pl_0

PL/0 (aka. PL_0)

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To begin with

This is the curriculum design of Compiler Principle course in Nanjing University of Aeronautics and Astronautics ( aka. NUAA).

Introduction

PL/0 is a subset language of Pascal.

This is a simple Rust implementation of PL/0 compiler.

BNF

<prog> -> program <id> ; <block>
<block> -> [<const-decl>][<var-decl>][<proc>]<body>
<const-decl> -> const <const> {, <const>} ;
<const> -> <id> := <integer>
<var-decl> -> var <id> {, <id>} ;
<proc> -> procedure <id> ([<id> {, <id>}]) ; <block> {; <proc>}
<body> -> begin <statement> {; <statement>} end
<statement> -> <id> := <exp>
              | if <l-exp> then <statement> [else <statement>]
              | while <l-exp> do <statement>
              | call <id> ([<exp> {, <exp>}])
              | <body>
              | read (<id> {, <id>})
              | write (<exp> {, <exp>})
<l-exp> -> <exp> <lop> <exp> | odd <exp>
<exp> -> [+|-] <term> {<aop> <term>}
<term> -> <factor> {<mop> <factor>}
<factor> -> <id> | <integer> | (<exp>)
<lop> -> = | <> | < | <= | > | >=
<aop> -> + | -
<mop> -> * | /
<id> -> <letter> {<letter> | <digit>}
<integer> -> <digit> {<digit>}
<letter> -> a | b | ... | z | A | B | ... | Z
<digit> -> 0 | 1 | ... | 9

Structure

$$ \set{Source Code} \Longrightarrow \textbf{Lexer} \stackrel{Token}{\Longrightarrow} \textbf{Parser} \stackrel{AST}{\Longrightarrow} \textbf{CodeGen} \Longrightarrow \set{PCode} \longrightarrow \textbf{VM} \longrightarrow \set{Result} $$

Part	Analysis List
Lexer	Lexical Analysis
Parser	Syntax Analysis
CodeGen	Semantic Analysis

Overview

Lexer/Tokenizer

This part is extreme easy, I’ve implemented it in my own hand without using any other tools.

(However, if you’d love to, you could use tools like flex or pest to generate lexer/tokenizer automatically)

Parser

With the help of Recursive Descent Algorithm, parser is also not that hard to implement.

However, it’s necessary to prove that the given BNF satisfy the definition of LL(1) before implementing parser in Recursive Descent Algorithm.

Proof will be given later.

Error Handling

I’ve adopted the welcomed panic-mode-liked error handling strategy for this part, to make sure that the compiler could find as many errors as possible in one run, instead of being halted by the first error.

To make sure error could be handled in a synchronous way, FIRST-FOLLOW table is a must (I’ve built this manually, which could be further improved by using auto-tools).

Codegen

AST to PCode code-generator is the default strategy for this part.

I’m working on a AST to Lua-Backend-Adapted-Representation (LBAR) code-generator as well (not implemented yet).

Virtual Machine (aka. VM / Interpreter)

Sense PCode is the default execution result of codegen, the Simple-PCode-Interpreter is the default implementation of Virtual Machine

Still, I’m trying to implement a Lua-VM-Liked-VM for LBAR

Feasibility Analysis

Proof: BNF is LL(1)

To satisfy this, 3 conditions should be met:

$$ \begin{align*} \text{Condition 1} &~\dots~ \text{No \textit{left recursion pattern} detected in the \textit{grammar}} \ \text{Condition 2} &~\dots~ \forall A \in V_N (A \rightarrow \alpha_1 | \alpha_2 | \dots | \alpha_n) \Rightarrow First(\alpha_i) \cap First(\alpha_j) = \Phi ~ (i \ne j) \ \text{Condition 3} &~\dots~ \forall A \in V_N (\epsilon \in First(A)) \Rightarrow First(A) \cap Follow(A) = \Phi \end{align*} $$

Now, let’s prove them one by one!

Condition 1 ~ No left recursion pattern detected in the grammar

After having a glance of the given BNF, we could easily prove that:

$$ \forall A \in V_N (A \rightarrow B ~\wedge~ B \in V_N ) \Rightarrow A \ne B $$

Which means that, there’s no left recursion pattern detected in the grammar.

Condition 2

This could be easy, with the reference of BNF and first_follow_table

Condition 3

Just the same as Condition 2

Fibonacci Demo

Source code:

program fibonacci;

const index := 30;

var return,i,a;

procedure fib(a,x);

var sum;
begin
  sum := 0;
  if x<2 then
    return := x
  else
    begin
      call fib(a+1,x-1);
      sum := sum+return;
      call fib(a+1,x-2);
      sum := sum+return;
      return := sum
    end
end

begin
  i := 1;
  a := 2;
  while i<=index do
    begin
      call fib(a+1,i);
      write(return);
      i := i+1
    end
end

Result:

• Console

1
1
2
3
5
8
13
21
34
55
89
144
233
377
610
987
1597
2584
4181
6765
10946
17711
28657
46368
75025
121393
196418
317811
514229
832040

• PCode

PCode List:
======================================================================
   0| JMP    0   39
   1| JMP    0   4
   2| STA    1   4
   3| STA    2   3
   4| INT    0   6
   5| LIT    0   0
   6| STO    0   5
   7| LOD    0   4
   8| LIT    0   2
   9| OPR    0   10
  10| JPC    0   14
  11| LOD    0   4
  12| STO    1   3
  13| JMP    0   38
  14| LOD    0   3
  15| LIT    0   1
  16| OPR    0   2
  17| LOD    0   4
  18| LIT    0   1
  19| OPR    0   3
  20| CAL    1   2
  21| LOD    0   5
  22| LOD    1   3
  23| OPR    0   2
  24| STO    0   5
  25| LOD    0   3
  26| LIT    0   1
  27| OPR    0   2
  28| LOD    0   4
  29| LIT    0   2
  30| OPR    0   3
  31| CAL    1   2
  32| LOD    0   5
  33| LOD    1   3
  34| OPR    0   2
  35| STO    0   5
  36| LOD    0   5
  37| STO    1   3
  38| OPR    0   0
  39| INT    0   7
  40| LIT    0   1
  41| STO    0   4
  42| LIT    0   2
  43| STO    0   5
  44| LOD    0   4
  45| LIT    0   30
  46| OPR    0   13
  47| JPC    0   61
  48| LOD    0   5
  49| LIT    0   1
  50| OPR    0   2
  51| LOD    0   4
  52| CAL    0   2
  53| LOD    0   3
  54| OPR    0   14
  55| OPR    0   15
  56| LOD    0   4
  57| LIT    0   1
  58| OPR    0   2
  59| STO    0   4
  60| JMP    0   44
  61| OPR    0   0
======================================================================

• Symbol Table

Symbol Table:
======================================================================
      name | type   | val  | level  | addr | size | scope_list
======================================================================
     index | const  | 30   | 0      | 3    | 0    | ["#"]
    return | var    | 0    | 0      | 3    | 0    | ["#"]
         i | var    | 0    | 0      | 4    | 0    | ["#"]
         a | var    | 0    | 0      | 5    | 0    | ["#"]
       fib | proc   | 2    | 0      | 6    | 2    | ["#"]
         a | var    | 0    | 1      | 3    | 0    | ["#", "fib"]
         x | var    | 0    | 1      | 4    | 0    | ["#", "fib"]
       sum | var    | 0    | 1      | 5    | 0    | ["#", "fib"]
======================================================================

Error Handling Demos

As is mentioned follow, this implementation of pl/0 compiler has a complete error handling strategy, which means that it could find as many errors as possible in one run, instead of being halted by the first error.

Here are some simple demos:

Syntax Error (may coexists with Lexical Error)

• src

program ;
var a, b, c;
begin
  a    1;
  b :=  ;
  é : 3;
  if 1 = 1 then
    write(1
  else
    write 0);
  write a + b + c;
  wrçte(1)
end

• console

SyntaxError{ Line: 1, Col: 9 }
  | ~~ Expected <id> field, but not found!

SyntaxError{ Line: 4, Col: 8 }
  | ~~ Expected `:=`, but got `Integer(1)`

SyntaxError{ Line: 5, Col: 9 }
  | ~~ Expected `<id>` / `<integer>` / `(<exp>)` field, but got an unmatchable token `;`

LexicalError{ Line: 6, Col: 3 }
  | ~~ 'é' is not an ASCII character

LexicalError{ Line: 6, Col: 5 }
  | ~~ ':' is an undefined sign, did you mean ':='?

SyntaxError{ Line: 6, Col: 7 }
  | ~~ Expected `:=`, but got `Integer(3)`

SyntaxError{ Line: 6, Col: 7 }
  | ~~ Expected <statement> field, but not found!

SyntaxError{ Line: 9, Col: 6 }
  | ~~ Expected `)`, but got `Else`

SyntaxError{ Line: 10, Col: 11 }
  | ~~ Expected `(`, but got `Integer(0)`

SyntaxError{ Line: 11, Col: 9 }
  | ~~ Expected `(`, but got `Identifier("a")`

SyntaxError{ Line: 11, Col: 18 }
  | ~~ Expected `)`, but got `;`

LexicalError{ Line: 12, Col: 5 }
  | ~~ 'ç' is not an ASCII character

SyntaxError{ Line: 12, Col: 7 }
  | ~~ Expected `:=`, but got `Identifier("te")`

SyntaxError{ Line: 12, Col: 7 }
  | ~~ Expected <statement> field, but not found!

thread 'main' panicked at src/parser/mod.rs:149:7:
|> Errors above occurred (during `parsing`), compiling stopped ... <|

note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace

Semantic Error

Duplicated Definition

• src

program MultiDef;

var a, a, a, a;

procedure proc();
begin
  write(1)
end;

procedure proc();
begin
  write(2)
end

begin
  write(1)
end

• console

SemanticError{ Line: 3, Col: 8 }
  | ~~ `a` is defined before

SemanticError{ Line: 3, Col: 11 }
  | ~~ `a` is defined before

SemanticError{ Line: 3, Col: 14 }
  | ~~ `a` is defined before

SemanticError{ Line: 10, Col: 14 }
  | ~~ `proc` is defined before

thread 'main' panicked at src/translator/mod.rs:116:7:
attempt to subtract with overflow
note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace

Undefined

• src

program undef;
begin
  a := 1;
  b := 2;
  write(c)
end

• console

SemanticError{ Line: 3, Col: 3 }
  | ~~ `a` is undefined

SemanticError{ Line: 4, Col: 3 }
  | ~~ `b` is undefined

SemanticError{ Line: 5, Col: 9 }
  | ~~ `c` is undefined

thread 'main' panicked at src/translator/mod.rs:73:7:
|> Errors above occurred (during `translation/codegen`), compiling stopped ... <|

note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace

args_list.length cannot match with definition(signature)

• src

program WrongArgsListLength;

var a;

procedure proc();
begin
  write(1)
end;

procedure procc(x, t, z);
begin
  write(1)
end

begin
  call proc(1, 1, 1);
  call procc(3)
end

• console

SemanticError{ Line: 16, Col: 11 }
  | ~~ `proc` expects 0 args, but received 3

SemanticError{ Line: 17, Col: 12 }
  | ~~ `procc` expects 3 args, but received 1

thread 'main' panicked at src/translator/mod.rs:73:7:
|> Errors above occurred (during `translation/codegen`), compiling stopped ... <|

Assign to const / procedure

• src

program AssignToConstProc;
const i := 1;

procedure proc();
begin
  write(i)
end

begin
  i := 16;
  proc := 16
end

• console

SemanticError{ Line: 10, Col: 3 }
  | ~~ `i` is not a variable

SemanticError{ Line: 11, Col: 6 }
  | ~~ `proc` is not a variable

thread 'main' panicked at src/translator/mod.rs:73:7:
|> Errors above occurred (during `translation/codegen`), compiling stopped ... <|