Chapter 3 Describing Syntax and Semantics Sections 1-3

1–2 Introduction Syntax: the form or structure of the expressions, statements, and program units Semantics: the meaning of the expressions, statements, and program units Syntax and semantics combined provide a language’s definition – Users of a language definition Other language designers Implementers Programmers (the users of the language)‏

1–3 Language Theory Chomsky identified four classes of language – Types 2 and 3 useful for programming language specification Backus (on ALGOL58 committee) developed notation for specifying programming languages Regular3 Context-free2 Context-sensitive1 Unrestricted0 CharacteristicsType

1–4 Terminology A metalanguage is a language used to describe another language A sentence is a string of characters over some alphabet A language is a set of sentences – a language is specified by a set of rules A lexeme is the lowest level syntactic unit of a language (e.g., *, sum, begin )‏ A token is a category of lexemes (e.g., identifier)‏

1–5 Two approaches to Language Definition Recognizers – Read a string and decide whether it follows the rules for the language – Example: syntax analysis part of a compiler (Chapter 4)‏ Generators – A device that generates sentences of a language (BNF)‏ – More useful for specifying the language than for checking a string

1–6 Formal Methods of Describing Syntax Backus-Naur Form and Context-Free Grammars – Most widely known method for describing programming language syntax – Developed as part of the process for specifying ALGOL – Define a class of languages called context-free languages Extended BNF – Improves readability and writability of BNF

1–7 BNF Fundamentals Non-terminals: BNF abstractions used to represent classes of syntactic structures Terminals: lexemes and tokens Grammar: a collection of rules – Examples of BNF rules: → identifier | identifier, → if then

1–8 BNF Rules A rule has a left-hand side (LHS) and a right-hand side (RHS), and consists of terminal and nonterminal symbols In a context-free grammar, there can only be one symbol on the LHS A grammar is a finite nonempty set of rules An abstraction (or nonterminal symbol) can have more than one RHS  | begin end

1–9 Describing Lists Syntactic lists are described using recursion -> |, -> |, -> |, -> |

1–11 Derivations BNF is a generative device – Use a grammar to generate sentences that belong to the language the grammar describes A derivation is a repeated application of rules, starting with the start symbol and ending with a sentence (all terminal symbols)‏

1–12 Derivation Every string of symbols in the derivation is a sentential form A sentence is a sentential form that has only terminal symbols A leftmost derivation is one in which the leftmost nonterminal in each sentential form is the one that is expanded A derivation may be neither leftmost nor rightmost

1–13 An Example Grammar -> -> | ; -> = -> a | b | c | d -> + | - -> | const

1–14 An Example Derivation => => => = => a = => a = + => a = b + => a = b + const

1–15 Parse Tree A hierarchical representation of a derivation const a = b +

1–18 Ambiguity in Grammars A grammar is ambiguous if and only if it generates a sentential form that has two or more distinct parse trees -> if then | if then else -> | | …

1–20 An Ambiguous Expression Grammar  | const  / | - const --//

1–21 An Unambiguous Expression Grammar If we build precedence of the operators into the grammar, we cannot have ambiguity  - |  / const | const const / -

1–22 Associativity of Operators Operator associativity can also be indicated by a grammar -> + | const (ambiguous)‏ -> + const | const (unambiguous)‏ const + +

1–23 Extended BNF Optional parts are placed in brackets [ ] -> ident ([ ])‏ Alternative parts of RHSs are placed inside parentheses and separated via vertical bars → (+|-) const Repetitions (0 or more) are placed inside braces { } → letter {letter|digit}

1–24 BNF and EBNF BNF  + | - |  * | / | EBNF  {(+ | -) }  {(* | /) }

1-25 Recent Variations in EBNF Alternative RHSs are put on separate lines Use of a colon instead of => Use of opt for optional parts Use of oneof for choices

Static Semantics Context-free grammars (CFGs) cannot describe all of the syntax of programming languages For example – the requirement that a variable be declared before it can be used is impossible to express in a grammar – information about variable and expression types could be included in a grammar but only at the cost of great complexity

Dynamic Semantics Describe the meaning of programs – English language descriptions neither precise nor complete – "Holy Grail" to be able to prove a program correct No universal notation for semantics – Operational semantics – Axiomatic semantics – Denotational semantics

Axiomatic Semantics Based on mathematical logic Assertions are attached to program statements describing constraints on variable at that point in program Postcondition assertions describe result of the statement Precondition assertions describe state before statement is executed Can derive the weakest precondition that guarantees a particular postcondition

Monkey Language -> b | d -> a -> | | a | a -> | -> | # Which are valid? ba#ababadada#bad#dabbada abdabaadab#ada dad#ad#abaadad#badadbaad