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3.2 Semantics . Semantics. Attribute Grammars The Meanings of Programs: Semantics Sebesta Chapter 3. Attribute Grammars. CFG cannot describe all necessary information An attribute grammar is a CFG G = (S, N, T, P) with the following additions:

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  • Attribute Grammars
  • The Meanings of Programs: Semantics
  • Sebesta Chapter 3
attribute grammars
Attribute Grammars
  • CFG cannot describe all necessary information
  • An attribute grammar is
    • a CFG G = (S, N, T, P) with the following additions:
      • For each grammar symbol xthere is a set A(x) of attribute values
      • Each rule has a set of functionsthat define certain attributes of the nonterminals in the rule
      • Each rule has a (possibly empty) set of predicates to check for attribute consistency
attribute grammars cont
Attribute Grammars (cont.)
  • Invented by Donald Knuth
  • Can carry complex syntactic and some semantic information along through parse trees
    • e.g. complex syntax rule (static semantics):

a variable must be defined before it is used

  • Primary value of AGs:
    • static semantics specification
    • compiler design (static semantics checking)
describing semantics
Describing Semantics
  • There is no single widely accepted notation or formalism for semantics
  • Different formalisms are used:
    • Operational Semantics
    • Axiomatic Semantics
    • Denotational Semantics
operational semantics
Operational Semantics
  • Describes the meaning of a program by executing its statements on a machine, either simulated or actual.
  • The meaning of a statement is defined by the change in the state of the machine (memory, registers, etc.)
operational semantics limitations
Operational Semantics Limitations
  • A virtual machine is needed
  • A hardware pure interpreter
    • too expensive for a high-level language
  • A software pure interpreter
    • too difficult to understand the actions because of the detailed characteristics of the particular computer used
    • machine-dependent
operational semantics1
Operational Semantics
  • A better alternative:

A complete computer simulation

  • The process:
    • Build a translator which translates source code to the machine code of an idealized computer
    • Build a simulator for the idealized computer
  • Evaluation of operational semantics:
    • Good if used informally (language manuals, etc.)
    • Extremely complex if used formally (e.g., VDL)
axiomatic semantics
Axiomatic Semantics
  • Based on formal logic - predicate calculus
    • Original purpose: formal program verification
  • Approach:
    • Define axioms or inference rules for each statement type in the language (to allow transformations of expressions to other expressions)
    • The expressions are called assertions
  • Prolog – logic programming language
  • Axiomatic semantics
  • Contains facts (assertions)
  • Contains inference rules
  • Inference process answers a query by generating new facts from known facts and rules
  • We will learn Prolog in this course to practice the logic programming paradigm
axiomatic semantics evaluation
Axiomatic Semantics Evaluation
  • Good for correctness proofs and for reasoning about programs
  • Too difficult to develop axioms and inference rules for all of the statements in a high-level language
  • Too difficult to understand the axioms and rules
  • It is not very useful for
    • language design
    • compiler/interpreter writers
    • programmers
denotational semantics
Denotational Semantics
  • Based on recursive function theory
  • The process:
    • Define a mathematical object for each language entity
    • Define a function that maps instances of the language entities onto instances of the corresponding mathematical objects
    • The meaning of language constructs are defined by the values of the program's variables
  • The state changes are defined by mathematical functions
    • (operational semantics defines them in program code)
denotational semantics evaluation
Denotational Semantics Evaluation
  • The most abstract method of describing semantics
  • Can be used to prove the correctness of programs
  • Provides a rigorous way to think about programs
  • Can aid language design
  • Has been used in compiler generators
  • Too complex to be useful to programmers
  • EBNF is an established formalism to define the syntax of PLs
  • There is no single commonly used way to define the semantics – all formalisms have disadvantages