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3 Pages

### ProblemSet8

Course: HIT 3315, Fall 2009
School: Allan Hancock College
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Word Count: 372

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2, HIT3315 Semester 2008 Dr. Markus Lumpe Swinburne University Of Technology Faculty of Information and Communication Technologies ASSIGNMENT COVER SHEET Subject Code: Subject Title: Assignment number and title: Due date: Lecturer: HIT3315 Languages in Software Development 8, Typed Lambda Calculus November 5, 2008, 11:30 am Dr. Markus Lumpe Your name: Marker's comments: Problem 1 Total Marks 100 100...

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2, HIT3315 Semester 2008 Dr. Markus Lumpe Swinburne University Of Technology Faculty of Information and Communication Technologies ASSIGNMENT COVER SHEET Subject Code: Subject Title: Assignment number and title: Due date: Lecturer: HIT3315 Languages in Software Development 8, Typed Lambda Calculus November 5, 2008, 11:30 am Dr. Markus Lumpe Your name: Marker's comments: Problem 1 Total Marks 100 100 Obtained Extension certification: This assignment has been given an extension and is now due on Signature of Convener: 1 HIT3315 Semester 2, 2008 Dr. Markus Lumpe Problem Set 8: Typed Lambda Calculus A Type System for the Lambda Calculus with Constants: Number: n : Int A number n has type Int. Variable: x : (x) If x dom(), then variable x has type (x). Abstraction: ; x : t e : t (lambda x t . e) : (t -> t) If under the extended typed environment ; x : t expression e has type t, then (lambda x t . e) has type (t -> t). Application: e1 : (t -> t) (e1 e2) : t e2 : t If under the same type environment e1 has type (t -> t) and e2 has type t, then (e1 e2) has type t. 2 HIT3315 Semester 2, 2008 Dr. Markus Lumpe Problem 1 Consider the following BNF specification: CompilationUnit LambdaExp ::= ::= | | | Type ::= | LambdaExp <EOF> <Number> <Identifier> LOOKAHEAD(2) ( lambda <Identifier> Type . LambdaExp ) ( LambdaExp LambdaExp ) Int ( Type -> Type ) Define front-end a in JavaCC for this grammar using TypedLambda as parser name. Define the corresponding abstract syntax tree classes that extend the following toplevel classes for lambda expressions and types: public abstract class TypedLambdaExpression { public abstract LambdaType typeCheck(Hashtable<String,LambdaType> aGamma); public abstract String toString(); } public abstract class LambdaType { public abstract boolean match( LambdaType aOtherType ); public abstract String toString(); } Incorporate the abstract syntax into the specification. Define the method typeCheck according to the rules defined above. Signal type errors by throwing a RuntimeException. 3 HIT3315 Semester 2, 2008 Dr. Markus Lumpe The main method: public static void main( String[] Args ) { try { TypedLambda lp = new TypedLambda (new FileInputStream( Args[0] )); Ty...

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