高完整性系统工程（三）： Logic Intro & Formal Specification

目录

1. Propositions 命题

 2.1 Propositional Connectives 命题连接词 

2.2 Variables 变量

2.3 Sets

 2.3.1 Set Operations

2.4 Predicates 

2.5 Quantification 量化

2.6 Relations

2.6.1 What Is A Relation?

2.6.2 Relations as Sets

2.6.3 Binary Relations as Pictures

2.6.4 Relation Example

2.6.5 Functions

2.6.6 Total vs Partial Functions 全函数 VS 部分函数

2.6.7 Relation Operations

2.6.8 Relation Joins 

3. TEMPORAL LOGIC 时序逻辑

3.1 Next State

3.1.1 Transitions and Traces

3.2 Temporal Operators 时间运算符

4. SPECIFICATIONS SAY “WHAT” DESIGNS SAY “HOW” 

4.1 Specifying Software

4.2 Aside: Functions as Relations

4.3 Modelling Data Types 

4.4 Sequences as Relations  作为关系的序列

4.5 Searching

4.6 Pre and Postconditions 前置条件和后置条件

4.7 Formal Model-Based Specs

4.8 Advantages

4.9 Effect on Cost

4.10 Disadvantages

4.11 Difficulty

5. SPECIFICATIONS IN ALLOY

5.1 Alloy

6. LASTPASS DEMO

6.1 Alloy Modelling Overview

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1. Propositions 命题

定义：A statement that is either true or false

 2.1 Propositional Connectives 命题连接词 

2.2 Variables 变量

Variables allow propositions to talk about state

Variables talk about different parts of the state of the formal model. (not state of the system/program)

2.3 Sets

A collection of things

 2.3.1 Set Operations

2.4 Predicates 

Extend propositions with the ability to quantify the values of a variable that a proposition is true for

all: Proposition P(x) holds for all values of x 

all x | P[x]

all city | Raining[city]

all city: AustralianCities | Raining[city]

some: Proposition P(x) holds for at least one value of x

some x | P[x]

some city | not Raining[city]

2.5 Quantification 量化

De Morgan’s Laws

all x | P[x]         is equivalent to         not some x | not P[x]

some x | P[x]    is equivalent to         not all x | not P[x]

Alloy Specific Quantifiers

one x | P[x] P(x)         holds for exactly one value x

lone x | P[x] P(x)        holds for at most one value x

none x | P[x] P(x)       holds for no value x

2.6 Relations

A proposition that relates things together =, <, etc.

arity: the number of things the relation relates =, < etc. are all binary relations; relate two numbers 3 < 4, (5 - 1) = (3 + 1), etc.

A relation that relates three things together: IsSum(x,y,z) <=> z = x + y

Relations are just predicate

2.6.1 What Is A Relation?

How would you write down unambiguously what a relation means?

Simplest answer: just list all of the things it relates together.