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1
Prof. Aiken
CS 143
Lecture 13
1
Operational Semantics of Cool
Lecture 13
Prof. Aiken
CS 143
Lecture 13
2
Lecture Outline
• COOL operational semantics
• Motivation
• Notation
• The rules
Prof. Aiken
CS 143
Lecture 13
3
Motivation
• We must specify for every Cool expression
what happens when it is evaluated
– This is the “meaning” of an expression
• The definition of a programming language:
– The tokens
lexical analysis
– The grammar
syntactic analysis
– The typing rules
semantic analysis
– The evaluation rules
code generation and optimization
Prof. Aiken
CS 143
Lecture 13
4
Evaluation Rules So Far
• We have specified evaluation rules indirectly
– The compilation of Cool to a stack machine
– The evaluation rules of the stack machine
• This is a complete description
– Why isn’t it good enough?
Prof. Aiken
CS 143
Lecture 13
5
Assembly Language Description of Semantics
• Assembly-language descriptions of language
implementation have irrelevant detail
– Whether to use a stack machine or not
– Which way the stack grows
– How integers are represented
– The particular instruction set of the architecture
• We need a complete description
– But not an overly restrictive specification
Prof. Aiken
CS 143
Lecture 13
6
Programming Language Semantics
• A multitude of ways to specify semantics
– All equally powerful
– Some more suitable to various tasks than others
• Operational semantics
– Describes program evaluation via execution rules
• on an abstract machine
– Most useful for specifying implementations
– This is what we use for Cool

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Prof. Aiken
CS 143
Lecture 13
7
Other Kinds of Semantics
• Denotational semantics
– Program’s meaning is a mathematical function
– Elegant, but introduces complications
• Need to define a suitable space of functions
• Axiomatic semantics
– Program behavior described via logical formulae
• If execution begins in state satisfying X, then it ends in
state satisfying Y
• X, Y formulas
– Foundation of many program verification systems
Prof. Aiken
CS 143
Lecture 13
8
Introduction to Operational Semantics
• Once again we introduce a formal notation
• Logical rules of inference, as in type checking
Prof. Aiken
CS 143
Lecture 13
9
Inference Rules
• Recall the typing judgment
Context
e : C
(in the given
context
, expression
e
has type
C
)
• We try something similar for evaluation
Context
e : v
(in the given
context
, expression
e
evaluates to
value
v
)
Prof. Aiken
CS 143
Lecture 13
10
Example Operational Semantics Rule
• Example:
• The result of evaluating an expression can
depend on the result of evaluating its
subexpressions
• The rules specify everything that is needed to
evaluate an expression
Context
e
1
: 5
Context
e
2
: 7
Context
e
1
+ e
2
: 12
Prof. Aiken
CS 143
Lecture 13
11
Contexts are Needed for Variables
• Consider the evaluation of
y
x + 1
– We need to keep track of values of variables

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