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An Introduction to ISETL Version 2.0 Gary Marc Levin Clarkson University Dept of Math and Computer Science Potsdam, NY 13676 (315) 268--2384 Bitnet: gary@clutx Internet: gary@clutx.clarkson.edu October 3, 1989 Abstract ISETL is an interactive implementation of SETL1, a programming language built around mathematical notation and objects, primarily sets and functions. It contains the usual collection of statements common to procedural languages, but a richer set of expressions. The objects of ISETL include: integers, floating point numbers, funcs (sub-programs), strings, sets, and tuples (finite anyumixture ofhISETLmobjects,bnested totarbitraryldepth.ay contain This introduction is intended for people who have had no previous experience with ISETL, but who are reasonably comfortable with learning a new programming language. Few examples are given here, but many examples are distributed with the software. This documentation is a useful supplement to Learning Discrete Mathematics with ISETL, a discrete math text written by Nancy Baxter, Ed Dubinsky, and Gary Levin, from Springer-Verlag. That text uses ISETL as a tool for teaching discrete mathematics. Copyright 1987, 1988, 1989. Gary Levin. Clarkson University. copied,nsubject toe theorestrictionothatritmnotbebersold for profit. (This would permit bulk copying and sale at cost.) The software is offered as-is, but we will attempt to correct errors in our code. aretderived fromsthenInteractiveeLineomEditor, whichwwas released with the following copyright restrictions. COPYRIGHT 1988 Evans & SuSaltlLakeCCity,eUtahrporation ---------------------------Rights Reserved. 1SETL was developed at the Courant Institute, by Schwartz. See Schwartz, J.T., et al. Programming with sets: An introduction to SETL. Springer-Verlag, 1986. 1 THE INFORMATION IN THIS SOFTWARE IS SUBJECT TO CHANGE WITHOUT NOTICE AND SHOULD NOT BE CONSTRUED AS A COMMITMENT BY EVANS & SUTHERLAND. EVANS & SUTHERLAND IFKETHEO SOFTWARETAISONMODIFIED TIN SAITMANNERY CREATING DERIVATIVEFCOPYRIGHTURIGHTS, APPROPRIATELILEGENDSSMAYSBE PLACEDTONXTHESSDERIVATIVEDWORKRAINYADDITION TO THAT SET PermissionEto use, copy, modify, and distribute this withoutefeenis iherebyugranted,nprovidednthaturtheeabove copyright notice appear in all copies and that both the copyright notice and this permission notice appear in supporting documentation, and that the name of Evans pertainingndtonodistributionn ofdvtheissoftwarepuwithout specific, written prior permission. Written by: Robert C. Pendleton Evans & Sutherland, Interactive Systems Division, Salt Lake City, Utah. Modified for ISETL by Gary Levin 2 CONTENTS Contents 1Running ISETL 4 2Characters, Keywords, and Identifiers 6 2.1Character Set : :: :: :: :: :: :: ::: :: :: :: :: :: :: :: : 6 2.2Keywords: :: :: :: :: :: :: :: :: ::: :: :: :: :: :: :: :: : 6 2.3Identifiers: :: :: :: :: :: :: :: ::: :: :: :: :: :: :: :: : 7 3Simple Data Types 7 3.1Integers: :: :: :: :: :: :: :: :: ::: :: :: :: :: :: :: :: : 7 3.2Floating_Point Numbers :: :: :: ::: :: :: :: :: :: :: :: : 7 3.3Booleans: :: :: :: :: :: :: :: :: ::: :: :: :: :: :: :: :: : 8 3.4Strings : :: :: :: :: :: :: :: :: ::: :: :: :: :: :: :: :: : 8 3.5Atoms: :: :: :: :: :: :: :: :: :: ::: :: :: :: :: :: :: :: : 9 3.6Files: :: :: :: :: :: :: :: :: :: ::: :: :: :: :: :: :: :: : 9 3.7Undefined :: :: :: :: :: :: :: :: ::: :: :: :: :: :: :: :: :10 4Compound Data Types 10 4.1Sets : :: :: :: :: :: :: :: :: :: ::: :: :: :: :: :: :: :: :10 4.2Tuples :: :: :: :: :: :: :: :: :: ::: :: :: :: :: :: :: :: :11 4.3Maps : :: :: :: :: :: :: :: :: :: ::: :: :: :: :: :: :: :: :12 5Funcs 12 6The ISETL Grammar --- Annotated 16 6.1Terminology: :: :: :: :: :: :: :: ::: :: :: :: :: :: :: :: :16 6.2Input at the Prompt : :: :: :: :: ::: :: :: :: :: :: :: :: :17 6.3Program : :: :: :: :: :: :: :: :: ::: :: :: :: :: :: :: :: :17 6.4Statements : :: :: :: :: :: :: :: ::: :: :: :: :: :: :: :: :17 6.5Iterators :: :: :: :: :: :: :: :: ::: :: :: :: :: :: :: :: :23 6.6Formers : :: :: :: :: :: :: :: :: ::: :: :: :: :: :: :: :: :25 6.7Selectors :: :: :: :: :: :: :: :: ::: :: :: :: :: :: :: :: :25 6.8Left Hand Sides :: :: :: :: :: :: ::: :: :: :: :: :: :: :: :27 6.9Expressions: :: :: :: :: :: :: :: ::: :: :: :: :: :: :: :: :27 6.1Function Constants :: :: :: :: :: ::: :: :: :: :: :: :: :: :33 7Pre-defined Functions 35 7.1Functions on Integers :: :: :: :: ::: :: :: :: :: :: :: :: :35 7.2Functions on Floating Point Numbers : :: :: :: :: :: :: :: :35 7.3Functions on Sets :: :: :: :: :: ::: :: :: :: :: :: :: :: :35 7.4Functions on Maps :: :: :: :: :: ::: :: :: :: :: :: :: :: :36 CONTENTS 3 7.5Standard Mathematical Functions : ::: :: :: :: :: :: :: :: :36 7.6Type Testers :: :: :: :: :: :: :: ::: :: :: :: :: :: :: :: :37 7.7Input/Output Functions : :: :: :: ::: :: :: :: :: :: :: :: :37 7.8Miscellaneous : :: :: :: :: :: :: ::: :: :: :: :: :: :: :: :39 7.9Tuple: :: :: :: :: :: :: :: :: :: ::: :: :: :: :: :: :: :: :39 8Precedence Rules 40 9Directives 41 9.1Brief Descriptions :: :: :: :: :: ::: :: :: :: :: :: :: :: :41 9.2!clear and !edit : :: :: :: :: :: ::: :: :: :: :: :: :: :: :43 9.3!allocate and !memory :: :: :: :: ::: :: :: :: :: :: :: :: :44 9.4!watch and !unwatch : :: :: :: :: ::: :: :: :: :: :: :: :: :44 9.5!record : :: :: :: :: :: :: :: :: ::: :: :: :: :: :: :: :: :45 9.6!system : :: :: :: :: :: :: :: :: ::: :: :: :: :: :: :: :: :45 1Editors 46 10.MSDOS Screen Editor : :: :: :: :: ::: :: :: :: :: :: :: :: :46 10.Mac Screen Editor :: :: :: :: :: ::: :: :: :: :: :: :: :: :47 10.Interactive Line Editor (ILE) :: ::: :: :: :: :: :: :: :: :48 1Runtime Errors 56 11.Fatal Errors :: :: :: :: :: :: :: ::: :: :: :: :: :: :: :: :56 11.Operator Related Messages : :: :: ::: :: :: :: :: :: :: :: :57 11.General Errors :: :: :: :: :: :: ::: :: :: :: :: :: :: :: :58 1The ISETL Grammar --- Compressed 63 12.Input at the Prompt : :: :: :: :: ::: :: :: :: :: :: :: :: :63 12.Program : :: :: :: :: :: :: :: :: ::: :: :: :: :: :: :: :: :63 12.Statements : :: :: :: :: :: :: :: ::: :: :: :: :: :: :: :: :63 12.Iterators :: :: :: :: :: :: :: :: ::: :: :: :: :: :: :: :: :64 12.Selectors :: :: :: :: :: :: :: :: ::: :: :: :: :: :: :: :: :64 12.Left Hand Sides :: :: :: :: :: :: ::: :: :: :: :: :: :: :: :64 12.Expressions and Formers :: :: :: ::: :: :: :: :: :: :: :: :65 12.Function Constants :: :: :: :: :: ::: :: :: :: :: :: :: :: :66 4 1 RUNNING ISETL 1 Running ISETL ISETL is an interpreted, interactive version of the programming language SETL. It is invoked by typing a command line with the executable name, say isetl, along with optional file names that are discussed below.2 There is no compiler for ISETL. When ISETL is running, it prompts for input with the character ``>''. Input consists of a sequence of expressions (each terminated by a semicolon ``;''), statements, and programs. Each input is acted upon as soon as it is entered. These actions are explained below. In the case of expressions, the result includes its value being printed. If you have not completed your entry, you will receive the prompt ``>>'', indicating that more is expected. 1. ISETL is exited by typing ``!quit''. It may also be exited by ending the standard input. In Unix, this is done by typing ctrl-D. In MS-DOS, ctrl-Z and ctrl-D will work. 2. A common mistake is omitting the semicolon after an expression. ISETL will wait until it gets a semicolon before proceeding. The doubled prompt ``>>'' indicates that ISETL is expecting more input. 3. ISETL can get its input from sources other than the standard input. (a) If there is an initialization file3 in the current directory, then the first thing ISETL will do is read this file. -2The-Macintosh-version-is-clickable. 3Initialization files are called either .isetlrc or isetl.ini. The file is looked for in: i. the current directory ii. the directory containing isetl.exe (MSDOS and Mac) ii. the home directory (Unix, VMS) or root (MSDOS) iv. in the symbol ISETLINI: (VMS only) Only one initialization file is read. The same pattern is searched for the ile initialization file. 5 (b) Next, if the command line has any file names listed, ISETL will read each of these in turn.4 Thus, if the command line reads, isetl file.1 blue green ISETL will first read from ``.isetlrc'' if it exists, and then from ``file.1'', then ``blue'', and then ``green''. Finally, it is ready for input from the terminal. (c) If there is a file available --- say ``file.2'' --- and ISETL is given (at any time), the following line of input, !include file.2 then it will take its input from ``file.2'' before being ready for any further input. The material in such a file is treated exactly as if it were typed directly at the keyboard, and it can be followed on subsequent lines by any additional information that the user would like to enter. Consider the following (rather contrived) example: Suppose that the file ``file.3'' contained the following data: 5, 6, 7, 3, -4, "the" Then if the user typed, > seta := { >> !include file.3 !include file.3 completed >> , x }; the effect would be exactly the same as if the user had entered, -4This-feature-is--system-dependent. To provide this feature in VMS, you must define isetl :== $your$disk:[your.dir]isetl.exe in your login.com. The leading $ makes this a foreign command. The rest is the complete path to the executable version of ISETL. 6 2 CHARACTERS, KEYWORDS, AND IDENTIFIERS > seta := {5, 6, 7, 3, -4, "the", x}; The line ``!include file.3 completed'' comes from ISETL and is always printed after an ``!include''. 4. Comments If a dollar sign ``$'' appears on a line, then everything that appears until the end of the line is ignored by ISETL. 5. After a program or statement has executed, the values of global variables persist. The user can then evaluate expressions in terms of these variables. (See section 5 for more detail on scope.) 2 Characters, Keywords, and Identifiers 2.1 Character Set The following is a list of characters used by ISETL. @ [ ] ; : = | { } ( ) . # ? * / + - _ " < > % ~ , a --- z A --- Z 0 --- 9 In addition, the following character-pairs are used. := .. ** /= <= >= -> The characters ``:'' and ``|'' may be used interchangably. 2.2 Keywords The following is a list of ISETL keywords. and false iff not program true div for impl notin read union do forall in of readf value else from inter om (OM) return where elseif fromb less opt subset while end frome local or take with exists func mod print then write if newat printf to writeln 2.3 Identifiers 7 2.3 Identifiers 1. An identifier is a sequence of alphanumeric characters along with the underscore, ``_''. It must begin with a letter. Upper or lower case may be used, and ISETL preserves the distinction. (I.e.: a_good_thing and A_Good_ Thing are both legal and are different.) 2. An identifier serves as a variable and can take on a value of any ISETL data type. The type of a variable is entirely determined by the value that is assigned to it and changes when a value of a different type is assigned. 3 Simple Data Types 3.1 Integers 1. There is no limit to the size of integers.5 2. An integer constant is a sequence of one or more digits. It represents an unsigned integer. 3. On input and output, long integers may be broken to accommodate limited line length. A backslash (``\'') at the end of a sequence of digits indicates that the integer is continued on the next line. > 123456\ >> 789; 123456789; 3.2 Floating_Point Numbers 1. The possible range of floating_ point numbers is machine dependent. At a minimum, the values will have 5 place accuracy, with a range of approximately 1 0 3. 2. A floating_ point constant is a sequence of one or more digits, followed by a decimal point, followed by zero or --------------------------- 5No practical limit. Actually limited to about 20,000 digits per integer. 8 3 SIMPLE DATA TYPES more digits. Thus, 2.0 and 2. are legal, but .5 is illegal. A floating_point constant may be followed by an exponent. An exponent consists of one of the characters ``e'', ``E'', ``f'', ``F'' followed by a signed or unsigned integer. The value of a floating_point constant is determined as in scientific notation. Hence, for example, 0.2, 2.0e-1, 20.0e-2 are all equivalent. As with integers, it is unsigned. 3. Different systems use different printed representations when floating point values are out of the machine's range. For example, when the value is too large, the Macintosh prints ``+++++'' and the Sun prints ``Infinity''. 3.3 Booleans 1. A Boolean constant is one of the keywords true or false, with the obvious meaning for its value. 3.4 Strings 1. A string constant is any sequence of characters preceded and followed by a double quote, ``"''. A string may not be split across lines. Large strings may be constructed using the operation of concatenation. Strings may also be surrounded by single quotes, ``'''. The backslash convention may be used to enter special characters. When pretty-printing, these conventions are used for output. In the case of formated output, the special characters are printed. 3.5 Atoms 9 \b backspace \f formfeed (new page) \n newline (prints as CR-LF) \q double quote \r carriage return (CR) \t tab \octal character represented by octal Refer to an ASCII chart for meaning. \other other --- may be any character not listed above. In particular, "\\" is a single backslash. You may type, "\"" for double quote, but the pretty printer will print as "\q". ASCII values are limited to '\001' to '\377'. > %+ [char(i): i in [1..127]]; "\001\002\003\004\005\006\007\b\t\n\013\f" +"\r\016\017\020\021\022\023\024\025\026" +"\027\030\031\032\033\034\035\036\037 !" +"\q#$%&'()*+,-./0123456789:;<=>?@ABCDEF" +"GHIJKLMNOPQRSTUVWXYZ[\\]^_`abcdefghijk" +"lmnopqrstuvwxyz{|}~\177"; 3.5 Atoms 1. Atoms are ``abstract points''. They have no identifying properties other than their individual existence. 2. The keyword newat has as its value an atom never before seen in this session of ISETL. 3.6 Files 1. A file is an ISETL value that corresponds to an external file in the operating system environment. 2. They are created as a result of applying one of the pre-defined functions openr, opena, openw. (See section 7.7.) 10 4 COMPOUND DATA TYPES 3.7 Undefined 1. The data type undefined has a single value --- OM. It may also be entered as om. 2. Any identifier that has not been assigned a value has the value OM. 4 Compound Data Types 4.1 Sets 1. Only finite sets may be represented in ISETL. The elements may be of any type, mixed heterogeneously. Elements occur at most once per set. 2. OM may not be an element of a set. Any set that would contain OM is considered to be undefined. 3. The order of elements is not significant in a set and printing the value of a set twice in succession could display the elements in different orders. 4. Zero or more expressions, separated by commas and enclosed in braces (``{'' and ``}'') evaluates to the set whose elements are the values of the enclosed expressions. Note that as a special case, the empty set is denoted by { }. 5. There are syntactic forms, explained in the grammar, for a finite set that is an arithmetic progression of integers, and also for a finite set obtained from a set former in standard mathematical notation. For example, the value of the following expression { x+y : x,y in {-1,-3..-100} | x /= y }; is the set of all sums of two different odd negative integers larger than ?1 0 0 . 4.2 Tuples 11 4.2 Tuples 1. A tuple is an infinite sequence of components, of which only a finite number are defined. The components may be of any type, mixed heterogeneously. The values of components may be repeated. 2. OM is a legal value for a component. 3. The order of the components of a tuple is significant. By treating the tuple as a function over the positive integers, you can extract individual components and contiguous subsequences (slices) of the tuple. 4. Zero or more expressions, separated by commas and enclosed in square brackets (``['' and ``]'') evaluates to the tuple whose defined components are the values of the enclosed expressions. Note that as a special case, the empty tuple is denoted by [ ]. This tuple is undefined everywhere. 5. The syntactic forms for tuples of finite arithmetic progressions and tuple formers are similar to those provided for sets. The only difference is the use of square, rather than curly, brackets. 6. The length of a tuple is the largest index (counting from 1) for which a component is defined (that is, is not equal to OM). It can change at run-time. 7. Tuples usually are indexed starting at 1, but they can have different starting indices. See page 33 and page 39 for definitions. 8. Tuples created by a FORMER have the default origin. See origin for how to redefine the default. 9. Tuples that result from operations on other tuples inherit their origin. Generally, the result inherits the origin of the leftmost tuple argument. 12 5 FUNCS 4.3 Maps Maps form a subclass of sets. 1. A map is a set that is either empty or whose elements are all ordered pairs. An ordered pair is a tuple whose first two components and no others are defined. 2. There are two special operators for evaluating a map at a point in its domain. Suppose that F is a map. (a) F(EXPR) will evaluate to the value of the second component of the ordered pair whose first component is the value of EXPR, provided there is exactly one such ordered pair in F; if there is no such pair, it evaluates to OM; if there are many such pairs, an error is reported. (b) F{EXPR} will evaluate to the set of all values of second components of ordered pairs in F whose first component is the value of EXPR. If there is no such pair, its value is the empty set. 3. A map in which no value appears more than once as the first component of an ordered pair is called a single-valued map or smap; otherwise, the map is called a multi-valued map or mmap. 5 Funcs 1. A func is an ISETL value that may be applied to zero or more values passed to it as arguments. It then returns a value specified by the definition of the func. Because it is a value, an ISETL func can be assigned to an identifier, passed as an argument, etc. Evaluation of an ISETL func can have side-effects determined by the statements in the definition of the func. Thus, it also serves the purpose of what is often called a procedure. 2. The return statement is only meaningful inside a func. Its effect is to terminate execution of the func and return a 13 value to the caller. The form ``return expr;'' returns the value of expr; ``return;'' returns OM. ISETL inserts return; just before the end of every func. 3. A func is the computational representation of a function, as a map is the ordered pair representation, and a tuple is the sequence representation. Just as tuples and maps may be modified at a point by assignment, so can funcs. However, if the value at a point is structured, you may not modify that at a point as well. > x := func(i); >> return char(i); >> end; > x(97); "a"; > x(97) := "q"; > x(97); "q"; > x(97)(1) := "abc"; ! Error: Only one level of selection allowed x may be modified at a point. The assignment to x(97) is legal. However, the following assignment is not supported at this time, because you are trying to modify the structure of the value returned. 4. A number of functions have been pre-defined as funcs in ISETL. A list of their definitions is given in section 7. These are not keywords and may be changed by the user. They may not be modified at a point, however. 5. It is possible for the user to define her/his own func. This is done with the following syntax: func(list-of-parameters); local list-of-local-ids; value list-of-global-ids; statements; end Alternately, one may write 14 5 FUNCS : list-of-parameters -> result : if the function simply consists of evaluating an expression. (a) The declaration of local ids may be omitted if no local variables are needed. The declaration of value ids represents global variables whose current values are to be remembered and used at the time of function invocation; these may be omitted if not needed. The list-of-parameters may be empty, but the pair of parentheses must be present. (b) Parameters and local-ids are local to the func. See below for a discussion of scope. (c) The syntax described above is for an expression of type func. As with any expression, it may be evaluated, but the value has no name. Thus, the definition will typically be part of an assignment statement or passed as a parameter. As a very simple example, consider: cube_plus := func(x,y); return x**3 + y; end; After having executed this input, ISETL will evaluate an expression such as cube_plus(2,5) as 1 3 . (d) Parameters are passed by value. It is an error to pass too many or too few arguments. It is possible to make some parameters optional. f := func(a,b,c opt x,y,z); ... end; f can be called with 3, 4, 5, or 6 arguments. If there are fewer than 6 arguments, the missing arguments are considered to be OM. (e) Scope is lexical (static) with retention. Lexical means that references to global variables are determined by where the func was created, not by where it will be evaluated. Retention means that even if the scope that created the func has been exited, its variables persist and can be used by the func. 15 By default, references to global variables will use the value of the variable at the time the function is invoked. The value declaration causes the value of the global variable at the time the func is created to be used. (f) Here is a more complicated example of the use of func. As defined below, compose takes two functions as arguments and creates their functional composition. The functions can be any ISETL values that may be applied to a single argument; e.g. func, tuple, smap. compose := func(f,g); return :x -> f(g(x)) : end; twice := :a -> 2*a: ; times4 := compose(twice,twice); Then the value of times4(3) would be 12. The value of times4 needs to refer to the values of f and g, and they remain accessible to times4, even though compose has returned. (g) Finally, here is an example of functions modified at a point and functions that capture the current value of a global. f := func(x); return x + 4; end func; gs := [ func(x); value N; return x+3*N; end : N in [1..3] ]; f(3) := 21; After this is executed, f(1) is 5, f(2) is 6, but f(3) is 21. gs(2)(4) is 10 (4+3*2). 16 6 THE ISETL GRAMMAR --- ANNOTATED 6 The ISETL Grammar --- Annotated 6.1 Terminology 1. In what follows, the symbol ID refers to identifiers, and INTEGER, FLOATING_POINT, BOOLEAN, and STRING refer to constants of type integer, floating_point, Boolean, and string, which have been explained above. Any other symbol in capital letters is explained in the grammar. 2. Definitions appear as: STMT --> LHS := EXPR ; STMT --> if EXPR then STMTS ELSE-IFS ELSE-PART end indicating that STMT can be either an assignment statement or a conditional statement. The definitions for ELSE-IFS and ELSE-PART are in the section for statements, and EXPR in the section for expressions. 3. Rules are sometimes given informally in English. The rule is then quoted. 4. Spaces are not allowed within any of the character pairs listed in section 2, nor within an ID, INTEGER constant, FLOATING_POINT constant, or keyword. Spaces are required between keywords, IDs, INTEGER constants, and FLOATING_POINT constants. 5. ISETL treats ends of line and tabs as spaces. Any input can be spread across lines without changing the meaning, and ISETL will not consider it to be complete until a semicolon (``;'') is entered. The only exceptions to this are the ! directives, which are ended with a carriage return, and the fact that a quoted string cannot be typed on more than one line. The annotated grammar below is divided into sections relating to the major parts of the language. 6.2 Input at the Prompt 17 6.2 Input at the Prompt INPUT --> PROGRAM INPUT --> STMT INPUT --> EXPR ; The EXPR is evaluated and the value is printed. 6.3 Program Programs are usually read from a file, only because they tend to be long. PROGRAM --> program ID ; LOCALS VALUES STMTS end ; Of course, it can appear on several lines. One may optionally close with end program. LOCALS and VALUES are defined in section 6.10. 6.4 Statements STMT --> LHS := EXPR ; First, the left hand side (LHS) is evaluated to determine the target(s) for the assignment, then the right hand side is evaluated. Finally, the assignment is made. If there are some targets for which there are no values to be assigned, they receive the value OM. If there are values to be assigned, but no corresponding targets, then the values are ignored. Examples: a := 4; a is changed to contain the value 4 . [a,b] := [1,2]; a is assigned 1 and b is assigned 2 . [x,y] := [y,x]; Swap x and y. 18 6 THE ISETL GRAMMAR --- ANNOTATED f(3) := 7; If f is a tuple, then the effect of this statement is to assign 7 as the value of the third component of f. If f is a map, then its effect is to replace all pairs beginning with 3 by the pair [3,7] in the set of ordered pairs f. If f is a func, then f(3) will be 7 , and all other values of f will be as they were before the assignment. STMT --> EXPR ; The expression is evaluated and the value ignored. This is usually used to invoke procedures. STMT --> if EXPR then STMTS ELSE-IFS ELSE-PART end ; The EXPRs after if and elseif are evaluated in order until one is found to be true. The STMTS following the associated then are executed. If no EXPR is found to be true, the STMTS in the ELSE-PART are executed. In this last case, if the ELSE-PART is omitted, this statement has no effect. One may optionally close with end if. See the end of this section for the definitions of ELSE-IFS and ELSE-PART. STMT --> for ITERATOR do STMTS end ; The STMTS are executed for each instance generated by the iterator. One may optionally close with end for. STMT --> while EXPR do STMTS end ; EXPR must evaluate to a Boolean value. EXPR is evaluated and the STMTS are executed repetitively as long as this value is equal to true. One may optionally close with end while. STMT --> read LHS-LIST ; ISETL gives a question mark (``?'') prompt and waits until an expression has been entered. This EXPR is evaluated and the result is assigned to the first item in LHS-LIST. This is repeated for each item in LHS-LIST. As usual, terminate the expressions with a semicolon. Note: If a read statement appears in an !include file, then ISETL will look at the next input in that file for the expression(s) to be read. 6.4 Statements 19 STMT --> read LHS-LIST from EXPR ; This is the same as read LHS-LIST; except that EXPR must have a value of type file. The values to be read are then taken from the external file specified by the value of EXPR. If there are more values in the file than items in LHS-LIST, then the extra values are left to be read later. If there are more items in LHS-LIST than values in the file, then the extra items are assigned the value OM. In the latter case, the function eof will return true when given the file as parameter. Before this statement is executed, the external file in question must have been opened for reading by the pre-defined function openr (see section 7.7). STMT --> readf PAIR-LIST ; STMT --> readf PAIR-LIST from EXPR ; The relation between these two forms is the same as the relation between the two forms of read, with the second one coming from a file. The elements in the PAIR-LIST define the formating used. See PAIR-LIST at the end of this section. STMT --> print EXPR-LIST ; Each expression in EXPR-LIST is evaluated and printed on standard output. The output values are formated to show their structure, with line breaks at reasonable positions and meaningful indentation. STMT --> print EXPR-LIST to EXPR ; As in read..from..., EXPR must be a value of type file. The values are written to the external file specified by the value of EXPR. Before executing this statement, the external file in question must have been opened for writing by one of the pre-defined functions openw or opena (see section 7.7). STMT --> printf PAIR-LIST ; STMT --> printf PAIR-LIST to EXPR ; The relation between these two forms is the same as the relation between the two forms of print, with the second one going to a file. The elements in the PAIR-LIST define the 20 6 THE ISETL GRAMMAR --- ANNOTATED formating used. See PAIR-LIST at the end of this section. See write and writeln below. STMT --> return ; return is only meaningful inside a func. Its effect is to terminate execution of the func and return OM to the caller. ISETL inserts return; just before the end of every func. If return appears at the ``top level'', e.g. as input at the keyboard, a run time error will occur. STMT --> return EXPR ; Same as return; except that EXPR is evaluated and its value is returned as the value of the func. STMT --> take LHS from LHS ; The second LHS must evaluate to a set. An arbitrary element of the set is assigned to the first LHS and removed from the set. STMT --> take LHS frome LHS ; The second LHS must evaluate to a tuple (or a string). The value of its last defined component (or last character) is assigned to the first LHS and replaced by OM in the tuple (deleted from the string). STMT --> take LHS fromb LHS ; The second LHS must evaluate to a tuple (or a string). The value of its first component (defined or not) (first character) is assigned to the first LHS and all components of the tuple (characters of the string) are shifted left one place. That is, the new value of the ithcomponent is the old value of the (i+1 )stcomponent (i = 1 ;2 ;.). STMT --> write PAIR-LIST ; STMT --> write PAIR-LIST to EXPR ; STMT --> writeln PAIR-LIST ; STMT --> writeln PAIR-LIST to EXPR ; write is equivalent to printf, provided for the convenience of the Pascal user. writeln is equivalent to write, with '\n' as the last item of the list. This is also provided for user convenience. 6.4 Statements 21 > readf x; 1.34 > x; 1.34000e+00; > readf y; 123,456 > y; "123,456"; Figure 1: readf example > printf 1/3: 15.10, 1/3:15.1, 1/3:15.01, "\n"; 0.3333333135 0.3333333135 0.3 printf 1/3: -17.10, 1/3:-17.1, 1/3:-17.01, "\n"; 3.3333331347e-01 3.3333331347e-01 3.3e-01 Figure 2: printf example STMTS --> ``One or more instances of STMT. The final semicolon is optional.'' ELSE-IFS --> ``Zero or more instances of ELSE-IF.'' ELSE-IF --> elseif EXPR then STMTS ELSE-PART --> else STMTS ``May be omitted.'' PAIR-LIST --> ``One or more instances of PAIR, separated by commas.'' PAIR --> EXPR : EXPR PAIR --> EXPR When a PAIR appears in a readf, the first EXPR must be a LHS. The meaning of the PAIR and the default value when the 22 6 THE ISETL GRAMMAR --- ANNOTATED > printf 3*[""]+[1..30] : 7*[3] with "\n"; 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 > x := [ [i,j,i+j] : i,j in [1..3] ]; > printf x: 5*[ [0,"+",0, "=", 0], "\t" ] >> with "\n", "\n"; 1+1=2 1+2=3 1+3=4 2+1=3 2+2=4 2+3=5 3+1=4 3+2=5 3+3=6 Figure 3: printf with structure example second EXPR is omitted depends on whether the PAIR occurs in readf or printf. The second EXPR (or its default value) defines the format. ? Input: Input formats are integers. The integer gives the maximum number of characters to be read. If the first sequence of non-white space characters can be interpreted as a number, that is the value read. Otherwise, the first non-white sequence is returned as a string. If the integer is negative (say ?i), exactly i characters will be read and returned as a string. Therefore c:-1 will read one character into c. If no integer is given, there is no maximum to the number of characters that will be read. See figure 1. ? Output: Output formats are: integers, floating_point numbers, strings, or tuples of output formats. Integers (and the integer part of floating_point numbers) represent the minimal number of columns to be used. The fractional part of a floating_ point number is used to specify precision, in terms of hundredths. The precision controls the number of places used in 6.5 Iterators 23 floating_point numbers, and where breaks occur in very long integers. Negative values cause floating_point numbers to be printed in scientific notation. Notice that there is a limit to the number of useful digits. Also notice that 15.1 is the same as 15.10; hence, both would use 15 columns and 10 decimal places. See figure 2. Strings should not be used as formats outside of tuples. Compound objects (tuples and sets) iterate over the format. If the format is a number, it is used as the format for each element. If the format is a tuple, the elements of the tuple are cycled among, with strings printed literally and other items used as formats. See figure 3. Default values are: ------------------------------------------------------- Float 20 5 Integer 10 50 (for breaking large ints) String 0 Anything else 10 6.5 Iterators These constructs are used to iterate through a collection of values, assigning these values one at a time to a variable. Iterators are used in the for statement, quantifiers, and set formers. A SIMPLE-ITERATOR generates a number of instances for which an assignment is made. These assignments are local to the iterator, and when it is exited, all previous values of IDs that were used as local variables are restored. That is, these IDs are ``bound variables'' whose scope is the construction containing the iterator. (e.g., for statements, quantifiers, formers, etc. ) ITERATOR --> ITER-LIST 24 6 THE ISETL GRAMMAR --- ANNOTATED ITERATOR --> ITER-LIST | EXPR EXPR must evaluate to a Boolean. Generates only those instances generated by ITER-LIST for which the value of EXPR is true. ITER-LIST --> ``One or more SIMPLE-ITERATORs separated by commas.'' Generates all possible instances for every combination of the SIMPLE-ITERATORs. The first SIMPLE-ITERATOR advances most slowly. Subsequent iterators may depend on previously bound values. SIMPLE-ITERATOR --> BOUND-LIST in EXPR EXPR must evaluate to a set, tuple, or string. The instances generated are all possibilities in which each BOUND in BOUND-LIST is assigned a value that occurs in EXPR. SIMPLE-ITERATOR --> BOUND = ID ( BOUND-LIST ) Here ID must have the value of an smap, tuple, or string, and BOUND-LIST must have the correct number of occurrences of BOUND corresponding to the parameters of ID. The resulting instances are those for which all occurrences of BOUND in BOUND-LIST have all possible legal values and BOUND is assigned the corresponding value. SIMPLE-ITERATOR --> BOUND = ID { BOUND-LIST } Same as the previous one for the case in which ID is an mmap. BOUND-LIST --> ``one or more BOUND, separated by commas'' BOUND --> ~ Corresponding value is thrown away. BOUND --> ID Corresponding value is assigned to ID. BOUND --> [ BOUND-LIST ] Corresponding value must be a tuple, and elements of the tuple are assigned to corresponding elements in the BOUND-LIST. 6.6 Formers 25 6.6 Formers Generates the elements of a set or tuple. FORMER --> ``Empty'' Generates the empty set or tuple. FORMER --> EXPR-LIST Values are explicitly listed. FORMER --> EXPR .. EXPR Both occurrences of EXPR must evaluate to integers. Generates all integers beginning with the first EXPR and increasing by 1 for as long as the second EXPR is not exceeded. If the first EXPR is larger than the second, no values are generated. FORMER --> EXPR , EXPR .. EXPR All three occurrences of EXPR must evaluate to integer. Generates all integers beginning with the first EXPR and incrementing by the value of the second EXPR minus the first EXPR. If this difference is positive, it generates those integers that are not greater than the third EXPR. If the difference is negative, it generates those integers that are not less than the third EXPR. If the difference is zero, no integers are generated. FORMER --> EXPR : ITERATOR The value of EXPR for each instance generated by the ITERATOR. 6.7 Selectors Selectors fall into three categories: function application, mmap images, and slices. A tuple, string, map, or func (pre- or user-defined) may be followed by a SELECTOR, which has the effect of specifying a value or group of values in the range of the tuple, string, map, or func. Not all of the following SELECTORs can be used in all four cases. SELECTOR --> ( EXPR-LIST ) Must be used with an smap, tuple, string, or func. 26 6 THE ISETL GRAMMAR --- ANNOTATED If used with a tuple or string, then EXPR-LIST can only have one element, which must evaluate to a positive integer. If used with a func, arguments are passed to corresponding parameters. There must be as many arguments as required parameters and no more than the optional parameters permit. If used with an smap and EXPR-LIST has more than one element, it is equivalent to what it would be if the list were enclosed in square brackets, [ ]. Thus a function of several variables is interpreted as a function of one variable --- the tuple whose components are the individual variables. SELECTOR --> { EXPR-LIST } Must be used with an mmap, tuple, or string. Tuples and strings will either select a singleton set or the empty set. The case in which the list has more than one element is handled as above. SELECTOR --> ( EXPR .. EXPR ) Must be used with a tuple or string, and both instances of EXPR must evaluate to a positive integer. The value is the slice of the original tuple or string in the range specified by the two occurrences of EXPR. There are some special rules in this case. To describe them, suppose that the first EXPR has the value a and the second has the value b so that the selector is (a..b). a<=b Value is the tuple or string with components defined only at the integers from 1 to b? a+ 1 , inclusive. The value of the ithcomponent is the value of the (a+ i? 1 )stcomponent of the value of EXPR. a = b+ 1 Value is the empty tuple. a > b+ 1 Run-time error. SELECTOR --> ( .. EXPR ) Means the same as (low .. EXPR), where low is 1 for strings and lo(T) for tuple T. SELECTOR --> ( EXPR .. ) Means the same as ( EXPR .. high ), where high is #s for string s and hi(T) for tuple T. 6.8 Left Hand Sides 27 SELECTOR --> ( ) Used with a func that has no parameters. It also works with an smap with [ ] in its domain. 6.8 Left Hand Sides The target for anything that has the effect of an assignment. LHS --> ID LHS --> LHS SELECTOR LHS must evaluate to a tuple, string, or map. LHS is modified by replacing the components designated by selector. LHS --> [ LHS-LIST ] LHS-LIST --> ``One or more instances of LHS, separated by commas'' Thus the input, [A, B, C] := [1, 2, 3]; has the effect of replacing A by 1 ,B by 2 , and C by 3 . Any LHS in the list can be replaced by ~. The effect is to omit any assignment to a LHS that has been so replaced. Thus the input, [A, ~, C] := [1, 2, 3]; replaces A by 1 ,C by 3 . 6.9 Expressions The first few in the following list are values of simple data types and they have been discussed before. EXPR --> ID EXPR --> INTEGER EXPR --> FLOATING-POINT EXPR --> STRING EXPR --> true EXPR --> false 28 6 THE ISETL GRAMMAR --- ANNOTATED EXPR --> OM EXPR --> newat The value is a new atom, different from any other atom that has appeared before. EXPR --> FUNC-CONST A user-defined func. See section 6.10. EXPR --> if EXPR then EXPR ELSE-IFS ELSE-PART end ; See definition of if under STMT, page18. ELSE-PART is required, and each part contains an expression rather than statements. EXPR --> ( EXPR ) Any expression can be enclosed in parentheses. The value is the value of EXPR. EXPR --> [ FORMER ] Evaluates to the tuple of those values generated by FORMER in the order that former generates them. EXPR --> { FORMER } Evaluates to the set of those values generated by FORMER. EXPR --> # EXPR EXPR must be a set, tuple, or string. The value is the cardinality of the set, the length of the tuple, or the length of the string. EXPR --> not EXPR Logical negation. EXPR must evaluate to Boolean. EXPR --> + EXPR Identity function. EXPR must evaluate to a number. EXPR --> - EXPR Negative of EXPR. EXPR must evaluate to a number. EXPR --> EXPR SELECTOR EXPR must evaluate to an ISETL value that is, in the general sense, a function. That is, it must be a map, tuple, string, or func. See section 6.7. EXPR --> EXPR . ID EXPR This is equivalent to ID(EXPR,EXPR). It lets you use a binary function as an infix operator. The space after the ``.'' is optional. 6.9 Expressions 29 EXPR --> EXPR . (EXPR) EXPR This is equivalent to (EXPR)(EXPR,EXPR). It lets you use a binary function as an infix operator. The space after the ``.'' is optional. In general, arithmetic operators and comparisons may mix integers and floating_ point. The result of an arithmetic operation is an integer if both operands are integers and floating_point otherwise. For simplicity, we will use the term number to mean a value that is either integer or floating_point. Possible operators are: + - * / div mod ** with less = /= < > <= >= union inter in notin subset and or impl iff See section 8 for precedence rules. Any cases not covered in the explanation for an operator will result in an error. For an explanation of errors, see section 11. EXPR --> EXPR + EXPR If both instances of EXPR evaluate to numbers, this is addition. If both instances of EXPR evaluate to sets, then this is union. If both instances of EXPR evaluate to tuples or strings, then this is concatenation. EXPR --> EXPR union EXPR An alternate form of +. It is intended that it be used with sets, but it is in all ways equivalent to +. EXPR --> EXPR - EXPR If both instances of EXPR evaluate to numbers, this is subtraction. If both instances of EXPR evaluate to sets, then this is set difference. EXPR --> EXPR * EXPR If both instances of EXPR evaluate to numbers, this is multiplication. If both evaluate to sets, this is intersection. If one instance of EXPR evaluates to integer and the other to a tuple or string, then the value is the 30 6 THE ISETL GRAMMAR --- ANNOTATED tuple or string, concatenated with itself the integer number of times, if the integer is positive; and the empty tuple or string, if the integer is less than or equal to zero. EXPR --> EXPR inter EXPR An alternate form of *. It is intended that it be used with sets, but it is in all ways equivalent to *. EXPR --> EXPR / EXPR Both instances of EXPR must evaluate to numbers. The value is the result of division and is of type floating_point. EXPR --> EXPR div EXPR Both instances of EXPR must evaluate to integer, and the second must be non-zero. The value is integer division defined by the following two relations, (adiv b)?b+ (a modb)= a for b > 0 adiv (?b)= ?(a div b) for b < 0 . EXPR --> EXPR mod EXPR Both instances of EXPR must evaluate to integer and the second must be non-zero. The result is the remainder, and the following condition is always satisfied, 0 <a modb < jbj. EXPR --> EXPR ** EXPR The values of the two expressions must be numbers. The operation is exponentiation. EXPR --> EXPR with EXPR The value of the first EXPR must be a set or tuple. If it is a set, the value is that set with the value of the second EXPR added as an element. If it is a tuple, the value of the second EXPR is assigned to the value of the first component after the last defined component of the tuple. EXPR --> EXPR less EXPR The value of the first EXPR must be a set. The value is that set with the value of the second EXPR removed, if it was present; the value of the first EXPR, if the second was not present. EXPR --> EXPR = EXPR The test for equality of any two ISETL values. 6.9 Expressions 31 EXPR --> EXPR /= EXPR Negation of EXPR=EXPR. EXPR --> EXPR < EXPR EXPR --> EXPR > EXPR EXPR --> EXPR <= EXPR EXPR --> EXPR >= EXPR For all the above inequalities, both instances of EXPR must evaluate to the same type, which must be number or string. For numbers, this is the test for the standard arithmetic ordering; for strings, it is the test for lexicographic ordering. EXPR --> EXPR in EXPR The second EXPR must be a set, tuple, or string. For sets and tuples, this is the test for membership of the first in the second. For strings, it is the test for substring. EXPR --> EXPR notin EXPR Negation of EXPR in EXPR. EXPR --> EXPR subset EXPR Both instances of EXPR must be sets. This is the test for the value of the first EXPR to be a subset of the value of the second EXPR. EXPR --> EXPR and EXPR Logical conjunction. Both instances of EXPR should evaluate to a Boolean. If the left operand is false, the right operand is not evaluated. Actually returns the second argument, if the first is true. While the user may depend on the left-to-right evaluation order, it is recommended that they not depend on the behavior when the second argument is not Boolean. EXPR --> EXPR or EXPR Logical disjunction. Both instances of EXPR should evaluate to a Boolean. If the left operand is true, the right operand is not evaluated. Actually returns the second argument, if the first is false. While the user may depend on the left-to-right evaluation order, it is recommended that they not depend on the behavior when the second argument is not Boolean. 32 6 THE ISETL GRAMMAR --- ANNOTATED EXPR --> EXPR impl EXPR Logical implication. Both instances of EXPR must evaluate to a Boolean. EXPR --> EXPR iff EXPR Logical equivalence. Both instances of EXPR should evaluate to a Boolean. It actually checks for equality, like =, but it has a different precedence. It is recommended that the user not depend on iff to work with arguments other than Booleans. EXPR --> % BINOP EXPR EXPR must evaluate to a set, tuple, or string. Say that the elements in EXPR are x1, x2,...,xN (N=#EXPR). If N=0, then the value is OM. If N=1, then the value is the single element. Otherwise, %? EXPR equals x1 ? x2 ? ??? ? xN associating to the left. If EXPR is a set, then the selection of elements is made in arbitrary order, otherwise it is made in the order of the components of EXPR. EXPR --> EXPR % BINOP EXPR The second instance of EXPR must evaluate to a set, tuple, or string. If the first EXPR is a, BINOP is ?, and the values in the second are x1, x2,..,xN as above, then the value is: a ? x1 ? x2 ? ???? xN associating to the left. EXPR --> EXPR ? EXPR The value of the first EXPR, if it is not OM; otherwise the value of the second EXPR. EXPR --> exists ITER-LIST | EXPR EXPR must evaluate to a Boolean. If ITER-LIST generates at least one instance in which EXPR evaluates to true, then the value is true; otherwise it is false. EXPR --> forall ITER-LIST | EXPR EXPR must evaluate to a Boolean. If every instance generated by ITER-LIST is such that EXPR evaluates to true, then the value is true; otherwise it is false. 6.10 Function Constants 33 EXPR --> EXPR where DEFNS end The value is the value of the EXPR preceding where, evaluated in the current environment with the IDs in the DEFNS added to the environment and initialized to the corresponding EXPRs. The scope of the IDs is limited to the where expression. The DEFNS can modify IDs defined in earlier DEFNS in the same where expression. EXPR --> EXPR @ EXPR The first expression must be an integer i and the second a tuple T. The result is a tuple consisting of the same sequence as T, but with the first index being i. BINOP --> ``Any binary operator or an ID or expression in parentheses whose value is a function of two parameters. The ID and parenthesized expression may be preceded by a period.'' The acceptable binary operators are: +, -, *, **, union, inter, /, div, mod, with, less, and, or, impl. DEFNS --> ``Zero or more instances of DEFN. The final semicolon is optional.'' DEFN --> BOUND := EXPR ; DEFN --> ID SELECTOR := EXPR ; EXPR-LIST --> ``One or more instances of EXPR separated by commas.'' 6.10 Function Constants FUNC-CONST --> FUNC-HEAD LOCALS VALUES STMTS end This is the syntax for user-defined funcs. One may optionally close with end func. VALUES and LOCALS may be repeated or omitted and appear in any order. See return on page 20. FUNC-CONST --> : ID-LIST OPT-PART -> EXPR : An abbreviation for func( ID-LIST OPT-PART ); return EXPR; end 34 6 THE ISETL GRAMMAR --- ANNOTATED FUNC-HEAD --> func ( ID-LIST OPT-PART ) ; In this case, there are parameters. The parameters in the OPT-PART receive the value om if there are no corresponding arguments. FUNC-HEAD --> func ( OPT-PART ) ; In this case, there are no required parameters. OPT-PART --> opt ID-LIST ``May be omitted.'' LOCALS --> local ID-LIST ; VALUES --> value ID-LIST ; ID-LIST --> ``One or more instances of ID separated by commas.'' 35 7 Pre-defined Functions 7.1 Functions on Integers In each of the following, EXPR must evaluate to integer. 1. even(EXPR) --- Is EXPR even? 2. odd(EXPR) --- Is EXPR odd? 3. float(EXPR) --- The value of EXPR converted to floating_point. 4. char(EXPR) --- The one-character string whose (machine dependent) index is the value of EXPR. 7.2 Functions on Floating Point Numbers In each of the following, EXPR must evaluate to floating_point. 1. ceil(EXPR) --- The smallest integer not smaller than the value of EXPR. 2. floor(EXPR) --- The largest integer not larger than the value of EXPR. 3. fix(EXPR) --- The same as floor(EXPR) if EXPR>=0, and the same as ceil(EXPR) if the value of EXPR<=0. In other words, the fractional part is discarded. 7.3 Functions on Sets In each of following, EXPR must evaluate to a set. 1. pow(EXPR) --- The set of all subsets of the value of EXPR. 2. npow(EXPR,EXPR) --- One EXPR must be a set and the other a non-negative integer. The set of all subsets of the set whose cardinality is equal to the integer. 36 7 PRE-DEFINED FUNCTIONS 7.4 Functions on Maps In each of the following, EXPR must evaluate to a map. 1. domain(EXPR) --- The set of all values that appear as the first component of an element of the value of EXPR. 2. image(EXPR) --- The set of all values that appear as the second component of an element of the value of EXPR. 7.5 Standard Mathematical Functions 1. Each of the following takes a single floating_point argument. The result is a floating_point approximation to the value of the corresponding mathematical function. exp, ln, log, sqrt, sin, cos, tan, asin, acos, atan, sinh, cosh, tanh, asinh, acosh, atanh. 2. In each of the following, EXPR must evaluate to integer or floating_point. The result is the value of the mathematical function in the same type as the value of EXPR. (a) sgn(EXPR) --- If EXPR is positive, then 1 ; if EXPR is zero, then 0 ; otherwise ?1 . (b) random(EXPR) --- The value is a number selected at random in the interval from 0 to the value of EXPR, inclusive. There has been no statistical study made of the generators. Don't depend on them for highly sensitive work. (c) randomize(EXPR) --- This resets the random number generator. EXPR should be an integer. This may be used to select a new sequence of random numbers. 3. In each of the following, both occurrences of EXPR must evaluate to a number or string. The result is always one of the two EXPR, according to the usual mathematical definition. (a) max(EXPR,EXPR) (b) min(EXPR,EXPR) 7.6 Type Testers 37 7.6 Type Testers In each of the following, the value of EXPR can be any ISETL data type. The function is the test for the value of EXPR being the type indicated. 1. is_atom(EXPR) 2. is_boolean(EXPR) 3. is_defined(EXPR) --- Negation of is_om. 4. is_file(EXPR) 5. is_floating(EXPR) 6. is_func(EXPR) 7. is_integer(EXPR) 8. is_map(EXPR) 9. is_number(EXPR) --- true for integer and floating_point. 10. is_om(EXPR) 11. is_set(EXPR) 12. is_string(EXPR) 13. is_tuple(EXPR) 7.7 Input/Output Functions 1. In each of the following functions, the value of EXPR must be a string that is a file name consistent with the operating system's naming conventions. The value of the function has ISETL type file and may be used in read... from.., readf... from..., print... to..., printf...to..., and the function eof to refer to that file. 38 7 PRE-DEFINED FUNCTIONS (a) openr(EXPR) --- If the file named by the value of EXPR exists, then it is opened for reading, and the value of the function is of type file. If the file named by the value of EXPR does not exist, then the value of the function is OM. A special case is the file named "CONSOLE". Opening "CONSOLE" for reading provides a way to read from the console, even if you are currently reading from an include file. If you have directed stdin from a file, it may read from that file or it may read from the console; this is machine dependent. (b) openw(EXPR) --- If the file named by the value of EXPR does not exist, then it is created by the operating system externally to ISETL. This file is opened for writing from the beginning, so that anything previously in the file is destroyed. The value of the function is of type file. (c) opena(EXPR) --- The same as openw(EXPR), except that if the file exists its contents are not destroyed. Anything that is written is added to the end of the file. 2. In the following function, the value of EXPR must be of type file. The file specified by this value is closed. Output files must be closed to guarantee that all output has been stored by the operating system. All files are closed automatically when ISETL is exited. There is usually a system-imposed limit on the number of files that may be open at one time, however, so it is a good idea to close files when finished using them. (a) close(EXPR) --- The value of the function is OM. 3. In the following function the value of EXPR must be of type file. (a) eof(EXPR) --- Test for having read past the end of an external file. 7.8 Miscellaneous 39 7.8 Miscellaneous 1. abs(EXPR) --- If the value of EXPR is integer or floating_point, then the value of the function is the standard absolute value. 2. ord(EXPR) --- The inverse of char. EXPR must be a string of length 1. 3. arb(EXPR) --- An element of EXPR selected arbitrarily. If the value of EXPR is empty, then the value of the function is OM. EXPR may be a set, tuple, or string. 4. random(EXPR) --- An element of EXPR selected with uniform probability. If the value of EXPR is empty, then the value of the function is OM. EXPR may be a set, tuple, or string. 5. max_line(EXPR) --- EXPR must be an integer. The maximum number of columns used when pretty-printing is set to the value of EXPR. 6. system(EXPR) --- EXPR must be a string. The string is passed to the operating system as a command line. Available under Unix, VMS, and MSDOS. 7. precision(EXPR) --- EXPR must be an integer. This sets the number of decimal places shown by print. If EXPR is negative, it indicates that print should use scientific notation. 8. video(EXPR) --- MSDOS only. EXPR must be a boolean. This controls how the screen is managed under MSDOS. Generally, true is faster output, and false is less likely to run into trouble with compatibility questions. Also controled by -v on the command line. See section 9.1. 7.9 Tuple 1. lo(EXPR) --- EXPR must be a tuple. Returns the low bound of the tuple. 2. hi(EXPR) --- EXPR must be a tuple. Returns the high bound of the tuple. 40 8 PRECEDENCE RULES 3. origin(EXPR) --- EXPR must be an integer. Sets the default lower bound for tuples. 8 Precedence Rules ? Operators are listed from highest priority to lowest priority. ? Operators are left associative unless otherwise indicated. ? ``nonassociative'' means that you cannot use two operators on that line without parentheses. anything that is a call to a function CALL --- func, tuple, string, map, etc. # - + unary operators ? nonassociative % nonassociative ** right associative * / mod div inter + - with less union .ID infix use of binary function in notin subset < <= = /= > >= nonassociative not unary and or impl iff exists forall where 41 9 Directives 9.1 Brief Descriptions There are a number of directives that can be given to ISETL to modify its behavior. On the command line, the following switches control aspects of ISETL. -d indicates direct input. This suppresses the interactive line editor or the screen editor in MSDOS. -e implies -d and provides the !edit directive described below. -s indicates silent mode. In silent mode, the header and all prompts are suppressed. -v (MSDOS only) controls the initial value of video. -v sets it to safe (on all PC compatibles), but slow (on most video boards). The rest of the directives are ! commands. [ a | b ] indicates a choice between a and b. 9.1.1 Commands ? !quit --- Exit ISETL. ? !include <filename> --- Replace <filename> with a file/pathname according to the rules of your operating system. ISETL will insert your file. ? !clear --- Throw away all input back to the last single prompt. ? !edit --- Edit all the input back to the last single prompt. Unavailable on systems with the interactive line editor. ? !memory [nnn] --- Change the legal upper bound to nnn. May not be lower than the currently allocated memory. Without nnn, shows how much memory has been allocated. 42 9 DIRECTIVES ? !allocate nnn --- Increase the currently allocated memory to nnn. Will not exceed the upper bound set by !memory, nor the actual limits of the machine. ? !record [ file-name ] --- Begins recording input to ``file-name''. This lets you experiment and keep a record of the work performed. ? !system command-line --- Sends the command-line to the system for execution. Not available on the Macintosh. ? !ids --- Lists all identifiers that have been defined. ? !oms --- Lists all identifiers that have been used, but not defined. ? !alias id command-line --- Makes !id equivalent to !command-line. ? !version --- Prints version information for ISETL. 9.1.2 Toggles Toggles take arguments on or off. Without arguments, they echo the toggle's current state. ? !verbose --- Controls the amount of information provided by runtime error messages. See section 11. Default is off. ? !echo --- When on, all input is echoed. This is particularly useful when trying to find a syntax error in an !include file or input for a read. It is also useful for pedagogical purposes, as it can be used to interleave input and output. ? !code --- When on, you get a pseudo-assembly listing for the program. Default is off. ? !trace --- When on, you get an execution trace, using the same notation as !code. When desperate, this can be used to trace the execution of your program. Really intended for debugging ISETL. Default is off. 9.2 !clear and !edit 43 ? !source --- Saves source for debugging. See !pp, !stack, and !slow. ? !stack --- Show calls when errors occur. 9.1.3 Debugging 1. !watch list-of-ids --- Traces assignment and evaluation of ids. 2. !unwatch list-of-ids --- Turns off tracing for ids. 3. !pp id [ file-name ] --- Prints the source for function id. When present, output goes to file-name; otherwise, output goes to last file. !pp returns the file to stdout (usually the screen). 4. !slow --- Execution steps by source lines. See section 9.1.3. 5. !fast --- Return to normal execution speed. When the system is stopped for debugging, in the !slow mode, you get the ?> prompt. Responses at this point are: f --- go to fast mode. l --- leap mode (calls are executed as one step). c --- crawl mode (trace execution within calls). e --- evaluate. Enter an expression at the ! prompt. RET --- Execute the next step. 9.2 !clear and !edit 1. The user can edit6 whatever has been entered since the beginning of the current syntactic object, in response to a syntax error message, or if the user wants to change something previously typed. If you prefer to start again, ``!clear'' will clear the typing buffer and allow you to start the input afresh. --------------------------- 6Turn this on with the -e switch. 44 9 DIRECTIVES 2. When the editor is invoked (by typing ``!edit''), the user is prompted for the string that is to be modified. The user types the desired string, and the editor finds its first occurrence in the lines being edited. 3. The user is then prompted for the replacement of this string. When it is entered, the change is made. 4. The process repeats until the user enters a blank search line, at which time control is returned to ISETL. 9.3 !allocate and !memory The !memory directive adjusts the upper limit on permitted memory allocation. This is mainly to protect mainframe systems, so that one user doesn't use all the available space. The !allocate directive increases the amount of memory currently available for ISETL objects. This space is automatically increased up to the limit set by !memory, but by allocating it early, some large programs may run more quickly. If you want to grab as much memory as possible, particularly on single user systems, this is what we would recommend. First, determine the amount of memory available, by attempting to allocate everything. Then subtract from that 10K for ISETL's scratch area plus any other space you may wish to save for use by the !system directive. You can then set the memory limit and pre-allocate in your isetl.ini (or .isetlrc) files. See figure 4. Having tried to allocate 800K, there was only room for 500K. Deciding to leave 200K for other work, a limit of 300K was placed on ISETL, and 150K was pre-allocated. The lines below ``...'' are in another session, because one cannot decrease the GC (garbage collected) memory. 9.4 !watch and !unwatch The two commands !watch and !unwatch control which identifiers are traced during execution. Tracing consists of reporting assignments and function evaluation. An identifier is watched by the directive: 9.5 !record 45 !watch id id1 id2 id3 where ``id'' is the name of the identifier to be watched. More than one identifier may be listed, separated by blanks. While being watched, any assignment to a variable named with that identifier is echoed on the standard output. This includes assignments to slices and maps. If the identifier is used as a function (smap, mmap, tuple, func), a line is printed indicating that the expression is being evaluated and a second line is printed reporting the value returned. It is significant that identifiers are watched, rather than variables. If i is being watched, then all variables named i are watched. You can stop watching an identifier with the directive: !unwatch id See figure 5 for an example of the output. 9.5 !record The !record directive channels all input from standard input into a file. This allows you to capture your work and later edit it for including. A directive of the form: !record test changes to recording on file test. If you had been recording elsewhere, the other file is closed. !record with no file name turns off recording altogether. The recording is appended to an existing file. By combining this with the !echo directive, one can create terminal sessions. 9.6 !system This allows you to execute one command in the operating system without leaving ISETL. This feature is not available on the Macintosh version. See section 9.3 for hints on making sure that there is enough room to invoke the command from the system. You could list your directory on MS-DOS using the command: !system dir 46 10 EDITORS Assuming that you had enough memory, you could escape to an editor, edit a file, exit the editor, and then include the file. If you type !system by itself, you will enter a new copy of your operating system. You can execute anything that fits in the remaining memory. 10 Editors The original view of ISETL was a program that read lines of text, recognizing programs and expressions, and then evaluating them. The introduction of editors adds a second level to this. In each of the editors, there is some way to send text to ISETL. This phrase refers to taking the text and treating it as if those lines had been typed directly in. 10.1 MSDOS Screen Editor In the MSDOS editor, you send lines to ISETL by typing RETURN. The text that is sent is called a region. The first line of a region is marked on the screen with a highlighted first character; this is called the TAG.7 The last line is the line containing the cursor. The TAG is automatically placed on the last line, so just typing normally will behave as expected. If you want to send earlier lines, edit them first, then TAG the first line you wish sent by typing ^ T, move to the last line that you wish sent, and type RETURN. Prompts at the beginning of a line are ignored.8 To make it easy to check a region, you can find TAG by typing ^ X (control-X). This will exchange the cursor and TAG. Type ^ X again to return. To make it easy to find the last region sent, type ^ B. This finds the BOOK_MARK, which is left behind at the old TAG after a region is sent to ISETL. --------------------------- 7If the line is completely empty. the whole line is h8N.B.:htIf.you try to type a line starting with `>', `?', or `!' you must leave a blank in front of them to prevent their removal. Blanks are automatically inserted after the prompts. 10.2 Mac Screen Editor 47 Table 1: Important keys for MSDOS Editor(^X = control-X) ESC Get menu Arrow Keys Motion INS Break line DEL Delete under Backspace Delete left Home Left of line End Right of line PgUp (PgDn) Up (down) 8 lines ^PgUp (^PgDn) Top (bottom) of buffer Return (LF) If below tag, execute; o.w. insert return ^A Mark previous region ^B Go back to bookmark (previous tag) ^E Erase current line ^L Refresh screen ^T Tag top of region ^X Exchange tag and cursor ^Z Escape to DOS. Use ``exit'' to return Help is available through menu or F1. There is a menu (ESC). You can execute commands from the menu by typing ESC followed by the capital letter in the command or by moving to the command with the arrows and then typing return. A hint. You can read a file that contains prompts and then execute it. Note that you cannot !include a file with prompts, because they are not syntactically correct, but prompts are stripped from the beginning of the line when the editor sends lines to ISETL. 10.2 Mac Screen Editor The Macintosh version has an editor that needs no introduction. All operations are reachable from the menus, and follow the standard Macintosh usages. The only unusual feature is that highlighted regions can be run --- sent to the execution window and sent to ISETL as input. 48 10 EDITORS Table 2: Menu for MSDOS Editor Copy region Copies region to the end of the buffer. Save region Appends region to a file. Omits prompts. Read file Placed at end of buffer. save Buffer Saves buffer, with prompts. Quit Like !quit. buffer Info Information on buffer size and cursor position. Help Describes key maps. You can run by: ? Typing RETURN, ? Selecting Run from the menu, or ? Typing clover-R. In addition, typing RETURN on the last line of the Execution window causes that line to be sent to ISETL. 10.3 Interactive Line Editor (ILE) 10.3.1 Brief description The left and right arrows will move you within a line, permitting insertions of characters. delete removes the character at the cursor, backspace deletes the character left of the cursor. The interesting feature is that the up arrow moves you back thru the last hundred lines entered, with down arrow moving you forward. You can't go past the last entered line. You need to use !clear if you want to throw away your current input (since the last >) so that you can edit it. Example: > a := b + 10.3 Interactive Line Editor (ILE) 49 >> c + >> !clear > =up=> c + =up=> a := b + >> =up=> a := b + =up=> c + =edit=> c; The !clear had ISETL throw away the earlier input, but left it for subsequent editting. =up=> means typing the up arrow, followed by the new value displayed on that line. =edit=> means editing the line to produce the desired result. Below is a complete description of the new editor. 10.3.2 Default key bindings The interactive line editor is an input line editor that provides both line editing and a history mechanism to edit and re-enter previous lines. ISETL looks in the ile initialization file. See page 4 for more information. Not everyone wants to have to figure out yet another initialization file format so we provide a complete set of default bindings for all its operations. The following table shows the default bindings of keys and key sequences provided by ile. These are based on the emacs key bindings for similar operations. 50 10 EDITORS Key Effect VMS differences del delete char under ^A start of line undefined ^B backward char ^E end of line ^F forward char ^K erase to end of line ^L retype line ^N forward history ^P backward history ^U erase line ^V quote ^X delete char under delete delete char under delete char before back space delete char before start of line return add to history line feed add to history home start of line undefined end end of line undefined ^C interrupt ^Z end of file ^D end of file left backward char right forward char up backward history down forward history 10.3.3 Initialization File The ile initialization file is a list of table numbers, characters, and actions or strings. ile has 4 action tables. Each action table contains an action or string for each possible character. ile decides what to do with a character by looking it up in the table and executing the action associated with the character or by passing the string one character at a time into ile as if it had been typed by the user. Normally only table 0 10.3 Interactive Line Editor (ILE) 51 is used. The escape actions cause the next character to be looked up in a different table. The escape actions make it possible to map multiple character sequences to actions. By default, all entries in table 0 are bound to the insert action, and all entries in the other tables are bound to the bell action. User specified bindings override these defaults. The example in Table 3 is an initialization file that sets up the same key and delimiter bindings as the ile default bindings. The first character on each key binding line is the index of the table to place the key binding in. Valid values for the index are 0, 1, 2, and 3. The second character on the line is either the character to bind or an indicator that tells how to find out what character to bind. If the second character is any character besides `^ ' or `\' then the action is bound to that character. If the second character on the line is `^ ' then the next character is taken as the name of a control character. So ^ H is backspace and ^ [ is escape. If the second character on the line is a `\' and the next character is a digit between 0 and 7 the the following characters are interpreted as an octal number that indicates which character to bind the action to. If the character immediately after the `\' is not an octal digit then the action is bound to that character. For example, to get the `^ ' character you would use `\^ '. The next character on the line is always `='. Following the equal sign is the name of an action or a string. The actions are defined in the following table. 10.3.4 Actions bell Send a bell (^ G) character to the terminal. Hopefully the bell will ring. This action is a nice way to tell the user that an invalid sequence of keys has been typed. insert Insert the character into the edit buffer. If there are already 75 characters in the buffer ile will beep and refuse to put the character in the buffer. 52 10 EDITORS 0\177=delete_char_under 0^@=escape_3 0^A=start_of_line 0^B=backward_char 0^C=pass_thru 0^D=pass_thru 0^E=end_of_line 0^F=forward_char 0^J=add_to_history 0^H=delete_char 0^K=erase_to_end_of_line 0^L=retype_line 0^M=add_to_history 0^N=forward_history 0^P=backward_history 0^U=erase_line 0^V=quote 0^X=delete_char_under 0^Z=pass_thru 0^[=escape_1 1[=escape_2 2A=backward_history 2B=forward_history 2C=forward_char 2D=backward_char 3\107=start_of_line 3\110=backward_history 3\113=backward_char 3\115=forward_char 3\117=end_of_line 3\120=forward_history 3\123=delete_char_under Table 3: Example ile.ini file 10.3 Interactive Line Editor (ILE) 53 delete_char Delete the character directly to the left of the cursor from the edit buffer. delete_char_under Delete the character under the cursor from the edit buffer. quote The next character to come into ile will be inserted into the edit buffer. This allows you to put characters into the edit buffer that are bound to an action other than insert. escape_1 Look up the next character in action table 1 instead of action table 0. escape_2 Look up the next character in action table 2 instead of action table 0. escape_3 Look up the next character in action table 3 instead of action table 0. start_of_line Move the cursor to the left most character in the edit buffer. backward_char Move the cursor to the left one character. end_of_line Move the cursor past the last character in the edit buffer. forward_char Move the cursor to the right one character. add_to_history Add the contents of the edit buffer to the history buffer and pass the line along to the program running under ile. erase_line Clear the line. Erase all characters on the line. erase_to_end_of_line Delete the character under the cursor and all character to the left of the cursor from the edit buffer. retype_line Retype the contents of the current edit buffer. This is handy when system messages or other asynchronous output has garbled the input line. 54 10 EDITORS forward_history Display the next entry in the history buffer. If you are already at the most recent entry display a blank line. If you try to go forward past the blank line this command will beep at you. backward_history Display the previous entry in the history buffer. If there are no older entries in the buffer, beep. 10.3.5 Strings In addition to being able to bind a character sequence to an action ile allows characters sequences to be bound to strings of characters. When a string is invoked the characters in the string are treated as if they were typed by the user. For example, if the line: 0^G=ring^Ma^Mbell^M was in your ile.ini file, typing control G would cause three lines to be typed as if the user typed them. Using the default bindings, unless there is a ^ J or ^ M in the string the string will be inserted in the current line but not sent along until the user actually presses return. 10.3.6 Error Messages When ile encounters errors it prints a message and terminates. ile can print several standard error message. It can also print a few messages that are specific to ile. ? ile: '=' missing on line # In a character binding line you left out the `=' character. Or, you did something that confused the initialization file reader into thinking there should be an `=' where you didn't think there should be one. ? ile: error in initialization file on line # This means that the first character of a character binding line wasn't a newline or a 0, 1, 2, or 3. It could also mean that the initialization file reader is confused. 10.3 Interactive Line Editor (ILE) 55 A misspelled action name in an ile.ini will be treated as a string. This means that typing the sequence of characters that should invoke the action will actually cause the misspelled name to be inserted in the input line. 10.3.7 Copyright ile and this documentation was adapted from the program called ile. Permission to modify and distribute the program and its documentation is granted, subject to the inclusion of its copyright notice, which has been reproduced at the front of this manual. 56 11 RUNTIME ERRORS 11 Runtime Errors Error messages describe most problems by printing the operation with the offending values of the arguments. If !source was on when the program was read, you will get the source line where the error occurred. If !stack is on, lines containing the calls leading to this error will also be printed. One possible problem is that some values are very big: {1..1000} for instance. Therefore, there are two forms of the error messages, controlled by the !verbose directive. By default, verbose is off and large values are represented by their type. The directive !verbose on results in full values being printed. !verbose off returns you to short messages. See figure 6 for an example. 11.1 Fatal Errors The following errors cause ISETL to exit. Generally they indicate that the problem is larger than ISETL can manage. Please report cases where internal limits are exceeded to the author. ------------------------------------------------------------------ Allocated data memory exhausted Use !memory to raise limit. Includes too deeply nested Probably file includes itself. Out of parsing space Internal limit exceeded. Parser out of memory Internal limit exceeded. Too many locals Internal limit exceeded. Too many variables Internal limit exceeded. 11.2 Operator Related Messages 57 11.2 Operator Related Messages Most errors print the offending expression with the values (or types) of the arguments. A few have additional information attached. ------------------------------------------------------------------- + May refer to union. * May refer to inter. <relation> Refers to any of the relational operators. Boolean expected May occur in if, while, and, or, ?, and iterators. Can't iterate over Error in iterator. in LHS of assignment Error in selector on LHS. Multiple images Smap had multiple images. 58 11 RUNTIME ERRORS 11.3 General Errors These errors do not provide context by printing the values involved, but they are generally more specific. * Used for self explanatory messages internal Messages the user should never see Please report to author. ------------------------------------------------------------------------------- Arithmetic error Relates to machine limits Bad arg to mcPrint internal Bad args in low,next..high * Bad args in low..high * Bad format in readf * Bad mmap in iterator MMap iterator over non-map Can't mmap string Cannot perform selection in assignment Can't mmap tuple Cannot perform selection in assignment Cannot edit except at top level Edit not permitted within an include Divide by zero * Exact format too big in readf * Floating point error * Input must be an expression * Internal object too large * Iter_Next internal Nesting too deep for pretty printer. * Only one level of selection allowed See section 5 Return at top level * RHS in mmap assignment must be set * RHS in string slice assignment * must be string RHS in tuple slice assignment * must be tuple Return at top level * Slice lower bound too big * Slice upper bound too big * Stack Overflow * Stack Underflow * Too few arguments * Too many arguments * Wrong number of args * 11.3 General Errors 59 > !memory Current GC memory = 50060, Limit = 1024000 > !allocate 800000 Current GC memory = 500600, Limit = 1024000 ... > !memory 300000 Current GC memory = 50060, Limit = 300000 > !allocate 150000 Current GC memory = 150180, Limit = 300000 Figure 4: Finding memory limits 60 11 RUNTIME ERRORS > f := func(i); return f(i-1)+f(i-2); end; > !watch f !'f' watched > f(1) := 1; ! f(1) := 1; > f(2) := 1; ! f(2) := 1; > f(4); ! Evaluate: f(4); ! Evaluate: f(3); ! Evaluate: f(2); ! Yields: 1; ! Evaluate: f(1); ! Yields: 1; ! f returns: 2; ! Evaluate: f(2); ! Yields: 1; ! f returns: 3; 3; Figure 5: !watch examples 11.3 General Errors 61 > !verbose on > {1..3} + 5; ! Error -- Bad arguments in: {3, 1, 2} + 5; > !verbose off > {1..3} + 5; ! Error -- Bad arguments in: !Set! + 5; Figure 6: Runtime errors 62 11 RUNTIME ERRORS 63 12 The ISETL Grammar --- Compressed 12.1 Input at the Prompt INPUT --> PROGRAM INPUT --> STMT INPUT --> EXPR ; 12.2 Program PROGRAM --> program ID ; LOCALS VALUES STMTS end ; 12.3 Statements STMT --> LHS := EXPR ; STMT --> EXPR ; STMT --> if EXPR then STMTS ELSE-IFS ELSE-PART end ; ELSE-IFS --> ``Zero or more repetitions of ELSE-IF.'' ELSE-IF --> elseif EXPR then STMTS ELSE-PART --> else STMTS STMT --> for ITERATOR do STMTS end ; STMT --> while EXPR do STMTS end ; STMT --> read LHS-LIST ; STMT --> read LHS-LIST from EXPR ; STMT --> readf PAIR-LIST ; STMT --> readf PAIR-LIST to EXPR ; STMT --> print EXPR-LIST ; STMT --> print EXPR-LIST to EXPR ; STMT --> printf PAIR-LIST ; STMT --> printf PAIR-LIST to EXPR ; STMT --> return ; STMT --> return EXPR ; STMT --> take LHS from LHS ; STMT --> take LHS frome LHS ; STMT --> take LHS fromb LHS ; STMT --> write PAIR-LIST ; STMT --> write PAIR-LIST to EXPR ; STMT --> writeln PAIR-LIST ; 64 12 THE ISETL GRAMMAR --- COMPRESSED STMT --> writeln PAIR-LIST to EXPR ; STMTS --> ``One or more instances of STMT. The final semicolon is optional.'' PAIR-LIST --> ``One or more instances of PAIR, separated by commas.'' PAIR --> EXPR : EXPR PAIR --> EXPR 12.4 Iterators ITERATOR --> ITER-LIST ITERATOR --> ITER-LIST | EXPR ITER-LIST --> ``One or more SIMPLE-ITERATORs separated by commas.'' SIMPLE-ITERATOR --> BOUND-LIST in EXPR SIMPLE-ITERATOR --> BOUND = ID ( BOUND-LIST ) SIMPLE-ITERATOR --> BOUND = ID { BOUND-LIST } BOUND-LIST --> ``One or more instances of BOUND, separated by commas.'' BOUND --> ~ BOUND --> ID BOUND --> [ BOUND-LIST ] 12.5 Selectors SELECTOR --> ( EXPR-LIST ) SELECTOR --> { EXPR-LIST } SELECTOR --> ( EXPR .. EXPR ) SELECTOR --> ( .. EXPR ) SELECTOR --> ( EXPR .. ) SELECTOR --> ( ) 12.6 Left Hand Sides LHS-LIST --> ``One or more instances of LHS, separated by commas.'' LHS --> ID LHS --> LHS SELECTOR LHS --> [ LHS-LIST ] 12.7 Expressions and Formers 65 12.7 Expressions and Formers EXPR-LIST --> ``One or more instances of EXPR separated by commas.'' EXPR --> ID EXPR --> INTEGER EXPR --> FLOATING-POINT EXPR --> STRING EXPR --> true EXPR --> false EXPR --> OM EXPR --> newat EXPR --> FUNC-CONST EXPR --> if EXPR then EXPR ELSE-IFS ELSE-PART end ; EXPR --> ( EXPR ) EXPR --> [ FORMER ] EXPR --> { FORMER } FORMER --> ``Empty'' FORMER --> EXPR-LIST FORMER --> EXPR .. EXPR FORMER --> EXPR , EXPR .. EXPR FORMER --> EXPR : ITERATOR EXPR --> # EXPR EXPR --> not EXPR EXPR --> + EXPR EXPR --> - EXPR EXPR --> EXPR SELECTOR EXPR --> EXPR . ID EXPR EXPR --> EXPR . (EXPR) EXPR 66 12 THE ISETL GRAMMAR --- COMPRESSED EXPR --> EXPR OP EXPR Possible operators (OP) are: + - * / div mod ** with less = /= < > <= >= union inter in notin subset and or impl iff EXPR --> % BINOP EXPR EXPR --> EXPR % BINOP EXPR EXPR --> EXPR ? EXPR EXPR --> exists ITER-LIST | EXPR EXPR --> forall ITER-LIST | EXPR EXPR --> EXPR where DEFNS end EXPR --> EXPR @ EXPR BINOP --> ``Any binary operator or an ID or expression in parentheses whose value is a function of two parameters. The ID and parenthesized expression may be preceded by a period.'' The acceptable binary operators are: +, -, *, **, union, inter, /, div, mod, with, less, and, or, impl. DEFNS --> ``Zero or more instances of DEFN. The final semicolon is optional.'' DEFN --> BOUND := EXPR ; DEFN --> ID SELECTOR := EXPR ; 12.8 Function Constants FUNC-CONST --> FUNC-HEAD LOCALS VALUES STMTS end FUNC-CONST --> : ID-LIST OPT-PART -> EXPR : FUNC-HEAD --> func ( ID-LIST OPT-PART ) ; FUNC-HEAD --> func ( OPT-PART ) ; OPT-PART --> opt ID-LIST ``May be omitted.'' LOCALS --> local ID-LIST ; VALUES --> value ID-LIST ; ID-LIST --> ``One or more instances of ID separated by commas.'' Index ?, 32, 66 cos, 36 ! (directives), 16, 41 @, 33, 66 DEFN, 33, 66 :=, 17, 63 DEFNS, 33, 66 -, 28, 65 difference (-) of two sets, %, 32, 66 29, 66 .., 25--26, 64--65 directives, 41 +, 28, 65 div, 6, 29, 66 /, 29, 66 do, 6, 18, 63 ~, 24, 64 dollar sign, 6 abs, 39 domain, 36 !alias, 42 !allocate, 42, 44 !echo, 42 and, 6, 29, 66 !edit, 41, 43 arb, 39 else, 6, 18, 63 atom, 9 ELSE-IF, 21, 63 elseif, 6, 18, 63 BINOP, 33, 66 ELSE-IFS, 21, 63 BOUND, 24, 64 ELSE-PART, 21, 63 bound variable, 23 empty BOUND-LIST, 24, 64 set (!1_2!, ;), 10 tuple ([]), 11 call by value, 14 end, 6, 18, 33, 63, 66 cardinality (#) of a set, 28, eof, 38 65 equal, 29, 66 ceil, 35 error messages, 56 char, 35 even, 35 character set, 6 exists, 6, 32, 66 !clear, 41, 43 exit, 4 close, 38 exponentiation (**), 29, 66 !code, 42 EXPR, 27, 65 comments ($), 6 EXPR-LIST, 33, 65 compound operator (%), 32, 66 concatenation (+) false, 6, 8, 27, 65 string, 29, 66 !fast, 43 tuple, 29, 66 file, 9 CONSOLE, 38 fix, 35 67 68 INDEX float, 35 Interactive Line Editor, FLOATING-POINT, 27, 65 48--55 floating-point number, 7 intersection (*, inter, \ ), floor, 35 29--30, 66 for, 6, 18, 63 is..., 37 forall, 6, 32, 66 isetl.ini, 4, 44 FORMER, 25, 65 .isetlrc, 4, 44 from, 6, 18, 20, 63 ITERATOR, 23, 64 fromb, 6, 20, 63 ITER-LIST, 24, 64 frome, 6, 20, 63 func, 6, 12--15, 34, 66 FUNC-CONST, 28, 33, 65--66 length (#) FUNC-HEAD, 34, 66 of a string, 28, 65 function, 12--15, 26 of a tuple, 28, 65 application, 25 less, 6, 29, 66 modified at a point, 15 LHS, 27, 64 of several variables, 26 LHS-LIST, 27, 64 generalize operation, 32, 66 ln, 36 grammar, 16 lo, 39 local, 6 hi, 39 LOCALS, 34, 66 hyperbolic functions, 36 log, 36 ID, 27, 65 map, 12, 25 ID-LIST, 34, 66 max, 36 !ids, 42 max_line, 39 if, 6, 18, 63 !memory, 44 iff, 6, 29, 66 min, 36 ile.ini, 49 mmap, 25 image, 36 mod, 6, 29, 66 image, 25 MSDOS, 39 impl, 6, 29, 66 in, 6, 24, 29, 64, 66 newat, 6, 28, 65 !include, 5, 41 not, 6, 28, 65 INPUT, 17, 63 notin, 6, 29, 66 INTEGER, 27, 65 npow, 35 integer, 7 number, 7 inter, 6, 29, 66 odd, 35 INDEX 69 of, 6 scope, 14, 23 om, 6, 28, 65 SELECTOR, 25, 64 !oms, 42 set former, 10 opena, 38 sgn, 36 openr, 38 SIMPLE-ITERATOR, 24, 64 openw, 38 sin, 36 opt, 6, 34, 66 slice, 25 optional parameters, 14 !slow, 43 OPT-PART, 34, 66 smap, 25 or, 6, 29, 66 !source, 43 ord, 39 sqrt, 36 origin, 40 !stack, 43 PAIR, 21, 64 STMT, 16--17, 63 PAIR-LIST, 21, 64 STMTS, 21, 64 parameter, 14 STRING, 27, 65 pow, 35 subset, 6, 29, 66 !pp, 43 !system, 42, 45 precedence rules, 40 system, 39 precision, 39 take, 6, 20, 63 print, 6, 19, 39, 63 then, 6, 18, 63 printf, 6, 19 to, 6, 19, 63 PROGRAM, 17, 63 !trace, 42 program, 6 trace, 43--44 prompts, 4 transcendental functions, 36 trig functions, 36 !quit, 4, 41 true, 6, 8, 27, 65 quit, 4 type test, 37 random, 36, 39 union, 6, 29, 66 randomize, 36 union (+, union, [ ), 29, 66 read, 6, 18, 63 !unwatch, 43--44 readf, 6 !record, 42, 45 value, 6 relational operators, 29, 66 value declaration, 15 replication (*) VALUES, 34, 66 string, 29, 66 !verbose, 42 tuple, 29, 66 !version, 42 return, 6, 12, 20, 63 video, 39 70 INDEX !watch, 43--44 where, 6, 33, 66 while, 6, 18, 63 with, 6, 29, 66 write, 6 writeln, 6