程序代写代做代考 Java data structure Program 1: Verification Condition Generator
Program 1: Verification Condition Generator
CSC 7101, Spring 2017
Due: 12 March 2017
Write a Verification Condition Generator (VCG) for our simple imperative language, IMP, using the
parser generator ANTLR. Use the Weakest (Liberal) Precondition Predicate Transformer semantics. This
allows you to use backward substitution over if-statements. For while-loops, simply print intermediate verifi-
cation conditions instead of combining them into a single verification condition using universal quantification.
Use the ANTLR attribute grammar mechanism as far as possible for generating the verfication conditions.
Reading Material
For information on ANTLR and the weakest precondition semantics see:
http://www.antlr.org/
https://en.wikipedia.org/wiki/Predicate_transformer_semantics
For using ANTLR, make sue you put antlr-4.6-complete.jar onto your CLASSPATH. For details,
see the Quick Start and Samples instructions on the ANTLR web page or read the Makefile I provided.
Code Structure
For constructing the verifications conditions, you need to build a parse tree data structure representing the
verification conditions. Since expressions may be be substituted for variables, and since boolean expressions
are used in assertions, you also need to build parse trees for all expressions in the program. When traversing
statements, you will then construct the verification conditions using the weakest precondition predicate
transformer. This may or may not require building the parse trees for statements as well.
For building parse trees, use the Composite Design Pattern, i.e., use a class hierarchy with an abstract
superclass and subclasses corresponding to the different language constructs, e.g.,
abstract class Node { … }
class Ident extends Node { … }
class IntLit extends Node { … }
class BinOp extends Node { … }
// etc.
For expressions, you will need methods for printing the expression and for performing a substitution. If you
decide to represent statements using parse tree nodes as well, it would be best to group expressions and
statements as two separate parts of the class hierarchy, since you will likely need different methods, e.g.,
abstract class Node { … }
abstract class Exp extends Node { … }
abstract class Stm extends Node { … }
class Ident extends Exp { … }
class IntLit extends Exp { … }
class BinOp extends Exp { … }
// etc.
class Assign extends Stm { … }
// etc.
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Grammar
Use the following grammar for the language IMP (in ANTLR syntax) with start symbol program as a starting
point. You may need to restructure the grammar based on how you propagate information using attributes.
program
: assertion statementlist assertion
;
statementlist
: statement
| statementlist ’;’ statement
;
statement
: ’skip’
| id ’:=’ arithexp
| ’begin’ statementlist ’end’
| ’if’ boolterm ’then’ statement ’else’ statement
| assertion ’while’ boolterm ’do’ statement
| ’assert’ assertion
;
assertion
: ’{’ quantexp ’}’
;
quantexp
: boolexp
| ’forall’ id ’.’ boolexp
| ’exists’ id ’.’ boolexp
;
boolexp
: boolterm
| boolterm ’=>’ boolterm
| boolterm ’<=>’ boolterm
;
boolterm
: boolterm2
| boolterm ’or’ boolterm2
;
boolterm2
: boolfactor
| boolterm2 ’and’ boolfactor
;
boolfactor
: ’true’
| ’false’
| compexp
| ’not’ quantexp
| ’(’ quantexp ’)’
;
2
compexp
: arithexp ’<’ arithexp | arithexp ’<=’ arithexp | arithexp ’=’ arithexp | arithexp ’!=’ arithexp | arithexp ’>=’ arithexp
| arithexp ’>’ arithexp
;
arithexp
: arithterm
| arithexp ’+’ arithterm
| arithexp ’-’ arithterm
;
arithterm
: arithfactor
| arithterm ’*’ arithfactor
| arithterm ’/’ arithfactor
;
arithfactor
: id
| integer
| ’-’ arithexp
| ’(’ arithexp ’)’
| id ’(’ arithexplist ’)’
;
arithexplist
: arithexp
| arithexplist ’,’ arithexp
;
id
: IDENT
;
integer
: INT
;
IDENT
: [A-Za-z][A-Za-z0-9_]*
;
INT
: [0]|[1-9][0-9]*
;
WS
: [
] -> skip
;
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Examples
The input to the VCG is a single Hoare triple. The output is a list of verification conditions, without
formatting, one VC per line. E.g., for the input
{ true } x := (2 * 3) * (3 + 4) { x = 42 }
The VCG should print
true => 2*3*(3+4)=42
Surround only the operators =>, <=>, and, and or with spaces, print a space after not, and print parentheses
only if the parent operator has higher precedence.
For loops, first print the exit condition, then the condition for the loop body, followed by the condition
for the code before the loop. E.g., for the input
{ x >= 0 and y > 0 }
q := 0;
r := x;
{ x = q*y + r and 0 <= r and y > 0 }
while r-y >= 0 do begin
q := q + 1;
r := r – y
end
{ x = q*y + r and 0 <= r and r < y }
the output should be:
x=q*y+r and 0<=r and y>0 and not r-y>=0 => x=q*y+r and 0<=r and r
x>=0 and y>0 => x=0*y+x and 0<=x and y>0
Administrative Stuff
Put your files into directory ~/prog1 in your cs7101xx account on classes.csc.lsu.edu, make sure that
you have a Makefile so that your code can be compiled and run using the commands
cd ~/prog1
make clean
make
java VCG test.vcg
and provide a file README.txt with anything that you want me or the grader to know about your project.
For submitting the code, simply use
cd ~/prog1
make clean
~cs7101_bau/bin/p_copy 1
Do not put the files into a ZIP file.
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