G22.2110 Programming Languages

• The main themes of programming language design and use:

– Model of computation– Expressiveness

• Abstraction mechanisms• control structures• tools for programming in the large

– Ease of use: Write-Debug / Readability / Maintainability

Models of Computation

• Imperative: programs have mutable storage (state) modified by assignments– by far the most common and familiar

• Functional (applicative): programs are pure functions– much use in AI, formal semantics, language research

• Declarative: programs are unordered sets of assertions and rules

– Prolog, rule-based systems, relational databases

Models of Computation

• Scalar: basic operations are on a single element; use loops for arrays and other bulk objects.– by far the most common and familiar

• Array: lists or arrays are first class.– Same operation adds two scalars as two vectors

or a scalar and a vector. Think linear algebra.

Linguist vs. Polyglot

• Polyglot: someone who can speak/write several languages (English, Chinese, Russian, etc.)

• Linguist: someone who understands the structure of language (e.g. use of case, formation of plural etc.)

• Goal: Make you a programming language linguist

Goals of Course

• Intellectual: help you understand benefit/pitfalls of different approaches/features to language design.

• Practical: you will design languages many times in your career, e.g. finance, science.

• Academic: good start on core exam

Language Embodies Thought

The majesty and grandeur of the English language; it’s the greatest possession we have. The noblest thoughts that ever flowed through the hearts of men are contained in its extraordinary, imaginative and musical mixtures of sounds. And that’s what you’ve set yourself out to conquer, X.

Who is X?

Genealogy

• FORTRAN (1957) => Fortran90, HPF• COBOL (1956) => COBOL2000

– still a large chunk of installed software• Algol60 => Algol68 => Pascal => Ada• APL => K (array language I use)• Simula => Smalltalk, C++• LISP => Scheme, ML, Haskell

– with plenty of cross-influences: Java inherits from C++, Smalltalk, LISP, Ada, etc.

Common Ideas

• Modern scalar imperative languages (Ada, C++, Java, but not K) have similar characteristics:– large number of features (grammar with several hundred

productions, 500 page reference manuals…)

– a rich type system

– procedural mechanisms

– object-oriented facilities

– abstraction mechanisms, with information hiding

– several storage-allocation mechanisms

– facilities for concurrent programming (not C++)

– facilities for generic programming (not Java)

Predictable performance vs. ease of writing

• Low-level languages mirror the physical machine:– Assembly, C, Fortran

• High-level languages model an abstract machine with useful capabilities:– ML, Setl, Prolog, Python, SQL

• Wide-spectrum languages try to do both, more or less well:– Ada, C++, Java, K

• High-level languages are often interpreted, have garbage collector,are dynamically typed,and cannot be used for real-time programming. Cost of operations is not directly visible.– Java is a hybrid

Language as a tool for thought

• Computing a sum in K: +/ 3 4 5 yields 12– Prefix sum: +\3 4 5 yields 3 7 12– Is it natural ? ( only if you happen to think that way)– Role of language as a communication vehicle among

programmers is more important than ease of writing– All languages have the same expressive power; arguments

of the form “you can’t do this in X” are meaningless.– But.. Idioms in language A may be useful inspiration when

writing in language B. Try multiplying in Roman numerals.– Ease of debugging very important – joys of interpretation.

The programming environment may be larger than the language

• The predefined libraries are indispensable to the proper use of many languages.

• The libraries are defined in the language itself, but they have to be internalized by a good programmer.

• the C++ standard template library

• The Java Swing classes

• The Ada I/O packages• There is a law of conservation of junk: whether it goes into

the language or in the library, the total amount of miscellaneous information is roughly the same from language to language. (Does not apply to Prolog or to K.)

Language Definition

• Different users have different needs:– programmers

• tutorials, reference manuals, programming guides (idioms)

– implementors• precise operational semantics

– verifiers• rigorous axiomatic or natural semantics

– language designers and language lawyers• all of the above

• Different levels of detail and precision– But none of them can be sloppy!

Syntax and Semantics

• Syntax refers to external representation• Semantics denotes meaning• Distinction is convenient but arbitrary: can describe

fully a programming language by syntactic means (Algol68 and W-grammars), but resulting grammar is hard to use.

• In practice, describe context-free aspects with a grammar, the rest with prose or a different formal notation (equations, pre/post conditions, assertions).

Syntax vs. Semantics

• Good syntax, unclear semantics: “Colorless green ideas sleep furiously”

• Good semantics, poor syntax: “Me go swimming now, sorry bye”

• In programming languages: syntax tells you what a well-formed program looks like. Semantic tells you relationship of output to input.

Grammars

• A set of non-terminal symbols• A distinguished non-terminal: the root symbol• A set of terminal symbols• A series of rewrite rules (productions) of the form:• ABC.. ::= XYZ..• where A, B, C, D, X, Y, Z terminals and non terminals.• The language is the set of sentences containing only terminal• symbols, that can be generated by applying the rewriting rules• starting from the root symbol

BNF: standard notation for context-free grammars

• A series of conventional abbreviations:– alternation: symb ::= Letter | Digit– option:

• if_stat ::= IF condition THEN statement [else_part] END IF – repetition:

• else_part ::= {elseif_part} [ELSE statement]• elsif_part ::= ELSIF condition THEN statement

– also noted with Kleene star:• id ::= Letter symb*

– Does not add to expressive power of grammar, could be done with recursion (tastes on readability differ)

– need convention for metasymbols: what if ‘|’ is in the language?

• Compare Barnes appendix 3, Stroustrup Appendix A.

The Chomsky hierarchy (“Three theories of language” 1957 –

beautiful paper)

• Regular grammars (noun phrases):– all productions have the form: N ::= TN

– (one non-terminal on left side; at most one on right)

• Context-free grammars (if-then)– all productions have the form: N ::= XYZ

– (one non-terminal on the left-hand side; mixture on right)

• Context-sensitive languages (passive transformation)– The number of symbols on the left is no greater than on the right

– (no production shrinks the size of the sentential form)

• Type-0 languages– no restrictions, full rewriting.

Less powerful languages can still generate infinite numbers of strings

• Regular grammars noun phrase:• NP ::= ‘the’ X | ‘a’ X• X ::= A N | A X• A ::= ‘big’ | ‘small’ | ‘beautiful’ | ‘splendid’ …• N ::= ‘house’ | ‘car’ | ‘friend’ | ….• Examples: the big beautiful big small big car• Show finite state representation.

However, not all languages

• Consider sentences of the form “if it is raining then I’ll take an umbrella else I’ll go in shorts”

• This is of the form “if S then S else S”• Chomsky showed there was no way to represent this

as a regular grammar. Needed a context-free grammar.

• Went on to show that context free grammars weren’t enough for all expressability. Need general rewriting rule of the form

• String of terminals and non-terminals ::= String

Where do Programming Languages Fit In?

• They are mostly context-free but sometimes more.• Professional compiler writers create grammars that

are overly permissive and then constrain them later.

Reverse Polish Notation Language

• 6 8 + yields 14• 31 6 8 + - yields 17because 6 8 + becomes 14 and

31 14 – yields 17• Line ::= newline | Exp newline• Exp ::= NUM | exp exp op• Op ::= ‘+’ | ‘-’ | ‘/’ | ‘*’• Try some examples.

How Would you Implement

• If line is empty return nothing else expr(line)• Expr(line)• Loop until end of line• if next symbol is a number then push to stack• else /* you have found an operation */

pop last two entries from stack, apply op put result back on stack

• end if• end loop

Lexical Grammars

• Lexical = formation of words/tokens.• Described mostly by regular grammar• Terminals are characters:

– need to specify character set: ASCII, Latin-1, ISO646, Unicode…

– need to specify if case is significant

– need to specify external source representation for portability

• Identifiers:– Id => letter

– Id => letter Id

• Context-free grammars can’t count: previous rule does not specify size limit

Parse trees

• A parse tree describes the grammatical structure of a sentence

– leaf nodes are terminal symbols

– root of tree is root symbol of grammar

– internal nodes are non-terminal symbols

– an internal node and its descendants correspond to some production for that non terminal

– top-down tree traversal represents the process of generating the given sentence from the grammar

– Reconstruction of tree from sentence is parsing

Ambiguity

• If the parse tree for a sentence is not unique, the grammar is ambiguous:– E ::= E + E | E * E | Id

– parse tree for A + B * C ?

– Either (A + B) * C) or (A + (B * C))

– Solution: non-terminals with different precedences

– E ::= E + T | T

– T ::= T * Id | Id

• Harder to resolve syntactically:– function_call ::= name (expression_list)

– indexed_component ::= name (index_list)

– type_conversion ::= name (expression)

The dangling else problem

• S ::= if E then S• S ::= if E then S else S• if E1 then if E2 then S1 else S2 is ambiguous

(if E1 holds then can S2 ever execute?)• Solutions:

– Pascal rule: else matches most recent if

– grammatical solution: different productions for balanced and unbalanced if-statements

– grammatical solution: introduce explicit end-marker

• general ambiguity problem is unsolvable