Download Hardware Verification Using HOL

Hardware Verification Using HOL
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G. Sivakumar
Computer Science Department
Indian Institute of Technology, Bombay
Mumbai 400076, India
[email protected]
http://www.cse.iitb.ac.in/∼siva
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Outline of Talk
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• Hardware Verification Overview
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• HOL Examples
– CMOS NOT Gate
– Ripple Carry Adder
– Parity Circuit
• HOL Tips for Lab Session
Formal Hardware
Verification
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the proof that a circuit or a system (the implementation) behaves according to a given set of requirements (the specification).
Abstraction Levels
• Large abstraction gap between Specification and Implementation.
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• Bridged in several layers (hierarchy).
• Automation tool for Lower Layers
• Catching Design flaws early is critical
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Level
Behavior
Architecture Algorithm
Structure
Process
RTL
Data Flow
FSM
Registers
ALU
Gate
Boolean
functions
Flip-flops
gates
Data
Numbers
Time
Causality
Bit Vectors Clock Cycles
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Transistor
Differential Capacitors
equations transistors
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area
Bits
Discrete delay
time
Voltage
current
Continuous
time
Hardware Verification
Method
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Classical method of hardware verification:
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1. write a specification of intended behaviour
Spec
2. write specifications of the design components
Part-1, . . . Part-n
3. define a formal model of the design
Design = Part-1 + . . . + Part-n
4. formulate and prove correctness
Design satisfies Spec
For now, ignore
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• fabrication defects
• inaccurate design models
• ...
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What is HOL?
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HOL is an interactive program for mechanized formal reasoning using higher
order logic.
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Current Version: HOL4 (June 2002) Home Page: http://hol.sf.net/ (Excellent
Tutorial: Lots of material borrowed from there in rest of talk)
The HOL system provides:
• an expressive and powerful notation for writing system specifications,
• flexible and general facilities for creating formal proofs of properties of
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specifications.
HOL Structure and Use
HOL is built on top of ML
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HOL is a programming environment
• system command = a programming language
• proof = computation of theorems
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Theory-creation in the HOL system
HOL Features
• rigorous and well-understood theoretical basis
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• powerful command language (the general purpose programming language
ML)
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• secure–can’t prove false theorems
• user-extendable, without compromising security
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• supports a variety of styles of reasoning
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• automates some low-level details of proofs
HOL applications include:
• hardware design and verification
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• reasoning about security
• reasoning about real-time systems
• semantics of HDLs (e.g. VHDL, Verilog)
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• software verification (e.g. Hoare logic)
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• modelling concurrency (e.g. CCS, CSP)
• automata theory. . .
Formal Specification in HOL
General Idea for a Hardware Device
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This is specified by a boolean term S(a, b, c, d) with free variables a, b, c, and
d.
Do not think of Inputs/Outputs.
S(a,b,c,d) is either True of False for some combination of a,b,c,d if that set of
values is externally observable on the wires.
Simple Examples
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Composing Behaviours
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Hiding Internal Strcuture
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CMOS Inverter Example
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We wish to verify o = ¬i
3 Steps
1. define a model of the circuit in logic
2. formulate the correctness of the circuit
3. prove the correctness of the circuit
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CMOS Primitives
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Inverter Model and
Correctness
Correctness Proof
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Proof(Ctd.)
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More Complex Example
Ripple Carry Adder (illustrates recursion)
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Model Definition
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Model Definition (Ctd.)
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Correctness Proof
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Time Dependent Behaviour
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Parity Circuit
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Trace working on sample input.
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HOL Demo
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Some simple demos now (including parity).
More in the lab.
HOL Tips (From Authors)
Skills needed to use the system:
• familiarity with basic logic notation
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• ability to use an interactive functional language
• intuitive grasp of reasons for logical truth
• you do not have to be an expert logician!
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Learning to use HOL:
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• gaining familiarity with the syntax of HOL’s logic
• learning to express specifications in this notation
• learning your way around HOL’s very large collection of built-in facts and
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proof procedures
• learning useful proof-tactics . . and recognizing the contexts in which they
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are useful
Main problems for beginners:
• don’t know how to prove it, even informally –solution: experience, seeing
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examples
• know the proof, but can’t get HOL to do it! –solution: the reference manual, examples