MiniTriangle. G52CMP: Lecture 6 Defining Programming Languages II. This Lecture. A MiniTriangle Program

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1 MiniTriangle G52CMP: Lecture 6 Defining Programming Languages II Henrik Nilsson Universit of Nottingham, UK In part II of the coursework, we are going to use a language called MiniTriangle: Originates from Watt & Brown (defined at pp. 6 20). Our version has evolved and is now quite different in some respects. We use MiniTriangle in this lecture to: - Illustrate the ideas of concrete and abstract sntax - Introduce ou to the language G52CMP: Lecture 6 p.1/30 G52CMP: Lecture 6 p.2/30 This Lecture Concrete Sntax - Lexical sntax for MiniTriangle - Context-free sntax for MiniTriangle Abstract Sntax - Abstract sntax for MiniTriangle Representing Abstract Sntax Trees (ASTs) A MiniTriangle Program This is an example of a valid MiniTriangle program: let in var : Integer := 0 begin := + 1 ; putint() end G52CMP: Lecture 6 p.3/30 G52CMP: Lecture 6 p.4/30

2 Concrete Sntax The Concrete Sntax, or surface sntax, of a language is usuall defined at two levels: The Lexical sntax: the sntax of - language smbols or tokens - white space - comments The Context-Free sntax. Regular Grammars Lexical sntax is usuall defined as a Regular Language (RL). A regular language can be described b - a Regular Expression - a Context-Free Grammar (as the RLs are a proper subset of the CFLs) If a grammar G is left-linear or right-linear, then G is a regular grammar and L(G) is a regular language. Regular languages are eas to recognise (DFA). G52CMP: Lecture 6 p.5/30 G52CMP: Lecture 6 p.6/30 Right-linear Grammar A CFG G = (N,T,P,S) is right-linear if all its productions are of the forms A wb A w where A,B N and w T. Example: The regular language 0(10) is generated b the right-linear grammar S 0A A 10A ǫ Left-linear Grammar A CFG G = (N,T,P,S) is left-linear if all its productions are of the forms A Bw A w where A,B N and w T. Example: The regular language 0(10) is generated b the left-linear grammar S S10 0 G52CMP: Lecture 6 p.7/30 G52CMP: Lecture 6 p.8/30

3 MiniTriangle Lexical Sntax (1) Program (Token Separator) Token Keword Identifier IntegerLiteral Operator, ; : := = ( ) eot Keword begin const do else end if in let then var while Identifier Letter Identifier Letter Identifier Digit except Keword IntegerLiteral Digit IntegerLiteral Digit Operator + - * / < <= ==!= >= > &&! Separator Comment space eol Comment // (an character except eol) eol G52CMP: Lecture 6 p.9/30 MiniTriangle Lexical Sntax (2) Notes: Essentiall a left-linear grammar. Not completel formal (e.g. the use of except for excluding kewords from identifiers). Note! Each individual character of a terminal is actuall a terminal smbol! I.e., reall: Keword b e g i n c o n s t... Special characters are written like this. Note! The are single terminal smbols! G52CMP: Lecture 6 p.10/30 MiniTriangle: Tokens Some valid MiniTriangle tokens: const3 (Identifier) const (Keword) 42 (Integer-Literal) + (Operator) Q: Is const3 reall a single token? The grammar is ambiguous! A: An implicit maximal munch rule used to disambiguate! MiniTriangle: Non Tokens Some non tokens: 123abc (two tokens: Integer-Literal 123 and Identifier abc) put_x (Identifier put, illegal character _, Identifier x) 3.14 (Integer-Literal 3, illegal character., Integer-Literal 14) 3e8 (two tokens: Integer-Literal 3 and Identifier e8) G52CMP: Lecture 6 p.11/30 G52CMP: Lecture 6 p.12/30

4 MiniTriangle Context-Free Sntax (1) MiniTriangle Context-Free Sntax (2) Program Command Commands Command Command ; Commands Command VarExpression := Expression VarExpression ( Expressions ) if Expression then Command else Command while Expression do Command let Declarations in Command begin Commands end Expressions Expression Expression, Expressions Expression PrimarExpression Expression Operator PrimarExpression PrimarExpression IntegerLiteral VarExpression Operator PrimarExpression ( Expression ) VarExpression Identifier G52CMP: Lecture 6 p.13/30 G52CMP: Lecture 6 p.14/30 MiniTriangle Context-Free Sntax (3) Another MiniTriangle Program Declarations Declaration Declaration ; Declarations Declaration const Identifier : TpeDenoter = Expression var Identifier : TpeDenoter var Identifier : TpeDenoter := Expression TpeDenoter Identifier The following is a sntacticall valid MiniTriangle program (slightl changed from earlier to save some space): let in var : Integer begin := + 1 ; putint() end G52CMP: Lecture 6 p.15/30 G52CMP: Lecture 6 p.16/30

5 Parse Tree for the Program Exercise 1 Program Command let Declarations in Command Draw the parse tree for the following MiniTriangle program: Declaration begin Commands end var Identifier : TpeDenoter Command Identifier VarExpression := Expression ; Commands Command while b do n := 0 Integer Identifier Expression Operator PrimarExpression VarExpression ( Expressions ) PrimarExpression + IntegerLiteral Identifier Expression VarExpression 1 putint PrimarExpression Identifier VarExpression Identifier G52CMP: Lecture 6 p.17/30 G52CMP: Lecture 6 p.18/30 Wh a Lexical Grammar? (1) Together, the lexical grammar and the context-free grammar specif the concrete sntax. In our case, both grammars are expressed in (E)BNF and looks similar. So... Wh not join them? Wh not do awa with scanning, and just do parsing? G52CMP: Lecture 6 p.19/30 Wh a Lexical Grammar? (2) Answer: Simplicit: dealing with white space and comments in the context free grammar becomes extremel complicated. (Tr it!) Efficienc: - Working on classified groups of characters (tokens) facilitates parsing: ma be possible to use a simpler parsing algorithm. - Grouping and classifing characters b as simple means as possible increases efficienc. G52CMP: Lecture 6 p.20/30

6 MiniTriangle Abstract Sntax (1) This grammar specifies the phrase structure of MiniTriangle. In addition, it gives node labels to be used when drawing Abstract Sntax Trees. Program Command Program Command Expression := Expression CmdAssign Expression ( Expression ) CmdCall Command CmdSeq if Expression then Command CmdIf else Command while Expression do Command CmdWhile let Declaration in Command CmdLet G52CMP: Lecture 6 p.21/30 MiniTriangle Abstract Sntax (2) Expression IntegerLiteral ExpLitInt ExpVar Expression ( Expression ) ExpApp Declaration const : TpeDenoter DeclConst = Expression var : TpeDenoter DeclVar (:= Expression ǫ) TpeDenoter TDBaseTpe Note: Kewords and other fixed-spelling terminals serve onl to make the connection with the concrete sntax clear. Identifier, Operator G52CMP: Lecture 6 p.22/30 Abstract Sntax Tree for the Program Exercise 2 Program CmdLet DeclVar TDBaseTpe ExpVar CmdAssign ExpApp CmdSeq ExpVar CmdCall ExpVar Draw the Abstract Sntax Tree for the following MiniTriangle program: while b do n := 0 Integer ExpVar ExpVar ExpLitInt IntegerLiteral putint + Note: fixed-spelling terminals are omitted because the are implied b the node labels. 1 G52CMP: Lecture 6 p.23/30 G52CMP: Lecture 6 p.24/30

7 Concrete AST Representation Mapping of abstract sntax to algebraic datatpes : Each non-terminal is mapped to a tpe. Each label is mapped to a constructor for the corresponding tpe. The constructors get one argument for each non-terminal and variable terminal in the RHS of the production. Sequences are represented b lists. Concrete AST Representation (2) data Command = CmdAssign Expression Expression CmdCall Expression [Expression] CmdSeq [Command] CmdIf Expression Command Command CmdWhile Expression Command CmdLet [Declaration] Command Options are represented b values of tpe Mabe. Literal terminals are ignored. G52CMP: Lecture 6 p.25/30 G52CMP: Lecture 6 p.26/30 Concrete AST Representation (3) data Expression = ExpLitInt Integer ExpVar ExpApp Expression [Expression] data Declaration = DeclConst TpeDenoter Expression DeclVar TpeDenoter (Mabe Expression) Concrete AST Representation (4) In fact, the lab code uses labelled fields: data Command = CmdAssign { cavar :: Expression, caval :: Expression, cmdsrcpos :: SrcPos } CmdCall { ccproc :: Expression, } ccargs :: [Expression], cmdsrcpos :: SrcPos G52CMP: Lecture 6 p.27/30... G52CMP: Lecture 6 p.28/30

8 Haskell Representation of the Program Exercise 3 CmdLet (DeclVar "" (TDBase "Integer") Nothing) (CmdSeq [CmdAssign (ExpVar "") Assumption: tpe = String (ExpApp (ExpVar "+") [ExpVar "", CmdCall (ExpVar "putint") [ExpVar ""]]) ExpLitInt 1]), Provide the Haskell representation of the following MiniTriangle fragment: while b do n := 0 G52CMP: Lecture 6 p.29/30 G52CMP: Lecture 6 p.30/30