Act07_Pf_Rules_and_Pfs

Act07_Pf_Rules_and_Pfs - CS 536: Proof Rules and Proofs...

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Unformatted text preview: CS 536: Proof Rules and Proofs Activity 7.1: Verification Proofs for Straight-Line Code A. Why? Verification of straight-line code (basically, a sequence of assignments/skips) is a good base for verifying larger and more complicated programs. B. Outcomes At the end of this activity you should: Be able to write a short proof of correctness for simple programs involving a sequence of assignments. C. Questions 1. Using the assignment and precondition strengthening rules, fill in the rest of the formal proof below. 1. { ??? } y := x { y } Ass i g n me n t ??? is (y 0)[x/y] is x 0 2. x = y x < 0 x Predicate logic 3. { ??? } y := x { y } Precond. Strengthening, lines 2, 1 x = y x < 0 2. Using the skip and precondition strengthening rules, fill in the rest of the formal proof below. 1. { ??? } skip { y } skip y 2. x = y x y Predicate logic 3. { ??? } skip { y } Precond. Strengthening, l in es 2, 1 x = y x 3. Using the (backward) assignment and composition rules, fill in the rest of the formal proof below. 1. { ??? i+1 n s+i+1 = sum(0,i+1) } Ass i g n me n t i := i+1 { i n s+i = sum(0,i) } Illinois Institute of Technology Activities for Lecture 7 CS 536: Science of Programming - 1 of 6 - James Sasaki, 2010 2. { ??? i n s+i = sum(0,i) } Ass i g n me n t s := s+i { i n s = sum(0,i) } 3. { ??? i+1 n s+i+1 = sum(0,i+1) } Compos i t i o n 1, 2 i:= i+1; s:= s+i { i n s = sum(0,i) } 4. Using the (backward) assignment and composition rules, fill in the rest of the formal proof below....
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This note was uploaded on 04/17/2011 for the course CS 536 taught by Professor Cs536 during the Fall '08 term at Illinois Tech.

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Act07_Pf_Rules_and_Pfs - CS 536: Proof Rules and Proofs...

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