Abstract Syntax Trees Synthetic and Inherited Attributes
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1 Abstract Syntax Trees Synthetic and Inherited Attributes Lecture 22 Sections Robb T. Koether Hampden-Sydney College Mon, Mar 16, 2015 Robb T. Koether (Hampden-Sydney College)Abstract Syntax TreesSynthetic and Inherited Attributes Mon, Mar 16, / 38
2 1 Abstract Syntax Trees 2 Syntax-Directed Definitions 3 Synthesized Attributes 4 Inherited Attributes 5 Examples 6 Assignment Robb T. Koether (Hampden-Sydney College)Abstract Syntax TreesSynthetic and Inherited Attributes Mon, Mar 16, / 38
3 Outline 1 Abstract Syntax Trees 2 Syntax-Directed Definitions 3 Synthesized Attributes 4 Inherited Attributes 5 Examples 6 Assignment Robb T. Koether (Hampden-Sydney College)Abstract Syntax TreesSynthetic and Inherited Attributes Mon, Mar 16, / 38
4 Parse Trees A parse tree shows the grammatical structure of a statement. It includes all of the grammar symbols (terminals and nonterminals) that were encountered during parsing. Robb T. Koether (Hampden-Sydney College)Abstract Syntax TreesSynthetic and Inherited Attributes Mon, Mar 16, / 38
5 Abstract Syntax Trees An abstract syntax tree (AST) shows the logical structure of the statement. Each node represents an action to be taken by the program or an object to be acted upon. The syntax tree may introduce operations that were not in the source code or the grammar. Dereferencing operations. Type-casting operations. Jump statements. Robb T. Koether (Hampden-Sydney College)Abstract Syntax TreesSynthetic and Inherited Attributes Mon, Mar 16, / 38
6 Syntax Trees vs. Parse Trees Example (Syntax Trees and Parse Trees) Consider the statement a = 2*b + c; stmt = lval = expr ; a + id expr + expr * DEREF expr * expr id 2 DEREF c num id b Parse Tree Syntax Tree Robb T. Koether (Hampden-Sydney College)Abstract Syntax TreesSynthetic and Inherited Attributes Mon, Mar 16, / 38
7 Syntax Trees vs. Parse Trees Our TreeBuilder program (Assignment 9) will convert the parse tree into the syntax tree. The parse tree never really exists, except insofar as the parser follows its logical order. The TreeBuilder will simply build the syntax tree from the information obtained by the parser. Then the code generator (Assignment 10) will write the assembly code from the syntax tree. Robb T. Koether (Hampden-Sydney College)Abstract Syntax TreesSynthetic and Inherited Attributes Mon, Mar 16, / 38
8 Abstract Syntax Trees Recursive descent parsers generally create a single AST for the entire program. They build the tree from root to leaf. Our parser will begin with the leaf nodes. The AST will be built from the bottom up. Robb T. Koether (Hampden-Sydney College)Abstract Syntax TreesSynthetic and Inherited Attributes Mon, Mar 16, / 38
9 Abstract Syntax Trees Our parser will generate a separate AST for each statement. It will create a list of ASTs. This will allow us to generate assembly code as the ASTs are created. The trees will be connected both sequentially and through jump statements. Robb T. Koether (Hampden-Sydney College)Abstract Syntax TreesSynthetic and Inherited Attributes Mon, Mar 16, / 38
10 Outline 1 Abstract Syntax Trees 2 Syntax-Directed Definitions 3 Synthesized Attributes 4 Inherited Attributes 5 Examples 6 Assignment Robb T. Koether (Hampden-Sydney College)Abstract Syntax TreesSynthetic and Inherited Attributes Mon, Mar 16, / 38
11 Syntax-Directed Definitions Definition A syntax-directed definition (SDD) is a context-free grammar with attributes added to the grammar symbols. These attributes are stored in the nodes of the syntax tree. Robb T. Koether (Hampden-Sydney College)Abstract Syntax TreesSynthetic and Inherited Attributes Mon, Mar 16, / 38
12 Example Example (Syntax-Directed Definitions) Let the grammar be E E + E num Then E derives its value from the num tokens in the expression. This is expressed formally by the rules E.val = E 1.val + E 2.val E.val = num.lexval Robb T. Koether (Hampden-Sydney College)Abstract Syntax TreesSynthetic and Inherited Attributes Mon, Mar 16, / 38
13 Syntax-Directed Definitions In a syntax-directed definition, each node has A set of synthesized attributes, and A set of inherited attributes. Robb T. Koether (Hampden-Sydney College)Abstract Syntax TreesSynthetic and Inherited Attributes Mon, Mar 16, / 38
14 Outline 1 Abstract Syntax Trees 2 Syntax-Directed Definitions 3 Synthesized Attributes 4 Inherited Attributes 5 Examples 6 Assignment Robb T. Koether (Hampden-Sydney College)Abstract Syntax TreesSynthetic and Inherited Attributes Mon, Mar 16, / 38
15 Synthesized Attributes Definition A synthesized attribute of a grammar symbol is a property that is determined by the attributes of the symbols below it in the parse tree. In other words, if A α is a production, then A s synthesized attributes are determined by the attributes of the symbols in α. Robb T. Koether (Hampden-Sydney College)Abstract Syntax TreesSynthetic and Inherited Attributes Mon, Mar 16, / 38
16 Synthesized Attributes If the AST represents a numerical expression, then the value of the root node is determined by the values of the nodes below it in the tree. Thus, the value of the root node is a synthesized attribute. Robb T. Koether (Hampden-Sydney College)Abstract Syntax TreesSynthetic and Inherited Attributes Mon, Mar 16, / 38
17 Example Example (Synthesized Attributes) The terminals get their values directly from the lexical analyzer. For example, a num token s value attribute would be the numerical value of the string of digits in the token. Robb T. Koether (Hampden-Sydney College)Abstract Syntax TreesSynthetic and Inherited Attributes Mon, Mar 16, / 38
18 Example Example (Synthesized Attributes) expr.val expr 1.val + expr 2.val num.lexval num.lexval Robb T. Koether (Hampden-Sydney College)Abstract Syntax TreesSynthetic and Inherited Attributes Mon, Mar 16, / 38
19 Example Example (Synthesized Attributes) expr.val expr 1.val + expr 2.val num.lexval num.lexval from lexer from lexer Robb T. Koether (Hampden-Sydney College)Abstract Syntax TreesSynthetic and Inherited Attributes Mon, Mar 16, / 38
20 Example Example (Synthesized Attributes) expr.val expr 1.val + expr 2.val synthesized synthesized num.lexval num.lexval from lexer from lexer Robb T. Koether (Hampden-Sydney College)Abstract Syntax TreesSynthetic and Inherited Attributes Mon, Mar 16, / 38
21 Example Example (Synthesized Attributes) expr.val synthesized synthesized expr 1.val + expr 2.val synthesized num.lexval num.lexval synthesized from lexer from lexer Robb T. Koether (Hampden-Sydney College)Abstract Syntax TreesSynthetic and Inherited Attributes Mon, Mar 16, / 38
22 Outline 1 Abstract Syntax Trees 2 Syntax-Directed Definitions 3 Synthesized Attributes 4 Inherited Attributes 5 Examples 6 Assignment Robb T. Koether (Hampden-Sydney College)Abstract Syntax TreesSynthetic and Inherited Attributes Mon, Mar 16, / 38
23 Inherited Attributes Definition An inherited attribute is a property of a symbol (node) that is determined by its parent node and its siblings in the parse tree. In other words, if β is symbol on the right side of the production A αβγ, then β s inherited attributes are determined by the attributes of A and the other symbols in α and γ. Robb T. Koether (Hampden-Sydney College)Abstract Syntax TreesSynthetic and Inherited Attributes Mon, Mar 16, / 38
24 Example Example (Inherited Attributes) Consider the grammar for a declaration containing one or more identifiers. dcl type list list list, id id type int float Robb T. Koether (Hampden-Sydney College)Abstract Syntax TreesSynthetic and Inherited Attributes Mon, Mar 16, / 38
25 Example Example (Inherited Attributes) For example, the declaration might be float a, b, c; The attribute float first appears as the type of the float token. From there it is passed to the identifiers a, then b, then c. Robb T. Koether (Hampden-Sydney College)Abstract Syntax TreesSynthetic and Inherited Attributes Mon, Mar 16, / 38
26 Example Example (Inherited Attributes) dcl type.type list.type FLOAT list.type, id 2.type float id 1.type Robb T. Koether (Hampden-Sydney College)Abstract Syntax TreesSynthetic and Inherited Attributes Mon, Mar 16, / 38
27 Example Example (Inherited Attributes) dcl type.type list.type FLOAT list.type, id 2.type from lexer float id 1.type Robb T. Koether (Hampden-Sydney College)Abstract Syntax TreesSynthetic and Inherited Attributes Mon, Mar 16, / 38
28 Example Example (Inherited Attributes) dcl type.type list.type synthesized FLOAT list.type, id 2.type from lexer float id 1.type Robb T. Koether (Hampden-Sydney College)Abstract Syntax TreesSynthetic and Inherited Attributes Mon, Mar 16, / 38
29 Example Example (Inherited Attributes) dcl type.type inherited list.type synthesized FLOAT list.type, id 2.type from lexer float id 1.type Robb T. Koether (Hampden-Sydney College)Abstract Syntax TreesSynthetic and Inherited Attributes Mon, Mar 16, / 38
30 Example Example (Inherited Attributes) dcl type.type inherited list.type synthesized inherited inherited FLOAT list.type, id 2.type from lexer float id 1.type Robb T. Koether (Hampden-Sydney College)Abstract Syntax TreesSynthetic and Inherited Attributes Mon, Mar 16, / 38
31 Example Example (Inherited Attributes) dcl type.type inherited list.type synthesized inherited inherited FLOAT list.type, id 2.type from lexer inherited float id 1.type Robb T. Koether (Hampden-Sydney College)Abstract Syntax TreesSynthetic and Inherited Attributes Mon, Mar 16, / 38
32 Some Questions Questions In an expression tree, is the type of the expression at the root inherited or is it synthesized? Is the type used in an arithmetic operation an inherited attribute or an synthesized attribute of the operator? In an assignment statement, is the type assigned by the operator an inherited attribute or a synthesized attribute of the operator? Robb T. Koether (Hampden-Sydney College)Abstract Syntax TreesSynthetic and Inherited Attributes Mon, Mar 16, / 38
33 Outline 1 Abstract Syntax Trees 2 Syntax-Directed Definitions 3 Synthesized Attributes 4 Inherited Attributes 5 Examples 6 Assignment Robb T. Koether (Hampden-Sydney College)Abstract Syntax TreesSynthetic and Inherited Attributes Mon, Mar 16, / 38
34 Synthesized Attributes Example (Synthesized Attributes) Let the grammar be E E + T E T T T * F T F F ( E ) F num Robb T. Koether (Hampden-Sydney College)Abstract Syntax TreesSynthetic and Inherited Attributes Mon, Mar 16, / 38
35 Synthesized Attributes Example (Synthesized Attributes) The attribute at every node is the value of the nonterminal. In every case, it is synthesized. E.val = E.val + T.val E.val = T.val T.val = T.val F.val T.val = F.val F.val = E.val F.val = num.lexval Robb T. Koether (Hampden-Sydney College)Abstract Syntax TreesSynthetic and Inherited Attributes Mon, Mar 16, / 38
36 Inherited Attributes Example (Inherited Attributes) Let the grammar be E T E E + T E E ε T F T T * F T T ε F ( E ) F num Robb T. Koether (Hampden-Sydney College)Abstract Syntax TreesSynthetic and Inherited Attributes Mon, Mar 16, / 38
37 Inherited Attributes Example (Inherited Attributes) The attribute at the nodes E, T, and F is the value of the nonterminal. In some cases, it is synthesized. In other cases, it is inherited. Robb T. Koether (Hampden-Sydney College)Abstract Syntax TreesSynthetic and Inherited Attributes Mon, Mar 16, / 38
38 Inherited Attributes Example (Inherited Attributes) For the production F num we have the rule F.val = num.lexval For the production F ( E ) we have the rule After that, it is not so simple. F.val = E.val Robb T. Koether (Hampden-Sydney College)Abstract Syntax TreesSynthetic and Inherited Attributes Mon, Mar 16, / 38
39 Inherited Attributes Example (Inherited Attributes) Consider the parse tree for the expression Robb T. Koether (Hampden-Sydney College)Abstract Syntax TreesSynthetic and Inherited Attributes Mon, Mar 16, / 38
40 Inherited Attributes Example (Inherited Attributes) E T E' F T' + T E' num * F T' F T' ε num ε num ε The parse tree Robb T. Koether (Hampden-Sydney College)Abstract Syntax TreesSynthetic and Inherited Attributes Mon, Mar 16, / 38
41 Inherited Attributes Example (Inherited Attributes) E T E' F T' + T E' num 3 * F T' F T' ε num 4 ε num 5 num gets its values from the lexer ε Robb T. Koether (Hampden-Sydney College)Abstract Syntax TreesSynthetic and Inherited Attributes Mon, Mar 16, / 38
42 Inherited Attributes Example (Inherited Attributes) E T E' F 3 T' + T E' num 3 * F 4 T' F 5 T' ε num 4 ε num 5 F.val = num.lexval ε Robb T. Koether (Hampden-Sydney College)Abstract Syntax TreesSynthetic and Inherited Attributes Mon, Mar 16, / 38
43 Inherited Attributes Example (Inherited Attributes) T.inh = F.val Robb T. Koether (Hampden-Sydney College)Abstract Syntax TreesSynthetic and Inherited Attributes Mon, Mar 16, / 38
44 Inherited Attributes Example (Inherited Attributes) How does T (in the production T F T ) get its value? It must multiply 3 and 4 to get 12. So, first T inherits 3 from F. Then, in the production T * F T 1, T 1 inherits 12 from T and F. Then, T turns around and synthesizes 12 from T 1. Then, back in the production T F T, T synthesizes 12 from T. Robb T. Koether (Hampden-Sydney College)Abstract Syntax TreesSynthetic and Inherited Attributes Mon, Mar 16, / 38
45 Inherited Attributes Example (Inherited Attributes) E T E' inh 3 F 3 T' 12 + T E' * 4 num 3 * F 4 T' F 5 T' ε num 4 ε num 5 ε T.inh = F.val Robb T. Koether (Hampden-Sydney College)Abstract Syntax TreesSynthetic and Inherited Attributes Mon, Mar 16, / 38
46 Inherited Attributes Example (Inherited Attributes) E T E' F 3 inh 3 T' inh 12 + T E' num 3 * F 4 T' 12 F 5 T' ε num 4 ε num 5 T 1.inh = T.inh F.val ε Robb T. Koether (Hampden-Sydney College)Abstract Syntax TreesSynthetic and Inherited Attributes Mon, Mar 16, / 38
47 Inherited Attributes Example (Inherited Attributes) E T E' F 3 inh 3 T' inh 12 + T E' num 3 * F 4 T' 12 F 5 T' ε num 4 ε num 5 ε T.syn = T.inh Robb T. Koether (Hampden-Sydney College)Abstract Syntax TreesSynthetic and Inherited Attributes Mon, Mar 16, / 38
48 Inherited Attributes Example (Inherited Attributes) E T E' F 3 inh 3 T' syn 12 + T E' num 3 * F 4 T' 12 F 5 T' ε num 4 ε num 5 ε T.syn = T 1.syn Robb T. Koether (Hampden-Sydney College)Abstract Syntax TreesSynthetic and Inherited Attributes Mon, Mar 16, / 38
49 Inherited Attributes Example (Inherited Attributes) E T syn 12 E' F 3 inh 3 T' syn 12 + T E' num 3 * F 4 T' 12 F 5 T' ε num 4 ε num 5 ε T.val = T.syn Robb T. Koether (Hampden-Sydney College)Abstract Syntax TreesSynthetic and Inherited Attributes Mon, Mar 16, / 38
50 Inherited Attributes Example (Inherited Attributes) E T syn 12 inh 12 E' F 3 inh 3 T' syn 12 + T E' num 3 * F 4 T' 12 F 5 T' ε num 4 ε num 5 ε E.inh = T.val Robb T. Koether (Hampden-Sydney College)Abstract Syntax TreesSynthetic and Inherited Attributes Mon, Mar 16, / 38
51 Inherited Attributes Example (Inherited Attributes) We now have the rules Production T F T T * F T 1 T ε F num Semantic Rules T.inh = F.val T.val = T.syn T 1.inh = T.inh F.val T.syn = T 1.syn T.syn = T.inh F.val = num.lexval Robb T. Koether (Hampden-Sydney College)Abstract Syntax TreesSynthetic and Inherited Attributes Mon, Mar 16, / 38
52 Inherited Attributes Example (Inherited Attributes) As well as the rules Production E T E E + T E 1 E ε Semantic Rules E.inh = T.val E.val = E.syn E 1.inh = E.inh + T.val E.syn = E 1.syn E.syn = E.inh Robb T. Koether (Hampden-Sydney College)Abstract Syntax TreesSynthetic and Inherited Attributes Mon, Mar 16, / 38
53 Outline 1 Abstract Syntax Trees 2 Syntax-Directed Definitions 3 Synthesized Attributes 4 Inherited Attributes 5 Examples 6 Assignment Robb T. Koether (Hampden-Sydney College)Abstract Syntax TreesSynthetic and Inherited Attributes Mon, Mar 16, / 38
54 Assignment Homework p. 309: 1, 2, 3 Robb T. Koether (Hampden-Sydney College)Abstract Syntax TreesSynthetic and Inherited Attributes Mon, Mar 16, / 38
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