Rule Formats for Structural Operational Semantics - A Very Short

33 Pages·2013·0.22 MB·English

Motivation
TailoringaRuleFormat
Conclusions
Rule Formats for Structural Operational Semantics
A Very Short Introduction
Luca Aceto
ICE-TCS, School of Computer Science, Reykjavik University
Chinese Academy of Sciences, Beijing, 21 November 2013
I have worked on rule formats for SOS with many
co-authors and thank them all!
LucaAceto RuleFormatsforSOS
Motivation
TailoringaRuleFormat
Conclusions
Message and Overview of the Talk
Message in a Nutshell
Rules rule! Using rule formats one can prove semantic properties
for classes of languages by purely syntactic means.
Overview
Motivation for developing rule formats
Introduction to rule formats with examples
Tailoring a rule format (unit elements)
Conclusion: Further and future work
LucaAceto RuleFormatsforSOS
Motivation
TailoringaRuleFormat WhatandWhy
Conclusions
The General Setting
Fact of (Computer Science) Life
In Computer Science, we use formal languages to communicate
with machines (programming languages) and describe expected
properties of computations (specification languages).
Like natural languages, the languages we use have
1 a syntax and
2 a semantics.
Question
How are those described in CS?
LucaAceto RuleFormatsforSOS
Motivation
TailoringaRuleFormat WhatandWhy
Conclusions
The General Setting
Fact of (Computer Science) Life
In Computer Science, we use formal languages to communicate
with machines (programming languages) and describe expected
properties of computations (specification languages).
Like natural languages, the languages we use have
1 a syntax and
2 a semantics.
Question
How are those described in CS?
LucaAceto RuleFormatsforSOS
Motivation
TailoringaRuleFormat WhatandWhy
Conclusions
Description of Programming and Specification Languages I
Syntax
Formally specified using, e.g., BNF notation. Example?
CCS nil 0 prefixing at
choice t +u parallel t(cid:107)u
where a is an action drawn from a non-empty set A.
Benefits: Too many to mention! For instance, compiler technology
was revolutionized and went from art to science, in the sense of
Knuth.
State of Play (Syntax)
The syntax of every language under the sky is formally specified.
Uncontroversial!
LucaAceto RuleFormatsforSOS
Motivation
TailoringaRuleFormat WhatandWhy
Conclusions
Semantics: Logic at Work
Operational Semantics: What the program does
Meaning of a program ≈ Execution on an idealized machine. How
is this specified?
Plotkin’s answer: Use logic! Define the semantics by using
inference rules.
Structural Operational Semantics for CCS
Given by transitions between terms of the form t →a u. These
associate a loop-free finite automaton with each term. How?
x →a x(cid:48) x →a x(cid:48) x →a x(cid:48), y →¯a y(cid:48)
ax →a x x +y →a x(cid:48) x(cid:107)y →a x(cid:48)(cid:107)y x(cid:107)y →τ x(cid:48)(cid:107)y(cid:48)
LucaAceto RuleFormatsforSOS
Motivation
TailoringaRuleFormat WhatandWhy
Conclusions
Semantics: Logic at Work
Operational Semantics: What the program does
Meaning of a program ≈ Execution on an idealized machine. How
is this specified?
Plotkin’s answer: Use logic! Define the semantics by using
inference rules.
Structural Operational Semantics for CCS
Given by transitions between terms of the form t →a u. These
associate a loop-free finite automaton with each term. How?
x →a x(cid:48) x →a x(cid:48) x →a x(cid:48), y →¯a y(cid:48)
ax →a x x +y →a x(cid:48) x(cid:107)y →a x(cid:48)(cid:107)y x(cid:107)y →τ x(cid:48)(cid:107)y(cid:48)
LucaAceto RuleFormatsforSOS
Motivation
TailoringaRuleFormat WhatandWhy
Conclusions
From SOS to Properties of Languages
Pay-off: Using the SOS rules one can prove properties of CCS!
Bisimilarity is a congruence.
+ and (cid:107) are commutative and associative modulo bisimilarity.
+ is an idempotent binary operation—that is, x +x = x holds
modulo bisimilarity.
0 is a left and right unit for + and (cid:107)—for example, 0+x = x
holds modulo bisimilarity.
The idempotent, commutative monoid laws axiomatize
bisimilarity over the “language of synchronization trees”.
Each program has an associated finite transition system.
LucaAceto RuleFormatsforSOS
Motivation
TailoringaRuleFormat WhatandWhy
Conclusions
Summary of the State of Play
A posteriori verification
Give the semantics and then use it to prove that the language
properties one desires are valid in the semantic model.
Cons
This is a lot of work that is repeated for many languages.
The work needs to be redone if we modify the inference rules
and/or add new operators.
Redoing the work does not give much insight as to why the
properties hold at all.
Can one do things differently?
LucaAceto RuleFormatsforSOS
Motivation
TailoringaRuleFormat WhatandWhy
Conclusions
Summary of the State of Play
A posteriori verification
Give the semantics and then use it to prove that the language
properties one desires are valid in the semantic model.
Cons
This is a lot of work that is repeated for many languages.
The work needs to be redone if we modify the inference rules
and/or add new operators.
Redoing the work does not give much insight as to why the
properties hold at all.
Can one do things differently?
LucaAceto RuleFormatsforSOS