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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