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CSCI 3171 Network Computing

创建日期：2024-06-25 11:46:32

所属分类：计算机computer science

标签： CSCI 3171

Network Computing

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CSCI 3171 Network Computing

Submission Instructions

This is an individual assignment. Just as with all other homework, submitted work should be your own. Course staff runs plagiarism detectors, and will treat excessive similarities between submissions as evidence of cheating. Submit in Submitty for autograding. Your Haskell file must be named Interpreter.hs. Submitty compiles your Interpreter module using The Glorious Glasgow Haskell Compilation System, version 8.0.2, and links it with various tests that call your functions.

Getting Started with Haskell

Download and install the Glasgow Haskell Compiler: https://www.haskell.org/ghc.

You can run GHC in interactive mode by running ghci from the command line. Type the following functions and save them in a file called fun.hs:

apply_n f n x = if n == 0 then x else apply_n f (n-1) (f x) plus a b = apply_n ((+) 1) b a mult a b = apply_n ((+) a) b 0 expon a b = apply_n ((*) a) b 1

Run ghci then load the file by typing

:l fun.hs

and call these functions, e.g., plus 2 3. You can reload the file after making a change

An Applicative Order Interpreter for the Lambda Calculus

Now, we get to the actual homework. In lecture, we wrote a normal order interpreter for the Lambda Calculus. It terminated when it returned an answer in Weak Head Normal Form. In this problem we will write an applicative order interpreter that yields an answer in Normal Form (i.e., the expression cannot be further reduced).

Problem 1. Applicative order interpreter

Your first task is to write the interpreter in the style we gave in lecture. Please include your answer in comments in your Haskell file under heading Problem 1.

Problem 2. Coding the applicative order interpreter in Haskell

Next, you will code the interpreter in Haskell. A lambda expression is of the following form, as we discussed in class:

data Expr = Var Name --- a variable | App Expr Expr --- function application | Lambda Name Expr --- lambda abstraction deriving (Eq,Show) --- the Expr data type derives from built-in Eq and Show classes, --- thus, we can compare and print expressions type Name = String --- a variable name

You are required to implement the following functions:

Free variables. As a first step, write the function

freeVars :: Expr -> [Name]

It takes an expression expr and returns the list of variables that are free in expr without repetition. For example freeVars (App (Var "x") (Var "x")) yields ["x"].

Generating new names. Next, generate fresh variables for a list of expressions by making use of the infinite list of positive integers [1..]. Write a function

freshVars :: [Expr] -> [Name]

It takes a list of expressions and generates an (infinite) list of variables that are not free in any of the expressions in the list. For example freshVars [Lambda "1_" (App (Var "x") (App (Var "1_") (Var "2_")))]yields the infinite list [1_,3_,4_,5_,..]. Remember, you will leverage [1..] to implement freshVars.

Substitution. Next, write the substitution function

subst :: (Name,Expr) -> Expr -> Expr

All functions in Haskell are curried: i.e., they take just one argument. The above function takes a variable x and an expression e, and returns a function that takes an expression E and returns E[e/x]. Important: subst must implement the algorithm we gave in class! Specifically, when performing a substitution on a lambda expression λy.E1, where y≠x, subst must always replace parameter y with the next fresh variable from the list of freshVars, even if y is not free in e and it would have been “safe” to leave it as is. This is necessary for autograding on Submitty.A single step. Now write a function to do a single step of reduction:

appNF_OneStep :: Expr -> Maybe Expr

where the built-in Maybe type is defined as follows:

data Maybe a = Nothing | Just a

appNF_OneStep takes an expression e. If there is a redex available in e, it picks the correct applicative order redex and reduces e. (Note that in applicative order we are pursuing the leftmost, innermost strategy as follows. Pick the leftmost redex R; if there are nested (inner) redexes within R, pick the leftmost one, and so on, until we reach a redex without nested ones.) If a reduction was carried out, resulting in a new expression expr', appNF_OneStep returns Just expr', otherwise it returns Nothing.

Repetition. Finally, write a function

appNF_n :: Int -> Expr -> Expr

Given an integer n and an expression e, appNF_n does n reductions (or as many as possible) and returns the resulting expression.

Write all functions described above, freeVars, freshVars, subst, appNF_OneStep, and appNF_n and include them in your Interpreter.hs file.
You are allowed to use all features of Haskell and import modules you find useful.
Just as with your Scheme homework, do comment your code! Write comments in the same style although there is one notable difference, namely that in Haskell type signatures are statically checked. Include type signatures for every function you write even though Haskell can infer those signatures.

Notes on grading: This homework is worth a total of 50 points: 40 points will be awarded for functional correctness by the autograder and 10 points will be awarded for quality and completeness of code and comments.

Errata

None yet. Check the Announcements on Submitty regularly.

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COMP532 MAS275 COMP5318 COMP4002 FIT5086 MAST20004 FIT3152 FIT5129 CIS2380 CS521 COMP 1005 EECMS CITS5501 ECE 462 ECON 6002 ENG 4051 CSC 648 CMT654 MECHENG 713 PHYS1002 AMME 2000 FP0060 DDES3200 MECHENG 743 BINF90002 FIT2081 ISYS90081 ELECTENG 722 BUS 360 ECOS3010 BUS2810 ETF2100 ENG2048 STAT5002 COMP2017 CEME 2003 MATS3004 COMP9319 PHYS1001 COMP5349 AMME2261 COMP-381 FIT3173 COSC2757 ENG4025 QBUS2820 COMP9414 MATH2021 EOSC118 MFIN6690 PMATH 321 CSE-141L MATH575A COMPSCI5002 COMP1511 management comp2123 FINS3616 COMP 3331 COMS30034 DTSC 71 AcF 702 AcF702 DTSC71 MAT021 ELE8083 ACFI213 EG-127J 127J FIT5163 FIT2001 ELE00113M CMT310 CS 245 ENGL 1101 MTH6115 EE497 CS 325 Math 124A MTH5130 MBA502 MGT 5380 ARCH 1261 F033800 20LLP109 ELE4009 FINANCIAL COMP3331 Computer ECE4179 20T3 COMP9311 COMP9311 UNSW MFIN6210 ACCT 5930 EE590 ENG2029 ECO100 SIT315 ACCT3610 COMP3600 STK2100 FIT2004 COMP30020 ACTL1101 Stat 101B BANA 200 COSC2473 ENGG1400 AI COMP90043 MMF 1914H PHYS 127 CS584 CIVL2010 ECMT2150 CS 333 CP1406 KIT308 Economics 701 ECON3740 ECE 5759 BFC3340 FINC2012 COMP4500 MATH3871 FIT3080 18-819C Economic ECO202Y5Y PHY100 FINC-780 Econ 100B EC602 IE582 EE450 COMP9517 WRDS 150B ECON 570 LECTURE 2 ECA5101 ECE 4420 ADAD9311 FIT3031 CS 544 MF 703 CS 6140 KIT501 ENGSCI 344 CSC171 IE 332 FINM8007 21S2 COSC 1114 FE545 E471 SIT102 CSC108 MAT301 IAE 101 COP3503 STAT2004 EC 303 CS1026 STAT1203 MATH3171 ISOM5160 IFN657 FIT2014 ACCT2102 DSCI550 STATS 330 ELEC421 COMP3670 QBUS6840 MEES:698B MAST30027 MIET1077 Economics IFT 6758 FIT5122 BUSN5101 CptS 111 HRMT5502 Math2018 PP 312 INFS3200 CZ3005 CSSE1001 SENG 2011 MKTG 553Q BUFN 640 COMP507 ETF5952 DATA 311 ECE4043 BANK3011 finance M3H623544 HW1 INFS 7410 AI6103 STAT3888 INFS3208 ACCT7103 ECOS3013 PSYCH 20B F79MA STAT3006 ENGG952 2X MGSC 7000 ECE4132 MSF 526 MATH 3033 CDS 511 EEEE4120 EEET2465 ECA5103 MATH2070 ELEC3104 BU51019 EEE8147 ENGR20003 COSC 1107 ETF3200 FNCE 435 MSFI 435 ISyE6420 GENG4405 HW ETC5523 IE 7315 MOEC0021 STA 106 ENGG 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BCPM0008 ECN 620 QBUS6830 ECSE-415 ECON5102 MGMT20005 MAT 653 ECO 480 COMP 5/600 CSSE 5600 ME 571 7CCMMS61 CS 550 COMP2865 MATH3075 STATS 506 QTM 220 ISYS2120 FIT5106 STAT 153 MKTG3112 ECON2102 ELE2018 COMP3031 MSIN0010 SCC461 MATH237 CS246 CSC3065 CSE 101 ICTWEB411 COMP9313 ECOS 2025 FN620 MATH11111 MATH 3018 KE1068 FINA 6112 C++ MISM 6202 MSIN0105 CSC8631 MECO6935 COMP4121 ACCT2011 DPBS1150 EEL 3701C F19PL OPM 661 CSE 310 CS918 BIOL30001 ACCT3563 BANK3600 MET CS622 MATH367 ACCT5907 Continuing COMP5048 COMP61021 CS3334 GSOE9210 CSCI-570 COMP 5322 HW 2 ALY-6020 IEOR 4706 DATA 200 EBUS504 CGE12412 COMP4108 7SSMM800 ECMM171P MATE50002 CS225 RS 6003 BH2274 ELEC3111 MAT6669 ECON-UA 227 PHIL 1012 7SSMM603 TB028A P6 ECS708 CSC 427 CS6476 CSE 250A A1A2 ITS61504 EECS 376 model HW6 UV0010 ECON 6074 MG4F7 CMP-7030Y INFO3008 BFIP013 ECON 5068 MATH6002 CS3483 PSTAT 131 C31FM CSOR W4246 AAEC 5307 DATA ELEC362 COMSM0047 ECN6006 MA20224 BST351 MATH 323 MATH323 AA2021 COMP3811 COMP2013 IB9X60 INVP001 EMATM0051 COMP220 BLAW1002 E20 TCP8001 ECON61001 EART40005 ECONM1022 MATH 365 MATH 367 ELEC6218 COMP 5812M EDUC 5061M ELEC ENG 1101 equation MATH6174 ST334 C4 EC9570 A33648 EBUS603 ECON47815 stata WFMS0001 PEM102 INF6060 ionically ELECTRICAL MATH 375 MMW 12 MKTG860 ECON60401 ALY6010 SOST20131 Introduction COM3524 MME2 GGR305 JNB 538 EECS101 COMM5030 IEOR E4601 2B CSC336 EN2315 LAW 432 CSC263 MATH2001 OLET1143 CSCB63 SIT772 COMM1170 STAT 441 MS930 INFT3050 GLBH0030 Stat 120B MAST10007 MGEC61 Machine GGR 252H1S ECON7030 Financial Marketing MGMT30019 ECON5120 SDSC 8009 CSC165H1S DSCI 551 3081W ACM41000 ECA 5304 MATH 1064 ECSE444 DATA 604 COMP7105 MIE1615 ECON4004 ENV200H1S EC481 MKT 306 EC1B1 MATH08051 ALY6140 CS260C CSE30 MSIN0226 CS4103 CSC3064 AM16 COMP11212 CSE4101 PSTAT 174 Math 380W CNT 5106C STAT 310 FIN2028 CS5014 STAT 425 COMP 4102A ELEC2140 MANF9544 QRM 9 QRM 8 ECON 457 COMPSCI 4091 MATH 523 DNSC-4211 PEAS 6000 MSIN0180 COMP2119 A2A HT 2022 IB93F0 MAS316/414 ACCT2522 MSIN0181 ATMS 201 COMP3425 MATH7861 SOLA2060 MA 325 7CCEMCTH ECON 432 INFT2051 SOLA 2060 ECOS2002 Stats141XP BIOA02H3 S2022 MA4601 K5 COMP5329 EG 284 IB3A70 WECO1020 COMP3027 Energy ACS61011 MAST20026 STAT 533 MATA31 ENVS257 BEM2031 EC 486 COMP0172 CS3214 EECE5644 IB2B20 COSC2536 COSC1147 COMP6214 5CCM242A COMP0130 AMME2000 MTMG50: EG238 ACF6006 QBUS2810 COSC2391 ECON7560 MATH377 STA305 CS 486 COMP1117B EL648 ELEC3909 ECON 241 COMP 4901W BUSI4428 ENEN20002 ENGN4524 ELEC3115 CSC 413 PSYC 100B ECON1002 MATH256 ANSC20005 MTHS2008 MATH40082 COSC 2406 FIT3174 STA 238 CMT202 Differential Equations MTHM017 GARCH 101 MATH2069 CSC336S ACSC12 ETF2121 CEME 2001 DB B474F ARHT1001 EECS 3311 3220 STATS 786 CS 484 COMP20008 MATH4091 ECE 455 CSCI 204 BUS B200F BA 875 BU5562 COSC 1147 X11 GEOG 101 IMM250F CSE 584A MATH38172 LAB 4 ELEC5882M FINS5523 EE 430 COMP 465 6CCS3PRE 7CCSMNSE FINANCE ACMB02H3 ENGG2112 ELEC5616 SCM B371 CHEM3120 CS22 ECMT2130 MAST30011 ADSPBF706 CENG0013 ACCOUNTING BUSS1040 CHEM 181 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