎇⎇
=
{{item1, item2, item4, item4, item5⎇⎇
.END
.SAMESEC
3. Sublists - There are two forms of sublist expressions
.INDENT1← 3
.INDENT2←6
.SKIP 1
a. listexpr [i1 TO i2] - the first integer expression (i1) stands for
the position of the first element to be taken and the second (i2)
stands for the position of the last element to be taken.
.INDENT1←6

E. G.
.SKIP 1
.ONCE COMPACT
{{itema,itemb,itemc,itemd⎇⎇[2 TO 3]={{itemb,itemc⎇⎇
.SKIP 1
.ONCE COMPACT
{{itema,itemb,itemc,itemd⎇⎇[3 TO 3]={{itemc⎇⎇
.SKIP 1
.INDENT1←3
b. listexpr [i1 FOR i2] - the first integer expression (i1) stands for
the position of the first element to be taken and the second (i2)
stands for the number of elements to be taken.
.INDENT1←6
E. G.
.SKIP 1
.ONCE COMPACT
{{itema,itemb,itemc,itemd⎇⎇[2 FOR 3]={{itemb,itemc,itemd⎇⎇
.SKIP 1
.ONCE COMPACT
{{itema,itemb,itemc,itemd⎇⎇[3 FOR 1]={{itemc⎇⎇
.SKIP 1
.ONCE COMPACT
{{itema,itemb,itemc,itemd⎇⎇[3 FOR 0]={{ ⎇⎇= NIL
.ENDSEC
.NEXT PAGE
LIST Selectors
.SKIP 1
It is often useful to think of a list as an untyped itemvar array with
a single dimension with lower bound 1 and upper bound variable.
.BEGSEC(5)
.INDENT2←3
1. Expression selector
.INDENT1←3
.SKIP 1
listexpr [i1] - returns the item which is the i1 element of the
list. If i1 is less than 0 or greater than the number of elements
of the list an error is signaled.

E. G.
.EXAMPLE
{{itema, itemb, itemc⎇⎇ [1] = itema
.EXAMPLE
{{itemb, itemc, itemd⎇⎇ [2] = itemc
.SKIP 1
Note the difference between  listexpr[i1] and listexpr[i1 FOR 1].
The former returns an item and the later returns a list containing
a single item.
.SAMESEC
2. Replacement selector
.INDENT1←3
.EXAMPLE
listvar[i1] ← itemexpr;
.SKIP 1
This removes the i1 element of the list and replaces it with the itemexpr
i1 must be between 1 and the number of elements in the list + 1.

E. G.
.BEGIN VERBATIM

   LIST1 ← {{ITEM1⎇⎇;
   LIST1[1] ← ITEM2; "NOW LIST1 = {{ITEM2⎇⎇"
   LIST1[2] ← ITEM3; "NOW LIST1 = {{ITEM2,ITEM3⎇⎇"
   LIST1[1] ← LIST1[2]; "NOW LIST1 = {{ITEM3,ITEM3⎇⎇"
.END
.ENDSEC
.NEXT PAGE
LIST BOOLEANS
.BEGIN INDENT2← 5
.SKIP 4
itm IN listexpr - TRUE if the itm is an element of the listexpr
.SKIP 3
listexpr1 = listexpr2 - TRUE if the lists contain
the same items in the same order.
.END
.SKIP 4
LIST FUNCTIONS

.BEGIN
.INDENT2 ← 5
LENGTH(listexpr) - this returns the current length of the list.
.SKIP 1

COP(listexpr) - this is identical in semantics
	with the expression  "listexpr[1]"
.SKIP 1
LOP(listvar) - this returns the first item in the list 
	variable and as a side effect removes the first element
	from the list variable. It is logically equivalent to the
	following procedure.

.BEGIN VERBATIM
	ITEMVAR PROCEDURE LOP(REFERENCE LIST ARG);
	BEGIN "LOP"
		ITEMVAR RESULT;
		RESULT ← ARG[1];
		ARG ← ARG[2 TO LENGTH(ARG)];
		RETURN(RESULT);
	END "LOP";

.END
.SKIP 1
LISTX(listexpr,itemexpr,intexpr) - this integer function
returns 0 if the "itemexpr" does not appear in the
"listexpr" at least "intexpr" different times.
Otherwise it returns the index of the "intexpr" occurence
of the "itemexpr" within the "listexpr".
Thus,
.EXAMPLE
LISTX({{FOO,BAZ,GARP,BAZ,BAZ⎇⎇,BAZ,2)  is 4.
.EXAMPLE
LISTX({{FOO,BAZ,GARP,BAZ,BAZ⎇⎇,GARP,2) IS 0.
.END
.NEXT PAGE
LIST PUT AND REMOVE STATEMENTS
.SKIP 2
When we insert items into a list we need to specify in some way
the position within the list where the item is to be placed.
We do this by specifying either an index position, or
item  BEFORE or AFTER which the item is to be inserted.
.SKIP 2

.BEGIN INDENT2←5
PUT itm1 IN  listvar AFTER n - will insert "itm1" after the "nth"
element of the "listvar". Thus to insert an item
into the list after every element in the list we would
execute:
.EXAMPLE
PUT itm1 IN  listvar AFTER LENGTH(listvar);
.skip 1
To insert the item at the head of the list we would use the index
0:
.EXAMPLE
PUT itm1 IN listvar AFTER  0;
.skip 1

If the index is less than 0 or greater than the length of the
list variable then an error message is generated.

.skip 3

PUT itm IN listvar BEFORE n - this is identical in semantics
	with:
.EXAMPLE
PUT itm IN listvar AFTER N-1;
.SKIP 3
PUT itm1 IN listvar  AFTER itm2;-- this statement searches
for the first occurrence of itm2 within the listvar
and inserts itm1 into the list following itm2. If
itm2 is not an element of the list then itm1 is inserted
at the end of the list. It is equivalent to :
.EXAMPLE
PUT itm1 IN listvar AFTER (IF LISTX(listvar,itm2,1) NEQ 0 THEN
.EXAMPLE
LISTX(listvar,itm2,1) ELSE LENGTH(listvar);
.skip 4
PUT itm1 IN listvar BEFORE itm2 - this statement 
searches the listvar for the first occurence of itm2 and
then inserts itm1 ahead of itm2 in the list.
It is logically equivalent to:
.EXAMPLE
PUT itm1 IN listvar BEFORE (IF LISTX(listvar,itm2,1) NEQ 0 THEN
.EXAMPLE
LISTX(listvar,itm2,1) ELSE 1;

.SKIP 5
REMOVE intexpr FROM listvar -- This removes the "intexpr" element
from the listvar. It is equivalent to:
.EXAMPLE
listvar ← listvar[0 to intexpr-1] &
.EXAMPLE
listvar[intexpr+1 to LENGTH(listvar)];
.skip 5
REMOVE itm FROM listvar - This removes the first 
occurrence of  "itm" from the list variable. It is equivalent
to:
.EXAMPLE
IF itm IN listvar THEN REMOVE LISTX(listvar,itm,1) FROM listvar;
.SKIP 5
REMOVE ALL itm FROM listvar - This removes all instances of
"itm"  from tthe listvar.
It is equivalent to:
.EXAMPLE
WHILE itm IN listvar DO REMOVE itm FROM  listvar;
.end
.next page
VI. ASSOCIATIONS
.SKIP 3
The associative power of LEAP comes from the use of associations,
also called triples or associative triples. A triple is a 3-tuple of items.
We write a triple as:
.EXAMPLE
A XOR O EQV V
.SKIP 1
where A, O, and V are items or item expressions. We call the first component
of the triple (A above) the "attribute"; the second component (O above), the
"object"; and the third component (V above), the "value". Triples are kept
in the "associative store". Triples are inserted into the associative store
by MAKE statements and removed from the associative store by ERASE statements.
.SKIP 3
MAKE
.SKIP 2
A MAKE statement is of the form:
.EXAMPLE
MAKE itmexpr1 XOR itmexpr2 EQV itemexpr3;
.SKIP 1
If the triple already exists in the associative store, the statement
does nothing, otherwise the triple is inserted into the store.
.SKIP 4
ERASE
.SKIP 2
To remove a triple from the associative store we execute an ERASE 
statement:
.EXAMPLE
ERASE itmexpr1 XOR itmexpr2 EQV itemexpr3;
.SKIP 1
If the triple is not in the associative store, the statement does nothing,
otherwise the triple is removed from the associative store. We often wish
to erase all the triples which have specific items as 1 or 2 of their components
but we don't care about the remaining components. To do this we may
use the token ANY to stand for the unspecified components.
.SKIP 1
E. G. to erase all associations with item2 as their object we could use:
.EXAMPLE
ERASE ANY XOR item2 EQV ANY;
.SKIP 1
to erase all associations with item1 as their attribute and item2 as 
their object we would use:
.EXAMPLE
ERASE item1 XOR item2 EQV ANY;
.SKIP 1
ANY may be used in 0, 1, 2, or all 3 positions in the triple. Thus,
.EXAMPLE
ERASE ANY XOR ANY EQV ANY;
.SKIP 1
would get rid of all associations in the UNIVERSE.
(Currently erases or searches with 3 ANY's are not implemented).
.NEXT PAGE
ASSOCIATIVE BOOLEANS
.SKIP 2
We may determine if a given triple exists by using the
boolean expression:
.EXAMPLE
itmexp1 XOR itmexp2 EQV itmexp3
.SKIP 1
which will evaluate to TRUE if the triple containing the items
exists in the associative store. As with ERASE 1 or 2 of the components
may be ANY. Thus,
.EXAMPLE
ANY XOR ANY EQV item1
.SKIP 1
will yield the value TRUE if any triple in the associative store contains
item1 as its value component.
.SKIP 4
BINDING ASSOCIATIVE BOOLEANS
.SKIP 2
Another form of the associative boolean takes one or more itemvars
(prefaced by the operator BIND) in place of corresponding item expressions.
The boolean value of this
expression is the same as that of the associative boolean formed
by replacing the "BIND ITEMVAR" terms with ANY. thus the
expression:
.example
FATHER XOR JOHN EQV BIND itv
.skip 1
would have the same truth value as the boolean expression:
.example
FATHER XOR JOHN EQV ANY
.skip 1
The binding boolean though, has an additional side effect if
the value returned is TRUE. In that case it assigns to the itemvar
(prefaced by BIND) the value of an item which makes the
associative boolean TRUE. For example above, the interpreter would
search to see if there was any triple in the associative store,
which had both FATHER as its attribute component and JOHN as its object 
component. If it found one, the interpreter would then assign the item in
the value component to the itemvar "itv".
.skip 1

Note that if there is more than one triple which satisfies the associative 
boolean, which one is selected is undefined. If there is no triple which
satisfies the boolean then the boolean returns FALSE and the value of the
BIND itemvar remains unchanged. Thus if we had a group of associations:
with attributes, the items CAR and CDR (representing a LISP like structure)
we could find the last cell in the CDR direction of the LISP-list pointed
to by first, using the very simple program:
.BEGIN VERBATIM

	LAST ← FIRST ;
	WHILE (CDR XOR LAST EQV BIND LAST ) DO;

.end
.SKIP 1
Note that each time the associative boolean is executed, the current value
of the itemvar LAST is used as the object component, and if successful
the value of LAST is changed to become the next element in the CDR direction.
.NEXT page
DERIVED SETS
.SKIP 2
In order to use the associative nature of triples we must have
ways of finding triples which have certain specified components. One way
we have discussed above is the use of binding associative booleans.
Another 
is to use derived sets. The third, FOREACH statements, will be discussed
later.
.SKIP 1
There are three forms of derived sets now implemented: the (') 
derived set, the ( XOR ) derived set, and the ( EQV ) derived set.
.EXAMPLE
itmexp1 ' itmexp2
.SKIP 1
produces the set of all items X, such that
.EXAMPLE
itmexp1 XOR X EQV itmexp2
.SKIP 1
is a triple currently in the associative store.
.EXAMPLE
itmexp1 XOR itmexp2
.SKIP 1
produces the set of all items Y such that,
.EXAMPLE
itmexp1 XOR itmexp2 EQV Y
.SKIP 1
is a triple in the associative store.
.EXAMPLE
itmexp1 EQV itmexp2 
.SKIP 1
produces the set of all items Y such that.
.EXAMPLE	
Y XOR itmexp1 EQV itmexp2
.SKIP 1
is a triple in the associative store
.SKIP 1
One or both of the item expressions may be the token ANY. Again this
means that we do not care about the value of that component. Thus,
.EXAMPLE
itmexp1 XOR ANY
.SKIP 1
will search the associative store for all associations which have itmexp1 as
their attribute component, and will return the set of value components of 
such associations.
.NEXT PAGE

EXAMPLE - DERIVED SETS
.SKIP 2
Let us represent a family tree using associations. We will have
the declared item PARENT and the sets MALE and FEMALE, as well as
items representing members of the family: JOE, TIM, TED, JOYCE, JANET,
ALICE, and HARRIET.
.SKIP 1
The familial relationships are represented by a the following tree.
.BEGIN VERBATIM

		TOM          ALICE             JOE        JAN
		 |             |                |          |
		 ---------------		------------
			|			      |
		  -------------			      |
		  |	      |			      |
		JOYCE	     TED		     TIM
		  |				      |
		  -------------------------------------
				     |
				  HARRIET

.END

Thus, the parents of HARRIET are JOYCE and TIM; the parents of JOYCE and TED
are TOM and ALICE and so forth.
.SKIP 1
We can represent this tree by making the following associations:
.SKIP 1
.BEGIN VERBATIM
		MAKE PARENT XOR HARRIET EQV JOYCE;
		MAKE PARENT XOR HARRIET EQV TIM;

		MAKE PARENT XOR JOYCE EQV TOM;
		MAKE PARENT XOR JOYCE EQV ALICE;
	
		MAKE PARENT XOR TED EQV ALICE;
		MAKE PARENT XOR TED EQV TOM;

		MAKE PARENT XOR TIM EQV JOE;
		MAKE PARENT XOR TIM EQV JAN;

.END
To keep track of the sexes of the various people we have the two
sets MALE and FEMALE.
.SKIP 1
.BEGIN VERBATIM
		MALE ← {TIM,TED,TOM,JOE⎇;
		FEMALE ← {JAN,JOYCE,ALICE⎇;
.END
.SKIP 1
NOTE: The above is merely one possible way we might represent the family tree.
For example instead of the MALE and FEMALE sets, we might have associations
of the form: SEX XOR person EQV MALE, where MALE is now an item. One of the
interesting difficulties in using LEAP is deciding how to represent a given
system of data as LEAP will often allow many different ways of representing
the same information. Some of the tradeoffs between the different representations
will be discussed later.
.SKIP 2
Now to use the structure we have built. Let us say that we wished to find the
parents of Harriet. We may easily do this by use of a derived set.
.SKIP 1
.BEGIN VERBATIM
		HARRIET!PARENTS ← PARENTS XOR HARRIET;
.END
.SKIP 1
where HARRIET!PARENTS has been declared to be a set variable.
.SKIP 1
To find Harriet's brothers is a little more complicated.
.BEGIN VERBATIM
	"find one parent"
	PARENT!ITMVR ← COP(PARENTS XOR HARRIET);
	    Comment the above could be replaced by 
	    the binding associative boolean.
	    IF NOT (PARENTS XOR HARRIET EQV BIND PARENT!ITMVR) THEN
	    	PRINT("HARRIET IS AN ANDROID")
	;
	"set of brothers,sisters"
	SIBLING!SET ← PARENT ' PARENT!ITMVR;

	"brother is a male sibling"
	BROTHER!SET ← SIBLING!SET INTER MALES;
.END
.SKIP 1
The above example illustrates the use of associations as binary relations between
items, in this case the relation "parent of". Often we wish to associate
several different pieces of data with an item. To do this we may declare items
which will be used to name the data and then allocate items which will contain
the corresponding data for each item. For example we may wish to record such
various attributes of a person such as weight, height, nickname. To do this
we will have items WEIGHT, HEIGHT, and NICKNAME which will be used to name the
attributes. We will allocate items whose datums are the corresponding values.
E.G.
.BEGIN VERBATIM

		MAKE WEIGHT XOR JOE EQV NEW(165);
		MAKE HEIGHT XOR JOE EQV NEW (70);
		MAKE NICKNAME XOR JOE EQV NEW("JOEY");

.END
Then to find the value of an attribute such as weight we would use the
expression:
.BEGIN VERBATIM
		DATUM(INT!ITMVR ← COP(WEIGHT XOR JOE))
.END

Remember that the assignment of the item to the integer itmvr is required
so that the compiler can tell what the data type of the datum is.
Again we could use a binding associative boolean instead of a COP of
a derived set. The binding boolean generates more efficient code, but has
the disadvantage of returning a boolean value rather than an item value
as does COP. However since COP will stop your program if you apply it
to an empty set, it is well worth the syntactic bother to use the associative
boolean.
.SKIP 1

FOREACH STATEMENTS
.skip 4

By using these operations and set variables we
have sufficient power to do any search on the associative data 
base. However one soon realizes that they are very
inconvenient to use in all but the most simple cases. Therefore
another technique is provided called FOREACH statements.
.SKIP 1
A FOREACH statement is similar to a FOR statement
in that it causes the iteration of a given SAIL statement to be
performed with a control variable receiving various values
for each iteration. These values are obtained by searching the
associative data base or enumerating the members of a set of items.
.SKIP 1
The most simple FOREACH statement has a single "local" itemvar
and a single "associative context". A local itemvar serves the
same purpose as the loop variable in a FOR statement. With each
iteration it will receive an item value and a SAIL statement will
be executed. A simple example of a FOR statement is:
.EXAMPLE
	FOREACH X | BROTHER XOR BOY1 EQV X DO
.ONCE CENTER
		<stmt>
.SKIP 1
This statement is equivalent to the following:
.SKIP 1
.BEGIN VERBATIM

	tlist← BROTHER XOR BOY;
	FOR j ← 1 step 1 until LENGTH(tlist) DO
	BEGIN  X←tlist[j];
		<stmt>
	END;

.END

.SKIP 1

ANY and BINDIT
.skip 1
There are two special "items" which may not be arguments to a make statement
(and thus may not be components of any association in the associative data
base). These are ANY and BINDIT. These items may appear anywhere else
an item might be legal, such as within sets, itemvars and lists.

We have mentioned ANY earlier. It essentially represents "don't care" when
we are doing pattern matching on the associative store. Thus
.example
FOREACH x | x XOR ANY EQV B DO

is to be iterated once for every distinct X which appears in associations with
B as the value component.
.skip 1
BINDIT is used to conditionally control ? searches. It also has importance
in MATCHING PROCEDURES  which will be discussed later.

There are special forms of the BINDING BOOLEANS and FOREACH statements,
are affected when an itemvar to be bound contains BINDIT.

The BINDING BOOLEAN B XOR C EQV ? x is identical in effect with the expression
.BEGIN CENTER
(IF x = BINDIT THEN (B XOR C EQV BIND x) 
ELSE (B XOR C EQV x))
.END
.skip 1
That is the value of  x is used if not equal to BINDIT and the itemvar x
is to be bound  if the value of x is equal to BINDIT.

.example
FOREACH ?x,y | A XOR x EQV y DO <stmt>
.example
is similarly equivalent to
.skip 1
.begin verbatim
		IF X=BINDIT THEN 
			FOREACH x,y | A XOR x EQV y DO <stmt>
		   else FOREACH y | A XOR x EQV y DO <stmt>
.end
.skip 1
Note that the FOREACH in the else part of the statement does not have "x"
in its binding list and thus x is considered to have a value. The reverse is
true in the THEN part of the statement.