5. Syntax-Directed Definitions & Type Analysis
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1 5. Syntax-Directed Definitions & Type Analysis Eva Rose Kristoffer Rose NYU Courant Institute Compiler Construction (CSCI-GA ) March 2, 2015 Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
2 1 Introduction 2 SDD: Syntax-Directed Definition 3 Type Systems 4 Types in Programming Languages 5 Types in the Compiler 6 Project Milestone 2 Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
3 Context Tokens Tree Tree source program IR IR IR Lexical Analysis Syntax Analysis Semantic Analysis Symbol Table Intermediate Representation Generator Optimizer Code Generator Machine-Dependent Code Optimizer target machine code Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
4 From Abstract Syntax Tree (AST) position = initial + rate * 60 = id, 1 + id, 2 id, 3 num, 60 id lexeme 1 position 2 initial 3 rate Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
5 Type Checking Gives Annotated AST... id, 1 t = float = t = float + id, 2 t = float t = float id lexeme t 1 position float 2 initial float 3 rate float t = float id, 3 num, 60 t = float t = int Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
6 1 Introduction 2 SDD: Syntax-Directed Definition 3 Type Systems 4 Types in Programming Languages 5 Types in the Compiler 6 Project Milestone 2 Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
7 Syntax-Directed Definition (SDD) Grammar Given a context-free grammar. Attributes Each grammar symbol (terminal or nonterminal) has a set of attributes associated. Semantic Rules Each production has a set of semantic rules associated for computing the attributes. If X is a symbol, a is an attribute, then X.a denotes the value of a at node X. Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
8 Synthesized and Inherited Attributes Synthesized attributes at node N are defined only in terms of the attribute values of the children of N, and N itself. Inherited attributes at node N is defined only in terms of attribute values at N s parent, N itself, and N s siblings. Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
9 Example: SDD for Desk Calculator PRODUCTION SEMANTIC RULE 1. L E $ L.val = E.val 2. E E 1 + T E.val = E 1.val + T.val 3. E T E.val = T.val 4. T T 1 F T.val = T 1.val F.val 5. T F T.val = F.val 6. F (E) F.val = E.val 7. F digit F.val = digit.lexval val and lexval are synthesized attributes. Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
10 Example: SDD for Desk Calculator PRODUCTION SEMANTIC RULE 1. L E $ L.val = E.val 2. E E 1 + T E.val = E 1.val + T.val 3. E T E.val = T.val 4. T T 1 F T.val = T 1.val F.val 5. T F T.val = F.val 6. F (E) F.val = E.val 7. F digit F.val = digit.lexval val and lexval are synthesized attributes. Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
11 Characteristics of Desk Calculator S-attributed (only synthesized attributes) attribute grammar (SDD/ no side-effects) S-attribute calculations: any bottom-up parsing is good (depth-first tree traversal). Note: In parser generator YACC, S-attributes are directly annotatable (as semantic actions). Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
12 Characteristics of Desk Calculator S-attributed (only synthesized attributes) attribute grammar (SDD/ no side-effects) S-attribute calculations: any bottom-up parsing is good (depth-first tree traversal). Note: In parser generator YACC, S-attributes are directly annotatable (as semantic actions). Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
13 Introduction SDD: Syntax-Directed Definition Type Systems Types in Programming Languages Types in the Compiler Project Milestone 2 Tree Traversal: Depth-First Post-order (default). Pre-order. Binary trees: also in-order. Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
14 Exercise: Desk Calculator Give annotated parse trees for the following expressions: (3 + 4) (5 + 6) $ (4 + 5) $ (Parse trees showing attributes and their values) Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
15 Exercise Construct an SDD that generates a (synthesized) attribute t in prefix notation for each expression expr, for arithmetic expressions. (You only need to consider: +,, and expressions). Prefix notation is where the operator comes before its operands; e.g., x y is the prefix notation for x y. Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
16 Solution: SDD for Infix Notation into Prefix Notation PRODUCTION SEMANTIC RULE expr expr 1 + term 2 expr.t = + expr 1.t term 2.t expr expr 1 term 2 expr.t = expr 1.t term 2.t expr expr 1 term 2 expr.t = expr 1.t term 2.t expr term expr.t = term.t term 0 term.t = 0 term 1 term.t = term 9 term.t = 9 Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
17 Solution: SDD for Infix Notation into Prefix Notation PRODUCTION SEMANTIC RULE expr expr 1 + term 2 expr.t = + expr 1.t term 2.t expr expr 1 term 2 expr.t = expr 1.t term 2.t expr expr 1 term 2 expr.t = expr 1.t term 2.t expr term expr.t = term.t term 0 term.t = 0 term 1 term.t = term 9 term.t = 9 Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
18 Solution: SDD for Infix Notation into Prefix Notation PRODUCTION SEMANTIC RULE expr expr 1 + term 2 expr.t = + expr 1.t term 2.t expr expr 1 term 2 expr.t = expr 1.t term 2.t expr expr 1 term 2 expr.t = expr 1.t term 2.t expr term expr.t = term.t term 0 term.t = 0 term 1 term.t = term 9 term.t = 9 Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
19 Solution: SDD for Infix Notation into Prefix Notation PRODUCTION SEMANTIC RULE expr expr 1 + term 2 expr.t = + expr 1.t term 2.t expr expr 1 term 2 expr.t = expr 1.t term 2.t expr expr 1 term 2 expr.t = expr 1.t term 2.t expr term expr.t = term.t term 0 term.t = 0 term 1 term.t = term 9 term.t = 9 Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
20 Exercise: Mingling with Inherited Attributes... PRODUCTION SEMANTIC RULES 1. T F T T.inh = F.val; T.val = T.syn T F T 1 T ɛ T 1.inh = T.inh F.val; T.syn = T 1.syn T.syn = T.inh 4. F digit F.val = digit.lexval inh is inherited, and val, syn are synthesized. Can you explain why? Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
21 Dependency Graphs Dependency graphs depicts the flow of information among attributes. Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
22 Introduction SDD: Syntax-Directed Definition Type Systems Types in Programming Languages Types in the Compiler Project Milestone 2 Example: Attributes Parse tree for 3 5 based on SDD: F 3 val digit 1 lexval T 9 val inh 5 8 syn T F 4 val 6 T inh 7 syn digit 2 lexval ɛ Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
23 Introduction SDD: Syntax-Directed Definition Type Systems Types in Programming Languages Types in the Compiler Project Milestone 2 Example: Attributes with Dependency Graph Parse tree for 3 5 based on SDD: F 3 val digit 1 lexval T 9 val inh 5 8 syn T F 4 val 6 T inh 7 syn digit 2 lexval ɛ Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
24 Dependency Graphs Central problem: Determining the efficient evaluation order for the attribute instances in a given parse tree. Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
25 Calculating Attributes Cycles possible! PRODUCTION SEMANTIC RULE A B A.s = B.i; B.i = A.s + 1 When dependency graphs have cycles, evaluation is stuck! Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
26 Well-behaved SDD Classes Given an SDD, hard to tell if there exists a parse tree whose dependency graphs have cycles! Safe way to go: use classes of SDDs that guarantee an evaluation order: S-Attributed Definitions all attributes are synthesized. L-Attributed Definitions left restrictions on dependency graph edges. Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
27 Well-behaved SDD Classes Given an SDD, hard to tell if there exists a parse tree whose dependency graphs have cycles! Safe way to go: use classes of SDDs that guarantee an evaluation order: S-Attributed Definitions all attributes are synthesized. L-Attributed Definitions left restrictions on dependency graph edges. Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
28 L-Attributed Definitions Suppose an attribute rule for A X 1 X 2... X i... X n produces inherited X i.a attribute. The rule may only use: inherited attributes associated with the head (A), inherited or synthesized attributes associated with the occurences of symbols X 1, X 2,..., X i 1 located left of X i. Inherited or synthesized attributes associated with the occurence of X i itself, as long as not part of a dependency graph cycle! or, the produced attribute is synthesized. Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
29 Example: Mingling with Inherited Attributes... Decide if the SDD is L-attributed and argue : PRODUCTION SEMANTIC RULES 1. T F T T.inh = F.val; T.val = T.syn T F T 1 T ɛ T 1.inh = T.inh F.val; T.syn = T 1.syn T.syn = T.inh 4. F digit F.val = digit.lexval inh is inherited, and val, syn are synthesized. Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
30 Example: Mingling with Inherited Attributes... Decide if the SDD is L-attributed and argue : PRODUCTION SEMANTIC RULES 1. T F T T.inh = F.val; T.val = T.syn T F T 1 T ɛ T 1.inh = T.inh F.val; T.syn = T 1.syn T.syn = T.inh 4. F digit F.val = digit.lexval inh is inherited, and val, syn are synthesized. Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
31 Example: Mingling with Inherited Attributes... Decide if the SDD is L-attributed and argue : PRODUCTION SEMANTIC RULES 1. T F T T.inh = F.val; T.val = T.syn T F T 1 T ɛ T 1.inh = T.inh F.val; T.syn = T 1.syn T.syn = T.inh 4. F digit F.val = digit.lexval inh is inherited, and val, syn are synthesized. Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
32 Another example The following SDD is NOT L-attributed. Why? PRODUCTION A B C SEMANTIC RULES A.s = B.b B.i = F(C.c, A.s) where B.i is inherited, and A.s, C.c are synthesized. Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
33 Another example The following SDD is NOT L-attributed. Why? PRODUCTION A B C SEMANTIC RULES A.s = B.b B.i = F(C.c, A.s) Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
34 Construction of Abstract Syntax Trees TREE INTERIOR NODES GRAMMAR parse tree nonterminals concrete syntax abstract syntax tree programming constructs abstract syntax Example (abstract syntax) + 2 E E + E E E digit 9 5 Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
35 Construction of AST Example 1: S-attributed SDD for simple expresssions. PRODUCTION SEMANTIC RULE 1. E E 1 + T 2 E.node = new Node( +, E 1.node, T 2.node) 2. E E 1 T 2 E.node = new Node(, E 1.node, T 2.node) 3. E T E.node = T.node 4. T ( E ) T.node = E.node 5. T id T.node = new Leaf(id, id.entry) 6. T num T.node = new Leaf(num, num.entry) Show the AST for a 4 + c Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
36 Construction of AST Example 1: S-attributed SDD for simple expresssions. PRODUCTION SEMANTIC RULE 1. E E 1 + T 2 E.node = new Node( +, E 1.node, T 2.node) 2. E E 1 T 2 E.node = new Node(, E 1.node, T 2.node) 3. E T E.node = T.node 4. T ( E ) T.node = E.node 5. T id T.node = new Leaf(id, id.entry) 6. T num T.node = new Leaf(num, num.entry) Show the AST for a 4 + c Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
37 Construction of AST Example 2: L-attributed SDD for simple expresssions. PRODUCTION SEMANTIC RULE 1. E T E E.node = E.syn; E.inh = T.node 2. E + T E 1 E 1.inh = new Node( +, E.node, T.node) 3. E T E 1 E.syn = E 1.syn E 1.inh = new Node(, E.node, T.node) E.syn = E 1.syn 4. E ɛ E.syn = E.inh 5. T ( E ) T.node = E.node 6. T id T.node = new Leaf(id, id.entry) 7. T num T.node = new Leaf(num, num.entry) Show AST and dependency graph for a 4 + c Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
38 Construction of AST Example 2: L-attributed SDD for simple expresssions. PRODUCTION SEMANTIC RULE 1. E T E E.node = E.syn; E.inh = T.node 2. E + T E 1 E 1.inh = new Node( +, E.node, T.node) 3. E T E 1 E.syn = E 1.syn E 1.inh = new Node(, E.node, T.node) E.syn = E 1.syn 4. E ɛ E.syn = E.inh 5. T ( E ) T.node = E.node 6. T id T.node = new Leaf(id, id.entry) 7. T num T.node = new Leaf(num, num.entry) Show AST and dependency graph for a 4 + c Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
39 Syntax-Directed Translation of Type Expressions PRODUCTION SEMANTIC RULE 1 T B C T.syn = C.syn C.inh = B.syn 2 B int B.syn = integer 3 B float B.syn = integer 4 C [num]c 1 C.syn = array(num.val, C 1.syn) C 1.inh = C.inh 5 C ɛ C.syn = C.inh Show AST and dependencies for int[2][3] Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
40 Syntax-Directed Translation of Type Expressions PRODUCTION SEMANTIC RULE 1 T B C T.syn = C.syn C.inh = B.syn 2 B int B.syn = integer 3 B float B.syn = integer 4 C [num]c 1 C.syn = array(num.val, C 1.syn) C 1.inh = C.inh 5 C ɛ C.syn = C.inh Show AST and dependencies for int[2][3] Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
41 1 Introduction 2 SDD: Syntax-Directed Definition 3 Type Systems 4 Types in Programming Languages 5 Types in the Compiler 6 Project Milestone 2 Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
42 Type Checking Languages come with type system: Set of rules What are the basic value types? How can existing values be composed and decomposed to form new types? Compiler s job: Assign type expressions to each component Determine that these type expressions conform to type systems Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
43 Type Checking Languages come with type system: Set of rules What are the basic value types? How can existing values be composed and decomposed to form new types? Compiler s job: Assign type expressions to each component Determine that these type expressions conform to type systems Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
44 Purpose of Types Development Help (completion, documentation) Error detection (static and dynamic checks) Error Prevention (disambiguate operations) Optimization purposes (storage layout) Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
45 Dynamic vs Static Type Checking Type checking can be done dynamically for any language (i.e., at run-time) compiler generates code to do runtime checks Usually preferred to do type checking statically (i.e., at compile-time) Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
46 Properties of Type Checking A sound type system eliminates the need for dynamic checking Examples: OCaml, Haskell A language is strongly typed if all type errors are caught. Examples: Java, C#, Ruby, Python, OCaml, Haskell Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
47 Rules for Type Checking Type Synthesis Builds the type system of an expression from the types of subexpressions Requires names to be declared before use Type Inference Determines the type of a construct from the way it is used Complex Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
48 Type Synthesis (Denotational Formulation) if f : S T and x : S then f(x) : T f : S T f(x) : T x : S Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
49 Type Synthesis (Denotational Formulation) if f : S T and x : S then f(x) : T f : S T f(x) : T x : S Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
50 Type Inference (Denotational Formulation) f(x) : T S[ f : S T x : S ] Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
51 1 Introduction 2 SDD: Syntax-Directed Definition 3 Type Systems 4 Types in Programming Languages 5 Types in the Compiler 6 Project Milestone 2 Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
52 Values in Programming Languages Some examples of types: short, int, long, char, bool, float,... int[2][3], struct Link, String,... class names,... Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
53 Type Concepts primitive types (boolean, integral, floating point, chars, strings*) composite types (arrays, records, strings*) reference types (pointers, object references) abstract data types aka. ADT (class) subtype (class hierarchies) recursive types (linked lists) function types (ordering)... Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
54 Type Concepts primitive types (boolean, integral, floating point, chars, strings*) composite types (arrays, records, strings*) reference types (pointers, object references) abstract data types aka. ADT (class) subtype (class hierarchies) recursive types (linked lists) function types (ordering)... Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
55 Type Specification Language manual Compiler manual Machine architecture Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
56 Type Specification Language manual Compiler manual Machine architecture Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
57 Type Specification Language manual Compiler manual Machine architecture Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
58 Some (Modern) Language Type Implementation Details Type Implementation (bit) Language Specifications byte 8 JVM-Spec: 8 short 16 (or 32) JVM-Spec: 16, C/C++ unspec. char 8 or 16 JVM-Spec: 16, C/C++: 8 int 32 or 64 JVM-Spec: 32, C/C++ 16 long 64 (or 128) JVM-Spec: 64, C/C++ 32 float 32 (or 64) JVM-Spec: 32, C/C++ unspec. double 64 (or 128) JVM-Spec: 64, C/C++ unspec. C: part of system read limits.h for min and max specifications. Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
59 Traditional/Old System (C-compiler) Type Details Type Implementation (bit) short 8 int 16 long 32 Today: unix systems : specify integers as 64 bit window systems : specify integers as 32 bit computers (AMD64): ALU datapath, registers are 64 bit, mobile phones (ARM): ditto, but 32 bit (moving to 64) Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
60 Type Conversions Widening (preservation) often implicit (coercions). Narrowing (lossy) often explicit (casts). Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
61 Introduction SDD: Syntax-Directed Definition Type Systems Types in Programming Languages Types in the Compiler Project Milestone 2 Widening Conversion Hierarchy (primitive Java types) short byte double float long int char Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
62 Introduction SDD: Syntax-Directed Definition Type Systems Types in Programming Languages Types in the Compiler Project Milestone 2 Narrowing Conversion Hierarchy (primitive Java types) byte double float long int short char Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
63 Example Type Conversion I 1 float position; 2 int initial; 3 float rate; position = initial + rate * 60.00; Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
64 Example Type Conversion II 1 float position; 2 int initial; 3 float rate; position = initial + rate * 60; Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
65 Example Type Conversion III 1 int position; 2 int initial; 3 float rate; position = initial + rate * 60; Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
66 Explicit Conversions (cast) Tell the compiler that you MEAN this type conversion (type cast) position = initial + (( int) rate) * 60; Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
67 Example Java Conversions... 1 "U" "U" 3 " friends are " + true 4 true + " types" Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
68 Example Java Conversions... 1 "U" + 2 OK "U" 3 " friends are " + true 4 true + " types" Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
69 Example Java Conversions... 1 "U" + 2 OK "U" Fail 3 " friends are " + true 4 true + " types" Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
70 Example Java Conversions... 1 "U" + 2 OK "U" Fail 3 " friends are " + true OK 4 true + " types" Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
71 Example Java Conversions... 1 "U" + 2 OK "U" Fail 3 " friends are " + true OK 4 true + " types" Fail Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
72 Operator and Function Overloading + meaning addition or string concatenation (Java) user defined functions (Java) 1 void err() {...} 2 void err(string s) {...} Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
73 Operator and Function Overloading + meaning addition or string concatenation (Java) user defined functions (Java) 1 void err() {...} 2 void err(string s) {...} Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
74 1 Introduction 2 SDD: Syntax-Directed Definition 3 Type Systems 4 Types in Programming Languages 5 Types in the Compiler 6 Project Milestone 2 Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
75 Type Equivalence Approaches What are the values in a type? Approach Denotational Abstract Data Types (ADT) Definition set of values (Type Theory) set of operations (OO-systems) When are two types considered the same? Approach Denotational Abstract Data Types (ADT) Named typing Definition set of values (Type Theory) set of operations (OO-systems) set of names Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
76 Type Expressions (TE) A way so assign structure to types: primitive types are TEs, type constructor operator assigned to a TE. Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
77 TE Examples short, int, long, float, char,... T[] Map S,T S T S T Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
78 Type structure: AST for int[2][3] T B C (1) B int float (2) C [num]c ɛ (3) T int [.]. 2 [.]. 3 ɛ Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
79 Type structure: AST for int[2][3] T B C (1) B int float (2) C [num]c ɛ (3) T int [.]. 2 [.]. 3 ɛ Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
80 Type structure: type expression for int[2][3] array 2 array 3 int Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
81 Example: SDD for array TEs PRODUCTION T B C B int B float C [num]c 1 C ɛ SEMANTIC RULES T.t = C.t; C.b = B.t B.t = integer B.t = float C.t = array(num.val, C 1.t); C 1.b = C.b C.t = C.b b-inherited; t-synthesized Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
82 Example: SDD for array TEs PRODUCTION T B C B int B float C [num]c 1 C ɛ SEMANTIC RULES T.t = C.t; C.b = B.t B.t = integer B.t = float C.t = array(num.val, C 1.t); C 1.b = C.b C.t = C.b b-inherited; t-synthesized Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
83 Example: SDD with Type Storage Attribute PRODUCTION SEMANTIC RULES T BC T.t = C.t; T.width = C.width; C.b = B.t; w = B.width; B int B.t = integer; B.width = 4; B float B.t = float; B.width = 8; C [num]c 1 C.t = array(num.val, C 1.t); C.width = num.val C 1.width; C ɛ C.t = C.b; C.width = w; b inherited; t, width synthesized Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
84 Example SDD: Declarations and Environment Attribute PRODUCTION SEMANTIC RULES S T 1 id 2 = E 3 ; S 4 E 3.e = S.e; S 4.e = Extend(S.e, id 2.sym, T 1 ) (1 E E 1 + E 2 E 1.e = E.e; E 2.e = E.e (2 id 1 id 1.t = Lookup(E.e, id 1.sym) (3 Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
85 1 Introduction 2 SDD: Syntax-Directed Definition 3 Type Systems 4 Types in Programming Languages 5 Types in the Compiler 6 Project Milestone 2 Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
86 Project Milestone 2 Project Milestone 2 Released! Two due dates: 3/9 (Monday) and 3/27 (Friday) Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
87 Project Milestone 2 Requirements for 3/9 1 SDD for type checking of JST: Pr2You-sdd.pdf... template is provided: Pr2Base-sdd.tex (or PDF). 2 Evaluation criteria: Are attributes explained? Are the dependencies between attributes explained? Are declarations recorded properly in type environments? Are all nodes that can be assigned a type annotated with one? Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
88 Project Milestone 2 Requirements for 3/9 1 SDD for type checking of JST: Pr2You-sdd.pdf... template is provided: Pr2Base-sdd.tex (or PDF). 2 Evaluation criteria: Are attributes explained? Are the dependencies between attributes explained? Are declarations recorded properly in type environments? Are all nodes that can be assigned a type annotated with one? Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
89 Project Milestone 2 Requirements for 3/27 1 Implementation: Pr2You.hx... template provided: Pr2Base.hx. 2 Documentation: Pr2You.pdf. 3 Evaluation criteria: HACS source is well structured and easy to read. Variation and difficulties documented. Planning documented. How to reproduce tests is documented. Choices documented. Collaborations documented. Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
90 Project Milestone 2 Requirements for 3/27 1 Implementation: Pr2You.hx... template provided: Pr2Base.hx. 2 Documentation: Pr2You.pdf. 3 Evaluation criteria: HACS source is well structured and easy to read. Variation and difficulties documented. Planning documented. How to reproduce tests is documented. Choices documented. Collaborations documented. Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
91 Project Milestone 2 Requirements for 3/27 1 Implementation: Pr2You.hx... template provided: Pr2Base.hx. 2 Documentation: Pr2You.pdf. 3 Evaluation criteria: HACS source is well structured and easy to read. Variation and difficulties documented. Planning documented. How to reproduce tests is documented. Choices documented. Collaborations documented. Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
92 Questions? Eva Rose, Kristoffer Rose Compiler Construction (CSCI-GA ) 5. Syntax-directed Definitions/Type Analysis March 2, / 67
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