Semantic Analysis II

Messages

Please check lecturer notices in the MoodleAppeals

Legitimate: “I don’t have the bug you mentioned…”

Illegitimate: “You took too many points for that…” No resubmissionTheoretical part to my box (floor 1 near the

elevator)

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Compiler

ICProgram

ic

x86 executable

exeLexicalAnalysi

s

Syntax Analysi

s

Parsing

AST Symbol

Tableetc.

Inter.Rep.(IR)

CodeGeneration

IC compiler

We saw: Scope Symbol tables

Today: Type checking

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Examples of type errors

int a; a = true;

void foo(int x) { int y; foo(5,7);}

1 < true

class A {…}class B extends A { void foo() { A a; B b; b = a; }}

argument list doesn’t match

formal parameters

a is not a subtype of b

assigned type doesn’t match declared type

relational operator applied to non-int

type

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Types

Type Set of possible values (and operations)

boolean = {true,false} int = {-231..231-1} void = {}

Type safety Type usage adheres to formally defined typing rules

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Type judgments

e : T e is a well-typed expression of type T

Examples 2 : int 2 * (3 + 4) : int true : bool “Hello” : string

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Type judgments

E e : T

In the context E, e is a well-typed expression of T

Examples:b:bool, x:int b:boolx:int 1 + x < 4:boolfoo:int->string, x:int foo(x) : string

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Typing rules

Premise

Conclusion[Name]

Conclusion[Name]

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Typing rules for expressions

E e1 : int E e2 : int

E e1+e2 : int[+]

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Expression rules

E true : bool

E e1 : int E e2 : int

E e1 op e2 : int

E false : bool

E int-literal : int E string-literal : string

op { +, -, /, *, %}

E e1 : int E e2 : int

E e1 rop e2 : boolrop { <=,<, >, >=}

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More expression rules

E e1 : bool E e2 : bool

E e1 lop e2 : boollop { &&,|| }

E e1 : int

E - e1 : int

E e1 : bool

E ! e1 : bool

E e1 : T[]

E e1.length : int

E e1 : T[] E e2 : int

E e1[e2] : T

E e1 : int

E new T[e1] : T[]

E new T() : T

E e:C (id : T) C

E e.id : T

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Subtyping

Inheritance induces subtyping relation ≤

S ≤ T values(S) values(T)

“A value of type S may be used wherever a value of type T is expected”

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Subtyping

For all types:

For reference types:

A ≤ A

A extends B {…}

A ≤ B

A ≤ B B ≤ C

A ≤ C null ≤ A

Examples1. int ≤ int ?

2. null ≤ A ?

3. null ≤ string ?

4. string ≤ null ?

5. null ≤ boolean ?

6. null ≤ boolean[] ?

7. A[] ≤ B[] ?

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Examples1. int ≤ int ?

2. null ≤ A ?

3. null ≤ string ?

4. string ≤ null ?

5. null ≤ boolean ?

6. null ≤ boolean[] ?

7. A[] ≤ B[] ?“Subtyping is not covariant for array types: if A is a subtype of B then A[ ] is not a

subtype of B[ ]. Instead, array subtyping is type invariant, which means that each array type is only a subtype of itself.”

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Expression rules with subtyping

E e1 : T1 E e2 : T2 T1 ≤ T2 or T2 ≤ T1

op {==,!=}

E e1 op e2 : bool

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Rules for method invocations

E e0 : T1 … Tn Tr

E ei : T’i T’

i ≤ Ti for all i=1..n

E e0(e1, … ,en): Tr

(m : static T1 … Tn Tr) CE ei : T’

i T’i ≤ Ti for all

i=1..nE C.m(e1, … ,en): Tr

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Statement rules

Statements have type voidJudgments of the form

E S In environment E, S is well typed

E e:bool E S

E while (e) S

E e:bool E S

E if (e) S

E e:bool E S1 E S2

E if (e) S1 else S2

E break E continue

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Return statements

ret:Tr represents return type of current method

ret:void E

E return;

ret:T’E T≤T’

E return e;

E e:T

More IC Rules

DeclarationsMethodClassProgram…

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Type-checking algorithm

1. Construct types1. Add basic types to a “type table”

2. Traverse AST looking for user-defined types (classes,methods,arrays) and store in table

3. Bind all symbols to types

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Type-checking algorithm

2. Traverse AST bottom-up (using visitor)1. For each AST node find corresponding rule

(there is only one for each kind of node)

2. Check if rule holds1. Yes: assign type to node according to consequent

2. No: report error

232345 > 32 && !false

BinopExpr UnopExpr

BinopExpr

…

op=AND

op=NEGop=GT

intLiteral

val=45

intLiteral

val=32

boolLiteral

val=false

: int : int

: bool

: bool

: bool

: bool

E false : bool

E int-literal : int

E e1 : int E e2 : int

E e1 > e2 : bool

E e1 : bool E e2 : bool

E e1 && e2 : bool

E e1 : bool

E !e1 : bool

Algorithm example

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Semantic analysis flow

Parsing and AST construction Combine library AST with IC program AST

Construct and initialize global type table Construct class hierarchy and verify the hierarchy is

tree Phase 1: Symbol table construction

Assign enclosing-scope for each AST node Phase 2: Scope checking

Resolve names Check scope rules using symbol table

Phase 3: Type checking Assign type for each AST node

Phase 4: Remaining semantic checks