CSC 1800 Organization of Programming Languages Semantics 1 - - PDF document

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CSC 1800 Organization of Programming Languages

Semantics

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Revisiting Syntax

⚫ Syntax: “look”, form/structure

– notation: context free grammar, BNF

⚫ Semantics: what programs do, their

behavior and meaning

– no standard notation

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Terminology: Tokens

⚫ Tokens are pieces of program text that we do not wish

to think of as being built from smaller pieces

⚫ Identifiers (count), keywords (if), operators (==),

constants (123.4), etc.

⚫ Programs stored in files are just sequences of

characters

⚫ How is such a file divided into a sequence of tokens? ⚫ Also know as… Terminals

(not Non-Terminals)

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Syntax can use BNF & EBNF

::= is defined as |

• r

< > syntactic category, grammatical category [ ] surround an optional part { } surround a repeated part, repeated 0 or more times ( ) are used to clarify hierarchy

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Examples of BNF & EBNF

⚫ BNF

<expr> ::= <expr> + <term> | <expr> - <term> | <term> <term> ::= <term> * <factor> | <term> / <factor> | <factor>

⚫ EBNF

<expr> ::= <term> {(+ | -) <term>} <term> ::= <factor> {(* | /) <factor>}

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Epsilon or ε or /*empty*/

⚫ There are places where you want the grammar

to generate nothing

⚫ For example, this grammar defines a typical if-

then construct with an optional else part: <ifstmt> : if <expr> then <stmt> <elsepart> <elsepart> : else <stmt> | ε

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Associativity

⚫ Operator associativity can also be indicated by

a grammar

<expr> -> <expr> + <expr> | const (ambiguous) <expr> -> <expr> + const | const (unambiguous)

<expr> <expr> <expr> <expr> const const const + +

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Moving Toward Semantics

⚫ Concrete syntax ⚫ Abstract syntax ⚫ Semantics: described in various ways

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Operational

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Denotational

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Axiomatic

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Program function (how it's done in the real world)

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Why Semantics?

⚫ Grammars cannot describe all of the syntax of

programming languages

⚫ Categories of constructs that are trouble:

• Context-free, but cumbersome (e.g.,

types of operands in expressions)

• Non-context-free (e.g., variables must

be declared before they are used)

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Semantics

⚫ There is no single widely acceptable notation or

formalism for describing semantics

⚫ Several needs for a methodology and notation for

semantics:

– Programmers need to know what statements mean – Compiler writers must know exactly what language constructs do – Correctness proofs would be possible – Compiler generators would be possible – Designers could detect ambiguities and inconsistencies

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Operational Semantics

⚫ Operational Semantics

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Describe the meaning of a program by executing its statements on a machine, either simulated or actual. The change in the state of the machine (memory, registers, etc.) defines the meaning of the statement ⚫ To use operational semantics for a high-level language,

a virtual machine is needed

⚫ A hardware pure interpreter would be too expensive ⚫ A software pure interpreter also has problems

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The detailed characteristics of the particular computer would make actions difficult to understand

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Such a semantic definition would be machine- dependent

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Operational Semantics – Useful?

⚫ Advantages:

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May be simple for small examples

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Good if used informally

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Useful for implementation ⚫ Disadvantages:

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Very complex for large programs

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Lacks mathematical rigor ⚫ Uses:

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Vienna Definition Language (VDL) used to define PL/I

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Compiler work

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Denotational Semantics

⚫ Based on recursive function theory ⚫ The most abstract semantics description method ⚫ Originally developed by Scott and Strachey (1970) ⚫ Building a denotational spec. for a language:

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Define a mathematical object for each language entity

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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 only

the values of the program's variables

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Denotational Example: Decimal Numbers

<dec_num> → '0' | '1' | '2' | '3' | '4' | '5' | '6' | '7' | '8' | '9' | <dec_num> ('0' | '1' | '2' | '3' | '4' | '5' | '6' | '7' | '8' | '9') Mdec('0') = 0, Mdec ('1') = 1, …, Mdec ('9') = 9 Mdec (<dec_num> '0') = 10 * Mdec (<dec_num>) Mdec (<dec_num> '1’) = 10 * Mdec (<dec_num>) + 1 … Mdec (<dec_num> '9') = 10 * Mdec (<dec_num>) + 9

Not a human-friendly notation

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Denotational Semantics – Useful?

⚫ Can be used to prove the correctness of programs ⚫ Provides a rigorous way to think about programs ⚫ Can be an aid to language design ⚫ Has been used in compiler generation systems ⚫ Because of its complexity, it are of little use to language

users

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Denotational vs. Operational

⚫ Denotational semantics is similar to operational

semantics except:

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There is no virtual machine

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Language is mathematics (lambda calculus) ⚫ Difference between denotational and operational

semantics:

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In operational semantics, the state changes are defined by coded algorithms for a virtual machine

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In denotational semantics, they are defined by rigorous mathematical functions

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Axiomatic Semantics

⚫ Based on formal logic (predicate calculus) ⚫ Original purpose: formal program verification ⚫ Axioms or inference rules are defined for each

statement type in the language (to allow transformations

• f logic expressions into more formal logic expressions)

⚫ The logic expressions are called assertions

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Axiomatic Semantics Form

⚫ Pre-, post form: {P} statement {Q} ⚫ An example

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a = b + 1 {a > 1}

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One possible precondition: {b > 10}

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Weakest precondition: {b > 0}

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Axiomatic Semantics – Useful?

⚫ Developing axioms or inference rules for all of the

statements in a language is difficult

⚫ It is a good tool for correctness proofs, and an excellent

framework for reasoning about programs, but it is not as useful for language users and compiler writers

⚫ Its usefulness in describing the meaning of a

programming language is limited for language users or compiler writers

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Program Function Semantics

⚫ How semantics are done in the real world ⚫ Describe in English (e.g.) as best as you can what each

particular syntax element in a language does, how you use it, what its meaning is in the language

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Example: Java If Statement

⚫ From the Java Language Specification:

14.9 The if Statement The if statement allows conditional execution of a statement or a conditional choice of two statements, executing one or the other but not both.

The Expression must have type boolean or Boolean, or a compile-time error occurs.

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Program Function Semantics – Useful?

⚫ Much easier to create that other semantic forms ⚫ Probably the only form of semantics that is useful to a

wide range of programmers

⚫ Danger: ambiguity of natural language

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