Erick Tryzelaar | 35295ff | 2008-03-31 08:44:50 +0000 | [diff] [blame] | 1 | <!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN" |
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| 3 | |
| 4 | <html> |
| 5 | <head> |
| 6 | <title>Kaleidoscope: Extending the Language: Control Flow</title> |
| 7 | <meta http-equiv="Content-Type" content="text/html; charset=utf-8"> |
| 8 | <meta name="author" content="Chris Lattner"> |
| 9 | <meta name="author" content="Erick Tryzelaar"> |
| 10 | <link rel="stylesheet" href="../llvm.css" type="text/css"> |
| 11 | </head> |
| 12 | |
| 13 | <body> |
| 14 | |
| 15 | <div class="doc_title">Kaleidoscope: Extending the Language: Control Flow</div> |
| 16 | |
| 17 | <ul> |
| 18 | <li><a href="index.html">Up to Tutorial Index</a></li> |
| 19 | <li>Chapter 5 |
| 20 | <ol> |
| 21 | <li><a href="#intro">Chapter 5 Introduction</a></li> |
| 22 | <li><a href="#ifthen">If/Then/Else</a> |
| 23 | <ol> |
| 24 | <li><a href="#iflexer">Lexer Extensions</a></li> |
| 25 | <li><a href="#ifast">AST Extensions</a></li> |
| 26 | <li><a href="#ifparser">Parser Extensions</a></li> |
| 27 | <li><a href="#ifir">LLVM IR</a></li> |
| 28 | <li><a href="#ifcodegen">Code Generation</a></li> |
| 29 | </ol> |
| 30 | </li> |
| 31 | <li><a href="#for">'for' Loop Expression</a> |
| 32 | <ol> |
| 33 | <li><a href="#forlexer">Lexer Extensions</a></li> |
| 34 | <li><a href="#forast">AST Extensions</a></li> |
| 35 | <li><a href="#forparser">Parser Extensions</a></li> |
| 36 | <li><a href="#forir">LLVM IR</a></li> |
| 37 | <li><a href="#forcodegen">Code Generation</a></li> |
| 38 | </ol> |
| 39 | </li> |
| 40 | <li><a href="#code">Full Code Listing</a></li> |
| 41 | </ol> |
| 42 | </li> |
| 43 | <li><a href="OCamlLangImpl6.html">Chapter 6</a>: Extending the Language: |
| 44 | User-defined Operators</li> |
| 45 | </ul> |
| 46 | |
| 47 | <div class="doc_author"> |
| 48 | <p> |
| 49 | Written by <a href="mailto:sabre@nondot.org">Chris Lattner</a> |
| 50 | and <a href="mailto:idadesub@users.sourceforge.net">Erick Tryzelaar</a> |
| 51 | </p> |
| 52 | </div> |
| 53 | |
| 54 | <!-- *********************************************************************** --> |
| 55 | <div class="doc_section"><a name="intro">Chapter 5 Introduction</a></div> |
| 56 | <!-- *********************************************************************** --> |
| 57 | |
| 58 | <div class="doc_text"> |
| 59 | |
| 60 | <p>Welcome to Chapter 5 of the "<a href="index.html">Implementing a language |
| 61 | with LLVM</a>" tutorial. Parts 1-4 described the implementation of the simple |
| 62 | Kaleidoscope language and included support for generating LLVM IR, followed by |
| 63 | optimizations and a JIT compiler. Unfortunately, as presented, Kaleidoscope is |
| 64 | mostly useless: it has no control flow other than call and return. This means |
| 65 | that you can't have conditional branches in the code, significantly limiting its |
| 66 | power. In this episode of "build that compiler", we'll extend Kaleidoscope to |
| 67 | have an if/then/else expression plus a simple 'for' loop.</p> |
| 68 | |
| 69 | </div> |
| 70 | |
| 71 | <!-- *********************************************************************** --> |
| 72 | <div class="doc_section"><a name="ifthen">If/Then/Else</a></div> |
| 73 | <!-- *********************************************************************** --> |
| 74 | |
| 75 | <div class="doc_text"> |
| 76 | |
| 77 | <p> |
| 78 | Extending Kaleidoscope to support if/then/else is quite straightforward. It |
| 79 | basically requires adding lexer support for this "new" concept to the lexer, |
| 80 | parser, AST, and LLVM code emitter. This example is nice, because it shows how |
| 81 | easy it is to "grow" a language over time, incrementally extending it as new |
| 82 | ideas are discovered.</p> |
| 83 | |
| 84 | <p>Before we get going on "how" we add this extension, lets talk about "what" we |
| 85 | want. The basic idea is that we want to be able to write this sort of thing: |
| 86 | </p> |
| 87 | |
| 88 | <div class="doc_code"> |
| 89 | <pre> |
| 90 | def fib(x) |
| 91 | if x < 3 then |
| 92 | 1 |
| 93 | else |
| 94 | fib(x-1)+fib(x-2); |
| 95 | </pre> |
| 96 | </div> |
| 97 | |
| 98 | <p>In Kaleidoscope, every construct is an expression: there are no statements. |
| 99 | As such, the if/then/else expression needs to return a value like any other. |
| 100 | Since we're using a mostly functional form, we'll have it evaluate its |
| 101 | conditional, then return the 'then' or 'else' value based on how the condition |
| 102 | was resolved. This is very similar to the C "?:" expression.</p> |
| 103 | |
| 104 | <p>The semantics of the if/then/else expression is that it evaluates the |
| 105 | condition to a boolean equality value: 0.0 is considered to be false and |
| 106 | everything else is considered to be true. |
| 107 | If the condition is true, the first subexpression is evaluated and returned, if |
| 108 | the condition is false, the second subexpression is evaluated and returned. |
| 109 | Since Kaleidoscope allows side-effects, this behavior is important to nail down. |
| 110 | </p> |
| 111 | |
| 112 | <p>Now that we know what we "want", lets break this down into its constituent |
| 113 | pieces.</p> |
| 114 | |
| 115 | </div> |
| 116 | |
| 117 | <!-- ======================================================================= --> |
| 118 | <div class="doc_subsubsection"><a name="iflexer">Lexer Extensions for |
| 119 | If/Then/Else</a></div> |
| 120 | <!-- ======================================================================= --> |
| 121 | |
| 122 | |
| 123 | <div class="doc_text"> |
| 124 | |
| 125 | <p>The lexer extensions are straightforward. First we add new variants |
| 126 | for the relevant tokens:</p> |
| 127 | |
| 128 | <div class="doc_code"> |
| 129 | <pre> |
| 130 | (* control *) |
| 131 | | If | Then | Else | For | In |
| 132 | </pre> |
| 133 | </div> |
| 134 | |
| 135 | <p>Once we have that, we recognize the new keywords in the lexer. This is pretty simple |
| 136 | stuff:</p> |
| 137 | |
| 138 | <div class="doc_code"> |
| 139 | <pre> |
| 140 | ... |
| 141 | match Buffer.contents buffer with |
| 142 | | "def" -> [< 'Token.Def; stream >] |
| 143 | | "extern" -> [< 'Token.Extern; stream >] |
| 144 | | "if" -> [< 'Token.If; stream >] |
| 145 | | "then" -> [< 'Token.Then; stream >] |
| 146 | | "else" -> [< 'Token.Else; stream >] |
| 147 | | "for" -> [< 'Token.For; stream >] |
| 148 | | "in" -> [< 'Token.In; stream >] |
| 149 | | id -> [< 'Token.Ident id; stream >] |
| 150 | </pre> |
| 151 | </div> |
| 152 | |
| 153 | </div> |
| 154 | |
| 155 | <!-- ======================================================================= --> |
| 156 | <div class="doc_subsubsection"><a name="ifast">AST Extensions for |
| 157 | If/Then/Else</a></div> |
| 158 | <!-- ======================================================================= --> |
| 159 | |
| 160 | <div class="doc_text"> |
| 161 | |
| 162 | <p>To represent the new expression we add a new AST variant for it:</p> |
| 163 | |
| 164 | <div class="doc_code"> |
| 165 | <pre> |
| 166 | type expr = |
| 167 | ... |
| 168 | (* variant for if/then/else. *) |
| 169 | | If of expr * expr * expr |
| 170 | </pre> |
| 171 | </div> |
| 172 | |
| 173 | <p>The AST variant just has pointers to the various subexpressions.</p> |
| 174 | |
| 175 | </div> |
| 176 | |
| 177 | <!-- ======================================================================= --> |
| 178 | <div class="doc_subsubsection"><a name="ifparser">Parser Extensions for |
| 179 | If/Then/Else</a></div> |
| 180 | <!-- ======================================================================= --> |
| 181 | |
| 182 | <div class="doc_text"> |
| 183 | |
| 184 | <p>Now that we have the relevant tokens coming from the lexer and we have the |
| 185 | AST node to build, our parsing logic is relatively straightforward. First we |
| 186 | define a new parsing function:</p> |
| 187 | |
| 188 | <div class="doc_code"> |
| 189 | <pre> |
| 190 | let rec parse_primary = parser |
| 191 | ... |
| 192 | (* ifexpr ::= 'if' expr 'then' expr 'else' expr *) |
| 193 | | [< 'Token.If; c=parse_expr; |
| 194 | 'Token.Then ?? "expected 'then'"; t=parse_expr; |
| 195 | 'Token.Else ?? "expected 'else'"; e=parse_expr >] -> |
| 196 | Ast.If (c, t, e) |
| 197 | </pre> |
| 198 | </div> |
| 199 | |
| 200 | <p>Next we hook it up as a primary expression:</p> |
| 201 | |
| 202 | <div class="doc_code"> |
| 203 | <pre> |
| 204 | let rec parse_primary = parser |
| 205 | ... |
| 206 | (* ifexpr ::= 'if' expr 'then' expr 'else' expr *) |
| 207 | | [< 'Token.If; c=parse_expr; |
| 208 | 'Token.Then ?? "expected 'then'"; t=parse_expr; |
| 209 | 'Token.Else ?? "expected 'else'"; e=parse_expr >] -> |
| 210 | Ast.If (c, t, e) |
| 211 | </pre> |
| 212 | </div> |
| 213 | |
| 214 | </div> |
| 215 | |
| 216 | <!-- ======================================================================= --> |
| 217 | <div class="doc_subsubsection"><a name="ifir">LLVM IR for If/Then/Else</a></div> |
| 218 | <!-- ======================================================================= --> |
| 219 | |
| 220 | <div class="doc_text"> |
| 221 | |
| 222 | <p>Now that we have it parsing and building the AST, the final piece is adding |
| 223 | LLVM code generation support. This is the most interesting part of the |
| 224 | if/then/else example, because this is where it starts to introduce new concepts. |
| 225 | All of the code above has been thoroughly described in previous chapters. |
| 226 | </p> |
| 227 | |
| 228 | <p>To motivate the code we want to produce, lets take a look at a simple |
| 229 | example. Consider:</p> |
| 230 | |
| 231 | <div class="doc_code"> |
| 232 | <pre> |
| 233 | extern foo(); |
| 234 | extern bar(); |
| 235 | def baz(x) if x then foo() else bar(); |
| 236 | </pre> |
| 237 | </div> |
| 238 | |
| 239 | <p>If you disable optimizations, the code you'll (soon) get from Kaleidoscope |
| 240 | looks like this:</p> |
| 241 | |
| 242 | <div class="doc_code"> |
| 243 | <pre> |
| 244 | declare double @foo() |
| 245 | |
| 246 | declare double @bar() |
| 247 | |
| 248 | define double @baz(double %x) { |
| 249 | entry: |
| 250 | %ifcond = fcmp one double %x, 0.000000e+00 |
| 251 | br i1 %ifcond, label %then, label %else |
| 252 | |
| 253 | then: ; preds = %entry |
| 254 | %calltmp = call double @foo() |
| 255 | br label %ifcont |
| 256 | |
| 257 | else: ; preds = %entry |
| 258 | %calltmp1 = call double @bar() |
| 259 | br label %ifcont |
| 260 | |
| 261 | ifcont: ; preds = %else, %then |
| 262 | %iftmp = phi double [ %calltmp, %then ], [ %calltmp1, %else ] |
| 263 | ret double %iftmp |
| 264 | } |
| 265 | </pre> |
| 266 | </div> |
| 267 | |
| 268 | <p>To visualize the control flow graph, you can use a nifty feature of the LLVM |
| 269 | '<a href="http://llvm.org/cmds/opt.html">opt</a>' tool. If you put this LLVM IR |
| 270 | into "t.ll" and run "<tt>llvm-as < t.ll | opt -analyze -view-cfg</tt>", <a |
| 271 | href="../ProgrammersManual.html#ViewGraph">a window will pop up</a> and you'll |
| 272 | see this graph:</p> |
| 273 | |
Benjamin Kramer | e15192b | 2009-08-05 15:42:44 +0000 | [diff] [blame] | 274 | <div style="text-align: center"><img src="LangImpl5-cfg.png" alt="Example CFG" width="423" |
| 275 | height="315"></div> |
Erick Tryzelaar | 35295ff | 2008-03-31 08:44:50 +0000 | [diff] [blame] | 276 | |
| 277 | <p>Another way to get this is to call "<tt>Llvm_analysis.view_function_cfg |
| 278 | f</tt>" or "<tt>Llvm_analysis.view_function_cfg_only f</tt>" (where <tt>f</tt> |
| 279 | is a "<tt>Function</tt>") either by inserting actual calls into the code and |
| 280 | recompiling or by calling these in the debugger. LLVM has many nice features |
| 281 | for visualizing various graphs.</p> |
| 282 | |
| 283 | <p>Getting back to the generated code, it is fairly simple: the entry block |
| 284 | evaluates the conditional expression ("x" in our case here) and compares the |
| 285 | result to 0.0 with the "<tt><a href="../LangRef.html#i_fcmp">fcmp</a> one</tt>" |
| 286 | instruction ('one' is "Ordered and Not Equal"). Based on the result of this |
| 287 | expression, the code jumps to either the "then" or "else" blocks, which contain |
| 288 | the expressions for the true/false cases.</p> |
| 289 | |
| 290 | <p>Once the then/else blocks are finished executing, they both branch back to the |
| 291 | 'ifcont' block to execute the code that happens after the if/then/else. In this |
| 292 | case the only thing left to do is to return to the caller of the function. The |
| 293 | question then becomes: how does the code know which expression to return?</p> |
| 294 | |
| 295 | <p>The answer to this question involves an important SSA operation: the |
| 296 | <a href="http://en.wikipedia.org/wiki/Static_single_assignment_form">Phi |
| 297 | operation</a>. If you're not familiar with SSA, <a |
| 298 | href="http://en.wikipedia.org/wiki/Static_single_assignment_form">the wikipedia |
| 299 | article</a> is a good introduction and there are various other introductions to |
| 300 | it available on your favorite search engine. The short version is that |
| 301 | "execution" of the Phi operation requires "remembering" which block control came |
| 302 | from. The Phi operation takes on the value corresponding to the input control |
| 303 | block. In this case, if control comes in from the "then" block, it gets the |
| 304 | value of "calltmp". If control comes from the "else" block, it gets the value |
| 305 | of "calltmp1".</p> |
| 306 | |
| 307 | <p>At this point, you are probably starting to think "Oh no! This means my |
| 308 | simple and elegant front-end will have to start generating SSA form in order to |
| 309 | use LLVM!". Fortunately, this is not the case, and we strongly advise |
| 310 | <em>not</em> implementing an SSA construction algorithm in your front-end |
| 311 | unless there is an amazingly good reason to do so. In practice, there are two |
| 312 | sorts of values that float around in code written for your average imperative |
| 313 | programming language that might need Phi nodes:</p> |
| 314 | |
| 315 | <ol> |
| 316 | <li>Code that involves user variables: <tt>x = 1; x = x + 1; </tt></li> |
| 317 | <li>Values that are implicit in the structure of your AST, such as the Phi node |
| 318 | in this case.</li> |
| 319 | </ol> |
| 320 | |
| 321 | <p>In <a href="OCamlLangImpl7.html">Chapter 7</a> of this tutorial ("mutable |
| 322 | variables"), we'll talk about #1 |
| 323 | in depth. For now, just believe me that you don't need SSA construction to |
| 324 | handle this case. For #2, you have the choice of using the techniques that we will |
| 325 | describe for #1, or you can insert Phi nodes directly, if convenient. In this |
| 326 | case, it is really really easy to generate the Phi node, so we choose to do it |
| 327 | directly.</p> |
| 328 | |
| 329 | <p>Okay, enough of the motivation and overview, lets generate code!</p> |
| 330 | |
| 331 | </div> |
| 332 | |
| 333 | <!-- ======================================================================= --> |
| 334 | <div class="doc_subsubsection"><a name="ifcodegen">Code Generation for |
| 335 | If/Then/Else</a></div> |
| 336 | <!-- ======================================================================= --> |
| 337 | |
| 338 | <div class="doc_text"> |
| 339 | |
| 340 | <p>In order to generate code for this, we implement the <tt>Codegen</tt> method |
| 341 | for <tt>IfExprAST</tt>:</p> |
| 342 | |
| 343 | <div class="doc_code"> |
| 344 | <pre> |
| 345 | let rec codegen_expr = function |
| 346 | ... |
| 347 | | Ast.If (cond, then_, else_) -> |
| 348 | let cond = codegen_expr cond in |
| 349 | |
| 350 | (* Convert condition to a bool by comparing equal to 0.0 *) |
| 351 | let zero = const_float double_type 0.0 in |
| 352 | let cond_val = build_fcmp Fcmp.One cond zero "ifcond" builder in |
| 353 | </pre> |
| 354 | </div> |
| 355 | |
| 356 | <p>This code is straightforward and similar to what we saw before. We emit the |
| 357 | expression for the condition, then compare that value to zero to get a truth |
| 358 | value as a 1-bit (bool) value.</p> |
| 359 | |
| 360 | <div class="doc_code"> |
| 361 | <pre> |
| 362 | (* Grab the first block so that we might later add the conditional branch |
| 363 | * to it at the end of the function. *) |
| 364 | let start_bb = insertion_block builder in |
| 365 | let the_function = block_parent start_bb in |
| 366 | |
| 367 | let then_bb = append_block "then" the_function in |
| 368 | position_at_end then_bb builder; |
| 369 | </pre> |
| 370 | </div> |
| 371 | |
| 372 | <p> |
| 373 | As opposed to the <a href="LangImpl5.html">C++ tutorial</a>, we have to build |
| 374 | our basic blocks bottom up since we can't have dangling BasicBlocks. We start |
| 375 | off by saving a pointer to the first block (which might not be the entry |
| 376 | block), which we'll need to build a conditional branch later. We do this by |
| 377 | asking the <tt>builder</tt> for the current BasicBlock. The fourth line |
| 378 | gets the current Function object that is being built. It gets this by the |
| 379 | <tt>start_bb</tt> for its "parent" (the function it is currently embedded |
| 380 | into).</p> |
| 381 | |
| 382 | <p>Once it has that, it creates one block. It is automatically appended into |
| 383 | the function's list of blocks.</p> |
| 384 | |
| 385 | <div class="doc_code"> |
| 386 | <pre> |
| 387 | (* Emit 'then' value. *) |
| 388 | position_at_end then_bb builder; |
| 389 | let then_val = codegen_expr then_ in |
| 390 | |
| 391 | (* Codegen of 'then' can change the current block, update then_bb for the |
| 392 | * phi. We create a new name because one is used for the phi node, and the |
| 393 | * other is used for the conditional branch. *) |
| 394 | let new_then_bb = insertion_block builder in |
| 395 | </pre> |
| 396 | </div> |
| 397 | |
| 398 | <p>We move the builder to start inserting into the "then" block. Strictly |
| 399 | speaking, this call moves the insertion point to be at the end of the specified |
| 400 | block. However, since the "then" block is empty, it also starts out by |
| 401 | inserting at the beginning of the block. :)</p> |
| 402 | |
| 403 | <p>Once the insertion point is set, we recursively codegen the "then" expression |
| 404 | from the AST.</p> |
| 405 | |
| 406 | <p>The final line here is quite subtle, but is very important. The basic issue |
| 407 | is that when we create the Phi node in the merge block, we need to set up the |
| 408 | block/value pairs that indicate how the Phi will work. Importantly, the Phi |
| 409 | node expects to have an entry for each predecessor of the block in the CFG. Why |
| 410 | then, are we getting the current block when we just set it to ThenBB 5 lines |
| 411 | above? The problem is that the "Then" expression may actually itself change the |
| 412 | block that the Builder is emitting into if, for example, it contains a nested |
| 413 | "if/then/else" expression. Because calling Codegen recursively could |
| 414 | arbitrarily change the notion of the current block, we are required to get an |
| 415 | up-to-date value for code that will set up the Phi node.</p> |
| 416 | |
| 417 | <div class="doc_code"> |
| 418 | <pre> |
| 419 | (* Emit 'else' value. *) |
| 420 | let else_bb = append_block "else" the_function in |
| 421 | position_at_end else_bb builder; |
| 422 | let else_val = codegen_expr else_ in |
| 423 | |
| 424 | (* Codegen of 'else' can change the current block, update else_bb for the |
| 425 | * phi. *) |
| 426 | let new_else_bb = insertion_block builder in |
| 427 | </pre> |
| 428 | </div> |
| 429 | |
| 430 | <p>Code generation for the 'else' block is basically identical to codegen for |
| 431 | the 'then' block.</p> |
| 432 | |
| 433 | <div class="doc_code"> |
| 434 | <pre> |
| 435 | (* Emit merge block. *) |
| 436 | let merge_bb = append_block "ifcont" the_function in |
| 437 | position_at_end merge_bb builder; |
| 438 | let incoming = [(then_val, new_then_bb); (else_val, new_else_bb)] in |
| 439 | let phi = build_phi incoming "iftmp" builder in |
| 440 | </pre> |
| 441 | </div> |
| 442 | |
| 443 | <p>The first two lines here are now familiar: the first adds the "merge" block |
| 444 | to the Function object. The second block changes the insertion point so that |
| 445 | newly created code will go into the "merge" block. Once that is done, we need |
| 446 | to create the PHI node and set up the block/value pairs for the PHI.</p> |
| 447 | |
| 448 | <div class="doc_code"> |
| 449 | <pre> |
| 450 | (* Return to the start block to add the conditional branch. *) |
| 451 | position_at_end start_bb builder; |
| 452 | ignore (build_cond_br cond_val then_bb else_bb builder); |
| 453 | </pre> |
| 454 | </div> |
| 455 | |
| 456 | <p>Once the blocks are created, we can emit the conditional branch that chooses |
| 457 | between them. Note that creating new blocks does not implicitly affect the |
Duncan Sands | 89f6d88 | 2008-04-13 06:22:09 +0000 | [diff] [blame] | 458 | IRBuilder, so it is still inserting into the block that the condition |
Erick Tryzelaar | 35295ff | 2008-03-31 08:44:50 +0000 | [diff] [blame] | 459 | went into. This is why we needed to save the "start" block.</p> |
| 460 | |
| 461 | <div class="doc_code"> |
| 462 | <pre> |
| 463 | (* Set a unconditional branch at the end of the 'then' block and the |
| 464 | * 'else' block to the 'merge' block. *) |
| 465 | position_at_end new_then_bb builder; ignore (build_br merge_bb builder); |
| 466 | position_at_end new_else_bb builder; ignore (build_br merge_bb builder); |
| 467 | |
| 468 | (* Finally, set the builder to the end of the merge block. *) |
| 469 | position_at_end merge_bb builder; |
| 470 | |
| 471 | phi |
| 472 | </pre> |
| 473 | </div> |
| 474 | |
| 475 | <p>To finish off the blocks, we create an unconditional branch |
| 476 | to the merge block. One interesting (and very important) aspect of the LLVM IR |
| 477 | is that it <a href="../LangRef.html#functionstructure">requires all basic blocks |
| 478 | to be "terminated"</a> with a <a href="../LangRef.html#terminators">control flow |
| 479 | instruction</a> such as return or branch. This means that all control flow, |
| 480 | <em>including fall throughs</em> must be made explicit in the LLVM IR. If you |
| 481 | violate this rule, the verifier will emit an error. |
| 482 | |
| 483 | <p>Finally, the CodeGen function returns the phi node as the value computed by |
| 484 | the if/then/else expression. In our example above, this returned value will |
| 485 | feed into the code for the top-level function, which will create the return |
| 486 | instruction.</p> |
| 487 | |
| 488 | <p>Overall, we now have the ability to execute conditional code in |
| 489 | Kaleidoscope. With this extension, Kaleidoscope is a fairly complete language |
| 490 | that can calculate a wide variety of numeric functions. Next up we'll add |
| 491 | another useful expression that is familiar from non-functional languages...</p> |
| 492 | |
| 493 | </div> |
| 494 | |
| 495 | <!-- *********************************************************************** --> |
| 496 | <div class="doc_section"><a name="for">'for' Loop Expression</a></div> |
| 497 | <!-- *********************************************************************** --> |
| 498 | |
| 499 | <div class="doc_text"> |
| 500 | |
| 501 | <p>Now that we know how to add basic control flow constructs to the language, |
| 502 | we have the tools to add more powerful things. Lets add something more |
| 503 | aggressive, a 'for' expression:</p> |
| 504 | |
| 505 | <div class="doc_code"> |
| 506 | <pre> |
| 507 | extern putchard(char); |
| 508 | def printstar(n) |
| 509 | for i = 1, i < n, 1.0 in |
| 510 | putchard(42); # ascii 42 = '*' |
| 511 | |
| 512 | # print 100 '*' characters |
| 513 | printstar(100); |
| 514 | </pre> |
| 515 | </div> |
| 516 | |
| 517 | <p>This expression defines a new variable ("i" in this case) which iterates from |
| 518 | a starting value, while the condition ("i < n" in this case) is true, |
| 519 | incrementing by an optional step value ("1.0" in this case). If the step value |
| 520 | is omitted, it defaults to 1.0. While the loop is true, it executes its |
| 521 | body expression. Because we don't have anything better to return, we'll just |
| 522 | define the loop as always returning 0.0. In the future when we have mutable |
| 523 | variables, it will get more useful.</p> |
| 524 | |
| 525 | <p>As before, lets talk about the changes that we need to Kaleidoscope to |
| 526 | support this.</p> |
| 527 | |
| 528 | </div> |
| 529 | |
| 530 | <!-- ======================================================================= --> |
| 531 | <div class="doc_subsubsection"><a name="forlexer">Lexer Extensions for |
| 532 | the 'for' Loop</a></div> |
| 533 | <!-- ======================================================================= --> |
| 534 | |
| 535 | <div class="doc_text"> |
| 536 | |
| 537 | <p>The lexer extensions are the same sort of thing as for if/then/else:</p> |
| 538 | |
| 539 | <div class="doc_code"> |
| 540 | <pre> |
| 541 | ... in Token.token ... |
| 542 | (* control *) |
| 543 | | If | Then | Else |
| 544 | <b>| For | In</b> |
| 545 | |
| 546 | ... in Lexer.lex_ident... |
| 547 | match Buffer.contents buffer with |
| 548 | | "def" -> [< 'Token.Def; stream >] |
| 549 | | "extern" -> [< 'Token.Extern; stream >] |
| 550 | | "if" -> [< 'Token.If; stream >] |
| 551 | | "then" -> [< 'Token.Then; stream >] |
| 552 | | "else" -> [< 'Token.Else; stream >] |
| 553 | <b>| "for" -> [< 'Token.For; stream >] |
| 554 | | "in" -> [< 'Token.In; stream >]</b> |
| 555 | | id -> [< 'Token.Ident id; stream >] |
| 556 | </pre> |
| 557 | </div> |
| 558 | |
| 559 | </div> |
| 560 | |
| 561 | <!-- ======================================================================= --> |
| 562 | <div class="doc_subsubsection"><a name="forast">AST Extensions for |
| 563 | the 'for' Loop</a></div> |
| 564 | <!-- ======================================================================= --> |
| 565 | |
| 566 | <div class="doc_text"> |
| 567 | |
| 568 | <p>The AST variant is just as simple. It basically boils down to capturing |
| 569 | the variable name and the constituent expressions in the node.</p> |
| 570 | |
| 571 | <div class="doc_code"> |
| 572 | <pre> |
| 573 | type expr = |
| 574 | ... |
| 575 | (* variant for for/in. *) |
| 576 | | For of string * expr * expr * expr option * expr |
| 577 | </pre> |
| 578 | </div> |
| 579 | |
| 580 | </div> |
| 581 | |
| 582 | <!-- ======================================================================= --> |
| 583 | <div class="doc_subsubsection"><a name="forparser">Parser Extensions for |
| 584 | the 'for' Loop</a></div> |
| 585 | <!-- ======================================================================= --> |
| 586 | |
| 587 | <div class="doc_text"> |
| 588 | |
| 589 | <p>The parser code is also fairly standard. The only interesting thing here is |
| 590 | handling of the optional step value. The parser code handles it by checking to |
| 591 | see if the second comma is present. If not, it sets the step value to null in |
| 592 | the AST node:</p> |
| 593 | |
| 594 | <div class="doc_code"> |
| 595 | <pre> |
| 596 | let rec parse_primary = parser |
| 597 | ... |
| 598 | (* forexpr |
| 599 | ::= 'for' identifier '=' expr ',' expr (',' expr)? 'in' expression *) |
| 600 | | [< 'Token.For; |
| 601 | 'Token.Ident id ?? "expected identifier after for"; |
| 602 | 'Token.Kwd '=' ?? "expected '=' after for"; |
| 603 | stream >] -> |
| 604 | begin parser |
| 605 | | [< |
| 606 | start=parse_expr; |
| 607 | 'Token.Kwd ',' ?? "expected ',' after for"; |
| 608 | end_=parse_expr; |
| 609 | stream >] -> |
| 610 | let step = |
| 611 | begin parser |
| 612 | | [< 'Token.Kwd ','; step=parse_expr >] -> Some step |
| 613 | | [< >] -> None |
| 614 | end stream |
| 615 | in |
| 616 | begin parser |
| 617 | | [< 'Token.In; body=parse_expr >] -> |
| 618 | Ast.For (id, start, end_, step, body) |
| 619 | | [< >] -> |
| 620 | raise (Stream.Error "expected 'in' after for") |
| 621 | end stream |
| 622 | | [< >] -> |
| 623 | raise (Stream.Error "expected '=' after for") |
| 624 | end stream |
| 625 | </pre> |
| 626 | </div> |
| 627 | |
| 628 | </div> |
| 629 | |
| 630 | <!-- ======================================================================= --> |
| 631 | <div class="doc_subsubsection"><a name="forir">LLVM IR for |
| 632 | the 'for' Loop</a></div> |
| 633 | <!-- ======================================================================= --> |
| 634 | |
| 635 | <div class="doc_text"> |
| 636 | |
| 637 | <p>Now we get to the good part: the LLVM IR we want to generate for this thing. |
| 638 | With the simple example above, we get this LLVM IR (note that this dump is |
| 639 | generated with optimizations disabled for clarity): |
| 640 | </p> |
| 641 | |
| 642 | <div class="doc_code"> |
| 643 | <pre> |
| 644 | declare double @putchard(double) |
| 645 | |
| 646 | define double @printstar(double %n) { |
| 647 | entry: |
| 648 | ; initial value = 1.0 (inlined into phi) |
| 649 | br label %loop |
| 650 | |
| 651 | loop: ; preds = %loop, %entry |
| 652 | %i = phi double [ 1.000000e+00, %entry ], [ %nextvar, %loop ] |
| 653 | ; body |
| 654 | %calltmp = call double @putchard( double 4.200000e+01 ) |
| 655 | ; increment |
| 656 | %nextvar = add double %i, 1.000000e+00 |
| 657 | |
| 658 | ; termination test |
| 659 | %cmptmp = fcmp ult double %i, %n |
| 660 | %booltmp = uitofp i1 %cmptmp to double |
| 661 | %loopcond = fcmp one double %booltmp, 0.000000e+00 |
| 662 | br i1 %loopcond, label %loop, label %afterloop |
| 663 | |
| 664 | afterloop: ; preds = %loop |
| 665 | ; loop always returns 0.0 |
| 666 | ret double 0.000000e+00 |
| 667 | } |
| 668 | </pre> |
| 669 | </div> |
| 670 | |
| 671 | <p>This loop contains all the same constructs we saw before: a phi node, several |
| 672 | expressions, and some basic blocks. Lets see how this fits together.</p> |
| 673 | |
| 674 | </div> |
| 675 | |
| 676 | <!-- ======================================================================= --> |
| 677 | <div class="doc_subsubsection"><a name="forcodegen">Code Generation for |
| 678 | the 'for' Loop</a></div> |
| 679 | <!-- ======================================================================= --> |
| 680 | |
| 681 | <div class="doc_text"> |
| 682 | |
| 683 | <p>The first part of Codegen is very simple: we just output the start expression |
| 684 | for the loop value:</p> |
| 685 | |
| 686 | <div class="doc_code"> |
| 687 | <pre> |
| 688 | let rec codegen_expr = function |
| 689 | ... |
| 690 | | Ast.For (var_name, start, end_, step, body) -> |
| 691 | (* Emit the start code first, without 'variable' in scope. *) |
| 692 | let start_val = codegen_expr start in |
| 693 | </pre> |
| 694 | </div> |
| 695 | |
| 696 | <p>With this out of the way, the next step is to set up the LLVM basic block |
| 697 | for the start of the loop body. In the case above, the whole loop body is one |
| 698 | block, but remember that the body code itself could consist of multiple blocks |
| 699 | (e.g. if it contains an if/then/else or a for/in expression).</p> |
| 700 | |
| 701 | <div class="doc_code"> |
| 702 | <pre> |
| 703 | (* Make the new basic block for the loop header, inserting after current |
| 704 | * block. *) |
| 705 | let preheader_bb = insertion_block builder in |
| 706 | let the_function = block_parent preheader_bb in |
| 707 | let loop_bb = append_block "loop" the_function in |
| 708 | |
| 709 | (* Insert an explicit fall through from the current block to the |
| 710 | * loop_bb. *) |
| 711 | ignore (build_br loop_bb builder); |
| 712 | </pre> |
| 713 | </div> |
| 714 | |
| 715 | <p>This code is similar to what we saw for if/then/else. Because we will need |
| 716 | it to create the Phi node, we remember the block that falls through into the |
| 717 | loop. Once we have that, we create the actual block that starts the loop and |
| 718 | create an unconditional branch for the fall-through between the two blocks.</p> |
| 719 | |
| 720 | <div class="doc_code"> |
| 721 | <pre> |
| 722 | (* Start insertion in loop_bb. *) |
| 723 | position_at_end loop_bb builder; |
| 724 | |
| 725 | (* Start the PHI node with an entry for start. *) |
| 726 | let variable = build_phi [(start_val, preheader_bb)] var_name builder in |
| 727 | </pre> |
| 728 | </div> |
| 729 | |
| 730 | <p>Now that the "preheader" for the loop is set up, we switch to emitting code |
| 731 | for the loop body. To begin with, we move the insertion point and create the |
| 732 | PHI node for the loop induction variable. Since we already know the incoming |
| 733 | value for the starting value, we add it to the Phi node. Note that the Phi will |
| 734 | eventually get a second value for the backedge, but we can't set it up yet |
| 735 | (because it doesn't exist!).</p> |
| 736 | |
| 737 | <div class="doc_code"> |
| 738 | <pre> |
| 739 | (* Within the loop, the variable is defined equal to the PHI node. If it |
| 740 | * shadows an existing variable, we have to restore it, so save it |
| 741 | * now. *) |
| 742 | let old_val = |
| 743 | try Some (Hashtbl.find named_values var_name) with Not_found -> None |
| 744 | in |
| 745 | Hashtbl.add named_values var_name variable; |
| 746 | |
| 747 | (* Emit the body of the loop. This, like any other expr, can change the |
| 748 | * current BB. Note that we ignore the value computed by the body, but |
| 749 | * don't allow an error *) |
| 750 | ignore (codegen_expr body); |
| 751 | </pre> |
| 752 | </div> |
| 753 | |
| 754 | <p>Now the code starts to get more interesting. Our 'for' loop introduces a new |
| 755 | variable to the symbol table. This means that our symbol table can now contain |
| 756 | either function arguments or loop variables. To handle this, before we codegen |
| 757 | the body of the loop, we add the loop variable as the current value for its |
| 758 | name. Note that it is possible that there is a variable of the same name in the |
| 759 | outer scope. It would be easy to make this an error (emit an error and return |
| 760 | null if there is already an entry for VarName) but we choose to allow shadowing |
| 761 | of variables. In order to handle this correctly, we remember the Value that |
| 762 | we are potentially shadowing in <tt>old_val</tt> (which will be None if there is |
| 763 | no shadowed variable).</p> |
| 764 | |
| 765 | <p>Once the loop variable is set into the symbol table, the code recursively |
| 766 | codegen's the body. This allows the body to use the loop variable: any |
| 767 | references to it will naturally find it in the symbol table.</p> |
| 768 | |
| 769 | <div class="doc_code"> |
| 770 | <pre> |
| 771 | (* Emit the step value. *) |
| 772 | let step_val = |
| 773 | match step with |
| 774 | | Some step -> codegen_expr step |
| 775 | (* If not specified, use 1.0. *) |
| 776 | | None -> const_float double_type 1.0 |
| 777 | in |
| 778 | |
| 779 | let next_var = build_add variable step_val "nextvar" builder in |
| 780 | </pre> |
| 781 | </div> |
| 782 | |
| 783 | <p>Now that the body is emitted, we compute the next value of the iteration |
| 784 | variable by adding the step value, or 1.0 if it isn't present. |
| 785 | '<tt>next_var</tt>' will be the value of the loop variable on the next iteration |
| 786 | of the loop.</p> |
| 787 | |
| 788 | <div class="doc_code"> |
| 789 | <pre> |
| 790 | (* Compute the end condition. *) |
| 791 | let end_cond = codegen_expr end_ in |
| 792 | |
| 793 | (* Convert condition to a bool by comparing equal to 0.0. *) |
| 794 | let zero = const_float double_type 0.0 in |
| 795 | let end_cond = build_fcmp Fcmp.One end_cond zero "loopcond" builder in |
| 796 | </pre> |
| 797 | </div> |
| 798 | |
| 799 | <p>Finally, we evaluate the exit value of the loop, to determine whether the |
| 800 | loop should exit. This mirrors the condition evaluation for the if/then/else |
| 801 | statement.</p> |
| 802 | |
| 803 | <div class="doc_code"> |
| 804 | <pre> |
| 805 | (* Create the "after loop" block and insert it. *) |
| 806 | let loop_end_bb = insertion_block builder in |
| 807 | let after_bb = append_block "afterloop" the_function in |
| 808 | |
| 809 | (* Insert the conditional branch into the end of loop_end_bb. *) |
| 810 | ignore (build_cond_br end_cond loop_bb after_bb builder); |
| 811 | |
| 812 | (* Any new code will be inserted in after_bb. *) |
| 813 | position_at_end after_bb builder; |
| 814 | </pre> |
| 815 | </div> |
| 816 | |
| 817 | <p>With the code for the body of the loop complete, we just need to finish up |
| 818 | the control flow for it. This code remembers the end block (for the phi node), then creates the block for the loop exit ("afterloop"). Based on the value of the |
| 819 | exit condition, it creates a conditional branch that chooses between executing |
| 820 | the loop again and exiting the loop. Any future code is emitted in the |
| 821 | "afterloop" block, so it sets the insertion position to it.</p> |
| 822 | |
| 823 | <div class="doc_code"> |
| 824 | <pre> |
| 825 | (* Add a new entry to the PHI node for the backedge. *) |
| 826 | add_incoming (next_var, loop_end_bb) variable; |
| 827 | |
| 828 | (* Restore the unshadowed variable. *) |
| 829 | begin match old_val with |
| 830 | | Some old_val -> Hashtbl.add named_values var_name old_val |
| 831 | | None -> () |
| 832 | end; |
| 833 | |
| 834 | (* for expr always returns 0.0. *) |
| 835 | const_null double_type |
| 836 | </pre> |
| 837 | </div> |
| 838 | |
| 839 | <p>The final code handles various cleanups: now that we have the |
| 840 | "<tt>next_var</tt>" value, we can add the incoming value to the loop PHI node. |
| 841 | After that, we remove the loop variable from the symbol table, so that it isn't |
| 842 | in scope after the for loop. Finally, code generation of the for loop always |
| 843 | returns 0.0, so that is what we return from <tt>Codegen.codegen_expr</tt>.</p> |
| 844 | |
| 845 | <p>With this, we conclude the "adding control flow to Kaleidoscope" chapter of |
| 846 | the tutorial. In this chapter we added two control flow constructs, and used |
| 847 | them to motivate a couple of aspects of the LLVM IR that are important for |
| 848 | front-end implementors to know. In the next chapter of our saga, we will get |
| 849 | a bit crazier and add <a href="OCamlLangImpl6.html">user-defined operators</a> |
| 850 | to our poor innocent language.</p> |
| 851 | |
| 852 | </div> |
| 853 | |
| 854 | <!-- *********************************************************************** --> |
| 855 | <div class="doc_section"><a name="code">Full Code Listing</a></div> |
| 856 | <!-- *********************************************************************** --> |
| 857 | |
| 858 | <div class="doc_text"> |
| 859 | |
| 860 | <p> |
| 861 | Here is the complete code listing for our running example, enhanced with the |
| 862 | if/then/else and for expressions.. To build this example, use: |
| 863 | </p> |
| 864 | |
| 865 | <div class="doc_code"> |
| 866 | <pre> |
| 867 | # Compile |
| 868 | ocamlbuild toy.byte |
| 869 | # Run |
| 870 | ./toy.byte |
| 871 | </pre> |
| 872 | </div> |
| 873 | |
| 874 | <p>Here is the code:</p> |
| 875 | |
| 876 | <dl> |
| 877 | <dt>_tags:</dt> |
| 878 | <dd class="doc_code"> |
| 879 | <pre> |
| 880 | <{lexer,parser}.ml>: use_camlp4, pp(camlp4of) |
| 881 | <*.{byte,native}>: g++, use_llvm, use_llvm_analysis |
| 882 | <*.{byte,native}>: use_llvm_executionengine, use_llvm_target |
| 883 | <*.{byte,native}>: use_llvm_scalar_opts, use_bindings |
| 884 | </pre> |
| 885 | </dd> |
| 886 | |
| 887 | <dt>myocamlbuild.ml:</dt> |
| 888 | <dd class="doc_code"> |
| 889 | <pre> |
| 890 | open Ocamlbuild_plugin;; |
| 891 | |
| 892 | ocaml_lib ~extern:true "llvm";; |
| 893 | ocaml_lib ~extern:true "llvm_analysis";; |
| 894 | ocaml_lib ~extern:true "llvm_executionengine";; |
| 895 | ocaml_lib ~extern:true "llvm_target";; |
| 896 | ocaml_lib ~extern:true "llvm_scalar_opts";; |
| 897 | |
| 898 | flag ["link"; "ocaml"; "g++"] (S[A"-cc"; A"g++"]);; |
| 899 | dep ["link"; "ocaml"; "use_bindings"] ["bindings.o"];; |
| 900 | </pre> |
| 901 | </dd> |
| 902 | |
| 903 | <dt>token.ml:</dt> |
| 904 | <dd class="doc_code"> |
| 905 | <pre> |
| 906 | (*===----------------------------------------------------------------------=== |
| 907 | * Lexer Tokens |
| 908 | *===----------------------------------------------------------------------===*) |
| 909 | |
| 910 | (* The lexer returns these 'Kwd' if it is an unknown character, otherwise one of |
| 911 | * these others for known things. *) |
| 912 | type token = |
| 913 | (* commands *) |
| 914 | | Def | Extern |
| 915 | |
| 916 | (* primary *) |
| 917 | | Ident of string | Number of float |
| 918 | |
| 919 | (* unknown *) |
| 920 | | Kwd of char |
| 921 | |
| 922 | (* control *) |
| 923 | | If | Then | Else |
| 924 | | For | In |
| 925 | </pre> |
| 926 | </dd> |
| 927 | |
| 928 | <dt>lexer.ml:</dt> |
| 929 | <dd class="doc_code"> |
| 930 | <pre> |
| 931 | (*===----------------------------------------------------------------------=== |
| 932 | * Lexer |
| 933 | *===----------------------------------------------------------------------===*) |
| 934 | |
| 935 | let rec lex = parser |
| 936 | (* Skip any whitespace. *) |
| 937 | | [< ' (' ' | '\n' | '\r' | '\t'); stream >] -> lex stream |
| 938 | |
| 939 | (* identifier: [a-zA-Z][a-zA-Z0-9] *) |
| 940 | | [< ' ('A' .. 'Z' | 'a' .. 'z' as c); stream >] -> |
| 941 | let buffer = Buffer.create 1 in |
| 942 | Buffer.add_char buffer c; |
| 943 | lex_ident buffer stream |
| 944 | |
| 945 | (* number: [0-9.]+ *) |
| 946 | | [< ' ('0' .. '9' as c); stream >] -> |
| 947 | let buffer = Buffer.create 1 in |
| 948 | Buffer.add_char buffer c; |
| 949 | lex_number buffer stream |
| 950 | |
| 951 | (* Comment until end of line. *) |
| 952 | | [< ' ('#'); stream >] -> |
| 953 | lex_comment stream |
| 954 | |
| 955 | (* Otherwise, just return the character as its ascii value. *) |
| 956 | | [< 'c; stream >] -> |
| 957 | [< 'Token.Kwd c; lex stream >] |
| 958 | |
| 959 | (* end of stream. *) |
| 960 | | [< >] -> [< >] |
| 961 | |
| 962 | and lex_number buffer = parser |
| 963 | | [< ' ('0' .. '9' | '.' as c); stream >] -> |
| 964 | Buffer.add_char buffer c; |
| 965 | lex_number buffer stream |
| 966 | | [< stream=lex >] -> |
| 967 | [< 'Token.Number (float_of_string (Buffer.contents buffer)); stream >] |
| 968 | |
| 969 | and lex_ident buffer = parser |
| 970 | | [< ' ('A' .. 'Z' | 'a' .. 'z' | '0' .. '9' as c); stream >] -> |
| 971 | Buffer.add_char buffer c; |
| 972 | lex_ident buffer stream |
| 973 | | [< stream=lex >] -> |
| 974 | match Buffer.contents buffer with |
| 975 | | "def" -> [< 'Token.Def; stream >] |
| 976 | | "extern" -> [< 'Token.Extern; stream >] |
| 977 | | "if" -> [< 'Token.If; stream >] |
| 978 | | "then" -> [< 'Token.Then; stream >] |
| 979 | | "else" -> [< 'Token.Else; stream >] |
| 980 | | "for" -> [< 'Token.For; stream >] |
| 981 | | "in" -> [< 'Token.In; stream >] |
| 982 | | id -> [< 'Token.Ident id; stream >] |
| 983 | |
| 984 | and lex_comment = parser |
| 985 | | [< ' ('\n'); stream=lex >] -> stream |
| 986 | | [< 'c; e=lex_comment >] -> e |
| 987 | | [< >] -> [< >] |
| 988 | </pre> |
| 989 | </dd> |
| 990 | |
| 991 | <dt>ast.ml:</dt> |
| 992 | <dd class="doc_code"> |
| 993 | <pre> |
| 994 | (*===----------------------------------------------------------------------=== |
| 995 | * Abstract Syntax Tree (aka Parse Tree) |
| 996 | *===----------------------------------------------------------------------===*) |
| 997 | |
| 998 | (* expr - Base type for all expression nodes. *) |
| 999 | type expr = |
| 1000 | (* variant for numeric literals like "1.0". *) |
| 1001 | | Number of float |
| 1002 | |
| 1003 | (* variant for referencing a variable, like "a". *) |
| 1004 | | Variable of string |
| 1005 | |
| 1006 | (* variant for a binary operator. *) |
| 1007 | | Binary of char * expr * expr |
| 1008 | |
| 1009 | (* variant for function calls. *) |
| 1010 | | Call of string * expr array |
| 1011 | |
| 1012 | (* variant for if/then/else. *) |
| 1013 | | If of expr * expr * expr |
| 1014 | |
| 1015 | (* variant for for/in. *) |
| 1016 | | For of string * expr * expr * expr option * expr |
| 1017 | |
| 1018 | (* proto - This type represents the "prototype" for a function, which captures |
| 1019 | * its name, and its argument names (thus implicitly the number of arguments the |
| 1020 | * function takes). *) |
| 1021 | type proto = Prototype of string * string array |
| 1022 | |
| 1023 | (* func - This type represents a function definition itself. *) |
| 1024 | type func = Function of proto * expr |
| 1025 | </pre> |
| 1026 | </dd> |
| 1027 | |
| 1028 | <dt>parser.ml:</dt> |
| 1029 | <dd class="doc_code"> |
| 1030 | <pre> |
| 1031 | (*===---------------------------------------------------------------------=== |
| 1032 | * Parser |
| 1033 | *===---------------------------------------------------------------------===*) |
| 1034 | |
| 1035 | (* binop_precedence - This holds the precedence for each binary operator that is |
| 1036 | * defined *) |
| 1037 | let binop_precedence:(char, int) Hashtbl.t = Hashtbl.create 10 |
| 1038 | |
| 1039 | (* precedence - Get the precedence of the pending binary operator token. *) |
| 1040 | let precedence c = try Hashtbl.find binop_precedence c with Not_found -> -1 |
| 1041 | |
| 1042 | (* primary |
| 1043 | * ::= identifier |
| 1044 | * ::= numberexpr |
| 1045 | * ::= parenexpr |
| 1046 | * ::= ifexpr |
| 1047 | * ::= forexpr *) |
| 1048 | let rec parse_primary = parser |
| 1049 | (* numberexpr ::= number *) |
| 1050 | | [< 'Token.Number n >] -> Ast.Number n |
| 1051 | |
| 1052 | (* parenexpr ::= '(' expression ')' *) |
| 1053 | | [< 'Token.Kwd '('; e=parse_expr; 'Token.Kwd ')' ?? "expected ')'" >] -> e |
| 1054 | |
| 1055 | (* identifierexpr |
| 1056 | * ::= identifier |
| 1057 | * ::= identifier '(' argumentexpr ')' *) |
| 1058 | | [< 'Token.Ident id; stream >] -> |
| 1059 | let rec parse_args accumulator = parser |
| 1060 | | [< e=parse_expr; stream >] -> |
| 1061 | begin parser |
| 1062 | | [< 'Token.Kwd ','; e=parse_args (e :: accumulator) >] -> e |
| 1063 | | [< >] -> e :: accumulator |
| 1064 | end stream |
| 1065 | | [< >] -> accumulator |
| 1066 | in |
| 1067 | let rec parse_ident id = parser |
| 1068 | (* Call. *) |
| 1069 | | [< 'Token.Kwd '('; |
| 1070 | args=parse_args []; |
| 1071 | 'Token.Kwd ')' ?? "expected ')'">] -> |
| 1072 | Ast.Call (id, Array.of_list (List.rev args)) |
| 1073 | |
| 1074 | (* Simple variable ref. *) |
| 1075 | | [< >] -> Ast.Variable id |
| 1076 | in |
| 1077 | parse_ident id stream |
| 1078 | |
| 1079 | (* ifexpr ::= 'if' expr 'then' expr 'else' expr *) |
| 1080 | | [< 'Token.If; c=parse_expr; |
| 1081 | 'Token.Then ?? "expected 'then'"; t=parse_expr; |
| 1082 | 'Token.Else ?? "expected 'else'"; e=parse_expr >] -> |
| 1083 | Ast.If (c, t, e) |
| 1084 | |
| 1085 | (* forexpr |
| 1086 | ::= 'for' identifier '=' expr ',' expr (',' expr)? 'in' expression *) |
| 1087 | | [< 'Token.For; |
| 1088 | 'Token.Ident id ?? "expected identifier after for"; |
| 1089 | 'Token.Kwd '=' ?? "expected '=' after for"; |
| 1090 | stream >] -> |
| 1091 | begin parser |
| 1092 | | [< |
| 1093 | start=parse_expr; |
| 1094 | 'Token.Kwd ',' ?? "expected ',' after for"; |
| 1095 | end_=parse_expr; |
| 1096 | stream >] -> |
| 1097 | let step = |
| 1098 | begin parser |
| 1099 | | [< 'Token.Kwd ','; step=parse_expr >] -> Some step |
| 1100 | | [< >] -> None |
| 1101 | end stream |
| 1102 | in |
| 1103 | begin parser |
| 1104 | | [< 'Token.In; body=parse_expr >] -> |
| 1105 | Ast.For (id, start, end_, step, body) |
| 1106 | | [< >] -> |
| 1107 | raise (Stream.Error "expected 'in' after for") |
| 1108 | end stream |
| 1109 | | [< >] -> |
| 1110 | raise (Stream.Error "expected '=' after for") |
| 1111 | end stream |
| 1112 | |
| 1113 | | [< >] -> raise (Stream.Error "unknown token when expecting an expression.") |
| 1114 | |
| 1115 | (* binoprhs |
| 1116 | * ::= ('+' primary)* *) |
| 1117 | and parse_bin_rhs expr_prec lhs stream = |
| 1118 | match Stream.peek stream with |
| 1119 | (* If this is a binop, find its precedence. *) |
| 1120 | | Some (Token.Kwd c) when Hashtbl.mem binop_precedence c -> |
| 1121 | let token_prec = precedence c in |
| 1122 | |
| 1123 | (* If this is a binop that binds at least as tightly as the current binop, |
| 1124 | * consume it, otherwise we are done. *) |
| 1125 | if token_prec < expr_prec then lhs else begin |
| 1126 | (* Eat the binop. *) |
| 1127 | Stream.junk stream; |
| 1128 | |
| 1129 | (* Parse the primary expression after the binary operator. *) |
| 1130 | let rhs = parse_primary stream in |
| 1131 | |
| 1132 | (* Okay, we know this is a binop. *) |
| 1133 | let rhs = |
| 1134 | match Stream.peek stream with |
| 1135 | | Some (Token.Kwd c2) -> |
| 1136 | (* If BinOp binds less tightly with rhs than the operator after |
| 1137 | * rhs, let the pending operator take rhs as its lhs. *) |
| 1138 | let next_prec = precedence c2 in |
| 1139 | if token_prec < next_prec |
| 1140 | then parse_bin_rhs (token_prec + 1) rhs stream |
| 1141 | else rhs |
| 1142 | | _ -> rhs |
| 1143 | in |
| 1144 | |
| 1145 | (* Merge lhs/rhs. *) |
| 1146 | let lhs = Ast.Binary (c, lhs, rhs) in |
| 1147 | parse_bin_rhs expr_prec lhs stream |
| 1148 | end |
| 1149 | | _ -> lhs |
| 1150 | |
| 1151 | (* expression |
| 1152 | * ::= primary binoprhs *) |
| 1153 | and parse_expr = parser |
| 1154 | | [< lhs=parse_primary; stream >] -> parse_bin_rhs 0 lhs stream |
| 1155 | |
| 1156 | (* prototype |
| 1157 | * ::= id '(' id* ')' *) |
| 1158 | let parse_prototype = |
| 1159 | let rec parse_args accumulator = parser |
| 1160 | | [< 'Token.Ident id; e=parse_args (id::accumulator) >] -> e |
| 1161 | | [< >] -> accumulator |
| 1162 | in |
| 1163 | |
| 1164 | parser |
| 1165 | | [< 'Token.Ident id; |
| 1166 | 'Token.Kwd '(' ?? "expected '(' in prototype"; |
| 1167 | args=parse_args []; |
| 1168 | 'Token.Kwd ')' ?? "expected ')' in prototype" >] -> |
| 1169 | (* success. *) |
| 1170 | Ast.Prototype (id, Array.of_list (List.rev args)) |
| 1171 | |
| 1172 | | [< >] -> |
| 1173 | raise (Stream.Error "expected function name in prototype") |
| 1174 | |
| 1175 | (* definition ::= 'def' prototype expression *) |
| 1176 | let parse_definition = parser |
| 1177 | | [< 'Token.Def; p=parse_prototype; e=parse_expr >] -> |
| 1178 | Ast.Function (p, e) |
| 1179 | |
| 1180 | (* toplevelexpr ::= expression *) |
| 1181 | let parse_toplevel = parser |
| 1182 | | [< e=parse_expr >] -> |
| 1183 | (* Make an anonymous proto. *) |
| 1184 | Ast.Function (Ast.Prototype ("", [||]), e) |
| 1185 | |
| 1186 | (* external ::= 'extern' prototype *) |
| 1187 | let parse_extern = parser |
| 1188 | | [< 'Token.Extern; e=parse_prototype >] -> e |
| 1189 | </pre> |
| 1190 | </dd> |
| 1191 | |
| 1192 | <dt>codegen.ml:</dt> |
| 1193 | <dd class="doc_code"> |
| 1194 | <pre> |
| 1195 | (*===----------------------------------------------------------------------=== |
| 1196 | * Code Generation |
| 1197 | *===----------------------------------------------------------------------===*) |
| 1198 | |
| 1199 | open Llvm |
| 1200 | |
| 1201 | exception Error of string |
| 1202 | |
Erick Tryzelaar | 1f3d276 | 2009-08-19 17:32:38 +0000 | [diff] [blame] | 1203 | let context = global_context () |
| 1204 | let the_module = create_module context "my cool jit" |
| 1205 | let builder = builder context |
Erick Tryzelaar | 35295ff | 2008-03-31 08:44:50 +0000 | [diff] [blame] | 1206 | let named_values:(string, llvalue) Hashtbl.t = Hashtbl.create 10 |
| 1207 | |
| 1208 | let rec codegen_expr = function |
| 1209 | | Ast.Number n -> const_float double_type n |
| 1210 | | Ast.Variable name -> |
| 1211 | (try Hashtbl.find named_values name with |
| 1212 | | Not_found -> raise (Error "unknown variable name")) |
| 1213 | | Ast.Binary (op, lhs, rhs) -> |
| 1214 | let lhs_val = codegen_expr lhs in |
| 1215 | let rhs_val = codegen_expr rhs in |
| 1216 | begin |
| 1217 | match op with |
| 1218 | | '+' -> build_add lhs_val rhs_val "addtmp" builder |
| 1219 | | '-' -> build_sub lhs_val rhs_val "subtmp" builder |
| 1220 | | '*' -> build_mul lhs_val rhs_val "multmp" builder |
| 1221 | | '<' -> |
| 1222 | (* Convert bool 0/1 to double 0.0 or 1.0 *) |
| 1223 | let i = build_fcmp Fcmp.Ult lhs_val rhs_val "cmptmp" builder in |
| 1224 | build_uitofp i double_type "booltmp" builder |
| 1225 | | _ -> raise (Error "invalid binary operator") |
| 1226 | end |
| 1227 | | Ast.Call (callee, args) -> |
| 1228 | (* Look up the name in the module table. *) |
| 1229 | let callee = |
| 1230 | match lookup_function callee the_module with |
| 1231 | | Some callee -> callee |
| 1232 | | None -> raise (Error "unknown function referenced") |
| 1233 | in |
| 1234 | let params = params callee in |
| 1235 | |
| 1236 | (* If argument mismatch error. *) |
| 1237 | if Array.length params == Array.length args then () else |
| 1238 | raise (Error "incorrect # arguments passed"); |
| 1239 | let args = Array.map codegen_expr args in |
| 1240 | build_call callee args "calltmp" builder |
| 1241 | | Ast.If (cond, then_, else_) -> |
| 1242 | let cond = codegen_expr cond in |
| 1243 | |
| 1244 | (* Convert condition to a bool by comparing equal to 0.0 *) |
| 1245 | let zero = const_float double_type 0.0 in |
| 1246 | let cond_val = build_fcmp Fcmp.One cond zero "ifcond" builder in |
| 1247 | |
| 1248 | (* Grab the first block so that we might later add the conditional branch |
| 1249 | * to it at the end of the function. *) |
| 1250 | let start_bb = insertion_block builder in |
| 1251 | let the_function = block_parent start_bb in |
| 1252 | |
| 1253 | let then_bb = append_block "then" the_function in |
| 1254 | |
| 1255 | (* Emit 'then' value. *) |
| 1256 | position_at_end then_bb builder; |
| 1257 | let then_val = codegen_expr then_ in |
| 1258 | |
| 1259 | (* Codegen of 'then' can change the current block, update then_bb for the |
| 1260 | * phi. We create a new name because one is used for the phi node, and the |
| 1261 | * other is used for the conditional branch. *) |
| 1262 | let new_then_bb = insertion_block builder in |
| 1263 | |
| 1264 | (* Emit 'else' value. *) |
| 1265 | let else_bb = append_block "else" the_function in |
| 1266 | position_at_end else_bb builder; |
| 1267 | let else_val = codegen_expr else_ in |
| 1268 | |
| 1269 | (* Codegen of 'else' can change the current block, update else_bb for the |
| 1270 | * phi. *) |
| 1271 | let new_else_bb = insertion_block builder in |
| 1272 | |
| 1273 | (* Emit merge block. *) |
| 1274 | let merge_bb = append_block "ifcont" the_function in |
| 1275 | position_at_end merge_bb builder; |
| 1276 | let incoming = [(then_val, new_then_bb); (else_val, new_else_bb)] in |
| 1277 | let phi = build_phi incoming "iftmp" builder in |
| 1278 | |
| 1279 | (* Return to the start block to add the conditional branch. *) |
| 1280 | position_at_end start_bb builder; |
| 1281 | ignore (build_cond_br cond_val then_bb else_bb builder); |
| 1282 | |
| 1283 | (* Set a unconditional branch at the end of the 'then' block and the |
| 1284 | * 'else' block to the 'merge' block. *) |
| 1285 | position_at_end new_then_bb builder; ignore (build_br merge_bb builder); |
| 1286 | position_at_end new_else_bb builder; ignore (build_br merge_bb builder); |
| 1287 | |
| 1288 | (* Finally, set the builder to the end of the merge block. *) |
| 1289 | position_at_end merge_bb builder; |
| 1290 | |
| 1291 | phi |
| 1292 | | Ast.For (var_name, start, end_, step, body) -> |
| 1293 | (* Emit the start code first, without 'variable' in scope. *) |
| 1294 | let start_val = codegen_expr start in |
| 1295 | |
| 1296 | (* Make the new basic block for the loop header, inserting after current |
| 1297 | * block. *) |
| 1298 | let preheader_bb = insertion_block builder in |
| 1299 | let the_function = block_parent preheader_bb in |
| 1300 | let loop_bb = append_block "loop" the_function in |
| 1301 | |
| 1302 | (* Insert an explicit fall through from the current block to the |
| 1303 | * loop_bb. *) |
| 1304 | ignore (build_br loop_bb builder); |
| 1305 | |
| 1306 | (* Start insertion in loop_bb. *) |
| 1307 | position_at_end loop_bb builder; |
| 1308 | |
| 1309 | (* Start the PHI node with an entry for start. *) |
| 1310 | let variable = build_phi [(start_val, preheader_bb)] var_name builder in |
| 1311 | |
| 1312 | (* Within the loop, the variable is defined equal to the PHI node. If it |
| 1313 | * shadows an existing variable, we have to restore it, so save it |
| 1314 | * now. *) |
| 1315 | let old_val = |
| 1316 | try Some (Hashtbl.find named_values var_name) with Not_found -> None |
| 1317 | in |
| 1318 | Hashtbl.add named_values var_name variable; |
| 1319 | |
| 1320 | (* Emit the body of the loop. This, like any other expr, can change the |
| 1321 | * current BB. Note that we ignore the value computed by the body, but |
| 1322 | * don't allow an error *) |
| 1323 | ignore (codegen_expr body); |
| 1324 | |
| 1325 | (* Emit the step value. *) |
| 1326 | let step_val = |
| 1327 | match step with |
| 1328 | | Some step -> codegen_expr step |
| 1329 | (* If not specified, use 1.0. *) |
| 1330 | | None -> const_float double_type 1.0 |
| 1331 | in |
| 1332 | |
| 1333 | let next_var = build_add variable step_val "nextvar" builder in |
| 1334 | |
| 1335 | (* Compute the end condition. *) |
| 1336 | let end_cond = codegen_expr end_ in |
| 1337 | |
| 1338 | (* Convert condition to a bool by comparing equal to 0.0. *) |
| 1339 | let zero = const_float double_type 0.0 in |
| 1340 | let end_cond = build_fcmp Fcmp.One end_cond zero "loopcond" builder in |
| 1341 | |
| 1342 | (* Create the "after loop" block and insert it. *) |
| 1343 | let loop_end_bb = insertion_block builder in |
| 1344 | let after_bb = append_block "afterloop" the_function in |
| 1345 | |
| 1346 | (* Insert the conditional branch into the end of loop_end_bb. *) |
| 1347 | ignore (build_cond_br end_cond loop_bb after_bb builder); |
| 1348 | |
| 1349 | (* Any new code will be inserted in after_bb. *) |
| 1350 | position_at_end after_bb builder; |
| 1351 | |
| 1352 | (* Add a new entry to the PHI node for the backedge. *) |
| 1353 | add_incoming (next_var, loop_end_bb) variable; |
| 1354 | |
| 1355 | (* Restore the unshadowed variable. *) |
| 1356 | begin match old_val with |
| 1357 | | Some old_val -> Hashtbl.add named_values var_name old_val |
| 1358 | | None -> () |
| 1359 | end; |
| 1360 | |
| 1361 | (* for expr always returns 0.0. *) |
| 1362 | const_null double_type |
| 1363 | |
| 1364 | let codegen_proto = function |
| 1365 | | Ast.Prototype (name, args) -> |
| 1366 | (* Make the function type: double(double,double) etc. *) |
| 1367 | let doubles = Array.make (Array.length args) double_type in |
| 1368 | let ft = function_type double_type doubles in |
| 1369 | let f = |
| 1370 | match lookup_function name the_module with |
| 1371 | | None -> declare_function name ft the_module |
| 1372 | |
| 1373 | (* If 'f' conflicted, there was already something named 'name'. If it |
| 1374 | * has a body, don't allow redefinition or reextern. *) |
| 1375 | | Some f -> |
| 1376 | (* If 'f' already has a body, reject this. *) |
| 1377 | if block_begin f <> At_end f then |
| 1378 | raise (Error "redefinition of function"); |
| 1379 | |
| 1380 | (* If 'f' took a different number of arguments, reject. *) |
| 1381 | if element_type (type_of f) <> ft then |
| 1382 | raise (Error "redefinition of function with different # args"); |
| 1383 | f |
| 1384 | in |
| 1385 | |
| 1386 | (* Set names for all arguments. *) |
| 1387 | Array.iteri (fun i a -> |
| 1388 | let n = args.(i) in |
| 1389 | set_value_name n a; |
| 1390 | Hashtbl.add named_values n a; |
| 1391 | ) (params f); |
| 1392 | f |
| 1393 | |
| 1394 | let codegen_func the_fpm = function |
| 1395 | | Ast.Function (proto, body) -> |
| 1396 | Hashtbl.clear named_values; |
| 1397 | let the_function = codegen_proto proto in |
| 1398 | |
| 1399 | (* Create a new basic block to start insertion into. *) |
| 1400 | let bb = append_block "entry" the_function in |
| 1401 | position_at_end bb builder; |
| 1402 | |
| 1403 | try |
| 1404 | let ret_val = codegen_expr body in |
| 1405 | |
| 1406 | (* Finish off the function. *) |
| 1407 | let _ = build_ret ret_val builder in |
| 1408 | |
| 1409 | (* Validate the generated code, checking for consistency. *) |
| 1410 | Llvm_analysis.assert_valid_function the_function; |
| 1411 | |
| 1412 | (* Optimize the function. *) |
| 1413 | let _ = PassManager.run_function the_function the_fpm in |
| 1414 | |
| 1415 | the_function |
| 1416 | with e -> |
| 1417 | delete_function the_function; |
| 1418 | raise e |
| 1419 | </pre> |
| 1420 | </dd> |
| 1421 | |
| 1422 | <dt>toplevel.ml:</dt> |
| 1423 | <dd class="doc_code"> |
| 1424 | <pre> |
| 1425 | (*===----------------------------------------------------------------------=== |
| 1426 | * Top-Level parsing and JIT Driver |
| 1427 | *===----------------------------------------------------------------------===*) |
| 1428 | |
| 1429 | open Llvm |
| 1430 | open Llvm_executionengine |
| 1431 | |
| 1432 | (* top ::= definition | external | expression | ';' *) |
| 1433 | let rec main_loop the_fpm the_execution_engine stream = |
| 1434 | match Stream.peek stream with |
| 1435 | | None -> () |
| 1436 | |
| 1437 | (* ignore top-level semicolons. *) |
| 1438 | | Some (Token.Kwd ';') -> |
| 1439 | Stream.junk stream; |
| 1440 | main_loop the_fpm the_execution_engine stream |
| 1441 | |
| 1442 | | Some token -> |
| 1443 | begin |
| 1444 | try match token with |
| 1445 | | Token.Def -> |
| 1446 | let e = Parser.parse_definition stream in |
| 1447 | print_endline "parsed a function definition."; |
| 1448 | dump_value (Codegen.codegen_func the_fpm e); |
| 1449 | | Token.Extern -> |
| 1450 | let e = Parser.parse_extern stream in |
| 1451 | print_endline "parsed an extern."; |
| 1452 | dump_value (Codegen.codegen_proto e); |
| 1453 | | _ -> |
| 1454 | (* Evaluate a top-level expression into an anonymous function. *) |
| 1455 | let e = Parser.parse_toplevel stream in |
| 1456 | print_endline "parsed a top-level expr"; |
| 1457 | let the_function = Codegen.codegen_func the_fpm e in |
| 1458 | dump_value the_function; |
| 1459 | |
| 1460 | (* JIT the function, returning a function pointer. *) |
| 1461 | let result = ExecutionEngine.run_function the_function [||] |
| 1462 | the_execution_engine in |
| 1463 | |
| 1464 | print_string "Evaluated to "; |
| 1465 | print_float (GenericValue.as_float double_type result); |
| 1466 | print_newline (); |
| 1467 | with Stream.Error s | Codegen.Error s -> |
| 1468 | (* Skip token for error recovery. *) |
| 1469 | Stream.junk stream; |
| 1470 | print_endline s; |
| 1471 | end; |
| 1472 | print_string "ready> "; flush stdout; |
| 1473 | main_loop the_fpm the_execution_engine stream |
| 1474 | </pre> |
| 1475 | </dd> |
| 1476 | |
| 1477 | <dt>toy.ml:</dt> |
| 1478 | <dd class="doc_code"> |
| 1479 | <pre> |
| 1480 | (*===----------------------------------------------------------------------=== |
| 1481 | * Main driver code. |
| 1482 | *===----------------------------------------------------------------------===*) |
| 1483 | |
| 1484 | open Llvm |
| 1485 | open Llvm_executionengine |
| 1486 | open Llvm_target |
| 1487 | open Llvm_scalar_opts |
| 1488 | |
| 1489 | let main () = |
Erick Tryzelaar | 4626268 | 2009-09-14 21:54:32 +0000 | [diff] [blame] | 1490 | ignore (initialize_native_target ()); |
| 1491 | |
Erick Tryzelaar | 35295ff | 2008-03-31 08:44:50 +0000 | [diff] [blame] | 1492 | (* Install standard binary operators. |
| 1493 | * 1 is the lowest precedence. *) |
| 1494 | Hashtbl.add Parser.binop_precedence '<' 10; |
| 1495 | Hashtbl.add Parser.binop_precedence '+' 20; |
| 1496 | Hashtbl.add Parser.binop_precedence '-' 20; |
| 1497 | Hashtbl.add Parser.binop_precedence '*' 40; (* highest. *) |
| 1498 | |
| 1499 | (* Prime the first token. *) |
| 1500 | print_string "ready> "; flush stdout; |
| 1501 | let stream = Lexer.lex (Stream.of_channel stdin) in |
| 1502 | |
| 1503 | (* Create the JIT. *) |
| 1504 | let the_module_provider = ModuleProvider.create Codegen.the_module in |
| 1505 | let the_execution_engine = ExecutionEngine.create the_module_provider in |
| 1506 | let the_fpm = PassManager.create_function the_module_provider in |
| 1507 | |
| 1508 | (* Set up the optimizer pipeline. Start with registering info about how the |
| 1509 | * target lays out data structures. *) |
| 1510 | TargetData.add (ExecutionEngine.target_data the_execution_engine) the_fpm; |
| 1511 | |
| 1512 | (* Do simple "peephole" optimizations and bit-twiddling optzn. *) |
| 1513 | add_instruction_combining the_fpm; |
| 1514 | |
| 1515 | (* reassociate expressions. *) |
| 1516 | add_reassociation the_fpm; |
| 1517 | |
| 1518 | (* Eliminate Common SubExpressions. *) |
| 1519 | add_gvn the_fpm; |
| 1520 | |
| 1521 | (* Simplify the control flow graph (deleting unreachable blocks, etc). *) |
| 1522 | add_cfg_simplification the_fpm; |
| 1523 | |
Erick Tryzelaar | 126d86b | 2009-09-14 21:54:15 +0000 | [diff] [blame] | 1524 | ignore (PassManager.initialize the_fpm); |
| 1525 | |
Erick Tryzelaar | 35295ff | 2008-03-31 08:44:50 +0000 | [diff] [blame] | 1526 | (* Run the main "interpreter loop" now. *) |
| 1527 | Toplevel.main_loop the_fpm the_execution_engine stream; |
| 1528 | |
| 1529 | (* Print out all the generated code. *) |
| 1530 | dump_module Codegen.the_module |
| 1531 | ;; |
| 1532 | |
| 1533 | main () |
| 1534 | </pre> |
| 1535 | </dd> |
| 1536 | |
| 1537 | <dt>bindings.c</dt> |
| 1538 | <dd class="doc_code"> |
| 1539 | <pre> |
| 1540 | #include <stdio.h> |
| 1541 | |
| 1542 | /* putchard - putchar that takes a double and returns 0. */ |
| 1543 | extern double putchard(double X) { |
| 1544 | putchar((char)X); |
| 1545 | return 0; |
| 1546 | } |
| 1547 | </pre> |
| 1548 | </dd> |
| 1549 | </dl> |
| 1550 | |
| 1551 | <a href="OCamlLangImpl6.html">Next: Extending the language: user-defined |
| 1552 | operators</a> |
| 1553 | </div> |
| 1554 | |
| 1555 | <!-- *********************************************************************** --> |
| 1556 | <hr> |
| 1557 | <address> |
| 1558 | <a href="http://jigsaw.w3.org/css-validator/check/referer"><img |
| 1559 | src="http://jigsaw.w3.org/css-validator/images/vcss" alt="Valid CSS!"></a> |
| 1560 | <a href="http://validator.w3.org/check/referer"><img |
| 1561 | src="http://www.w3.org/Icons/valid-html401" alt="Valid HTML 4.01!"></a> |
| 1562 | |
| 1563 | <a href="mailto:sabre@nondot.org">Chris Lattner</a><br> |
| 1564 | <a href="mailto:idadesub@users.sourceforge.net">Erick Tryzelaar</a><br> |
| 1565 | <a href="http://llvm.org">The LLVM Compiler Infrastructure</a><br> |
Dan Gohman | 523e392 | 2010-02-03 17:27:31 +0000 | [diff] [blame] | 1566 | Last modified: $Date$ |
Erick Tryzelaar | 35295ff | 2008-03-31 08:44:50 +0000 | [diff] [blame] | 1567 | </address> |
| 1568 | </body> |
| 1569 | </html> |