Project 4 - Adding Type Checking and Recursion EECS 662 - Programming Languages
The objective of this project is to add Boolean operations, type checking, and a fixed point operation to FBAE from Project 3. You will first add boolean operations to the FBAE interpreter by extending the AST and updating the evaluator. You will then add a fixed point operator to your AST and interpreter. Finally, you will define a type checker for the extended FBAE language and integrate type checking into the FBAE interpreter. Specifically, you will parse your FBAE expression, type check the resulting AST, elaborate to FBAE, and evaluate the result.
The base language for this project is the extension of FBAE defined as follows:
None of these operations is new. We have implemented them in some form in earlier projects or in class.
Implement and evaluator with the signature
eval :: Env -> FBAE ->
FBAValue that performs call-by-value function interpretation
using static scoping. Your interpreter need only do minimal
runtime error checking as it will be integrated with a type
inference function later in the project.
eval function, implement a function
interp :: String
-> FBAEValue that parses its input and evaluates the resulting
The syntax for
lambda in FBAE includes specification of a type.
Lambda has a placeholder for the domain type. While this will
be populated by the parser and you must include types in your AST,
they are ignored by the evaluator. Note specifically that
has no domain type specified. Think carefully about why this is the
A parser and data structures for FBAE are provided in the project
utilities file. If you choose to you may continue to use the
elaborator from Project 3 to implement
bind and reuse your evaluator
for CFAE. Alternatively, you may extend the CFAE interpreter to
bind as the beginning of your new interpreter.
In this exercise you will add recursion to CFWAE by adding a
operator to CFWAE. This is accomplished by adding the term:
to the original FBAE language from Exercise 1. Note that the parser and AST provided for Project 4 already include these constructs. Thus, you need not change you parser or your AST for this exercise.
evalfunction from Exercise 1 to include the
interp function need not be updated. Once again types must be
included, but will be ignored by the evaluator and interpreter.
In this exercise you will write a type checker for the FBAE language identical to that used in Project 2 with the addition of syntax for types.
typeof :: Cont -> FBAE -> TFBAE, that takes an FBAE data structure and returns its type given a context. If no type can be found,
typeofshould throw an error indicating why. Think of this as an interpreter that produces type values rather than traditional values.
An AST for the type values is included in the Project 3 utilities file.
In this exercise you will put all the pieces together to write an interpreter for FBAE and its extensions.
evalfunctions into a function
interp :: String -> FBAEValuethat parses its input, finds the type of the result, and evaluates the result if a type is found.
Note that the type inference function is called after parsing, but before evaluation. Evaluation should only occur if type inference works.
You can get quite a bit of your code from class notes or the text.
However, you will need to write
eval cases for Boolean
operations on your own.
Keep error checking in
eval to a minimum. If the purpose of
typeof is to predict errors, then very little error checking need be
performed during evaluation. This is one advantage of type inference
and type checking.
I strongly suggest writing this project either using
error to throw
errors or using the
Either monad. You can use
treating it as a monad, but you will end up writing quite a bit more
code. It’s not complicated, just bigger.
contains a parser and data structures for
free to roll your own if you prefer. The parser
utilities file used in previous projects is no longer needed. Just
use the project utilities file by itself.
Following are the AST structures defined in the utilities file.