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...