Dataflow Analysis代写 Homework代写 paper代写 Essay代写

Reasoning about Software January 29, 2019

Dataflow Analysis代写 Collaboration is permitted, but you must write the solutions by yourself without assistance. Getting solutions from outside sources

Rice University COMP 503, Spring 2018

Swarat Chaudhuri Homework 2 Dataflow Analysis代写

Homework 2: Type Systems and Dataflow Analysis Due Wednesday, February 13, 2019

Reminders Dataflow Analysis代写

• Please submit your homework on
• Collaboration is permitted, but you must write the solutions by yourself without assistance. Getting solutions from outside sources such as the Web or students not enrolled in the class is forbidden.

1.Consider the information flow type system that you studied in the paper “A Sound Type System for Secure Flow Analysis”,

by Volpano, Smith, and Irvine. Now suppose that you have a func- tional rather than imperative language.  The grammar of programs e  in the language is given      by

e ::= x | c | (e₁ e₂) | λx.e₁ | e₁ + e₂ | e₁ ≥ 0 | let x = e₁ in e₂ | if e₁ then e₂ else e₃

where x represents variables and c represents constants.Dataflow Analysis代写

Present a type system for information flow analysis of programs in this language. Your answer should clarify the following points.

(a)What is the form of a type judgment in thissetting?

(b)What does a type environment looklike?

(c)Doesthe grammar of the language need to be augmented with additional type annotations? Recall that while type-checking the λ-calculus, we needed to add a type annotation to the input variable x in λ-terms.

(d)What are the typing rules? Please present the rules formally, and also write a sentence or two explaining each

2.Define a data flow analysis Dataflow Analysis代写

that can be used to compute two  sets of variables for each statement  in a program: those which are definitely not defined before use, and those which may not be defined before use. These sets can be used to provide extra error checking of programs. Your answer should answer the following

(a)What is the dataflow lattice for thissetting?

(b)What are the dataflowequations?Dataflow Analysis代写

(c)Why does your analysisterminate?

(d)How do you use the information computed by your analysis to construct the two sets specified above for output to theuser?

(e)How does your dataflow analysis operate on the following program, and what are the variable sets of interest for the label c in thecode?

s := 0

c: while (i < n) { s := s + i

i :=  i + 1

}

3.Consider any lattice L = (S, ±, H, H) where S is a set, ± is a partial order,

and H and H are respectively the join and meet operators. Show that the following identitieshold:

(a)For all x, y,z,

x H (y H z) = (x H y) H z  Dataflow Analysis代写

(b)For all x,y,

(x H y) H x = x.Homework

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