CSE P 501 Compilers. Parsing & ContextFree Grammars Hal Perkins Winter UW CSE P 501 Winter 2016 C1


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1 CSE P 501 Compilers Parsing & ContextFree Grammars Hal Perkins Winter 2016 UW CSE P 501 Winter 2016 C1
2 Administrivia Project partner signup: please find a partner and fill out the signup form by noon tomorrow if not done yet (only one form per group, please) Watch for spam from CSE GitLab as repos are set up (save and ignore for now) WriQen HW2 out now, due in a week HW1 soluron posted in a couple of days First part of project scanner out later this week, due in two weeks Programming is fairly simple; this is the infrastructure shakedown cruise UW CSE P 501 Winter 2016 C2
3 Agenda for Today Parsing overview Context free grammars Ambiguous grammars Reading: Cooper & Torczon Dragon book is also parrcularly strong on grammars and languages UW CSE P 501 Winter 2016 C3
4 SyntacRc Analysis / Parsing Goal: Convert token stream to an abstract syntax tree Abstract syntax tree (AST): Captures the structural features of the program Primary data structure for next phases of compilaron Plan Study how contextfree grammars specify syntax Study algorithms for parsing and building ASTs UW CSE P 501 Winter 2016 C4
5 Contextfree Grammars The syntax of most programming languages can be specified by a contextfree grammar (CGF) Compromise between REs: can t nest or specify recursive structure General grammars: too powerful, undecidable Contextfree grammars are a sweet spot Powerful enough to describe nesrng, recursion Easy to parse; restricrons on general CFGs improve speed Not perfect Cannot capture semanrcs, like must declare every variable or must be int requires later semanrc pass Can be ambiguous (something we ll deal with) UW CSE P 501 Winter 2016 C5
6 DerivaRons and Parse Trees DerivaRon: a sequence of expansion steps, beginning with a start symbol and leading to a sequence of terminals Parsing: inverse of derivaron Given a sequence of terminals (aka tokens) recover (discover) the nonterminals and structure, i.e., the parse tree (concrete syntax) UW CSE P 501 Winter 2016 C6
7 Old Example program G program ::= statement program statement statement ::= assignstmt ifstmt assignstmt ::= id = expr ; ifstmt ::= if ( expr ) statement expr ::= id int expr + expr id ::= a b c i j k n x y z int ::= program statement statement ifstmt assignstmt expr id expr expr expr statement assignstmt id expr int id int int w a = 1 ; if ( a + 1 ) b = 2 ; UW CSE P 501 Winter
8 Parsing Parsing: Given a grammar G and a sentence w in L(G), traverse the derivaron (parse tree) for w in some standard order and do something useful at each node The tree might not be produced explicitly, but the control flow of the parser will correspond to a traversal UW CSE P 501 Winter 2016 C8
9 Standard Order For pracrcal reasons we want the parser to be determinis6c (no backtracking), and we want to examine the source program from le8 to right. (i.e., parse the program in linear Rme in the order it appears in the source file) UW CSE P 501 Winter 2016 C9
10 Common Orderings Topdown Start with the root Traverse the parse tree depthfirst, lebtoright (lebmost derivaron) LL(k), recursivedescent BoQomup Start at leaves and build up to the root EffecRvely a rightmost derivaron in reverse(!) LR(k) and subsets (LALR(k), SLR(k), etc.) UW CSE P 501 Winter 2016 C10
11 Something Useful At each point (node) in the traversal, perform some semanrc acron Construct nodes of full parse tree (rare) Construct abstract syntax tree (AST) (common) Construct linear, lowerlevel representaron (oben produced in later phases of producron compilers by traversing iniral AST ) Generate target code on the fly (done in 1pass compilers; not common in producron compilers) Can t generate great code in one pass, but useful if you need a quick n dirty working compiler UW CSE P 501 Winter 2016 C11
12 ContextFree Grammars Formally, a grammar G is a tuple <N,Σ,P,S> where N is a finite set of nonterminal symbols Σ is a finite set of terminal symbols (alphabet) P is a finite set of produc6ons A subset of N (N Σ )* S is the start symbol, a disrnguished element of N If not specified otherwise, this is usually assumed to be the nonterminal on the leb of the first producron UW CSE P 501 Winter 2016 C12
13 Standard NotaRons a, b, c elements of Σ w, x, y, z elements of Σ* A, B, C elements of N X, Y, Z elements of N Σ α, β, γ elements of (N Σ )* A α or A ::= α if <A, α> P UW CSE P 501 Winter 2016 C13
14 DerivaRon RelaRons (1) α A γ => α β γ iff A ::= β in P derives A =>* α if there is a chain of producrons starrng with A that generates α transirve closure UW CSE P 501 Winter 2016 C14
15 DerivaRon RelaRons (2) w A γ => lm w β γ iff A ::= β in P derives lebmost α A w => rm α β w iff A ::= β in P derives rightmost We will only be interested in lebmost and rightmost derivarons not random orderings UW CSE P 501 Winter 2016 C15
16 Languages For A in N, L(A) = { w A =>* w } If S is the start symbol of grammar G, define L(G) = L(S) Nonterminal on leb of first rule is taken to be the start symbol if one is not specified explicitly UW CSE P 501 Winter 2016 C16
17 Reduced Grammars Grammar G is reduced iff for every producron A ::= α in G there is a derivaron S =>* x A z => x α z =>* xyz i.e., no producron is useless ConvenRon: we will use only reduced grammars There are algorithms for pruning useless producrons from grammars see a formal language or compiler book for details UW CSE P 501 Winter 2016 C17
18 Ambiguity Grammar G is unambiguous iff every w in L(G ) has a unique lebmost (or rightmost) derivaron Fact: unique lebmost or unique rightmost implies the other A grammar without this property is ambiguous Note that other grammars that generate the same language may be unambiguous, i.e., ambiguity is a property of grammars, not languages We need unambiguous grammars for parsing UW CSE P 501 Winter 2016 C18
19 Example: Ambiguous Grammar for ArithmeRc Expressions expr ::= expr + expr expr  expr expr * expr expr / expr int int ::= Exercise: show that this is ambiguous How? Show two different lebmost or rightmost derivarons for the same string Equivalently: show two different parse trees for the same string UW CSE P 501 Winter 2016 C19
20 Example (cont) expr ::= expr + expr expr  expr expr * expr expr / expr int int ::= Give a lebmost derivaron of 2+3*4 and show the parse tree UW CSE P 501 Winter 2016 C20
21 Example (cont) expr ::= expr + expr expr  expr expr * expr expr / expr int int ::= Give a different lebmost derivaron of 2+3*4 and show the parse tree UW CSE P 501 Winter 2016 C21
22 Another example expr ::= expr + expr expr  expr expr * expr expr / expr int int ::= Give two different derivarons of UW CSE P 501 Winter 2016 C22
23 What s going on here? The grammar has no noron of precedence or associarvely TradiRonal soluron Create a nonterminal for each level of precedence Isolate the corresponding part of the grammar Force the parser to recognize higher precedence subexpressions first Use leb or rightrecursion for leb or rightassociarve operators (nonassociarve operators are not recursive) UW CSE P 501 Winter 2016 C23
24 Classic Expression Grammar (first used in ALGOL 60) expr ::= expr + term expr term term term ::= term * factor term / factor factor factor ::= int ( expr ) int ::= UW CSE P 501 Winter 2016 C24
25 Check: Derive * 4 expr ::= expr + term expr term term term ::= term * factor term / factor factor factor ::= int ( expr ) int ::= UW CSE P 501 Winter 2016 C25
26 Check: Derive expr ::= expr + term expr term term term ::= term * factor term / factor factor factor ::= int ( expr ) int ::= Note interacron between leb vs rightrecursive rules and resulrng associarvity UW CSE P 501 Winter 2016 C26
27 Check: Derive 5 + (6 + 7) expr ::= expr + term expr term term term ::= term * factor term / factor factor factor ::= int ( expr ) int ::= UW CSE P 501 Winter 2016 C27
28 Another Classic Example Grammar for condironal statements stmt ::= if ( expr ) stmt if ( expr ) stmt else stmt (This is the dangling else problem found in many, many grammars for languages beginning with Algol 60) Exercise: show that this is ambiguous How? UW CSE P 501 Winter 2016 C28
29 One DerivaRon stmt ::= if ( expr ) stmt if ( expr ) stmt else stmt if ( expr ) if ( expr ) stmt else stmt UW CSE P 501 Winter 2016 C29
30 Another DerivaRon stmt ::= if ( expr ) stmt if ( expr ) stmt else stmt if ( expr ) if ( expr ) stmt else stmt UW CSE P 501 Winter 2016 C30
31 Solving if Ambiguity Fix the grammar to separate if statements with else clause and if statements with no else Done in Java reference grammar Adds lots of nonterminals or, Change the language But it d beqer be ok to do this you need to own the language or get permission from owner or, Use some adhoc rule in the parser else matches closest unpaired if UW CSE P 501 Winter 2016 C31
32 Resolving Ambiguity with Grammar (1) Stmt ::= MatchedStmt UnmatchedStmt MatchedStmt ::=... if ( Expr ) MatchedStmt else MatchedStmt UnmatchedStmt ::= if ( Expr ) Stmt if ( Expr ) MatchedStmt else UnmatchedStmt formal, no addironal rules beyond syntax can be more obscure than original grammar UW CSE P 501 Winter 2016 C32
33 Check Stmt ::= MatchedStmt UnmatchedStmt MatchedStmt ::=... if ( Expr ) MatchedStmt else MatchedStmt UnmatchedStmt ::= if ( Expr ) Stmt if ( Expr ) MatchedStmt else UnmatchedStmt if ( expr ) if ( expr ) stmt else stmt UW CSE P 501 Winter 2016 C33
34 Resolving Ambiguity with Grammar (2) If you can (re)design the language, just avoid the problem enrrely Stmt ::=... if Expr then Stmt end if Expr then Stmt else Stmt end formal, clear, elegant allows sequence of Stmts in then and else branches, no {, } needed extra end required for every if (But maybe this is a good idea anyway?) UW CSE P 501 Winter 2016 C34
35 Parser Tools and Operators Most parser tools can cope with ambiguous grammars Makes life simpler if used with discipline Usually can specify precedence & associarvity Allows simpler, ambiguous grammar with fewer nonterminals as basis for parser let the tool handle the details (but only when it makes sense) (i.e., expr ::= expr+expr expr*expr with assoc. & precedence declararons can be the best soluron) UW CSE P 501 Winter 2016 C35
36 Parser Tools and Ambiguous Grammars Possible rules for resolving other problems: Earlier producrons in the grammar preferred to later ones (some danger here if grammar changes) Longest match used if there is a choice (good soluron for dangling if) Parser tools normally allow for this But be sure that what the tool does is really what you want And that it s part of the tool spec, so that v2 won t do something different (that you don t want!) UW CSE P 501 Winter 2016 C36
37 Coming AQracRons Next topic: LR parsing ConRnue reading ch. 3 UW CSE P 501 Winter 2016 C37
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