CS/OS代写、代写ESSAY、代写CS/OS程序、代写留学生OSAssignment

日期：2018-09-09 02:16

COMP3161/9161 18s2 Assignment 1

In this assignment you will implement an interpreter for MinHs, a small functional

language similar to ML and Haskell. It is fully typed, with types specified by the

programmer. The assignment consists of a base compulsory component, worth 70%,

and five additional components, each worh 10%, which collectively are worth 50%,

meaning that only three of them have to be completed to earn full marks. You can earn

bonus marks by completing more tasks.

• Task 1 (70%)

Implement an interpreter for the MinHs language presented in the lectures, using

an environment semantics, including support for recursion and closures.

• Task 2 (10%)

Extend the interpreter to support partially applied prim-ops.

• Task 3 (10%)

Extend the interpreter to support n-ary functions

• Task 4 (10%)

Extend the interpreter to support multiple bindings in the one let form.

• Task 5 (10%)

Extend the interpreter to support let bindings that take parameters, definining

non-recursive functions.

• Task 6 (10%)

Extend the interpreter to support mutually recursive bindings.

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Each of these parts is explained in detail below.

The front end of the interpreter (lexer, parser, type checker) is provided for you, along

with the type of the evaluate function (found in the file Evaluator.hs). The function

evaluate returns an object of type Value. You may modify the constructors for

Value if you wish, but not the type for evaluate. The return value of evaluate is used

to check the correctness of your assignment.

You must provide an implementation of evaluate, in Evaluator.hs. It is this

file you will submit for Task 1. No other files can be modified.

You can assume the typechecker has done its job and will only give you correct

programs to evaluate. The type checker will, in general, rule out incorrect programs,

so the interpreter does not have to consider them.

Please use the Piazza forum for questions about this assignment.

1 Task 1

This is the core part of the assignment. You are to implement an interpreter for MinHs.

The following expressions must be handled:

• variables. v, u

• integer constants. 1, 2, ..

• boolean constants. True, False

• some primitive arithmetic and boolean operations. +, ∗, <, <=, ..

• constructors for lists. Nil, Cons

• destructors for lists. head, tail

• inspectors for lists. null

• function application. f x

• if e then e1 else e2

• let x :: τx = e1; y :: τy = e2; . . . in e2

• recfun f :: (τ1 → τ2) x = e expressions

These cases are explained in detail below. The abstract syntax defining these syntactic

entities is in Syntax.hs. You should understand the data type Exp and Bind

well.

Your implementation is to follow the dynamic semantics described in the lectures,

and this document. You are not to use substitution as the evaluation strategy, but must

use an environment/heap semantics. If a runtime error occurs, which is possible, you

should use Haskell’s error :: String → a function to emit a suitable error message

(the error code returned by error is non-zero, which is what will be checked for – the

actual error message is not important).

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1.1 Program structure

A program in MinHs may evaluate to either an integer, a list of integers, or a boolean,

depending on the type assigned to the main function. The main function is always

defined (this is checked by the implementation). In Task 1 programs, you need only

consider the case of a single top-level binding for main, like so:

main :: Int = 1 + 2;

or

main :: Bool

= let x :: Int = 1;

in if x + ((recfun f :: (Int -> Int) y = y * y) 2) == 0

then True

else False;

1.2 Variables, Literals and Constants

MinHs is a spartan language. We only have to consider 4 types:

Int

Bool

t1 -> t2

[Int]

The only literals you will encounter are integers. The only non-literal constructors are

True and False for the Bool type, and Nil and Cons for the [Int] type.

1.3 Function application

MinHs is, by virtue of its Haskell implementation, a non-strict language. An argument

to a function is only evaluated when needed — when the function tries to inspect its

value. This does not add a great deal of complexity to your implementation — it will

occur naturally as you will be writing the interpreter in Haskell, which is also a nonstrict

language.

The result of a function application may in turn be a function.

1.4 Primitive operations

You need to implement the following primitive operations:

+ :: Int -> Int -> Int

- :: Int -> Int -> Int

* :: Int -> Int -> Int

/ :: Int -> Int -> Int

negate :: Int -> Int

> :: Int -> Int -> Bool

>= :: Int -> Int -> Bool

< :: Int -> Int -> Bool

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<= :: Int -> Int -> Bool

== :: Int -> Int -> Bool

/= :: Int -> Int -> Bool

head :: [Int] -> Int

tail :: [Int] -> [Int]

null :: [Int] -> Bool

These operations are defined over Ints, [Int]s, and Bools, as usual. negate is the

primop representation of the unary negation function, i.e. -1. The abstract syntax for

primops is defined in Syntax.hs.

1.5 if - then - else

MinHs has an if e then e1 else e2 construct. The types of e1 and e2 are the same.

The type of e is Bool.

1.6 let

For the first task you only need to handle simple let s of the kind we have discussed

in the lectures. Like these:

main :: Int

= let

x :: Int = 1 + 2;

in x;

or

main :: Int

= let f :: (Int -> Int)

= recfun f :: (Int -> Int) x = x + x;

in f 3;

For the base component of the assignment, you do not need to handle let bindings

of more than one variable at a time (as is possible in Haskell). Remember, a let may

bind a recursive function defined with recfun .

1.7 recfun

The recfun expression introduces a new, named function value. It has the form:

(recfun f :: (Int -> Int) x = x + x)

A recfun value is a first-class value, and may be bound to a variable with let .

The value ‘f’ is bound in the body of the function, so it is possible to write recursive

functions:

recfun f :: (Int -> Int) x =

if x < 10 then f (x+1) else x

Be very careful when implementing this construct, as there can be problems when using

environments in a language allowing functions to be returned by functions.

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1.8 Evaluation strategy

We have seen in the tutorials how it is possible to evaluate expressions via substitution.

This is an extremely inefficient way to run a program. In this assignment you are

to use an environment instead. You will be penalised for an interpreter that operates

via substitution. The module Env.hs provides a data type suitable for most uses.

Consult the lecture notes on how environments are to be used in dynamic semantics.

The strategy is to bind variables to values in the environment, and look them up when

requried.

In general, you will need to use: empty, lookup and addAll to begin with an

empty environment, lookup the environment, or to add a binding to the environment,

respectively. As these functions clash with functions in the Prelude, a good idea is

to import the module Env qualified:

import qualified Env

This makes the functions accessible as Env.empty and Env.lookup, to disambiguate

from the Prelude versions.

2 Dynamic Semantics of MinHs

Big-step semantics

We define a relation ⇓ which relates an environment mapping variables to values1 Γ

and an expression E to the resultant value of that expression V . Our value set for V

will, to start with, consist of:

• Machine integers

• Boolean values

• Lists of integers

We will also need to add closures, or function values to our value set to deal with the

recfun construct in a sound way. See the section on Function Values for details.

Environment

The environment Γ maps variables to values, and is used in place of substitution. It is

specified as follows:

Γ ::= · | Γ, x=v

Values bound in the environment are closed – they contain no free variables. This requirement

creates a problem with function values created with recfun whose bodies

contain variables bound in an outer scope. We must bundle them with their associated

environment as a closure.

1Or, possibly, to an unevaluated computation of the value, but in Haskell these two things are indistinguishable.

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Constants and Boolean Constructors

Γ ` Num n ⇓ n Γ ` Con True ⇓ True Γ ` Con False ⇓ False

Primitive operations

Γ ` e1 ⇓ v1 e2 ⇓ v2

Γ ` Plus e1 e2 ⇓ v1 + v2

Similarly for the other arithmetic and comparison operations (as for the language of

arithmetic expressions)

Note that division by zero should cause your interpreter to throw an error using

Haskell’s error function.

The abstract syntax of the interpreter re-uses function application to represent application

of primitive operations, so Plus e1 e2 is actually represented as:

App (App (Prim Plus e1) e2)

For this first part of the assignment, you may assume that prim-ops are never partially

applied — that is, they are fully saturated with arguments, so the term App (Prim Plus e1)

will never occur in isolation.

Evaluation of if -expression

Γ ` e1 ⇓ True Γ ` e2 ⇓ x

Γ ` If e1 e2 e3 ⇓ x

Γ ` e1 ⇓ False Γ ` e3 ⇓ x

Γ ` If e1 e2 e3 ⇓ x

Variables

Γ(x) = v

Γ ` Var x ⇓ v

List constructors and primops

Γ ` Con Nil ⇓ []

Γ ` x ⇓ vx Γ ` xs ⇓ vxs

Γ ` Cons x xs ⇓ vx : vxs

Γ ` x ⇓ v : vs

Γ ` head x ⇓ v

Γ ` x ⇓ v : vs

Γ ` tail x ⇓ vs

Γ ` x ⇓ v : vs

Γ ` null x ⇓ False

Γ ` x ⇓ []

Γ ` head x ⇓ error

Γ ` x ⇓ []

Γ ` tail x ⇓ error

Γ ` x ⇓ []

Γ ` null x ⇓ True

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For the first part of the assignment, you may assume that Cons is also never partially

applied, as with prim-ops.

Variable Bindings with Let

Γ ` e1 ⇓ v1 Γ, x=v1 ` e2 ⇓ v2

Γ ` Let e1 (x.e2) ⇓ v2

Function values

To maintain soundness with function values, we need to pair a function with its environment,

forming a closure. We introduce the following syntax for function values:

(the types are included for completeness, but are not required at runtime):

hhΓ; Recfun τ1 τ2 f.x.eii

You will need to decide on a suitable representation of closures as a Haskell data type.

Now we can specify how to introduce closed function values:

Γ ` Recfun τ1 τ2 f.x.e1 ⇓ hhΓ; Recfun τ1 τ2 f.x.e1ii

We also re-use the recfun syntax, only without arguments, to construct infinite structures

like infinite lists. Here, the recursive reference is provided but no function value

is necessary:

Γ, f = v ` e ⇓ v

Γ ` Recfun τ f.e ⇓ v

Function Application

Γ ` e1 ⇓ v1 v1 = hhΓ

0

; Recfun τ1 τ2 f.x.ef ii

Γ ` e2 ⇓ v2 Γ

0

, f =v1, x=v2 ` ef ⇓ r

Γ ` App e1 e2 ⇓ r

3 Additional Tasks

In order to get full marks in the assignment, you must do three of the following five

tasks:

3.1 Task 2: Partial Primops

In the base part of the assignment, you are allowed to assume that all primitive operations

(and the constructor Cons) are fully saturated with arguments. In this task

you are to implement partial application of primitive operations (and Cons), which

removes this assumption. For example:

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main :: Int

= let inc :: (Int -> Int)

= recfun inc :: (Int -> Int) = (+) 1;

in inc 2; -- returns 3

Note that the expression (+) 1 partially applies the primop Plus to 1, returning a

function from Int to Int.

You will need to develop a suitable dynamic semantics for such expressions and

implement it in your evaluator. The parser and type checker are already capable of

dealing with expressions of this form.

3.2 Task 3: n-ary functions

In this task you are to implement n-ary functions. In other words, you should modify

the interpreter to handle bindings of functions of more than 1 argument.

main :: Bool

= let eq :: (Int -> Int -> Bool)

= recfun eq :: (Int -> Int -> Bool)

x y = x == y;

in eq 3 4;

We haven’t discussed the semantics of such functions in the lectures so you will

need to work out a reasonable dynamic semantics for n-ary functions on your own,

based on the semantics for unary functions. The parser and type checker are once again

already capable of handling expressions of this form, so the only extension necessary

is in the evaluator component.

Hint: Is the following example semantically different to the previous?

main :: Bool

= let eq :: (Int -> Int -> Bool)

= recfun eq :: (Int -> Int -> Bool)

x = recfun eq2 :: (Int -> Bool)

y = x == y;

in eq 3 4;

3.3 Task 4: Multiple bindings in let

In the base part of the assignment, we specify that let expressions contain only one

binding. In this task, you are to extend the interpreter so that let expressions with

multiple bindings, like:

main :: Int

= let a :: Int = 3;

b :: Int = 2;

in a + b;

are evaluated the same way as multiple nested let expressions:

main :: Int

= let a :: Int = 3;

in let b :: Int = 2;

in a + b;

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Once again the only place where extensions need to be made are in the evaluator, as

the type checker and parser are already capable of handling multiple let bindings.

3.4 Task 5: let bindings declare functions

In this task you are to extend the let construct further so that let bindings can take

parameters — defining non-recursive functions. This makes programming in MinHs

much less verbose, as recfun is only necessary for defining recursive functions. For

example:

main :: Int

= let y :: Int = 3;

in let f :: (Int -> Int) x = x + 1;

in f y; -- returns 4

Note that these bindings are non-recursive, so let x = x is a scope error, as the x

in the binding is not in scope.

3.5 Task 6: Mutually recursive bindings

Currently bindings must be specified in dependency order. However, in Haskell, the order

of declarations is irrelevant, which allows mutually recursive bindings. Implement

Haskell-style mutually recursive bindings, like so:

main :: Int

= letrec a :: Int = b;

b :: Int = c;

c :: Int = 7;

in c + a;

Syntax for letrec bindings is already defined, typechecked, and parsed by the provided

code. To implement this part, you simply need to implement the evaluator portion.

4 Testing

Your assignments will be tested very rigorously: correctness is a theme of this subject,

after all. You are encouraged to test yourself. minhs comes with a regress tester

script, and you should add your own tests to this.

The tests that come with this assignment tarball, which are also run on submission

as a dryrun, cover the base part (the first 70%) of the assignment only. You will be

responsible for testing each extension adequately.

5 Building minhs

minhs (the compiler/interpreter) is written in Haskell, and requires GHC 7.4 or higher,

and the cabal build tool included in the Haskell Platform, or the stack tool that is

also popular for building Haskell projects. If you are using CSE machines, follow

instructions for cabal, however if you are working on your own machine you may

find it more convenient to use stack.

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5.1 Building with cabal on CSE machines

In order to build the assignment, first enter a COMP3161 subshell by typing the following

into a CSE terminal:

$ 3161

All testing will occur on standard CSE Linux machines. Make sure you test your

program on a CSE Linux machine. Once in a COMP3161 subshell, MinHS can be

built with:

• cabal configure to set up the build environment

• cabal build to build the compiler

• ./dist/build/minhs-1/minhs-1 --help will help you find any useful

debugging options.

To run the interpreter:

$ ./dist/build/minhs-1/minhs-1 foo.mhs

You may wish to experiment with some of the debugging options to see, for example,

how your program is parsed, and what abstract syntax is generated.

To run the test driver, a short shell script is provided. For usage information, type:

$ ./run_tests_cabal.sh --help

5.2 Building with stack

You should be able to build the compiler by simply invoking:

$ stack build

To see the debugging options, run (after building):

$ stack exec minhs-1

To run the compiler with a particular file, run:

$ stack exec minhs-1 -- foo.mhs

And to run all of our tests, type:

$ ./run_tests_stack.sh

6 Late Penalty

Unless otherwise stated if you wish to submit an assignment late, you may do so, but

a late penalty reducing the maximum available mark applies to every late assignment.

The maximum available mark is reduced by 10% if the assignment is one day late, by

25% if it is 2 days late and by 50% if it is 3 days late. Assignments that are late 4

days or more will be awarded zero marks. So if your assignment is worth 88% and you

submit it one day late you still get 88%, but if you submit it two days late you get 75%,

three days late 50%, and four days late zero.

Assignment extensions are only awarded for serious and unforeseeable events.

Having the flu for a few days, deleting your assignment by mistake, going on holiday,

work commitments, etc do not qualify. Therefore aim to complete your assignments

well before the due date in case of last minute illness, and make regular backups of

your work.

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7 Plagiarism

Many students do not appear to understand what is regarded as plagiarism. This is

no defense. Before submitting any work you should read and understand the UNSW

plagiarism policy https://student.unsw.edu.au/plagiarism.

All work submitted for assessment must be entirely your own work. We regard

unacknowledged copying of material, in whole or part, as an extremely serious offence.

In this course submission of any work derived from another person, or solely or jointly

written by and or with someone else, without clear and explicit acknowledgement, will

be severely punished and may result in automatic failure for the course and a mark of

zero for the course. Note this includes including unreferenced work from books, the

internet, etc.

Do not provide or show your assessable work to any other person. Allowing another

student to copy from you will, at the very least, result in zero for that assessment. If

you knowingly provide or show your assessment work to another person for any reason,

and work derived from it is subsequently submitted you will be penalized, even if the

work was submitted without your knowledge or consent. This will apply even if your

work is submitted by a third party unknown to you. You should keep your work private

until submissions have closed.

If you are unsure about whether certain activities would constitute plagiarism ask

us before engaging in them!

References

[1] Report on the Programming Language Haskell 98, eds. Simon Peyton Jones, John

Hughes, (1999) http://www.haskell.org/onlinereport/

[2] Robert Harper, Programming Languages: Theory and Practice, (Draft of Jan

2003), http://www-2.cs.cmu.edu/˜rwh/plbook/.

[3] The Implementation of Functional Programming Languages, Simon Peyton

Jones, published by Prentice Hall, 1987. Full text online (as jpg page images).

[4] Simon Peyton-Jones, Implementing Functional Languages : a tutorial, 2000.

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A Lexical Structure

The lexical structure of MinHS is an small subset of Haskell98. See section 2.2 of the

Haskell98 report [1]. The lexical conventions are implemented by the Parsec parser

library, which we use for our Parser implementation.

B Concrete syntax

The concrete syntax is based firstly on Haskell. It provides the usual arithmetic and

boolean primitive operations (most of the Int-type primitive operations of GHC). It

has conventional let bindings. At the outermost scope, the let is optional. As

a result, multiple outer-level bindings are treated as nested let bindings down the

page. It is required that a distinguished main function, of atomic type, exist. There

is an if-then-else conditional expression. The primitive types of MinHS are

Int,Bool and [Int]. MinHS also implements, at least partially, a number of extensions

to MinML: inline comments, n-ary functions, infix notation, more primitive

numerical operations and a non-mutually recursive, simultaneous let declaration

(treated as a nested-let ). Function values may be specified with recfun .

The concrete syntax is described and implemented in the Parser.hs module, a

grammar specified using the Parser combinator library Parsec.

Features of Haskell we do not provide:

• No nested comments

• No layout rule. Thus, semi-colons are required to terminate certain expressions.

Consult the grammar.

C Abstract syntax

The (first-order) abstract syntax is based closely on the MinHs syntax introduced in the

lectures. It is implemented in the file Syntax.hs. Extensions to the MinHs abstract

syntax take their cue from the Haskell kernel language. Presented below is the abstract

syntax, with smatterings of concrete syntax for clarity.

D Static semantics

The static semantics are based on those of the lecture, and of and MinML, from Bob

Harper’s book. They are implemented by the module TypeChecker.hs.

D.1 n-ary functions

Functions may be declared to take more than 1 argument at a time.

E Environments

Environments are required by typechecker and possibly by the interpreter. The typechecker

needs to map variables to types, and the interpreter might need to map variables

to functions or values (like a heap). This latter structure is used to provide a fast

alternative to substitution.

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Types τ → Int | Bool | τ → τ

Literals n → . . . | 0 | 1 | 2 | . . .

b → True | False

Primops o → + | - | * | / | % |

| > | >= | == | /= | < | <=

Expressions exp → Var x

| Lit n

| Con b

| Apply e1 e2

| Let decl exp

| Recfun decl

| If exp exp1 exp2

Decl decl → Fun f τ [arg] e

| Val v τ e

Figure 1: The expression abstract syntax of MinHS

We provide a general environment module, keyed by identifiers, in Env.hs.

Environments are generally simpler in MinHs than in real Haskell. We still need to

bind variables to partially evaluated functions, however.

F Dynamic semantics

The dynamic semantics are described in this document, the lectures, and resemble that

of Harper [2]. Implemented in the module Evaluator.hs.

F.1 Interpreter

The interpreter is the backend that runs by default. It should implement the dynamic

semantics of MinHs.

G Interfaces

The basic types are found in Syntax.hs, which contains definitions for the structure

of terms, types, primOps, and others.

Printing

Most structures in MinHS need to be printed at some point. The easiest way to do this

is to make that type an instance of class Pretty. See Pretty.hs for an example.

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Testing

./run tests cabal.sh

Check directories may have an optional ‘Flag’ file, containing flags you wish to

pass to minhs in that directory, or the magic flag, ‘expect-fail’, which inverts the sense

in which success is defined by the driver.