ASTs, Regex, Parsing, and Pretty Printing

Transcription

1 ASTs, Regex, Prsing, nd Pretty Printing CS 2112 Fll Algeric Expressions To strt, consider integer rithmetic. Suppose we hve the following 1. The lphet we will use is the digits {0, 1, 2, 3, 4, 5, 6, 7, 8, We will llow the unry opertor (one rgument) for negtion. 3. We will llow the inry opertors: + ddition sutrction multipliction / division For ese nd clrity of presenttion, when we represent expressions s Astrct Syntx Trees (AST), we will only llow for two children for given opertion. In this is the mximum llowed, s we only hve inry opertors. However, we will see ASTs lter tht will e more flexile. Consider the following AST for integer lger We prse it left to right, nd ottom up, so it represents the expression (3 + 5) 4 eqully importnt, it is very much not

2 Another exmple: + / This exmple represents the expression ( (3 + 5) (32/2) ) Before continuing with more exmples, lets revisit regulr expressions. 2 Regulr Expression Review 2.1 The lphet of regulr expressions The lphet of regulr expression is denoted y Σ. This set is wht defines wht re vlid components of the regulr expression. For exmple, 1. Σ = {0, 1 This is the lphet of ll inry strings, encoded s 0 s nd 1 s. 2. Σ = {,, c This is the lphet of ll strings tht contin either i) ll s ii) ll s iii) ll c s iv) ll s nd s v) ll s nd c s 2

3 vi) ll s nd c s vii) ll s nd s nd c s As you cn see, the ility to define the lphet of regulr expression using set nottion is exceptionlly convenient. 2.2 The Kleene Str () is post-fix opertor This opertor represents 0 or more occurrences of whtever it opertes on. For exmple, 1. d {ε, d, dd, ddd, 2. (01) {ε, 01, 0101, , 3. If Σ = {,, then Σ = {ε,,,,,,,, where ε is the empty string. Lter, we will use to represent the empty set. 2.3 A plus sign (+) represents union Reclling tht regulr expressions re sets, we use the nottion For exmple, 1. {, + {c, d = {,, c, d A + B A B 2. {,, c + {, c, d = {,, c, d When we use +, it is inry opertor (it requires two rguments). Additionlly, note tht the unions produced do not hve duplicted elements in the second exmple, we do not hve duplicte or c. 2.4 A dot product ( ) represents conctention We use the nottion A B {xy x A, y B For exmple, 1. {, {c, d = {c, d, c, d 2. {,, c {, c, d = {, c, d,, c, d, c, cc, cd 3

4 3 AST s nd regulr expressions Consider the AST + This descries the regulr expression ( + ( ) ) which, when written s prsed from ove with prentheses to group (prentheses colored to help hit e little more understndle): ( + (( (( ) ) ) )) 4

5 4 Alternte interprettion As it turns out, we cn use (deterministic) finite stte mchines to represent the regulr expression presented in Section 3. The stte mchine would e s follows: Strt S 0 S 1 So in this exmple, the strt stte nd the ccept stte (doule circle) re the sme thing. Convince yourself tht the regulr expression ( + ( ) ) is correctly represented y the finite stte mchine ove y following the rrows. For exmple, if we sw the string then we would go from the Strt stte, to stte S 0, to stte S 1. This string would not e ccepted y the finite stte mchine, which is good ecuse it is not descried y the regulr expression. On the other hnd, consider the string. Follow the edges to see. The input will put you t the following sttes: Strt S 0 Strt S 0 S 1 S 1 S 1 S 1 S 1 S 1 S 1 S 1 S 0 Strt So we cn see tht there is direct reltionship etween the Kleene Str nd self-loops in stte mchine. Astrct Syntx Trees nd Finite Stte Mchines re oth excellent conceptul models for understnding regulr expressions, ut they re not the only ones. In fct, they re just rely the tip of the iceerg! 5

6 5 Pretty Printing When it comes to pretty printing ASTs, recursion should feel the most nturl. Accompnying this PDF is full version of the snippet elow, in PrettyPrint.jv. An excerpt from the progrm is sufficient for explining the ide: / Clss Node hs Node[] children = new Node[2]; where the following invrint is mintined: - Index 0 nd 1 re null: terminl node - Index 0 hs vlue nd index 1 is null: unry opertor - Index 0 is null nd index 1 hs vlue: post-fix opertor - Index 0 nd index 1 oth hve vlues: inry opertor Clerly this tctic does not scle well, ut illustrtes the concept. / pulic sttic void prettyprint(node n) { // terminl nodes just get printed if(n.isterminl()) { System.out.print(n); // print the unry op followed y its only child else if(n.isunryop()) { System.out.print(n); prettyprint(n.children[0]); // post-fix opertors get printed fter their only child else if(n.ispostfixop()) { prettyprint(n.children[1]); System.out.print(n); // inry opertors, print the left child first, the op, then right else if(n.isbinryop()) { System.out.print("("); prettyprint(n.children[0]); 6

7 System.out.print(" " + n + " "); prettyprint(n.children[1]); System.out.print(")"); 7