1<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"> 2<html> 3<head> 4<title>Introdution to Poly</title> 5<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> 6</head> 7 8<body><strong>Note to online version</strong><br> 9This document was originally published as a Cambridge University Technical Report 10(TR29) and as part of my PhD thesis, Programming Language Design with Polymorphism, 11Cambridge University Technical Report TR49. It describes an early version of the 12Poly language. David C. J. Matthews, August 2003. 13<h1 align="center">INTRODUCTION TO POLY</h1> 14<h2 align="center">D.C.J. Matthews,May 1982<br> 15 Computer Laboratory,<br> 16 University of Cambridge </h2> 17 18<p><strong>Abstract</strong><br> 19 This report is a tutorial introduction to the programming language <strong>Poly</strong>. 20 It describes how to write and run programs in Poly using the VAX/UNIX implementation. 21 Examples given include polymorphic list functions, a double precision integer 22 package and a subrange type constructor.</p> 23<h2>Introduction to Poly</h2> 24<p>Poly is a programming language which supports polymorphic operations. This 25 document explains how it is used on the VAX. </p> 26<h4>1. Commands and Declarations</h4> 27<p>The system is entered by running the appropriate program (e.g.<strong> /mnt/dcjm/poly</strong> 28 at Cambridge). The compiler will then reply with a prompt (<font face="Courier New, Courier, mono">></font>). 29 To exit from Poly at any time type ctrl-D (end-of-text) or ctrl-C (interrupt). 30 There are three types of instructions which can be typed to Poly; declarations 31 of identifiers, statements (commands), or expressions. An example of a command 32 and the output it produces is</p> 33<pre>> print("Hello"); 34Hello</pre> 35<p>Note the closing semicolon which must be present to indicate the end of the 36 command. If you forget it the compiler will print a <font face="Courier New, Courier, mono">#</font> 37 as a prompt to indicate that the command is not yet complete.</p> 38<p>An example of an expression is</p> 39<pre>> "Hi"; 40Hi </pre> 41<p>Poly prints the value of an expression without the need to type the word 'print'. 42</p> 43<p>Commands can be grouped by enclosing them with the bracketing symbols <strong>begin</strong> 44 and <strong>end</strong> or <strong>(</strong> and <strong>)</strong>. For instance 45<pre>> begin 46# print("Hello"); 47# print(" again") 48# end; 49Hello again</pre> 50Any object in Poly can be bound to an identifier by writing a declaration. For 51instance 52<pre>> let message == "Hello "; </pre> 53declares an identifier 'message' to have the value of the string 'Hello '. It 54can be printed in the same way as the string constant. 55<pre>> message; 56Hello </pre> 57<p>Names can be either a sequence of letters and digits starting with a letter, 58 or a sequence of the special characters + - * = < > etc. Certain names are reserved 59 to have special meanings and cannot be used in declarations. Those words can 60 be written in upper, lower or mixed case, all other words are considered to 61 be different if written in different cases. When declaring a name made up of 62 the special characters remember to put a space between the name and the == or 63 colon which follows it. Comments are enclosed in curly brackets <strong>{</strong> 64 and <strong>}</strong>. They are ignored by the compiler and are equivalent 65 to a single space or newline between words.</p> 66<h3> 2. Procedures</h3> 67<p>Statements or groups of statements can be declared by making them into procedures. 68</p> 69<pre>> let printmessage == 70# proc() 71# (print("A message ")); </pre> 72<p>A procedure consists of a procedure header (in this case the word <strong>proc</strong> 73 and parentheses <strong>(</strong> and <strong>)</strong> ) and a body. The 74 procedure body must be enclosed in bracketing symbols (in this case '(' and 75 ')') even if there is only one statement. </p> 76<p> This is simply another example of a declaration. Just as previously 'message' 77 was declared to have the value "Hello#", 'printmessage' has been declared with 78 the value of the procedure. </p> 79<p> The procedure is called by typing the procedure name followed by <strong>()</strong>. 80</p> 81<pre>> printmessage(); 82A message </pre> 83 84<p>The effect of this is execute the body of the procedure and so print the string. 85</p> 86<p>Procedures can take arguments so that values can be passed to them when they 87 are called. </p> 88<pre>> let pmessage == 89# proc(m : string) 90# begin 91# print("The message is :"); 92# print(m) 93# end; </pre> 94This can be called by typing 95<pre>> pmessage("Hello"); 96The message is :Hello </pre> 97or by typing 98<pre>> pmessage("Goodbye"); 99The message is :Goodbye </pre> 100<h3>3. Specifications</h3> 101<p>As well as having a value all objects in Poly have a specification, analogous 102 to a type in other languages. It is used by the compiler to ensure that only 103 meaningful statements will be accepted. You can find the specification of a 104 declared name x by typing <strong>? "x";</strong>. </p> 105<pre>> ? "message"; 106message : string </pre> 107This means that message is a constant belonging to the type 'string'. 108<pre>> ? "pmessage"; 109pmessage : PROC(string) </pre> 110This means that pmessage is a procedure taking a value of type string as its argument. 111Since message has that specification the call 112<pre>> pmessage(message); 113The message is :Hello </pre> 114will work. Likewise the call 115<pre>> pmessage("Hi"); 116The message is :Hi </pre> 117will work because "Hi" also belongs to type string. However 118<pre>> pmessage(pmessage); 119Error - specifications have different forms </pre> 120 121<p>will fail because 'pmessage' has the wrong specification. Incidentally, the 122 specification of the procedure is the same as the header used when it was declared, 123 ignoring the differences in the case of some of the words.</p> 124<h3>4. Integer and Boolean</h3> 125<p>So far the only constants used have been those belonging to the type string. 126 Another type, <strong>integer</strong> provides operations on integral numbers. 127</p> 128<pre>> print(42); 12942 </pre> 130The usual arithmetic operations +, -, *, div, mod, succ and pred are available. 131<pre>> 42+10-2; 50 </pre> 132However, unlike other languages all infix operators have the same precedence so 133<pre>> 4+3*2; 14 </pre> 134 135<p>prints 14 rather than 10. Also - is an infix operator only, there is a procedure 136 neg which complements its argument. </p> 137<p>Another 'standard' type is <strong>boolean</strong> which has only two values 138 <strong>true</strong> and <strong>false</strong>. Its main use is in tests for 139 equality (the <strong>=</strong> operator), inequality (<strong><></strong>) 140 and magnitude (<strong>> < >= <=</strong>). </p> 141<pre>> let two == 2; 142> 1 = two; 143false 144> 2 = two; 145true 146> 3 <> 4; 147true 148> 4 >= 5; 149false </pre> 150The expression '1 = two' has type boolean. Identifiers can be declared to have 151boolean values in the same way as integers and strings. 152<pre>> let testtwo == two > 1; </pre> 153<p>declares testtwo to be 'true' since 'two' is greater than 1. There are three 154 operators which work on boolean values, <strong>&</strong>, <strong>|</strong> 155 and <strong>~</strong>. <strong>~</strong> is a prefix operator which complements 156 its argument (i.e. if its argument was false the result is true, and vice-versa). 157 <strong>&</strong> is an infix operator which returns true only if both its 158 arguments are true. <strong>|</strong> is also an infix operator which returns 159 true if either of its arguments is true. </p> 160<h3>5. If-Statement</h3> 161<p>Boolean values are particularly useful since they can be tested using <strong>if</strong>. 162 The if-statement causes different statements to be obeyed depending on a condition. 163</p> 164<pre>> if two = 2 165# then print("It is two") 166# else print("It isn't two"); 167It is two </pre> 168tests the value of the expression 'two = 2' and executes the statement after the 169word <strong>then</strong> if it is true, and the statement after the word <strong>else</strong> 170if it is false. This could be written as a procedure, 171<pre>> let iszero == 172# proc(i: integer) 173# (if i = 0 then print("It is zero") 174# else print("It isn't zero")); </pre> 175which could then be called to test a value. 176<pre>> iszero(4); 177It isn't zero</pre> 178since 4 is not zero. If-statements can return values as well as perform actions 179in the then and else parts. An alternative way of writing 'iszero' could have 180been 181<pre>> let iszero == 182# proc(i: integer) 183# (print( 184# if i = 0 185# then "It is zero" 186# else "It isn't zero" 187# )); </pre> 188 189<p>This version tests the condition, and returns one or other of the strings for 190 printing. This can only be used if both the then and else parts return values 191 with similar specifications (in this case both sides return string constants). 192 The version of the if-statement which does not return a value can be written 193 with only a then-part. If the then-part returns a value there must be an else-part 194 (otherwise what value would be returned if the condition were false?). </p> 195<h3>6. More on Procedures</h3> 196<p>Procedures can be written which return results. For instance a further way 197 of writing 'iszero' would be to allow it to return the value of the string. 198</p> 199<pre>> let iszero == 200# proc(i: integer)string 201# (if i = 0 then "It is zero" 202# else "It isn't zero"); 203> ? "iszero"; 204iszero : PROC(integer)string</pre> 205Calling it would then cause it to return the appropriate string which would then 206be printed. 207<pre>> iszero(0); 208It is zero </pre> 209Another example is a procedure which returns the square of its argument. 210<pre>> let sqr == 211# proc(i: integer)integer (i*i); </pre> 212declares sqr to be a procedure which takes an argument with type integer and returns 213a result with type integer. The body of the procedure evaluates the square of 214the argument i, and the result is the value of the expression. The call 215<pre>> sqr(4); 21616 </pre> 217<p>will therefore print out the value 16. </p> 218<p> Procedures in Poly can be written which call themselves, i.e. recursive procedures. 219 These are declared using <strong>letrec</strong> rather than <strong>let</strong>. 220</p> 221<pre>> letrec fact == 222# proc(i: integer)integer 223# (if i = 1 then 1 224# else i*fact(i-1)); </pre> 225This is the recursive definition of the factorial function. The procedure can 226be called by using 227<pre>> fact(5); 228120 </pre> 229 230<p>which prints the result. <strong>letrec</strong> has the effect of making the 231 name being declared available in the expression following the <strong>==</strong>, 232 whereas <strong>let</strong> does not declare it until after the closing semicolon. 233</p> 234<h3>7. Variables</h3> 235<p>Constants are objects whose value cannot be changed. There are also objects 236 whose value can change, these are variables. Variables are created by declarations 237 such as </p> 238<pre>> let v == new(0); </pre> 239The procedure 'new' returns a variable whose initial value is the argument. 240<pre>> v; 2410 </pre> 242A new value can be given to v by using the assignment operator. 243<pre>> v := 3; 244> v; 2453 </pre> 246Thus v now has the value 3. The new value can depend on the old value. 247<pre>> v := (v+2); </pre> 248Sets the value to be 5. The parentheses are necessary because otherwise the order 249of evaluation would be strictly left-to-right. Variables can be of any type. 250<pre>> let sv == new("A string"); </pre> 251 252<p>declares sv to be a string variable. The specification of a variable is not 253 as simple as it may seem and will be dealt with later.</p> 254<h3>8. The While Loop</h3> 255<p> It is often necessary to repeat some statements more than once. This can be 256 done using the <strong>while</strong> statement. For instance </p> 257<pre>> let x == new(10); 258> while x <> 0 259# do 260# begin 261# print(x*x); 262# print(" "); 263# x := pred(x) 264# end; 265100 81 64 49 25 16 9 4 1 </pre> 266prints the square of all the numbers from 10 down to 1. The body of the loop (the 267statement after the word <strong>do</strong>) is executed repeatedly while the 268condition (the expression after the word <strong>while</strong>) is true. The 269condition is tested before the loop is entered, so 270<pre>> while false 271# do print("Looping"); </pre> 272 273<p>will not print anything.</p> 274<h3> 9. Operators</h3> 275<p>We have already seen examples of operators such as + and &. In Poly operators 276 are just procedures whose specifications include the words <strong>infix</strong> 277 or <strong>prefix</strong>. They are declared in a similar way to procedures, 278 for instance </p> 279<pre>> let sq == proc prefix (i : integer)integer (i*i); </pre> 280has declared sq as a prefix operator. It can be used like any other prefix operator: 281<pre>> sq 3; 2829 </pre> 283 284<p>The difference between a prefix operator and other procedures is that the argument 285 to a prefix operator does not need to be in parentheses. Infix operators can 286 be defined similarly.</p> 287<h3>10. The Specifications of Types</h3> 288<p>All objects in Poly have specifications. This includes types such as string, 289 integer and boolean. </p> 290<pre> > ? "boolean"; 291boolean : TYPE (boolean) 292 & : PROC INFIX (boolean; boolean)boolean; 293 false : boolean; 294 print : PROC (boolean); 295 true : boolean; 296 | : PROC INFIX (boolean; boolean)boolean; 297 ~ : PROC PREFIX (boolean)boolean 298END </pre> 299Types in Poly are regarded as sets of "attributes". These attributes are usually 300procedures or constants but could be other types. The attributes of a type can 301be used exactly like ordinary objects with the same specification. However, since 302different types may have attributes with the same name, it is necessary to prefix 303the name of the attribute with the name of the type separated by <strong>$</strong>. 304<pre>> integer$print(5); 3055 </pre> 306This invokes the attribute 'print' belonging to integer and prints the number. 307Most types have a print attribute which prints a value of that type in an appropriate 308format. $ acts a selector which finds the attribute belonging to a particular 309type. It is not an operator so operators always work on the selected name rather 310than the type name. 311<pre>> ~ boolean$true; 312false </pre> 313<h3>11. Records</h3> 314<p>Poly allows new types to be created in the same way as new procedures, constants 315 or variables. One way of creating a new type is by making a record. A record 316 is a group of similar or dissimilar objects. </p> 317<pre>> let rec == record(a, b: integer);</pre> 318This declares 'rec' to be a record with two components, a and b, both of type 319integer. 320<pre>> ? "rec"; 321rec : TYPE (rec) 322 a : PROC(rec)integer; 323 b : PROC(rec)integer; 324 constr : PROC(integer;integer)rec 325END </pre> 326'constr' is a procedure which makes a record by taking two integers, and 'a' and 327'b' are procedures which return the 'a' and 'b' values of the record. 328<pre>> let recv == rec$constr(3, 4); </pre> 329creates a new record with 3 in the first field (a) and 4 in the second field (b). 330The result is given the name 'recv'. 331<pre>> rec$a(recv); 3323 333> rec$b(recv); 3344 </pre> 335<p>show that the values of the individual fields can be found by using 'a' and 336 'b' as procedures. They must of course be prefixed by 'rec$' to show the type 337 they belong to.</p> 338<p>Records can be made with fields of any specification, not just constants. </p> 339<pre>> let arec == 340# record(x:integer; p: proc(integer)integer); </pre> 341declares a record with fields x and p, x being an integer constant and p a procedure. 342<pre>> let apply == 343# proc(z : arec)integer 344# begin 345# let pp == arec$p(z); 346# pp(arec$x(z)) 347# end; </pre> 348is a procedure which takes a constant of this record type and applies the procedure 349p to the value x and returns the result. In fact, it is not necessary to declare 350pp in the body of the procedure. An alternative way of writing apply is 351<pre>> let apply == 352# proc(z : arec)integer 353# (arec$p(z)(arec$x(z))); </pre> 354<h3>12. Unions</h3> 355<p>Another way of constructing a type is using a 'union'. A union is a type whose 356 values can be constructed from the values of several other types. For instance 357 a value of a union of integer and string could be either an integer or a string. 358</p> 359<pre>> let un == union(int: integer; str: string); </pre> 360This has created a type which is the union of integer and string. A value of the 361union type can be constructed by using an injection function. This union type 362has two such functions, their names made by appending 'int' and 'str' onto the 363letters 'inj_', making 'inj_int' and 'inj_str'. ('int' and 'str' were the 'tags' 364given in the declaration, in a similar way to fields in a record). 365<pre>> let intunion == un$inj_int(3); </pre> 366This has created a value with type 'un' containing the integer value 3. 367<pre>> let stringunion == un$inj_str("The string"); </pre> 368creates a value, also with type 'un', but this time containing a string. Given 369a value of a union type it is often useful to be able to decide which of its constituent 370types it was made from. For each of the 'tags' there is a procedure whose name 371is made by prefixing with the letters 'is_', which returns 'true' or 'false' depending 372on whether its argument was made from the corresponding injection function. 373<pre>> un$is_int(intunion); true </pre> 374prints 'true' because intunion was made from 'inj_int'. However 375<pre>> un$is_str(intunion); 376false </pre> 377Values of the original types can be obtained by using 'projection' functions, 378which are the reverse of the 'injection' functions. Their names are made by prefixing 379the tags with 'proj_' to make names like 'proj_str' and 'proj_int'. 380<pre>> un$proj_int(intunion); 3813 382> un$proj_str(stringunion); 383The string </pre> 384print the original values. It is possible to write 385<pre>> un$proj_str(intunion); 386Exception projecte raised </pre> 387because 'intunion' has type 'un', just like 'stringunion'. However, 'proj_str' 388is expected to return a value with type string so when this is run it will cause 389an error. The effect will be to raise an 'exception' called 'projecterror' which 390means that a projection procedure was given an argument constructed using a different 391injection procedure. 392<pre>> let unprojstr == un$proj_str; 393> ? "unprojstr"; 394unprojstr : PROC(un)string RAISES projecterror </pre> 395<p>shows that 'proj_str' may raise 'projecterror'. Exceptions will be dealt with 396 in more detail later on. </p> 397<h3>13. The Type-Constructor</h3> 398<p>It is often useful to be able to construct a type which is similar to an existing 399 one but with additional attributes. This can be done by using the type-constructor. 400</p> 401<pre>> let nrec == 402# type (r) extends rec; 403# let print == 404# proc(v : r) 405# begin 406# print(r$a(v)); 407# print(","); 408# print(r(v)) 409# end 410# end; 411> ? "nrec"; 412 nrec : TYPE (nrec) 413 a : PROC (nrec)integer; 414 b : PROC (nrec)integer; 415 constr : PROC (integer; integer)nrec; 416 print : PROC (nrec) 417END </pre> 418This declares 'nrec' to be a new type which is an 'extension' of an existing type 419'rec'. It then lists the new attributes, in this case just the procedure 'print', 420which are declared just as though they were ordinary declarations. The name 'r' 421in parentheses which follows the word 'type' is the name for the new type within 422the body of the type constructor, so the argument of the procedure 'print' is 423given the type 'r'. It is important to remember that the new type is a completely 424separate type from 'rec'. Values <em>can</em> be changed from the old to the new 425type and vice versa, but they cannot be used interchangeably. The specification 426of nrec is similar to that of rec except that there is now an extra procedure 427'print'. 428<pre>> let nrecv == nrec$constr(5,6); 429> nrec$print(nrecv); 4305,6 </pre> 431makes a value with type nrec, and prints it using the new 'print' attribute. It 432is possible to write simply 433<pre>> print(nrecv); 4345,6 </pre> 435because there is a procedure 'print' which looks for the 'print' attribute of 436the type of the value given, and then calls it. This is the way integers and strings 437are printed (they both have 'print' attributes). Many of the other operations 438such as ':=' and '+' work in a similar way. A further alternative is to write 439an expression. 440<pre>> nrecv; 4415,6 </pre> 442 443<p>In this case the compiler looks for the 'print' attribute and applies it. </p> 444<h3>14. A Further Example</h3> 445<p>This record could be extended in a different way, to make a double-precision 446 integer. Suppose that the maximum range of numbers which could be held in a 447 single integer was from -9999 to 9999. Then a double-precision number could 448 be defined by representing it as a record with two fields, a high and low order 449 part, and the actual number would have value (high)*10000 + (low). This can 450 be implemented as follows. </p> 451<pre> > let dp == 452# type (d) extends record(hi, lo: integer); 453# let succ == 454# proc(x:d)d 455# begin 456# if d$lo(x) = 9999 457# then d$constr(succ(d$hi(x)), 0) 458# else if (d$hi(x) < 0) & (d$lo(x) = 0) 459# then d$constr(succ(d$hi(x)), neg(9999)) 460# else d$constr(d$hi(x), succ(d$lo(x))) 461# end; 462# let pred == 463# proc(x:d)d 464# begin 465# if d$lo(x) = neg(9999) 466# then d$constr(pred(d$hi(x)), 0) 467# else if (d$hi(x) > 0) & (d$lo(x) = 0) 468# then d$constr(pred(d$hi(x)), 9999) 469# else d$constr(d$hi(x), pred(d$lo(x))) 470# end; 471# let print == 472# proc(x:d) 473# begin 474# if d$hi(x) <> 0 475# then 476# begin 477# print(d$hi(x)); 478# if abs(d$lo(x)) < 10 479# then print("000") 480# else if abs(d$lo(x)) < 100 481# then print("00") 482# else if abs(d$lo(x)) < 1000 483# then print("0"); 484# print(abs(d$lo(x))) 485# end 486# else print(d$lo(x)) 487# end; 488# let zero == d$constr(0,0); 489# let iszero == 490# proc(x:d) boolean 491# ((d$hi(x) = 0) & (d$lo(x) = 0)) 492# end; </pre> 493 494<p>This is sufficient to provide the basis of all the arithmetic operations, since 495 +,-,* etc. can all be defined in terms of succ, pred, zero and iszero.</p> 496<h3>15. Exceptions</h3> 497<p>In the section on union types above mention was made of exceptions. In the 498 case of the projection operations of a union type an exception is raised when 499 attempting to project a union value onto a type which was not the one used in 500 the injection. An exception is simply a name and any exception can be raised 501 by writing 'raise' followed by the name of the exception. </p> 502<pre>> raise somefault; 503Exception somefault raised </pre> 504raises an exception called 'somefault'. 505<pre>> let procraises 506# == proc(b: boolean) 507# (if b then raise afault); </pre> 508has specification 509<pre>PROC(b: boolean) RAISES afault </pre> 510<p>Various operations, as well as projection, may raise exceptions. For instance 511 many of the attributes of integer, such as 'succ' raise the exception 'rangeerror' 512 if the result of the operation is outside the range which can be held in an 513 integer constant. 'div' will raise 'divideerror' if it is asked to divide something 514 by 0.</p> 515<p>As well as being raised exceptions can also be caught, which allows a program 516 to recover from an error. A group of statements enclosed in brackets or 'begin' 517 and 'end' can have a 'catch phrase' as the last item. A catch phrase is the 518 word <strong>catch</strong> followed by a procedure. e.g. 'catch p' will catch 519 any exception raised in the group of statements and apply p to its name. </p> 520<pre>>let proccatches == 521# proc(excp: string) (print(excp)); 522> begin 523# procraises(true); 524# catch proccatches 525# end; 526afault </pre> 527'proccatches' has been declared as a procedure which takes a argument of type 528string. The exception is raised by 'procraises' and, since it is not caught in 529that procedure it propagates back to the point at which 'procraises' was called. 530The catch phrase catches the exception and calls the procedure with the name of 531the exception as the argument. The catching procedure can then look at the argument 532and decide what to do. 533<pre>> begin 534# procraises(false); 535# catch proccatches 536# end; </pre> 537<p>does not print anything because an exception has not been raised and so the 538 procedure is not called.</p> 539<p>If the block containing the catch phrase returns a value, then the catching 540 procedure must return a similar value. </p> 541<pre>> let infinity == 99999; 542> let divi == 543# proc infix(a, b: integer)integer 544# begin 545# a div b 546# catch proc(string)integer (infinity) 547# end; </pre> 548<p>This declares 'divi' to be similar to 'div' except that instead of raising 549 an exception it returns a large number. Since 'a div b' returns an integer value 550 the catch phrase must also return an integer.</p> 551<h3>16. The Specification of Variables</h3> 552<p>The specification of a variable in Poly is not, as one might expect, a constant 553 of some reference type or a separate kind of specification, but each variable 554 is in fact a separate type. Since a type in Poly is simply a set of constants, 555 procedures or other types, a type can be used simply as a way of conveniently 556 grouping together objects. </p> 557<pre>> let intpair == 558# type 559# let first == 1; 560# let second == 2 561# end; </pre> 562<p>This has declared 'intpair' to be a pair of integers containing the values 563 1 and 2. 'intpair$first' and 'intpair$second' can be used as integer values 564 directly. </p> 565<p> The specification of an integer variable is </p> 566<pre>TYPE 567assign: PROC(integer); 568content: PROC()integer 569END </pre> 570A variable is a pair of procedures, 'assign' which stores a new value in the variable, 571and 'content' which extracts the current value from it. The standard assignment 572operator ':=' simply calls 'assign' on the variable. The compiler inserts a call 573to 'content' automatically when a variable is used when a constant is expected. 574'assign' and 'content' can both be called explicitly. 575<pre>> let vx == new(5); 576> vx$assign(vx$content() + 1); 577> vx$content(); 5786 </pre> 579As an example of a more complicated variable, suppose we wanted to write a subrange 580variable, similar to a subrange in Pascal, which could hold values between 0 and 58110. 582<pre>> let sr == 583# begin 584# let varbl == new(0); 585# type 586# let content == varbl$content; 587# let assign == 588# proc(i: integer) 589# (if (i < 0) | (i > 10 590# then raise rangeerror 591# else varbl$assign(i)) 592# end 593# end; </pre> 594'varbl' is an integer variable which is initially set to 0. 'assign' checks the 595value before assigning it to 'varbl', and raises an exception if it is out of 596range. 'content' is just the 'content' procedure of the variable. It can be used 597in a similar way to a simple variable. 598<pre>> sr := 2; 599> sr; 6002 601> sr := 20; 602Exception rangeerror raised 603> sr; 6042 </pre> 605<h3>17. Specifications in Declarations</h3> 606<p>The double-precision type declared above has one drawback. The specification 607 contains the 'hi', 'lo' and 'constr' attributes in the specification of the 608 type which would allow someone to construct a value which had the type 'dp', 609 but had, for instance, fields outside the range -9999 to 9999 or with different 610 signs. This could make some of the operations fail to work. We need a way of 611 hiding details of the internals of a type declaration so that they do not appear 612 in the specification, and so cannot be used outside. In Poly a specification 613 can be given to something explicitly as well as having it inferred from the 614 declaration. </p> 615<pre>> let aconst: integer == 2; </pre> 616declares 'aconst' and forces it to have type 'integer'. The specification is written 617in the same way as the specification of the argument of a procedure. 618<pre>> let quote : proc(string) 619# == proc(x: string) 620# begin 621# print("`"); 622# print(x); 623# print("'") 624# end; </pre> 625is another example of explicitly giving a specification to a value. An explicitly 626written specification is the specification of the name which is being declared. 627It need not be identical to the specification of the value following the '=='. 628However it must be possible to convert the specification of the value to the explicit 629specification (the 'context'). 630<pre>> let avar == new(3); 631> let bconst: integer == avar; </pre> 632declares 'avar' to be an integer variable and 'bconst' to be an integer constant. 633In the latter case the specification is necessary, otherwise 'bconst' would have 634been a variable and would have been another name for 'avar'. The conversion of 635a variable to a constant in order to match a given specification is one example 636of a 'coercion' of a value to match a 'context'. There are several others which 637can be applied depending on the particular specification. For instance the specification 638of a procedure may be changed from an operator to a simple procedure or vice versa. 639<pre>> let plus: 640# proc(integer;integer)integer raises rangeerror 641# == integer$+ ; </pre> 642declares 'plus' as a procedure which is the same as the '+' attribute of integer 643except that it is not an infix operator. 644<pre>> plus(3,4); 6457 </pre> 646<p>The list of exceptions raised by the procedure must be included in the specification. 647 The exception list in the specification given must include all the exceptions 648 which may be raised, but may include others as well. A special exception name 649 <strong>any</strong> can be used to indicate that a procedure can raise any 650 exception. Any exception list will match a context with exception list 'raises 651 any'. </p> 652<p> The specifications of the arguments and result must all match. </p> 653<pre>> let dble: 654# type (d) 655# succ, pred: proc(d)d raises rangeerror; 656# print: proc(d) raises rangeerror; 657# zero: d; 658# iszero: proc(d)boolean; 659# end 660# == dp; </pre> 661 662<p>creates a new type 'dble' with the specification given. The specification is 663 the same as that of 'dp' but with some of the attributes of dp missing. </p> 664<p> In the case of types the specification of the value must possess all the attributes 665 of the explicit specification, but the explicit specification need not include 666 all the attributes of the value. If a type is regarded as a set of named attributes 667 then it is possible to take a subset of them and make them into a new type, 668 simply by giving the new type the required specification. The specification 669 of each attribute must itself match the specification that is given for it. 670</p> 671<p> This mechanism provides a way of 'hiding' internal operations from the specification 672 of a type. The specification of 'dble' above has only those attributes which 673 are necessary to use it, and none of the operations which are used internally.</p> 674<h3>18. Types as Results of Procedures</h3> 675<p>So far we have considered procedures which take constants as arguments or return 676 constants as results. In Poly values of any specification can be passed to or 677 returned from a procedure. For instance </p> 678<pre>> let subrange 679# == proc(min, max, initial: integer) 680# type (s) 681# content: proc()integer; 682# assign: proc(integer) raises outofrange 683# end 684# begin 685# type 686# let varbl == new(initial); 687# let content == varbl$content; 688# let assign == 689# proc(i: integer) 690# (if (i < min) | (i > max) 691# then raise outofrange 692# else varbl$assign(i)) 693# end 694# end; </pre> 695This procedure is similar to the definition of the subrange type 'sr' previously. 696However the bounds of the type are now arguments of a procedure so their values 697can be supplied when the program is run. Also new subrange variables can be created 698by calling the procedure. 699<pre>> let sv == subrange(0,10,0); </pre> 700<p>This creates 'sv' as a variable of this subrange type. As with any procedure 701 the arguments can be arbitrary expressions provided they return results with 702 the correct specification. </p> 703<h3>19. Types as Arguments to Procedures</h3> 704<p>Types can be passed as arguments as well as being returned from procedures. 705</p> 706<pre>> let copy == 707# proc(atype: type end) 708# type (t) 709# into: proc(atype)t; 710# outof: proc(t)atype 711# end 712# begin 713# type (t) extends atype; 714# let into == t$up 715# let outof == t$down 716# end 717# end; </pre> 718This procedure takes a type and returns a type with two operations 'into' and 719'outof'. 'up' and 'down' are procedures which are created when 'extends' is used, 720and provide a way of converting between the original and the resulting types. 721The specification of 'atype' merely says that it must be passed a type as an argument, 722but since it does not list any attributes then any type can be used as an actual 723argument (this is effectively saying that the empty set is a subset of every set). 724The procedure can be called, giving it an actual type as argument. 725<pre>> let copyint == copy(integer);</pre> 726The specification of the result is 727<pre>TYPE (copyint) 728into: PROC(integer)copyint; 729outof: PROC(copyint)integer 730END; </pre> 731The specification of copyint allows mapping between integer and copyint since 732the type integer has been included in the specification. 733<pre>> let copy5 == copyint$into(5); 734> copyint$outof(copy5); 7355 </pre> 736has mapped the integer constant 5 into and out of 'copyint'. 737<pre>> let copychar == copy(char); </pre> 738 739<p>creates a similar type which maps between char and copychar.</p> 740<h3>20. Polymorphic Procedures</h3> 741<p>There are often cases where, in addition to passing a type as a argument, one 742 or more values of that type are passed as well. For instance a procedure to 743 find the second successor of a value might be written as </p> 744<pre>> let add2 == 745# proc(atype: 746# type (t) 747# succ: proc(t)t raises rangeerror 748# end; 749# val: atype) 750# (atype$succ(atype$succ(val)));</pre> 751The specification of 'val' is that it must be a constant, and its type is 'atype'. 752However 'atype' is also an argument to the procedure so the specification really 753means that this procedure could be called by giving it any type with the required 754attributes, and a constant which must be of the same type as the first argument. 755<pre>> add2(integer, 2); 7564 </pre> 757Similarly 758<pre>> add2(char, 'A'); C </pre> 759However 760<pre>> add2(integer, 'A'); </pre> 761and 762<pre>> add2(string, "A string"); </pre> 763 764<p>both fail, in the first case because 'A' is not integer, and in the second 765 because string does not have a successor function.</p> 766<h3> 21. Implied Arguments</h3> 767<p>Many types have a 'print' attribute which prints a constant of the type. </p> 768<pre>> let pri == 769# proc(printable: type (t) print(t) end; val: printable) 770# (printable$print(val)); </pre> 771declares 'pri' as a procedure which takes as arguments a type and a constant of 772that type and prints the constant using the 'print' attribute. This can be called 773by writing 774<pre>> pri(integer, 3); or > pri(char, 'a'); </pre> 775since both 'integer' and 'char' have a 'print' attribute. Having to pass the type 776explicitly is really unnecessary, since it is possible for the system to find 777the type from the specification of the constant. It would be possible for the 778system to convert 'pri(3)' into 'pri(integer,3)' since '3' has type integer. In 779Poly types which can be deduced from the specifications of other arguments can 780be declared as 'implied' arguments. A argument list written in square brackets, 781<strong>[</strong> and <strong>]</strong>, can precede the normal argument list 782and those parameters, which must be all be types, are inferred from the other 783actual arguments when the procedure is called. 784<pre>> let prin == 785# proc [printable: type (t) print: proc(t) end] 786# (val: printable) 787# (printable$print(val)); 788 </pre> 789This can now be called by writing 790<pre>> prin(3); 791or 792> prin("hello");</pre> 793and is in fact the definition of 'print' in the standard library. Alternatively 794'prin' could have been declared by giving it an explicit specification and using 795'pri'. 796<pre>> let prin: proc[printable: type (t) print: proc(t) end] 797# (printable) 798# == pri; </pre> 799This is another form of conversion which can be made using an explicit specification. 800Using implied parameters can simplify considerably the use of procedures with 801types as arguments, and allow infix or prefix operators to be used in cases where 802they could not otherwise be used. For instance, consider an addition operation 803defined as 804<pre>> let add == 805# proc(summ: type (s) + : proc infix (s;s) raises rangeerror 806# end; 807# i, j: summ)summ 808# (i + j); </pre> 809would be used by writing 810<pre>> add(integer, 1, 2); 8113 </pre> 812However, by writing 813<pre>> let + 814# : proc infix [summ: type(s) 815# + : proc infix (s;s)raises rangeerror 816# end] 817# (i, j: summ)summ raises rangeerror 818# == add; </pre> 819 820<p>'+' can become an infix operator, since it has only two actual arguments. Similar 821 definitions are used for many of the other declarations in the library. </p> 822<h3>22. Literals</h3> 823<p>We have already seen how constants can be written as "Hello" or 42. These are 824 known as literal constants, because their values are given by the characters 825 which form them, rather than by some previous declaration. They are however, 826 only sequences of characters, it is only by convention that "Hello" is a string 827 constant and 42 an integer constant. This is only important when we wish to 828 use some other definition than the 'standard' one. For instance, if the type 829 integer were restricted to the range -9999 to 9999 then the constant 100000 830 would be an error if it were treated as an integer. The definition of double-precision 831 integer above, would, however, be able to represent it.</p> 832<p>In Poly, therefore, literals have no intrinsic type, they must be converted 833 into a value by the use of a conversion routine. The compiler recognises certain 834 sequences of characters as literals rather than names or special symbols. The 835 three forms of literal constants recognised by the compiler are 'numbers', 'double-quoted 836 sequences' and 'single-quoted sequences'. 'Numbers' begin with a digit and may 837 consist of numbers or letters. </p> 838<pre>42 0H3F6A 3p14159 </pre> 839are examples of 'numbers'. 'Double-quoted sequences' are sequences of characters 840contained in double-quotes. A double-quote character inside the sequence must 841be written twice. 842<pre>"Hello" "" "He said ""Hello"""</pre> 843'Single-quoted sequences' are similar to double-quoted sequences but single rather 844than double-quotes are used. 845<pre>'Hello' '' 'He said ''Hello''' </pre> 846When the compiler recognises one of these literals it tries to construct a call 847to a conversion routine which can interpret it as a value of some type. For instance, 848the standard library contains a definition of 'convertn' which the compiler calls 849if it finds a 'number'. That definition has specification 850<pre>PROC(string)integer </pre> 851<p>All conversion routines must have similar specifications, but the result type 852 will differ and some exceptions may be raised. The literal is supplied as a 853 constant of type 'string'. The conversion routine can examine the characters 854 which form the literal and return the appropriate value. It may of course raise 855 an exception if the characters do not form a valid value, if either the value 856 would be out of range or if the literal contains illegal characters. </p> 857<p> There are also two other conversion routines in the standard library, 'converts' 858 which converts double-quoted sequences into string values, and 'convertc' which 859 converts single-quoted sequences into values of the type 'char'. These definitions 860 can be overridden by preceding the literal by the name of a type and a $ sign. 861 For instance </p> 862<pre>> let int == integer; 863> let one == int$1; </pre> 864 865<p>applies the 'convertn' routine belonging to 'int', so that 'one' has type int 866 rather than integer. </p> 867<h3>23. Lists</h3> 868<p>Lists are a convenient example for polymorphic operations. List types can be 869 constructed by the following procedure. </p> 870<pre>> let list == 871# proc(base: type end) 872# type (list) 873# car : proc(list)base raises nil_list; 874# cdr : proc(list)list raises nil_list; 875# cons: proc(base; list)list; 876# nil : list; 877# null: proc(list)boolean 878# end 879# begin 880# type (list) 881# let node == record(cr: base; cd: list); 882# extends union(nl : void; nnl : node); 883# let cons == # proc(bb: base; ll: list)list 884# (list$inj_nnl(node$constr(bb, ll))); 885# let car == 886# proc(ll: list)base 887# begin 888# node$cr(list$proj_nnl(ll)) 889# catch proc(string)base (raise nil_list) 890# end; 891# let cdr == 892# proc(ll: list)list 893# begin 894# node$cd(list$proj_nnl(ll)) 895# catch proc(string)list (raise nil_list) 896# end; 897# let nil == list$inj_nl(void$empty); 898# let null == list$is_nl 899# end 900# end; </pre> 901<p>'void' is a standard type which has only one value (empty), and is used to 902 represent the 'nil' value of the list. The list structure is made using a recursive 903 union with each node containing a value of the 'base' type and the next item 904 of the list, or containing a nil value. 'cons' makes a new node of the list, 905 'car' and 'cdr' find the 'base' and 'list' parts of a node respectively, and 906 'null' tests for the value 'nil'. 'car' and 'cdr' both trap the exception which 907 would be raised if a projection error occurred and raise 'nil_value' in its 908 place. </p> 909<p> A particular list type can now be created, for instance a list of integers. 910</p> 911<pre>> let ilist == list(integer); 912> let il == ilist$cons(1, ilist$cons(2, ilist$cons(3, ilist$nil))); </pre> 913A polymorphic 'cons' function could be declared to work on lists of any base type. 914<pre>> let cons == 915# proc[base: type end; 916# list: type (l) cons: proc(base; l)l end] 917# (bb: base; ll: list)list # (list$cons(bb, ll)); </pre> 918It is now possible to write simply 919<pre>> let il == cons(1, cons(2, cons(3, ilist$nil))); </pre> 920Polymorphic 'car', 'cdr' and 'null' functions can be written similarly. As further 921examples some other polymorphic list functions are given. 922<pre>> letrec append == 923# proc[base: type end; 924# list: type (l) 925# car: proc(l)base raises nil_list; 926# cdr: proc(l)l raises nil_list; 927# cons: proc(base; l)l; 928# null: proc(l)boolean end] 929# (first, second: list)list 930# ( if null(first) then second 931# else cons(car(first), append(cdr(first), second)) ); 932> letrec reverse == 933# proc[base: type end; 934# list: type (l) 935# car: proc(l)base raises nil_list; 936# cdr: proc(l)l raises nil_list; 937# cons: proc(base; l)l; 938# nil: l; 939# null: proc(l)boolean end] 940# (ll: list)list 941# ( if null(ll) then list$nil 942# else append(reverse(cdr(ll)), cons(car(ll), list$nil)) ); </pre> 943A useful function would be one which would print the data part of a list if the 944base type could be printed. 945<pre>> letrec pr == 946# proc [base: type(b) print: proc(b) end; 947# list: type(l) car: proc(l)base raises nil_list; 948# cdr: proc(l)l raises nil_list; 949# null: proc(l)boolean 950# end ] 951# (ll: list) 952# begin 953# if null(ll) 954# then print("nil") 955# else 956# begin 957# print("( "); 958# print(list$car(ll)); 959# print(". "); 960# pr(list$cdr(ll)); 961# print(") ") 962# end 963# catch proc(string) () 964# end; </pre> 965The list created above can now be printed. 966<pre>> pr(il); 967( 1. ( 2. ( 3. nil) ) ) </pre> 968 969<p>Other polymorphic functions on lists can be declared in a similar way.</p> 970<h3>24. Conclusion</h3> 971<p>This document is intended as an introduction to Poly and to give some idea 972 of the ways in which it can be used. It is not a rigorous description and various 973 details, such as the precise checking rules for specifications, have been deliberately 974 skated over in order to explain the language simply. A companion document, the 975 Poly Report, is the reference for the precise details of the language. </p> 976</p> 977</body> 978</html> 979