Add first draft of Homework 3 (CS325)

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code/cs325-langs/hws/hw1.txt

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+CS 325-001, Analysis of Algorithms, Fall 2019
+HW1 - Python 3, qsort, BST, and qselect
+Due electronically on flip on Monday 9/30 at 11:59pm. 
+No late submission will be accepted.
+
+Need to submit on flip: report.txt, qsort.py, and qselect.py.
+qselect.py will be automatically graded for correctness (1%).
+
+flip $ /nfs/farm/classes/eecs/fall2019/cs325-001/submit hw1 qselect.py qsort.py report.txt
+
+Note:
+
+1. You can ssh to flip machines from your own machine by:
+   $ ssh access.engr.oregonstate.edu
+
+2. You can add /nfs/farm/classes/eecs/fall2019/cs325-001/ to your $PATH:
+   $ export PATH=$PATH:/nfs/farm/classes/eecs/fall2019/cs325-001/
+   and add the above command to your ~/.bash_profile,
+   so that you don't need to type it every time.
+
+   (alternatively, you can use symbolic links or aliases to avoid typing the long path)
+
+3. You can choose to submit each file separately, or submit them together.
+
+Textbooks for References:
+[1] CLRS Ch. 9.2 and Ch. 12
+
+0. Q: What's the best-case, worst-case, and average-case time complexities of quicksort.
+   Briefly explain each case.
+
+1. [WILL BE GRADED] 
+   Quickselect with Randomized Pivot (CLRS Ch. 9.2).
+
+   >>> from qselect import *
+   >>> qselect(2, [3, 10, 4, 7, 19])
+   4
+   >>> qselect(4, [11, 2, 8, 3])
+   11
+
+   Q: What's the best-case, worst-case, and average-case time complexities? Briefly explain.
+
+   Filename: qselect.py
+
+
+2. Buggy Qsort Revisited
+
+   In the slides we showed a buggy version of qsort which is weird in an interesting way:
+   it actually returns a binary search tree for the given array, rooted at the pivot:
+
+   >>> from qsort import *
+   >>> tree = sort([4,2,6,3,5,7,1,9])
+   >>> tree
+   [[[[], 1, []], 2, [[], 3, []]], 4, [[[], 5, []], 6, [[], 7, [[], 9, []]]]]
+
+   which encodes a binary search tree:
+
+                      4
+                    /   \
+                  2       6
+                 / \     / \
+                1   3   5   7
+                             \
+                              9
+   
+   Now on top of that piece of code, add three functions: 
+   * sorted(t): returns the sorted order (infix traversal)
+   * search(t, x): returns whether x is in t
+   * insert(t, x): inserts x into t (in-place) if it is missing, otherwise does nothing.
+
+   >>> sorted(tree)
+   [1, 2, 3, 4, 5, 6, 7, 9]
+   >>> search(tree, 6)
+   True
+   >>> search(tree, 6.5)
+   False
+   >>> insert(tree, 6.5)
+   >>> tree
+   [[[[], 1, []], 2, [[], 3, []]], 4, [[[], 5, []], 6, [[[], 6.5, []], 7, [[], 9, []]]]]
+   >>> insert(tree, 3)
+   >>> tree
+   [[[[], 1, []], 2, [[], 3, []]], 4, [[[], 5, []], 6, [[[], 6.5, []], 7, [[], 9, []]]]]
+
+   Hint: both search and insert should depend on a helper function _search(tree, x) which 
+   returns the subtree (a list) rooted at x when x is found, or the [] where x should 
+   be inserted.
+
+   e.g., 
+   >>> tree = sort([4,2,6,3,5,7,1,9])        # starting from the initial tree
+   >>> _search(tree, 3)
+   [[], 3, []]
+   >>> _search(tree, 0)
+   []
+   >>> _search(tree, 6.5)
+   []
+   >>> _search(tree, 0) is _search(tree, 6.5)
+   False
+   >>> _search(tree, 0) == _search(tree, 6.5)
+   True
+   
+   Note the last two []'s are different nodes (with different memory addresses): 
+   the first one is the left child of 1, while the second one is the left child of 7
+   (so that insert is very easy).
+   
+   Filename: qsort.py
+   
+   Q: What are the time complexities for the operations implemented?
+
+Debriefing (required!): --------------------------
+
+1. Approximately how many hours did you spend on this assignment?
+2. Would you rate it as easy, moderate, or difficult?
+3. Did you work on it mostly alone, or mostly with other people?
+4. How deeply do you feel you understand the material it covers (0%–100%)? 
+5. Any other comments?
+
+This section is intended to help us calibrate the homework assignments. 
+Your answers to this section will *not* affect your grade; however, skipping it
+will certainly do.
+

code/cs325-langs/hws/hw10.txt

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+CS 325, Algorithms (MS/MEng-level), Fall 2019
+
+HW10 - Challenge Problem - RNA Structure Prediction (6%)
+This problem combines dynamic programming and priority queues.
+
+Due Wednesday 12/4, 11:59pm.
+No late submission will be accepted.
+
+Include in your submission: report.txt, rna.py.
+Grading: 
+* report.txt -- 1%
+* 1-best structure -- 2%
+* number of structures -- 1%
+* k-best structures -- 2%
+
+Textbooks for References:
+[1] KT Ch. 6.5 (DP over intervals -- RNA structure)    
+[2] KT slides: DP I (RNA section)
+    http://www.cs.princeton.edu/~wayne/kleinberg-tardos/
+
+***Please analyze time/space complexities for each problem in report.txt.
+
+1. Given an RNA sequence, such as ACAGU, we can predict its secondary structure 
+   by tagging each nucleotide as (, ., or ). Each matching pair of () must be 
+   AU, GC, or GU (or their mirror symmetries: UA, CG, UG). 
+   We also assume pairs can _not_ cross each other. 
+   The following are valid structures for ACAGU:
+
+   ACAGU
+   .....
+   ...()
+   ..(.)
+   .(.).
+   (...)
+   ((.))    
+
+   We want to find the structure with the maximum number of matching pairs. 
+   In the above example, the last structure is optimal (2 pairs). 
+
+   >>> best("ACAGU")
+   (2, '((.))')
+
+   Tie-breaking: arbitrary. Don't worry as long as your structure
+   is one of the correct best structures.
+
+   some other cases (more cases at the bottom):
+
+   GCACG
+   (2, '().()')
+   UUCAGGA
+   (3, '(((.)))')
+   GUUAGAGUCU
+   (4, '(.()((.)))')
+   AUAACCUUAUAGGGCUCUG
+   (8, '.(((..)()()((()))))')
+   AACCGCUGUGUCAAGCCCAUCCUGCCUUGUU
+   (11, '(((.(..(.((.)((...().))()))))))')
+   GAUGCCGUGUAGUCCAAAGACUUCACCGUUGG
+   (14, '.()()(()(()())(((.((.)(.))()))))')
+   CAUCGGGGUCUGAGAUGGCCAUGAAGGGCACGUACUGUUU
+   (18, '(()())(((((.)))()(((())(.(.().()()))))))')
+   ACGGCCAGUAAAGGUCAUAUACGCGGAAUGACAGGUCUAUCUAC
+   (19, '.()(((.)(..))(((.()()(())))(((.)((())))))())')
+   AGGCAUCAAACCCUGCAUGGGAGCACCGCCACUGGCGAUUUUGGUA
+   (20, '.(()())...((((()()))((()(.()(((.)))()())))))()')
+
+2. Total number of all possible structures
+
+   >>> total("ACAGU")
+   6
+
+3. k-best structures: output the 1-best, 2nd-best, ... kth-best structures.
+
+   >>> kbest("ACAGU", 3)
+   [(2, '((.))'), (1, '(...)'), (1, '.(.).')]
+   
+   The list must be sorted. 
+   Tie-breaking: arbitrary.
+
+   In case the input k is bigger than the number of possible structures, output all.
+
+   Sanity check: kbest(s, 1)[0][0] == best(s)[0] for each RNA sequence s.
+
+All three functions should be in one file: rna.py.
+
+See more testcases at the end.
+   
+Debriefing (required!): --------------------------
+
+0. What's your name?
+1. Approximately how many hours did you spend on this assignment?
+2. Would you rate it as easy, moderate, or difficult?
+3. Did you work on it mostly alone, or mostly with other people?
+4. How deeply do you feel you understand the material it covers (0%-100%)? 
+5. Any other comments?
+
+This section is intended to help us calibrate the homework assignments. 
+Your answers to this section will *not* affect your grade; however, skipping it
+will certainly do.
+
+
+TESTCASES:
+
+for each sequence s, we list three lines:
+best(s)
+total(s)
+kbest(s, 10)
+
+
+
+ACAGU
+(2, '((.))')
+6
+[(2, '((.))'), (1, '.(.).'), (1, '..(.)'), (1, '...()'), (1, '(...)'), (0, '.....')]
+------
+AC
+(0, '..')
+1
+[(0, '..')]
+------
+GUAC
+(2, '(())')
+5
+[(2, '(())'), (1, '()..'), (1, '.().'), (1, '(..)'), (0, '....')]
+------
+GCACG
+(2, '().()')
+6
+[(2, '().()'), (1, '(..).'), (1, '()...'), (1, '.(..)'), (1, '...()'), (0, '.....')]
+------
+CCGG
+(2, '(())')
+6
+[(2, '(())'), (1, '(.).'), (1, '.().'), (1, '.(.)'), (1, '(..)'), (0, '....')]
+------
+CCCGGG
+(3, '((()))')
+20
+[(3, '((()))'), (2, '((.)).'), (2, '(.()).'), (2, '.(()).'), (2, '.(().)'), (2, '.((.))'), (2, '((.).)'), (2, '(.(.))'), (2, '(.().)'), (2, '((..))')]
+------
+UUCAGGA
+(3, '(((.)))')
+24
+[(3, '(((.)))'), (2, '((.).).'), (2, '((..)).'), (2, '(.(.)).'), (2, '((.))..'), (2, '.((.)).'), (2, '.((.).)'), (2, '.((..))'), (2, '((..).)'), (2, '((.)..)')]
+------
+AUAACCUA
+(2, '.((...))')
+19
+[(2, '((.)..).'), (2, '(()...).'), (2, '()(...).'), (2, '().(..).'), (2, '()....()'), (2, '.()(..).'), (2, '.()...()'), (2, '.(.)..()'), (2, '.((...))'), (2, '.(.(..))')]
+------
+UUGGACUUG
+(4, '(()((.)))')
+129
+[(4, '(())(.)()'), (4, '(()((.)))'), (3, '(().)..()'), (3, '(().).(.)'), (3, '(().)(..)'), (3, '((.))..()'), (3, '((.)).(.)'), (3, '((.))(..)'), (3, '(())(..).'), (3, '(())(.)..')]
+------
+UUUGGCACUA
+(4, '(.()()(.))')
+179
+[(4, '((()).).()'), (4, '((.)()).()'), (4, '(.()()).()'), (4, '.(()()).()'), (4, '.(()()(.))'), (4, '((()).(.))'), (4, '((.)()(.))'), (4, '((()())..)'), (4, '(.()()(.))'), (3, '((()).)...')]
+------
+GAUGCCGUGUAGUCCAAAGACUUC
+(11, '(((()()((()(.))))((.))))')
+2977987
+[(11, '(()())(((()().))(((.))))'), (11, '(()())(((()()).)(((.))))'), (11, '(()())(((()(.)))(((.))))'), (11, '(()()()((()(.)))(((.))))'), (11, '(((()()((()().)))((.))))'), (11, '(((()()((()(.))))((.))))'), (11, '(()()()((()()).)(((.))))'), (11, '(()()()((()().))(((.))))'), (11, '(((()()((()()).))((.))))'), (10, '(()()()((()().).)((.))).')]
+------
+AGGCAUCAAACCCUGCAUGGGAGCG
+(10, '.(()())...((((()()))).())')
+560580
+[(10, '.(()())...((((())())).)()'), (10, '.(()())...((((()()))).)()'), (10, '.(()())...(((()(()))).)()'), (10, '.(()())...(((()(()))).())'), (10, '.(()())...((((())())).())'), (10, '.(()())...((((()()))).())'), (9, '((.).)(...(.((()()))).)()'), (9, '((.).)(...(((.)(()))).)()'), (9, '((.).)(...(.(()(()))).)()'), (9, '((.).)(...((.(()()))).)()')]
+------

code/cs325-langs/hws/hw11.txt

@@ -0,0 +1,42 @@
+HW11 -- OPTIONAL (for your practice only -- solutions will be released on Tuesday)
+
+Edit Distance (see updated final review solutions)
+
+flip $ /nfs/farm/classes/eecs/fall2019/cs325-001/submit hw11 edit.py
+
+Implement two functions:
+* distance1(s, t): Viterbi-style (either top-down or bottom-up)
+* distance2(s, t): Dijkstra-style (best-first)
+
+For Dijkstra, you can use either heapdict or heapq (see review problem 7).
+Given that this graph is extremely sparse (why?), heapq (ElogE) might be faster than heapdict (ElogV)
+because the latter has overhead for hash.
+
+They should return the same result (just return the edit distance).
+
+We have 10 testcases (listed below); the first 5 test distance1(), 
+and the second 5 test distance2() on the same 5 string pairs.
+
+My solutions (on flip2):
+Testing Case  1 (open)...	  0.001 s, Correct
+Testing Case  2 (open)...	  0.000 s, Correct
+Testing Case  3 (open)...	  0.012 s, Correct
+Testing Case  4 (open)...	  0.155 s, Correct
+Testing Case  5 (open)...	  0.112 s, Correct
+Testing Case  6 (hidden)...	  0.000 s, Correct
+Testing Case  7 (hidden)...	  0.000 s, Correct
+Testing Case  8 (hidden)...	  0.004 s, Correct
+Testing Case  9 (hidden)...	  0.009 s, Correct
+Testing Case 10 (hidden)...	  0.021 s, Correct
+Total Time: 0.316 s
+
+distance1("abcdefh", "abbcdfg") == 3
+distance1("pretty", "prettier") == 3
+distance1("aaaaaaadaaaaaaaaaaaaaaaaacaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa", "aaaaaaaaaaaabaaaaaaaaaaaaaaaaaaaaaaaaaaaaaxaaaaaaaaaaaaaaaaaaaaaa") == 5
+distance1('cpuyedzrwcbritzclzhwwabmlyresvewkdxwkamyzbxtwiqzvokqpkecyywrbvhlqgxzutdjfmvlhsezfbhfjbllmfhzlqlcwibubyyjupbwhztskyksfthkptxqlmhivfjbgclwsombvytdztapwpzmdqfwwrhqsgztobeuiatcwmrzfbwhfnpzzasomrhotoqiwvexlgxsnafiagfewmopdzwanxswfsmbxsmsczbwsgnwy', 'cpuyedzrwcbritzclzhwwabmlyresvewkdxwkamyzbtwiqzvokqpkecyywrbvhlqgxzutdjfmvlhsezfbhfjbllmfhzlqlcwibubyyjupbwhztskyksfthkptxqlmhivfbgclwsombvytdztapwpzmdqfwwrhqsgztobeuiatcwmrzfbwhfnpzzasonrhotoqiwvexlgxsnafiagfewmopdzwanxswfsmbxsmsczbwsgnwy') == 3
+distance1('cpuyedzrwcbritzclzhwwabmlyresvewkdxwkamyzbtwiqzvokqpasdfkecyywrbvhlqgxzutdjfmvlhsezfbhbllmfhzlqlcwibubyyjupbwhztsxyksfthkptxqlmhivfjbgclhombvytdztapwpzmdqfwwrhqsgztobeuiatcwmrzfbwhfnpzzasomrttoqiwvexlgxsnafiagfewmopdzwanxswfsmbxsmsczbwsgnwydmbihjkvziitusmkjljrsbafytsinql', 'cpuyedzrwcbritzclzhwwabmlyresvewkdxwkamyzbtwiqzvokqpkecyywrbvhlqgxzutdjfmvlhsezfbhfjbllmfhzlqlcwibubyyjupbwhztskyksfthkptxqlmhivfjbgclwsombvytdztapwpzmdqfwwrhqsgztobeuiatcwmrzfbwhfnpzzasomrhotoqiwvexlgxsnafiagfewmopdzwanxswfsmbxsmsczbwsgnwydmbihjkvziitusmkjljrsbafytsinql') == 11
+distance2("abcdefh", "abbcdfg") == 3
+distance2("pretty", "prettier") == 3
+distance2("aaaaaaadaaaaaaaaaaaaaaaaacaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa", "aaaaaaaaaaaabaaaaaaaaaaaaaaaaaaaaaaaaaaaaaxaaaaaaaaaaaaaaaaaaaaaa") == 5
+distance2('cpuyedzrwcbritzclzhwwabmlyresvewkdxwkamyzbxtwiqzvokqpkecyywrbvhlqgxzutdjfmvlhsezfbhfjbllmfhzlqlcwibubyyjupbwhztskyksfthkptxqlmhivfjbgclwsombvytdztapwpzmdqfwwrhqsgztobeuiatcwmrzfbwhfnpzzasomrhotoqiwvexlgxsnafiagfewmopdzwanxswfsmbxsmsczbwsgnwy', 'cpuyedzrwcbritzclzhwwabmlyresvewkdxwkamyzbtwiqzvokqpkecyywrbvhlqgxzutdjfmvlhsezfbhfjbllmfhzlqlcwibubyyjupbwhztskyksfthkptxqlmhivfbgclwsombvytdztapwpzmdqfwwrhqsgztobeuiatcwmrzfbwhfnpzzasonrhotoqiwvexlgxsnafiagfewmopdzwanxswfsmbxsmsczbwsgnwy') == 3
+distance2('cpuyedzrwcbritzclzhwwabmlyresvewkdxwkamyzbtwiqzvokqpasdfkecyywrbvhlqgxzutdjfmvlhsezfbhbllmfhzlqlcwibubyyjupbwhztsxyksfthkptxqlmhivfjbgclhombvytdztapwpzmdqfwwrhqsgztobeuiatcwmrzfbwhfnpzzasomrttoqiwvexlgxsnafiagfewmopdzwanxswfsmbxsmsczbwsgnwydmbihjkvziitusmkjljrsbafytsinql', 'cpuyedzrwcbritzclzhwwabmlyresvewkdxwkamyzbtwiqzvokqpkecyywrbvhlqgxzutdjfmvlhsezfbhfjbllmfhzlqlcwibubyyjupbwhztskyksfthkptxqlmhivfjbgclwsombvytdztapwpzmdqfwwrhqsgztobeuiatcwmrzfbwhfnpzzasomrhotoqiwvexlgxsnafiagfewmopdzwanxswfsmbxsmsczbwsgnwydmbihjkvziitusmkjljrsbafytsinql') == 11

code/cs325-langs/hws/hw2.txt

@@ -0,0 +1,80 @@
+CS 325-001, Analysis of Algorithms, Fall 2019
+HW2 - Divide-n-conquer: mergesort, number of inversions, longest path
+
+Due Monday Oct 7, 11:59pm (same submission instructions as HW1).
+No late submission will be accepted.
+
+Need to submit: report.txt, msort.py, inversions.py, and longest.py.
+longest.py will be graded for correctness (1%).
+
+To submit:
+flip $ /nfs/farm/classes/eecs/fall2019/cs325-001/submit hw2 report.txt {msort,inversions,longest}.py
+(You can submit each file separately, or submit them together.)
+
+To see your best results so far:
+flip $ /nfs/farm/classes/eecs/fall2019/cs325-001/query hw2
+
+
+Textbooks for References:
+[1] CLRS Ch. 2
+
+0. Which of the following sorting algorithms are (or can be made) stable?
+   (a) mergesort
+   (b) quicksort with the first element as pivot
+   (c) quicksort with randomized pivot
+   (d) selection sort
+   (e) insertion sort
+   (f) heap sort --- not covered yet (see CLRS Ch. 6)
+
+1. Implement mergesort.
+   
+   >>> mergesort([4, 2, 5, 1, 6, 3])
+   [1, 2, 3, 4, 5, 6]   
+   
+   Filename: msort.py
+   
+2. Calculate the number of inversions in a list.
+
+   >>> num_inversions([4, 1, 3, 2])
+   4
+   >>> num_inversions([2, 4, 1, 3])
+   3
+
+   Filename: inversions.py
+   Must run in O(nlogn) time.
+
+3. [WILL BE GRADED] 
+
+   Length of the longest path in a binary tree (number of edges).
+   
+   We will use the "buggy qsort" representation of binary trees from HW1:
+   [left_subtree, root, right_subtree]
+
+   >>> longest([[], 1, []])
+   0
+
+   >>> longest([[[], 1, []], 2, [[], 3, []]])
+   2
+
+   >>> longest([[[[], 1, []], 2, [[], 3, []]], 4, [[[], 5, []], 6, [[], 7, [[], 9, []]]]])
+   5
+
+   Note the answer is 5 because the longest path is 1-2-4-6-7-9.   
+
+   Filename: longest.py
+   Must run in O(n) time.
+
+Debriefing (required!): --------------------------
+
+1. Approximately how many hours did you spend on this assignment?
+2. Would you rate it as easy, moderate, or difficult?
+3. Did you work on it mostly alone, or mostly with other people?
+   Note you are encouraged to discuss with your classmates, 
+   but each students should submit his/her own code.
+4. How deeply do you feel you understand the material it covers (0%–100%)? 
+5. Any other comments?
+
+This section is intended to help us calibrate the homework assignments. 
+Your answers to this section will *not* affect your grade; however, skipping it
+will certainly do.
+

code/cs325-langs/hws/hw3.txt

@@ -0,0 +1,83 @@
+CS 325, Algorithms, Fall 2019
+HW3 - K closest numbers; Two Pointers
+
+Due Monday Oct 14, 11:59pm. (same submission instructions as HW1-2).
+No late submission will be accepted.
+
+Need to submit: report.txt, closest_unsorted.py, closest_sorted.py, xyz.py.
+closest_sorted.py will be graded for correctness (1%).
+
+To submit:
+flip $ /nfs/farm/classes/eecs/fall2019/cs325-001/submit hw3 report.txt {closest*,xyz}.py
+(You can submit each file separately, or submit them together.)
+
+To see your best results so far:
+flip $ /nfs/farm/classes/eecs/fall2019/cs325-001/query hw3
+
+
+1. Given an array A of n numbers, a query x, and a number k,
+   find the k numbers in A that are closest (in value) to x.
+   For example:
+
+   find([4,1,3,2,7,4], 5.2, 2)	returns   [4,4]
+   find([4,1,3,2,7,4], 6.5, 3)	returns   [4,7,4]
+   find([5,3,4,1,6,3], 3.5, 2)	returns   [3,4]
+
+
+   Filename: closest_unsorted.py
+   Must run in O(n) time. 
+   The elements in the returned list must be in the original order.
+   In case two numbers are equally close to x, choose the earlier one.
+
+
+2. [WILL BE GRADED]
+   Now what if the input array is sorted? Can you do it faster?
+
+   find([1,2,3,4,4,7], 5.2, 2) returns   [4,4]
+   find([1,2,3,4,4,7], 6.5, 3) returns   [4,4,7]
+
+   Filename: closest_sorted.py
+   Must run in O(logn + k) time.
+   The elements in the returned list must be in the original order.
+
+   Note: in case two numbers are equally close to x, choose the smaller one:
+   find([1,2,3,4,4,6,6], 5, 3) returns   [4,4,6]
+   find([1,2,3,4,4,5,6], 4, 5) returns   [2,3,4,4,5]
+
+   Hint: you can use Python's bisect.bisect for binary search.
+
+
+3. For a given array A of n *distinct* numbers, find all triples (x,y,z) 
+   s.t. x + y = z. (x, y, z are distinct numbers)
+
+   e.g.,
+   
+   find([1, 4, 2, 3, 5]) returns [(1,3,4), (1,2,3), (1,4,5), (2,3,5)]
+
+   Note that:
+   1) no duplicates in the input array
+   2) you can choose any arbitrary order for triples in the returned list.
+
+   Filename: xyz.py
+   Must run in O(n^2) time.
+
+   Hint: you can use any built-in sort in Python.
+
+
+Debriefing (required!): --------------------------
+
+0. What's your name?
+1. Approximately how many hours did you spend on this assignment?
+2. Would you rate it as easy, moderate, or difficult?
+3. Did you work on it mostly alone, or mostly with other people?
+   Note you are encouraged to discuss with your classmates, 
+   but each students should submit his/her own code.
+4. How deeply do you feel you understand the material it covers (0%-100%)? 
+
+5. Which part(s) of the course you like the most so far?
+6. Which part(s) of the course you dislike the most so far?
+
+This section is intended to help us calibrate the homework assignments. 
+Your answers to this section will *not* affect your grade; however, skipping it
+will certainly do.
+

code/cs325-langs/hws/hw4.txt

@@ -0,0 +1,114 @@
+CS 325-001, Algorithms, Fall 2019
+HW4 - Priority Queue and Heaps
+
+Due via the submit program on Monday Oct 21, 11:59pm.
+No late submission will be accepted.
+
+Need to submit: report.txt, nbest.py, kmergesort.py, datastream.py.
+datastream.py will be graded for correctness (1%).
+
+To submit:
+flip $ /nfs/farm/classes/eecs/fall2019/cs325-001/submit hw4 report.txt {nbest,kmergesort,datastream}.py
+(You can submit each file separately, or submit them together.)
+
+To see your best results so far:
+flip $ /nfs/farm/classes/eecs/fall2019/cs325-001/query hw4
+
+
+Textbooks for References:
+[1] CLRS Ch. 6
+[2] KT slides for binary heaps (only read the first 20 pages!): 
+    https://www.cs.princeton.edu/~wayne/kleinberg-tardos/pdf/BinomialHeaps.pdf
+[3] Python heapq module 
+
+0. There are two methods for building a heap from an unsorted array:
+   (1) insert each element into the heap  --- O(nlogn) -- heapq.heappush()
+   (2) heapify (top-down)                 --- O(n)     -- heapq.heapify()
+
+   (a) Derive these time complexities.
+   (b) Use a long list of random numbers to show the difference in time. (Hint: random.shuffle or random.sample)
+   (c) What about sorted or reversely-sorted numbers?
+
+1. Given two lists A and B, each with n integers, return
+   a sorted list C that contains the smallest n elements from AxB:
+
+     AxB = { (x, y) | x in A, y in B }
+
+   i.e., AxB is the Cartesian Product of A and B.
+
+   ordering:  (x,y) < (x',y') iff. x+y < x'+y' or (x+y==x'+y' and y<y')
+
+   You need to implement three algorithms and compare:
+
+   (a) enumerate all n^2 pairs, sort, and take top n.
+   (b) enumerate all n^2 pairs, but use qselect from hw1.
+   (c) Dijkstra-style best-first, only enumerate O(n) (at most 2n) pairs.
+       Hint: you can use Python's heapq module for priority queue.
+
+   Q: What are the time complexities of these algorithms? 
+
+   >>> a, b = [4, 1, 5, 3], [2, 6, 3, 4]
+   >>> nbesta(a, b)   # algorithm (a), slowest
+   [(1, 2), (1, 3), (3, 2), (1, 4)]
+   >>> nbestb(a, b)   # algorithm (b), slow
+   [(1, 2), (1, 3), (3, 2), (1, 4)]
+   >>> nbestc(a, b)   # algorithm (c), fast
+   [(1, 2), (1, 3), (3, 2), (1, 4)]
+
+   Filename: nbest.py
+
+2. k-way mergesort (the classical mergesort is a special case where k=2).
+
+   >>> kmergesort([4,1,5,2,6,3,7,0], 3)  # k=3
+   [0,1,2,3,4,5,6,7]
+
+   Q: What is the complexity? Write down the detailed analysis in report.txt.
+
+   Filename: kmergesort.py
+
+3. [WILL BE GRADED]
+   
+   Find the k smallest numbers in a data stream of length n (k<<n),
+   using only O(k) space (the stream itself might be too big to fit in memory).
+
+   >>> ksmallest(4, [10, 2, 9, 3, 7, 8, 11, 5, 7])
+   [2, 3, 5, 7]
+   >>> ksmallest(3, range(1000000, 0, -1))
+   [1, 2, 3]
+
+   Note: 
+   a) it should work with both lists and lazy lists
+   b) the output list should be sorted
+
+   Q: What is your complexity? Write down the detailed analysis in report.txt.
+   
+   Filename: datastream.py
+
+   [UPDATE] The built-in function heapq.nsmallest() is _not_ allowed for this problem.
+   	    The whole point is to implement it yourself. :)
+
+
+4. (optional) Summarize the time complexities of the basic operations (push, pop-min, peak, heapify) for these implementations of priority queue:
+   
+   (a) unsorted array
+   (b) sorted array (highest priority first)
+   (c) reversly sorted array (lowest priority first)
+   (d) linked list
+   (e) binary heap
+
+Debriefing (required!): --------------------------
+
+0. What's your name?
+1. Approximately how many hours did you spend on this assignment?
+2. Would you rate it as easy, moderate, or difficult?
+3. Did you work on it mostly alone, or mostly with other people?
+   Note you are encouraged to discuss with your classmates, 
+   but each students should submit his/her own code.
+4. How deeply do you feel you understand the material it covers (0%-100%)? 
+5. Which part(s) of the course you like the most so far?
+6. Which part(s) of the course you dislike the most so far?
+
+This section is intended to help us calibrate the homework assignments. 
+Your answers to this section will *not* affect your grade; however, skipping it
+will certainly do.
+

code/cs325-langs/hws/hw5.txt

@@ -0,0 +1,130 @@
+CS 532-001, Algorithms, Fall 2019
+HW5 - DP (part 1: simple)
+
+HWs 5-7 are all on DPs.
+
+Due Monday Oct 28, 11:59pm.
+No late submission will be accepted.
+
+Need to submit report.txt, mis.py, bsts.py, bitstrings.py.
+mis.py will be graded for correctness (1%).
+
+To submit:
+flip $ /nfs/farm/classes/eecs/fall2019/cs325-001/submit hw5 report.txt {mis,bsts,bitstrings}.py
+(You can submit each file separately, or submit them together.)
+
+To see your best results so far:
+flip $ /nfs/farm/classes/eecs/fall2019/cs325-001/query hw5
+
+
+Textbooks for References:
+[1] CLRS Ch. 15
+[2] KT Ch. 6
+    or Ch. 5 in a previous version:
+    http://cs.furman.edu/~chealy/cs361/kleinbergbook.pdf   
+
+Hint: Among the three coding questions, p3 is the easiest, and p1 is similar to p3.
+      You'll realize that both are very similar to p0 (Fibonacci).
+      p2 is slightly different from these, but still very easy.
+
+0. (Optional) Is Fibonacci REALLY O(n)?
+   Hint: the value of f(n) itself grows exponentially.	    
+
+1. [WILL BE GRADED]
+   Maximum Weighted Independent Set 
+
+   [HINT] independent set is a set where no two numbers are neighbors in the original list.
+   	  see also https://en.wikipedia.org/wiki/Independent_set_(graph_theory)
+
+   input:  a list of numbers (could be negative)
+   output: a pair of the max sum and the list of numbers chosen
+
+   >>> max_wis([7,8,5])
+   (12, [7,5])
+
+   >>> max_wis([-1,8,10])
+   (10, [10])
+
+   >>> max_wis([])
+   (0, [])
+
+   [HINT] if all numbers are negative, the optimal solution is 0,
+          since [] is an independent set according to the definition above.
+
+   >>> max_wis([-5, -1, -4])
+   (0, [])
+
+   Q: What's the complexity?
+   
+   Include both top-down (max_wis()) and bottom-up (max_wis2()) solutions, 
+   and make sure they produce exact same results. 
+   We'll only grade the top-down version.
+
+   Tie-breaking: any best solution is considered correct.
+
+   Filename: mis.py
+
+   [HINT] you can also use the naive O(2^n) exhaustive search method to verify your answer.
+   
+
+2. Number of n-node BSTs
+
+   input: n
+   output: number of n-node BSTs
+
+   >>> bsts(2)
+   2
+   >>> bsts(3)
+   5
+   >>> bsts(5)
+   42
+
+   [HINT] There are two 2-node BSTs:
+      2    1
+     /      \
+    1        2
+   Note that all other 2-node BSTs are *isomorphic* to either one.
+      
+   Qa: What's the complexity of this DP?
+   
+   Qb: What's the name of this famous number series?
+
+   Feel free to use any implementation style.
+   
+   Filename: bsts.py
+
+3. Number of bit strings of length n that has
+
+   1) no two consecutive 0s.
+   2) two consecutive 0s.
+   
+   >>> num_no(3)
+   5
+   >>> num_yes(3)
+   3
+
+   [HINT] There are three 3-bit 0/1-strings that have two consecutive 0s.
+            001  100  000
+          The other five 3-bit 0/1-strings have no two consecutive 0s:
+	    010  011  101  110  111
+
+   Feel free to choose any implementation style.
+
+   Filename: bitstrings.py
+
+   [HINT] Like problem 1, you can also use the O(2^n) exhaustive search method to verify your answer.
+
+
+Debriefing (required!): --------------------------
+
+0. What's your name?
+1. Approximately how many hours did you spend on this assignment?
+2. Would you rate it as easy, moderate, or difficult?
+3. Did you work on it mostly alone, or mostly with other people?
+4. How deeply do you feel you understand the material it covers (0%-100%)? 
+5. Which part(s) of the course you like the most so far?
+6. Which part(s) of the course you dislike the most so far?
+
+This section is intended to help us calibrate the homework assignments. 
+Your answers to this section will *not* affect your grade; however, skipping it
+will certainly do.

code/cs325-langs/hws/hw6.txt

@@ -0,0 +1,114 @@
+CS 325-001, Algorithms, Fall 2019
+HW6 - DP (part 2)
+
+Due on Monday Nov 4, 11:59pm.
+No late submission will be accepted.
+
+Need to submit: report.txt, knapsack_unbounded.py, knapsack_bounded.py.
+knapsack_bounded.py will be graded for correctness (1%).
+
+To submit:
+flip $ /nfs/farm/classes/eecs/fall2019/cs325-001/submit hw6 report.txt knapsack*.py
+(You can submit each file separately, or submit them together.)
+
+To see your best results so far:
+flip $ /nfs/farm/classes/eecs/fall2019/cs325-001/query hw6
+
+Textbooks for References:
+[1] KT Ch. 6.4
+    or Ch. 5.3 in a previous version:
+    http://cs.furman.edu/~chealy/cs361/kleinbergbook.pdf   
+[2] KT slides for DP (pages 1-37):
+    https://www.cs.princeton.edu/~wayne/kleinberg-tardos/pdf/06DynamicProgrammingI.pdf
+[3] Wikipedia: Knapsack (unbounded and 0/1)
+[4] CLRS Ch. 15
+
+Please answer time/space complexities for each problem in report.txt.
+
+0. For each of the coding problems below:
+   (a) Describe a greedy solution.
+   (b) Show a counterexample to the greedy solution.
+   (c) Define the DP subproblem 
+   (d) Write the recurrence relations
+   (e) Do not forget base cases
+   (f) Analyze the space and time complexities
+
+1. Unbounded Knapsack
+
+   You have n items, each with weight w_i and value v_i, and each has infinite copies.
+   **All numbers are positive integers.**
+   What's the best value for a bag of W?
+
+   >>> best(3, [(2, 4), (3, 5)])
+   (5, [0, 1])
+
+   the input to the best() function is W and a list of pairs (w_i, v_i).
+   this output means to take 0 copies of item 1 and 1 copy of item 2.
+
+   tie-breaking: *reverse* lexicographical: i.e., [1, 0] is better than [0, 1]:
+   (i.e., take as many copies from the first item as possible, etc.)
+
+   >>> best(3, [(1, 5), (1, 5)])
+   (15, [3, 0])
+
+   >>> best(3, [(1, 2), (1, 5)])
+   (15, [0, 3])
+
+   >>> best(3, [(1, 2), (2, 5)])
+   (7, [1, 1])
+
+   >>> best(58, [(5, 9), (9, 18), (6, 12)])
+   (114, [2, 4, 2])
+
+   >>> best(92, [(8, 9), (9, 10), (10, 12), (5, 6)])
+   (109, [1, 1, 7, 1])
+
+   Q: What are the time and space complexities?
+
+   filename: knapsack_unbounded.py
+
+2. [WILL BE GRADED] 
+   Bounded Knapsack
+
+   You have n items, each with weight w_i and value v_i, and has c_i copies.
+   **All numbers are positive integers.**
+   What's the best value for a bag of W?
+
+   >>> best(3, [(2, 4, 2), (3, 5, 3)])
+   (5, [0, 1])
+
+   the input to the best() function is W and a list of triples (w_i, v_i, c_i).
+
+   tie-breaking: same as in p1:
+
+   >>> best(3, [(1, 5, 2), (1, 5, 3)])
+   (15, [2, 1])
+
+   >>> best(3, [(1, 5, 1), (1, 5, 3)])
+   (15, [1, 2])
+
+   >>> best(20, [(1, 10, 6), (3, 15, 4), (2, 10, 3)])
+   (130, [6, 4, 1])
+
+   >>> best(92, [(1, 6, 6), (6, 15, 7), (8, 9, 8), (2, 4, 7), (2, 20, 2)])
+   (236, [6, 7, 3, 7, 2])
+
+   Q: What are the time and space complexities?
+
+   filename: knapsack_bounded.py
+
+   You are encouraged to come up with a few other testcases yourself to test your code!
+   
+Debriefing (required!): --------------------------
+
+0. What's your name?
+1. Approximately how many hours did you spend on this assignment?
+2. Would you rate it as easy, moderate, or difficult?
+3. Did you work on it mostly alone, or mostly with other people?
+4. How deeply do you feel you understand the material it covers (0%-100%)? 
+5. Which part(s) of the course you like the most so far?
+6. Which part(s) of the course you dislike the most so far?
+
+This section is intended to help us calibrate the homework assignments. 
+Your answers to this section will *not* affect your grade; however, skipping it
+will certainly do.

code/cs325-langs/hws/hw8.txt

@@ -0,0 +1,147 @@
+CS 325-001, Algorithms, Fall 2019
+HW8 - Graphs (part I); DP (part III)
+
+Due on Monday November 18, 11:59pm.
+No late submission will be accepted.
+
+Include in your submission: report.txt, topol.py, viterbi.py.
+viterbi.py will be graded for correctness (1%).
+
+To submit:
+flip $ /nfs/farm/classes/eecs/fall2019/cs325-001/submit hw8 report.txt {topol,viterbi}.py
+(You can submit each file separately, or submit them together.)
+
+To see your best results so far:
+flip $ /nfs/farm/classes/eecs/fall2019/cs325-001/query hw8
+
+Textbooks for References:
+[1] CLRS Ch. 23 (Elementary Graph Algorithms)
+[2] KT Ch. 3 (graphs), or Ch. 2 in this earlier version:
+    http://cs.furman.edu/~chealy/cs361/kleinbergbook.pdf
+[3] KT slides (highly recommend!):
+    https://www.cs.princeton.edu/~wayne/kleinberg-tardos/pdf/03Graphs.pdf
+[4] Jeff Erickson: Ch. 5 (Basic Graph Algorithms):
+    http://jeffe.cs.illinois.edu/teaching/algorithms/book/05-graphs.pdf
+[5] DPV Ch. 3, 4.2, 4.4, 4.7 (Dasgupta, Papadimitriou, Vazirani)
+    https://www.cs.berkeley.edu/~vazirani/algorithms/chap3.pdf (decomposition of graphs)
+    https://www.cs.berkeley.edu/~vazirani/algorithms/chap4.pdf (paths, shortest paths)
+[6] my advanced DP tutorial (up to page 16):
+    http://web.engr.oregonstate.edu/~huanlian/slides/COLING-tutorial-anim.pdf
+
+Please answer non-coding questions in report.txt.
+
+0. For the following graphs, decide whether they are
+   (1) directed or undirected, (2) dense or sparse, and (3) cyclic or acyclic:
+
+   (a) Facebook
+   (b) Twitter
+   (c) a family
+   (d) V=airports, E=direct_flights
+   (e) a mesh
+   (f) V=courses, E=prerequisites
+   (g) a tree
+   (h) V=linux_software_packages, E=dependencies
+   (i) DP subproblems for 0-1 knapsack
+
+   Can you name a very big dense graph?
+
+1. Topological Sort
+   
+   For a given directed graph, output a topological order if it exists.
+   
+   Tie-breaking: ARBITRARY tie-breaking. This will make the code 
+   and time complexity analysis a lot easier. 
+
+   e.g., for the following example:
+
+     0 --> 2 --> 3 --> 5 --> 6
+        /    \   |  /    \
+       /      \  v /      \
+     1         > 4         > 7
+
+   >>> order(8, [(0,2), (1,2), (2,3), (2,4), (3,4), (3,5), (4,5), (5,6), (5,7)])
+   [0, 1, 2, 3, 4, 5, 6, 7]
+
+   Note that order() takes two arguments, n and list_of_edges, 
+   where n specifies that the nodes are named 0..(n-1).
+
+   If we flip the (3,4) edge:
+
+   >>> order(8, [(0,2), (1,2), (2,3), (2,4), (4,3), (3,5), (4,5), (5,6), (5,7)])
+   [0, 1, 2, 4, 3, 5, 6, 7]
+
+   If there is a cycle, return None
+
+   >>> order(4, [(0,1), (1,2), (2,1), (2,3)])
+   None
+
+   Other cases:
+
+   >>> order(5, [(0,1), (1,2), (2,3), (3,4)])
+   [0, 1, 2, 3, 4]
+
+   >>> order(5, [])
+   [0, 1, 2, 3, 4]  # could be any order   
+
+   >>> order(3, [(1,2), (2,1)])
+   None
+
+   >>> order(1, [(0,0)]) # self-loop
+   None
+
+   Tie-breaking: arbitrary (any valid topological order is fine).
+   
+   filename: topol.py 
+
+   questions: 
+   (a) did you realize that bottom-up implementations of DP use (implicit) topological orderings?
+       e.g., what is the topological ordering in your (or my) bottom-up bounded knapsack code?
+   (b) what about top-down implementations? what order do they use to traverse the graph?
+   (c) does that suggest there is a top-down solution for topological sort as well? 
+
+2. [WILL BE GRADED]
+   Viterbi Algorithm For Longest Path in DAG (see DPV 4.7, [2], CLRS problem 15-1)
+   
+   Recall that the Viterbi algorithm has just two steps:
+   a) get a topological order (use problem 1 above)
+   b) follow that order, and do either forward or backward updates
+
+   This algorithm captures all DP problems on DAGs, for example,
+   longest path, shortest path, number of paths, etc.
+
+   In this problem, given a DAG (guaranteed acyclic!), output a pair (l, p) 
+   where l is the length of the longest path (number of edges), and p is the path. (you can think of each edge being unit cost)
+
+   e.g., for the above example:
+
+   >>> longest(8, [(0,2), (1,2), (2,3), (2,4), (3,4), (3,5), (4,5), (5,6), (5,7)])
+   (5, [0, 2, 3, 4, 5, 6])
+
+   >>> longest(8, [(0,2), (1,2), (2,3), (2,4), (4,3), (3,5), (4,5), (5,6), (5,7)])
+   (5, [0, 2, 4, 3, 5, 6]) 
+
+   >>> longest(8, [(0,1), (0,2), (1,2), (2,3), (2,4), (4,3), (3,5), (4,5), (5,6), (5,7), (6,7)])
+   (7, [0, 1, 2, 4, 3, 5, 6, 7])  # unique answer
+
+   Note that longest() takes two arguments, n and list_of_edges, 
+   where n specifies that the nodes are named 0..(n-1).
+
+   Tie-breaking: arbitrary. any longest path is fine.   
+
+   Filename: viterbi.py
+
+   Note: you can use this program to solve MIS, knapsacks, coins, etc.
+
+
+Debriefing (required!): --------------------------
+
+0. What's your name?
+1. Approximately how many hours did you spend on this assignment?
+2. Would you rate it as easy, moderate, or difficult?
+3. Did you work on it mostly alone, or mostly with other people?
+4. How deeply do you feel you understand the material it covers (0%-100%)? 
+5. Any other comments?
+
+This section is intended to help us calibrate the homework assignments. 
+Your answers to this section will *not* affect your grade; however, skipping it
+will certainly do.

code/cs325-langs/hws/hw9.txt

@@ -0,0 +1,166 @@
+CS 325, Algorithms, Fall 2019
+HW9 - Graphs (part 2), DP (part 4)
+
+Due Monday Nov 25, 11:59pm. 
+No late submission will be accepted.
+
+Include in your submission: report.txt, dijkstra.py, nbest.py.
+dijkstra.py will be graded for correctness (1%).
+
+Textbooks for References:
+[1] CLRS Ch. 22 (graph)
+[2] my DP tutorial (up to page 16):
+    http://web.engr.oregonstate.edu/~huanlian/slides/COLING-tutorial-anim.pdf
+[3] DPV Ch. 3, 4.2, 4.4, 4.7, 6 (Dasgupta, Papadimitriou, Vazirani)
+    https://www.cs.berkeley.edu/~vazirani/algorithms/chap3.pdf
+    https://www.cs.berkeley.edu/~vazirani/algorithms/chap4.pdf
+    https://www.cs.berkeley.edu/~vazirani/algorithms/chap6.pdf
+[4] KT Ch. 6 (DP)
+    http://www.aw-bc.com/info/kleinberg/assets/downloads/ch6.pdf
+[5] KT slides: Greedy II (Dijkstra)
+    http://www.cs.princeton.edu/~wayne/kleinberg-tardos/
+
+***Please answer time/space complexities for each problem in report.txt.
+
+1. [WILL BE GRADED]
+   Dijkstra (see CLRS 24.3 and DPV 4.4)
+   
+   Given an undirected graph, find the shortest path from source (node 0)
+   to target (node n-1). 
+   
+   Edge weights are guaranteed to be non-negative, since Dijkstra doesn't work
+   with negative weights, e.g.
+ 
+       3
+   0 ------ 1   
+     \    /
+    2 \  / -2
+       \/
+       2
+   
+   in this example, Dijkstra would return length 2 (path 0-2), 
+   but path 0-1-2 is better (length 1).
+
+   For example (return a pair of shortest-distance and shortest-path):
+   
+       1
+   0 ------ 1   
+     \    /  \
+    5 \  /1   \6
+       \/   2  \
+       2 ------ 3
+            
+   >>> shortest(4, [(0,1,1), (0,2,5), (1,2,1), (2,3,2), (1,3,6)])
+   (4, [0,1,2,3])
+
+   If the target node (n-1) is unreachable from the source (0),
+   return None:
+
+   >>> shortest(5, [(0,1,1), (0,2,5), (1,2,1), (2,3,2), (1,3,6)])
+   None
+
+   Another example:
+
+      1          1
+   0-----1    2-----3
+
+   >>> shortest(4, [(0,1,1), (2,3,1)])
+   None
+
+   Tiebreaking: arbitrary. Any shortest path would do.
+
+   Filename: dijkstra.py
+
+   Hint: please use heapdict from here:
+   https://raw.githubusercontent.com/DanielStutzbach/heapdict/master/heapdict.py
+
+   >>> from heapdict import heapdict
+   >>> h = heapdict()
+   >>> h['a'] = 3
+   >>> h['b'] = 1
+   >>> h.peekitem()
+   ('b', 1)
+   >>> h['a'] = 0
+   >>> h.peekitem()
+   ('a', 0)
+   >>> h.popitem()
+   ('a', 0)
+   >>> len(h)
+   1
+   >>> 'a' in h
+   False
+   >>> 'b' in h 
+   True
+
+   You don't need to submit heapdict.py; we have it in our grader.
+
+
+2. [Redo the nbest question from Midterm, preparing for HW10 part 3]
+
+   Given k pairs of lists A_i and B_i (0 <= i < k), each with n sorted numbers,
+   find the n smallest pairs in all the (k n^2) pairs.
+   We say (x,y) < (x', y') if and only if x+y < x'+y'.
+   Tie-breaking: lexicographical (i.e., prefer smaller x).
+
+   You can base your code on the skeleton from the Midterm:
+
+    from heapq import heappush, heappop
+    def nbest(ABs):    # no need to pass in k or n
+        k = len(ABs)
+        n = len(ABs[0][0])
+        def trypush(i, p, q):  # push pair (A_i,p, B_i,q) if possible
+            A, B = ABs[i] # A_i, B_i
+            if p < n and q < n and ______________________________:
+                heappush(h, (________________, i, p, q, (A[p],B[q])))
+                used.add((i, p, q))
+        h, used = ___________________                 # initialize
+        for i in range(k):  # NEED TO OPTIMIZE
+            trypush(______________)
+        for _ in range(n): 
+            _, i, p, q, pair = ________________
+            yield pair     # return the next pair (in a lazy list)
+            _______________________
+            _______________________
+
+
+    But recall we had two optimizations to speed up the first for-loop (queue initialization):
+
+    (1) using heapify instead of k initial pushes. You need to implement this (very easy).
+
+    (2) using qselect to choose top n out of the k bests. This one is OPTIONAL.
+
+    Analyze the time complexity for the version you implemented.
+ 
+    >>> list(nbest([([1,2,4], [2,3,5]), ([0,2,4], [3,4,5])])) 
+
+    [(0, 3), (1, 2), (0, 4)]
+
+    >>> list(nbest([([-1,2],[1,4]), ([0,2],[3,4]), ([0,1],[4,6]), ([-1,2],[1,5])])) 
+    [(-1, 1), (-1, 1)]
+
+    >>> list(nbest([([5,6,10,14],[3,5,10,14]),([2,7,9,11],[3,8,12,16]),([1,3,8,10],[5,9,10,11]),([1,2,3,5],[3,4,9,10]),([4,5,9,10],[2,4,6,11]),([4,6,10,13],[2,3,5,9]),([3,7,10,12],[1,2,5,10]),([5,9,14,15],[4,8,13,14])]))
+
+    [(1, 3), (3, 1), (1, 4), (2, 3)]
+
+    >>> list(nbest([([1,6,8,13],[5,8,11,12]),([1,2,3,5],[5,9,11,13]),([3,5,7,10],[4,6,7,11]),([1,4,7,8],[4,9,11,15]),([4,8,10,13],[4,6,10,11]),([4,8,12,15],[5,10,11,13]),([2,3,4,8],[4,7,11,15]),([4,5,10,15],[5,6,7,8])]))
+
+    [(1, 4), (1, 5), (1, 5), (2, 4)]
+
+    This problem prepares you for the hardest question in HW10 (part 3).
+
+    Filename: nbest.py
+       
+
+
+Debriefing (required!): --------------------------
+
+0. What's your name?
+1. Approximately how many hours did you spend on this assignment?
+2. Would you rate it as easy, moderate, or difficult?
+3. Did you work on it mostly alone, or mostly with other people?
+4. How deeply do you feel you understand the material it covers (0%-100%)? 
+5. Any other comments?
+
+This section is intended to help us calibrate the homework assignments. 
+Your answers to this section will *not* affect your grade; however, skipping it
+will certainly do.

code/cs325-langs/sols/hw1.lang

@@ -0,0 +1,19 @@
+qselect(xs,k) =
+    ~xs -> {
+        pivot <- xs[0]!
+        left <- xs[#0 <= pivot]
+        right <- xs[#0 > pivot]
+    } ->
+        if k > |left| + 1 then qselect(right, k - |left| - 1)
+        else if k == |left| + 1 then [pivot]
+        else qselect(left, k);
+
+_search(xs, k) =
+    if xs[1] == k then xs
+    else if xs[1] > k then _search(xs[0], k)
+    else _search(xs[2], k);
+
+sorted(xs) = sorted(xs[0]) ++ [xs[1]] ++ sorted(xs[2]);
+search(xs, k) = |_search(xs, k)| != 0;
+insert(xs, k) = _insert(k, _search(xs, k));
+_insert(k, xs) = if |xs| == 0 then xs << [] << k << [] else xs

code/cs325-langs/sols/hw2.lang

@@ -0,0 +1,11 @@
+state 0;
+
+effect {
+    if(SOURCE == R) {
+        STATE = STATE + |LEFT|;
+    }
+}
+
+combine {
+    STATE = STATE + LSTATE + RSTATE;
+}

code/cs325-langs/sols/hw3.lang

@@ -0,0 +1,95 @@
+function qselect(xs, k, c) {
+    if xs == [] {
+        return 0;
+    }
+
+    traverser bisector(list: xs, span: (0,len(xs)));
+    traverser pivot(list: xs, random: true);
+
+    let pivotE = pop!(pivot);
+    let (leftList, rightList) = bisect!(bisector, (x) -> c(x) < c(pivotE));
+    
+    if k > len(leftList) + 1 {
+        return qselect(rightList, k - len(leftList) - 1, c);
+    } elsif k == len(leftList) + 1 {
+        return pivotE;
+    } else {
+        return qselect(leftList, k, c);
+    }
+}
+
+function closestUnsorted(xs, k, n) {
+    let min = qselect(list(xs), k, (x) -> abs(x - n));
+    let out = [];
+    let countEqual = k;
+
+    traverser iter(list: xs, span: (0, len(xs)));
+    while valid!(iter) {
+        if abs(at!(iter)-n) < abs(min-n) {
+            let countEqual = countEqual - 1;
+        }
+        step!(iter);
+    }
+
+    traverser iter(list: xs, span: (0, len(xs)));
+    while valid!(iter) {
+        if abs(at!(iter)-n) == abs(min-n) and countEqual > 0 {
+            let countEqual = countEqual - 1;
+            let out = out + [at!(iter)];
+        } elsif abs(at!(iter)-n) < abs(min-n) {
+            let out = out + [at!(iter)];
+        }
+        step!(iter);
+    }
+
+    return out;
+}
+
+function closestSorted(xs, k, n) {
+    let start = bisect(xs, n);
+    let counter = 0;
+    traverser left(list: xs, span: (0, start), reverse: true);
+    traverser right(list: xs, span: (start, len(xs)));
+
+    while counter != k and canstep!(left) and valid!(right) {
+        if abs(at!(left, 1) - n) < abs(at!(right) - n) {
+            step!(left);
+        } else {
+            step!(right);
+        }
+        let counter = counter + 1;
+    }
+
+    while counter != k and (canstep!(left) or valid!(right)) {
+        if canstep!(left) { step!(left); }
+        else { step!(right); }
+        let counter = counter + 1;
+    }
+
+    return subset!(left, right);
+}
+
+sorted function xyz(xs, k) {
+    traverser x(list: xs, span: (0,len(xs)));
+    let dest = [];
+
+    while valid!(x) {
+        traverser z(list: xs, span: (pos!(x)+2,len(xs)));
+        traverser y(list: xs, span: (pos!(x)+1,pos!(z)));
+
+        while valid!(y) and valid!(z) {
+            if at!(x) + at!(y) == at!(z) {
+                let dest = dest + [(at!(x), at!(y), at!(z))];
+                step!(z);
+            } elsif at!(x) + at!(y) > at!(z) {
+                step!(z);
+            } else {
+                step!(y);
+            }
+        }
+
+        step!(x);
+    }
+
+    return dest;
+}

code/cs325-langs/src/Common.hs

@@ -0,0 +1,15 @@
+module Common where
+import PythonAst
+import PythonGen
+import Text.Parsec
+
+compile :: (String -> String -> Either ParseError p) -> (p -> [PyStmt]) -> String -> IO ()
+compile p t f = do
+    let inputName = f ++ ".lang"
+    let outputName = f ++ ".py"
+    file <- readFile inputName
+    let either = p inputName file
+    case either of
+        Right prog -> writeFile outputName (translate $ t prog)
+        Left e -> print e
+

code/cs325-langs/src/CommonParsing.hs

@@ -0,0 +1,90 @@
+module CommonParsing where
+import Data.Char
+import Data.Functor
+import Text.Parsec
+import Text.Parsec.Char
+import Text.Parsec.Combinator
+
+type Parser a b = Parsec String a b
+
+kw :: String -> Parser a ()
+kw s = try $ string s <* spaces $> ()
+
+kwIf :: Parser a ()
+kwIf = kw "if"
+
+kwThen :: Parser a ()
+kwThen = kw "then"
+
+kwElse :: Parser a ()
+kwElse = kw "else"
+
+kwElsif :: Parser a ()
+kwElsif = kw "elsif"
+
+kwWhile :: Parser a ()
+kwWhile = kw "while"
+
+kwState :: Parser a ()
+kwState = kw "state"
+
+kwEffect :: Parser a ()
+kwEffect = kw "effect"
+
+kwCombine :: Parser a ()
+kwCombine = kw "combine"
+
+kwRand :: Parser a ()
+kwRand = kw "rand"
+
+kwFunction :: Parser a ()
+kwFunction = kw "function"
+
+kwSorted :: Parser a ()
+kwSorted = kw "sorted"
+
+kwLet :: Parser a ()
+kwLet = kw "let"
+
+kwTraverser :: Parser a ()
+kwTraverser = kw "traverser"
+
+kwReturn :: Parser a ()
+kwReturn = kw "return"
+
+op :: String -> op -> Parser a op
+op s o = string s $> o
+
+int :: Parser a Int
+int = read <$> (many1 digit <* spaces)
+
+var :: [String] -> Parser a String
+var reserved =
+    do
+        c <- satisfy $ \c -> isLetter c || c == '_'
+        cs <- many (satisfy isLetter <|> digit) <* spaces
+        let name = c:cs
+        if name `elem` reserved
+        then fail "Can't use reserved keyword as identifier"
+        else return name
+
+list :: Char -> Char -> Char -> Parser a b -> Parser a [b]
+list co cc cd pe = surround co cc $ sepBy pe (char cd >> spaces)
+
+surround :: Char -> Char -> Parser a b -> Parser a b
+surround c1 c2 pe =
+    do
+        char c1 >> spaces
+        e <- pe
+        spaces >> char c2 >> spaces
+        return e
+
+level :: (o -> e -> e -> e) -> Parser a o -> Parser a e -> Parser a e
+level c po pe =
+    do
+        e <- pe <* spaces
+        ops <- many $ try $ (flip . c <$> (po <* spaces) <*> pe) <* spaces
+        return $ foldl (flip ($)) e ops
+
+precedence :: (o -> e -> e -> e) -> Parser a e -> [ Parser a o ] -> Parser a e
+precedence = foldl . flip . level

code/cs325-langs/src/LanguageOne.hs

@@ -0,0 +1,393 @@
+module LanguageOne where
+import qualified PythonAst as Py
+import qualified CommonParsing as P
+import Data.Bifunctor
+import Data.Char
+import Data.Functor
+import qualified Data.Map as Map
+import Data.Maybe
+import qualified Data.Set as Set
+import Text.Parsec
+import Text.Parsec.Char
+import Text.Parsec.Combinator
+import Control.Monad.State
+
+{- Data Types -}
+data PossibleType = List | Any deriving Eq
+
+data SelectorMarker = None | Remove
+
+data Op
+    = Add
+    | Subtract
+    | Multiply
+    | Divide
+    | Insert
+    | Concat
+    | LessThan
+    | LessThanEq
+    | GreaterThan
+    | GreaterThanEq 
+    | Equal
+    | NotEqual
+    | And
+    | Or
+
+data Selector = Selector String Expr
+
+data Expr
+    = Var String
+    | IntLiteral Int
+    | ListLiteral [Expr]
+    | Split Expr [Selector] Expr
+    | IfElse Expr Expr Expr
+    | BinOp Op Expr Expr
+    | FunctionCall Expr [Expr]
+    | LengthOf Expr
+    | Random
+    | Access Expr Expr SelectorMarker
+    | Parameter Int
+
+data Function = Function String [String] Expr
+
+data Prog = Prog [Function]
+
+{- Parser -}
+type Parser = Parsec String (Maybe Int)
+
+parseVar :: Parser String
+parseVar = P.var ["if", "then", "else", "var"]
+
+parseThis :: Parser Expr
+parseThis =
+    do
+        char '&'
+        contextNum <- getState
+        spaces
+        return (Var $ "context_" ++ show contextNum)
+
+parseList :: Parser Expr
+parseList = ListLiteral <$>
+    do
+        char '[' >> spaces
+        es <- sepBy parseExpr (char ',' >> spaces)
+        spaces >> char ']' >> spaces
+        return es
+
+parseSplit :: Parser Expr
+parseSplit =
+    do
+        char '~' >> spaces
+        e <- parseExpr
+        spaces >> string "->"
+        spaces >> char '{'
+        contextNum <- getState
+        putState $ return $ 1 + fromMaybe (-1) contextNum
+        es <- many1 (spaces >> parseSelector)
+        putState contextNum
+        spaces >> char '}' >> spaces >> string "->" >> spaces
+        e' <- parseExpr
+        spaces
+        return $ Split e es e'
+
+parseSelectorMarker :: Parser SelectorMarker
+parseSelectorMarker = (char '!' >> return Remove) <|> return None
+
+parseSelector :: Parser Selector
+parseSelector =
+    do
+        name <- parseVar
+        spaces >> string "<-" >> spaces
+        expr <- parseExpr
+        spaces
+        return $ Selector name expr
+
+parseIfElse :: Parser Expr
+parseIfElse =
+    do
+        P.kwIf >> spaces
+        ec <- parseExpr
+        spaces >> P.kwThen >> spaces
+        et <- parseExpr
+        spaces >> P.kwElse >> spaces
+        ee <- parseExpr
+        spaces
+        return $ IfElse ec et ee
+
+parseLength :: Parser Expr
+parseLength =
+    do
+        char '|' >> spaces
+        e <- parseExpr
+        spaces >> char '|' >> spaces
+        return $ LengthOf e
+
+parseParameter :: Parser Expr
+parseParameter =
+    do
+        char '#'
+        d <- digit
+        spaces
+        return $ Parameter $ read [d]
+
+parseParenthesized :: Parser Expr
+parseParenthesized =
+    do
+        char '(' >> spaces
+        e <- parseExpr
+        spaces >> char ')' >> spaces
+        return e
+
+parseBasicExpr :: Parser Expr
+parseBasicExpr = choice
+    [ IntLiteral <$> P.int
+    , parseThis
+    , parseList
+    , parseSplit
+    , parseLength
+    , parseParameter
+    , parseParenthesized
+    , Var <$> try parseVar
+    , P.kwRand $> Random
+    , parseIfElse
+    ] 
+
+parsePostfix :: Parser (Expr -> Expr)
+parsePostfix = parsePostfixAccess <|> parsePostfixCall
+
+parsePostfixAccess :: Parser (Expr -> Expr)
+parsePostfixAccess =
+    do
+        char '[' >> spaces
+        e <- parseExpr
+        spaces >> char ']' >> spaces
+        marker <- parseSelectorMarker
+        spaces
+        return $ \e' -> Access e' e marker
+
+parsePostfixCall :: Parser (Expr -> Expr)
+parsePostfixCall =
+    do
+        char '(' >> spaces
+        es <- sepBy parseExpr (char ',' >> spaces)
+        char ')' >> spaces
+        return $ flip FunctionCall es
+
+parsePostfixedExpr :: Parser Expr
+parsePostfixedExpr =
+    do
+        eb <- parseBasicExpr
+        spaces
+        ps <- many parsePostfix
+        return $ foldl (flip ($)) eb ps
+
+parseExpr :: Parser Expr
+parseExpr = P.precedence BinOp parsePostfixedExpr
+    [ P.op "*" Multiply, P.op "/" Divide
+    , P.op "+" Add, P.op "-" Subtract
+    , P.op "<<" Insert
+    , P.op "++" Concat
+    , try (P.op "<=" LessThanEq) <|> try (P.op ">=" GreaterThanEq) <|>
+        P.op "<" LessThan <|> P.op ">" GreaterThan <|>
+        P.op "==" Equal <|> P.op "!=" NotEqual
+    , P.op "&&" And <|> P.op "||" Or
+    ]
+
+parseFunction :: Parser Function
+parseFunction =
+    do
+        name <- parseVar
+        spaces >> char '(' >> spaces
+        vs <- sepBy parseVar (char ',' >> spaces)
+        spaces >> char ')' >> spaces >> char '=' >> spaces
+        body <- parseExpr
+        spaces
+        return $ Function name vs body
+
+parseProg :: Parser Prog
+parseProg = Prog <$> sepBy1 parseFunction (char ';' >> spaces)
+
+parse :: SourceName -> String -> Either ParseError Prog
+parse = runParser parseProg Nothing 
+
+{- "Type" checker -}
+mergePossibleType :: PossibleType -> PossibleType -> PossibleType
+mergePossibleType List _ = List
+mergePossibleType _ List = List
+mergePossibleType _ _ = Any
+
+getPossibleType :: String -> Expr -> PossibleType
+getPossibleType s (Var s') = if s == s' then List else Any
+getPossibleType _ (ListLiteral _) = List
+getPossibleType s (Split _ _ e) = getPossibleType s e
+getPossibleType s (IfElse i t e) =
+    foldl1 mergePossibleType $ map (getPossibleType s) [i, t, e]
+getPossibleType _ (BinOp Insert _ _) = List
+getPossibleType _ (BinOp Concat _ _) = List
+getPossibleType _ _ = Any
+
+{- Translator -}
+type Translator = Control.Monad.State.State (Map.Map String [String], Int)
+
+currentTemp :: Translator String
+currentTemp = do
+    t <- gets snd
+    return $ "temp" ++ show t
+
+incrementTemp :: Translator String
+incrementTemp = do
+    modify (second (+1))
+    currentTemp
+
+hasLambda :: Expr -> Bool
+hasLambda (ListLiteral es) = any hasLambda es
+hasLambda (Split e ss r) =
+    hasLambda e || any (\(Selector _ e') -> hasLambda e') ss || hasLambda r
+hasLambda (IfElse i t e) = hasLambda i || hasLambda t || hasLambda e
+hasLambda (BinOp o l r) = hasLambda l || hasLambda r
+hasLambda (FunctionCall e es) = any hasLambda $ e : es
+hasLambda (LengthOf e) = hasLambda e
+hasLambda (Access e _ _) = hasLambda e
+hasLambda Parameter{} = True
+hasLambda _ = False
+
+translate :: Prog -> [Py.PyStmt]
+translate p = fst $ runState (translateProg p) (Map.empty, 0)
+
+translateProg :: Prog -> Translator [Py.PyStmt]
+translateProg (Prog fs) = concat <$> traverse translateFunction fs
+
+translateFunction :: Function -> Translator [Py.PyStmt]
+translateFunction (Function n ps ex) = do
+    let createIf p = Py.BinOp Py.Equal (Py.Var p) (Py.ListLiteral [])
+    let createReturn p = Py.IfElse (createIf p) [Py.Return (Py.Var p)] [] Nothing
+    let fastReturn = [createReturn p | p <- take 1 ps, getPossibleType p ex == List]
+    (ss, e) <- translateExpr ex
+    return $ return $ Py.FunctionDef n ps $ fastReturn ++ ss ++ [Py.Return e]
+
+translateSelector :: Selector -> Translator Py.PyStmt
+translateSelector (Selector n e) =
+    let
+        cacheCheck = Py.NotIn (Py.StrLiteral n) (Py.Var "cache")
+        cacheAccess = Py.Access (Py.Var "cache") [Py.StrLiteral n]
+        cacheSet = Py.Assign (Py.AccessPat (Py.Var "cache") [Py.StrLiteral n])
+        body e' = [ Py.IfElse cacheCheck [cacheSet e'] [] Nothing, Py.Return cacheAccess]
+    in
+        do
+            (ss, e') <- translateExpr e
+            vs <- gets fst
+            let callPrereq p = Py.Standalone $ Py.FunctionCall (Py.Var p) []
+            let prereqs = maybe [] (map callPrereq) $ Map.lookup n vs
+            return $ Py.FunctionDef n [] $ ss ++ prereqs ++ body e'
+
+translateExpr :: Expr -> Translator ([Py.PyStmt], Py.PyExpr)
+translateExpr (Var s) = do
+    vs <- gets fst
+    let sVar = Py.Var s
+    let expr = if Map.member s vs then Py.FunctionCall sVar [] else sVar
+    return ([], expr) 
+translateExpr (IntLiteral i) = return ([], Py.IntLiteral i)
+translateExpr (ListLiteral l) = do
+    tl <- mapM translateExpr l
+    return (concatMap fst tl, Py.ListLiteral $ map snd tl)
+translateExpr (Split e ss e') = do
+    vs <- gets fst
+    let cacheAssign = Py.Assign (Py.VarPat "cache") (Py.DictLiteral [])
+    let cacheStmt = [ cacheAssign | Map.size vs == 0 ]
+    let vnames = map (\(Selector n es) -> n) ss
+    let prereqs = snd $ foldl (\(ds, m) (Selector n es) -> (n:ds, Map.insert n ds m)) ([], Map.empty) ss
+    modify $ first $ Map.union prereqs
+    fs <- mapM translateSelector ss
+    (sts, te) <- translateExpr e'
+    modify $ first $ const vs
+    return (cacheStmt ++ fs ++ sts, te)
+translateExpr (IfElse i t e) = do
+    temp <- incrementTemp
+    let tempPat = Py.VarPat temp
+    (ists, ie) <- translateExpr i
+    (tsts, te) <- translateExpr t
+    (ests, ee) <- translateExpr e
+    let thenSts = tsts ++ [Py.Assign tempPat te]
+    let elseSts = ests ++ [Py.Assign tempPat ee]
+    let newIf = Py.IfElse ie thenSts [] $ Just elseSts
+    return (ists ++ [newIf], Py.Var temp)
+translateExpr (BinOp o l r) = do
+    (lsts, le) <- translateExpr l
+    (rsts, re) <- translateExpr r
+    (opsts, oe) <- translateOp o le re
+    return (lsts ++ rsts ++ opsts, oe)
+translateExpr (FunctionCall f ps) = do
+    (fsts, fe) <- translateExpr f
+    tps <- mapM translateExpr ps
+    return (fsts ++ concatMap fst tps, Py.FunctionCall fe $ map snd tps)
+translateExpr (LengthOf e) =
+    second (Py.FunctionCall (Py.Var "len") . return) <$> translateExpr e
+translateExpr (Access e Random m) = do
+    temp <- incrementTemp
+    (sts, ce) <- translateExpr e
+    let lenExpr = Py.FunctionCall (Py.Var "len") [Py.Var temp]
+    let randExpr = Py.FunctionCall (Py.Var "randint") [ Py.IntLiteral 0,  lenExpr ]
+    return (sts, singleAccess ce randExpr m)
+translateExpr (Access c i m) = do
+    (csts, ce) <- translateExpr c
+    (ists, ie) <- translateExpr i
+    temp <- incrementTemp
+    if hasLambda i
+    then return (csts ++ ists ++ [createFilterLambda temp ie m], Py.FunctionCall (Py.Var temp) [ce])
+    else return (csts ++ ists, singleAccess ce ie m)
+translateExpr (Parameter i) = return $ ([], Py.Var $ "arg" ++ show i)
+translateExpr _ = fail "Invalid expression"
+
+singleAccess :: Py.PyExpr -> Py.PyExpr -> SelectorMarker -> Py.PyExpr
+singleAccess c i None = Py.Access c [i]
+singleAccess c i Remove = Py.FunctionCall (Py.Member c "pop") [i]
+
+createFilterLambda :: String -> Py.PyExpr -> SelectorMarker -> Py.PyStmt
+createFilterLambda s e None = Py.FunctionDef s ["arg"]
+    [ Py.Assign (Py.VarPat "out") (Py.ListLiteral [])
+    , Py.For (Py.VarPat "arg0") (Py.Var "arg")
+        [ Py.IfElse e
+            [ Py.Standalone $ Py.FunctionCall (Py.Member (Py.Var "out") "append")
+                [ Py.Var "arg0" ]
+            ]
+            []
+            Nothing
+        ]
+    , Py.Return $ Py.Var "out"
+    ]
+createFilterLambda s e Remove = Py.FunctionDef s ["arg"]
+    [ Py.Assign (Py.VarPat "i") $ Py.IntLiteral 0
+    , Py.Assign (Py.VarPat "out") (Py.ListLiteral [])
+    , Py.While (Py.BinOp Py.LessThan (Py.Var "i") $ Py.FunctionCall (Py.Var "len") [Py.Var "arg"])
+        [ Py.IfElse e
+            [ Py.Standalone $ Py.FunctionCall (Py.Member (Py.Var "out") "append")
+                [ singleAccess (Py.Var "arg") (Py.Var "i") Remove
+                ]
+            ]
+            []
+            Nothing
+        , Py.Assign (Py.VarPat "i") (Py.BinOp Py.Add (Py.Var "i") (Py.IntLiteral 1))
+        ]
+    , Py.Return $ Py.Var "out"
+    ]
+
+translateOp :: Op -> Py.PyExpr -> Py.PyExpr -> Translator ([Py.PyStmt], Py.PyExpr)
+translateOp Add l r = return ([], Py.BinOp Py.Add l r)
+translateOp Subtract l r = return ([], Py.BinOp Py.Subtract l r)
+translateOp Multiply l r = return ([], Py.BinOp Py.Multiply l r)
+translateOp Divide l r = return ([], Py.BinOp Py.Divide l r)
+translateOp LessThan l r = return ([], Py.BinOp Py.LessThan l r)
+translateOp LessThanEq l r = return ([], Py.BinOp Py.LessThanEq l r)
+translateOp GreaterThan l r = return ([], Py.BinOp Py.GreaterThan l r)
+translateOp GreaterThanEq  l r = return ([], Py.BinOp Py.GreaterThanEq  l r)
+translateOp Equal l r = return ([], Py.BinOp Py.Equal l r)
+translateOp NotEqual l r = return ([], Py.BinOp Py.NotEqual l r)
+translateOp And l r = return ([], Py.BinOp Py.And l r)
+translateOp Or l r = return ([], Py.BinOp Py.Or l r)
+translateOp Concat l r = return ([], Py.BinOp Py.Add l r)
+translateOp Insert l r = do
+    temp <- incrementTemp
+    let assignStmt = Py.Assign (Py.VarPat temp) l
+    let appendFunc = Py.Member (Py.Var temp) "append"
+    let insertStmt = Py.Standalone $ Py.FunctionCall appendFunc [r]
+    return ([assignStmt, insertStmt], Py.Var temp)

code/cs325-langs/src/LanguageThree.hs

@@ -0,0 +1,461 @@
+module LanguageThree where
+import qualified CommonParsing as P
+import qualified PythonAst as Py
+import Control.Monad.State
+import Data.Bifunctor
+import Data.Foldable
+import Data.Functor
+import qualified Data.Map as Map
+import Data.Maybe
+import Text.Parsec hiding (State)
+import Text.Parsec.Char
+import Text.Parsec.Combinator
+
+{- Data Types -}
+data Op
+    = Add
+    | Subtract
+    | Multiply
+    | Divide
+    | LessThan
+    | LessThanEqual
+    | GreaterThan
+    | GreaterThanEqual
+    | Equal
+    | NotEqual
+    | And
+    | Or
+
+data Expr
+    = TraverserCall String [Expr]
+    | FunctionCall String [Expr]
+    | BinOp Op Expr Expr
+    | Lambda [String] Expr
+    | Var String
+    | IntLiteral Int
+    | BoolLiteral Bool
+    | ListLiteral [Expr]
+    | TupleLiteral [Expr]
+
+type Branch = (Expr, [Stmt])
+
+data Stmt
+    = IfElse Branch [Branch] [Stmt]
+    | While Branch
+    | Traverser String [(String, Expr)]
+    | Let Pat Expr
+    | Return Expr
+    | Standalone Expr
+
+data Pat
+    = VarPat String
+    | TuplePat [Pat]
+
+data SortedMarker = Sorted | Unsorted deriving Eq
+
+data Function = Function SortedMarker String [String] [Stmt]
+
+data Prog = Prog [Function]
+
+{- Parser -}
+type Parser = Parsec String ()
+
+parseVar :: Parser String
+parseVar = P.var
+    [ "if", "elif", "else"
+    , "while", "let", "traverser"
+    , "function", "sort"
+    , "true", "false"
+    ]
+
+parseBool :: Parser Bool
+parseBool = (string "true" $> True) <|> (string "false" $> False)
+
+parseList :: Parser Expr
+parseList = ListLiteral <$> P.list '[' ']' ',' parseExpr
+
+parseTupleElems :: Parser [Expr]
+parseTupleElems = P.list '(' ')' ',' parseExpr
+
+parseTuple :: Parser Expr
+parseTuple = do
+    es <- parseTupleElems
+    return $ case es of
+        e:[] -> e
+        _ -> TupleLiteral es
+
+parseLambda :: Parser Expr
+parseLambda = try $ do
+    vs <- P.list '(' ')' ',' parseVar
+    string "->" >> spaces
+    Lambda vs <$> parseExpr
+
+parseCall :: Parser Expr
+parseCall = try $ do
+    v <- parseVar
+    choice
+        [ TraverserCall v <$> (char '!' *> parseTupleElems)
+        , FunctionCall v <$> parseTupleElems
+        ]
+
+parseBasic :: Parser Expr
+parseBasic = choice
+    [ IntLiteral <$> P.int
+    , BoolLiteral <$> parseBool
+    , try parseCall
+    , Var <$> parseVar
+    , parseList
+    , parseLambda
+    , parseTuple
+    ]
+
+parseExpr :: Parser Expr
+parseExpr = P.precedence BinOp parseBasic
+    [ P.op "*" Multiply <|> P.op "/" Divide
+    , P.op "+" Add <|> P.op "-" Subtract
+    , P.op "==" Equal <|> P.op "!=" NotEqual <|>
+        try (P.op "<=" LessThanEqual) <|>  P.op "<" LessThan <|>
+        try (P.op ">=" GreaterThanEqual) <|>  P.op ">" GreaterThan
+    , P.op "and" And
+    , P.op "or" Or
+    ]
+
+parseBlock :: Parser [Stmt]
+parseBlock = char '{' >> spaces >> many parseStmt <* char '}' <* spaces
+
+parseBranch :: Parser Branch
+parseBranch = (,) <$> (parseExpr <* spaces) <*> parseBlock
+
+parseIf :: Parser Stmt
+parseIf = do
+    i <- P.kwIf >> parseBranch
+    els <- many (P.kwElsif >> parseBranch)
+    e <- try (P.kwElse >> parseBlock) <|> return []
+    return $ IfElse i els e
+
+parseWhile :: Parser Stmt
+parseWhile = While <$> (P.kwWhile >> parseBranch)
+
+parseTraverser :: Parser Stmt
+parseTraverser = Traverser
+    <$> (P.kwTraverser *> parseVar)
+    <*> (P.list '(' ')' ',' parseKey) <* char ';' <* spaces
+
+parseKey :: Parser (String, Expr)
+parseKey = (,)
+    <$> (parseVar <* spaces <* char ':' <* spaces)
+    <*> parseExpr
+
+parseLet :: Parser Stmt
+parseLet = Let
+    <$> (P.kwLet >> parsePat <* char '=' <* spaces)
+    <*> parseExpr <* char ';' <* spaces
+
+parseReturn :: Parser Stmt
+parseReturn = Return <$> (P.kwReturn >> parseExpr <* char ';' <* spaces)
+
+parsePat :: Parser Pat
+parsePat = (VarPat <$> parseVar) <|> (TuplePat <$> P.list '(' ')' ',' parsePat)
+
+parseStmt :: Parser Stmt
+parseStmt = choice
+    [ parseTraverser
+    , parseLet
+    , parseIf
+    , parseWhile
+    , parseReturn
+    , Standalone <$> (parseExpr <* char ';' <* spaces)
+    ]
+
+parseFunction :: Parser Function
+parseFunction = Function
+    <$> (P.kwSorted $> Sorted <|> return Unsorted)
+    <*> (P.kwFunction >> parseVar)
+    <*> (P.list '(' ')' ',' parseVar)
+    <*> parseBlock
+
+parseProg :: Parser Prog
+parseProg = Prog <$> many parseFunction
+
+parse :: String -> String -> Either ParseError Prog
+parse = runParser parseProg ()
+
+{- Translation -}
+data TraverserBounds = Range Py.PyExpr Py.PyExpr | Random
+
+data TraverserData = TraverserData
+    { list :: Maybe String
+    , bounds :: Maybe TraverserBounds 
+    , rev :: Bool
+    }
+
+data ValidTraverserData = ValidTraverserData
+    { validList :: String
+    , validBounds ::  TraverserBounds
+    , validRev :: Bool
+    }
+
+type Translator = State (Map.Map String ValidTraverserData, [Py.PyStmt], Int)
+
+getScoped :: Translator (Map.Map String ValidTraverserData)
+getScoped = gets (\(m, _, _) -> m)
+
+setScoped :: Map.Map String ValidTraverserData -> Translator ()
+setScoped m = modify (\(_, ss, i) -> (m, ss, i))
+
+scope :: Translator a -> Translator a
+scope m = do
+    s <- getScoped
+    a <- m
+    setScoped s
+    return a
+
+clearTraverser :: String -> Translator ()
+clearTraverser s = modify (\(m, ss, i) -> (Map.delete s m, ss, i))
+
+putTraverser :: String -> ValidTraverserData -> Translator ()
+putTraverser s vtd = modify (\(m, ss, i) -> (Map.insert s vtd m, ss, i))
+
+getTemp :: Translator String
+getTemp = gets $ \(_, _, i) -> "temp" ++ show i
+
+freshTemp :: Translator String
+freshTemp = modify (second (+1)) >> getTemp
+
+emitStatement :: Py.PyStmt -> Translator ()
+emitStatement = modify . first . (:)
+
+collectStatements :: Translator a -> Translator ([Py.PyStmt], a)
+collectStatements t = do
+    modify (first $ const [])
+    a <- t
+    ss <- gets $ \(_, ss, _) -> ss
+    modify (first $ const [])
+    return (ss, a)
+
+withdrawStatements :: Translator (Py.PyStmt) -> Translator [Py.PyStmt]
+withdrawStatements ts =
+    (\(ss, s) -> ss ++ [s]) <$> (collectStatements ts)
+
+requireTraverser :: String -> Translator ValidTraverserData
+requireTraverser s = gets (\(m, _, _) -> Map.lookup s m) >>= handleMaybe
+    where
+        handleMaybe Nothing = fail "Invalid traverser"
+        handleMaybe (Just vtd) = return vtd
+
+traverserIncrement :: Bool -> Py.PyExpr -> Py.PyExpr -> Py.PyExpr
+traverserIncrement rev by e =
+    Py.BinOp op e (Py.BinOp Py.Multiply by (Py.IntLiteral 1))
+    where op = if rev then Py.Subtract else Py.Add
+
+traverserValid :: Py.PyExpr -> ValidTraverserData -> Py.PyExpr
+traverserValid e vtd =
+    case validBounds vtd of
+        Range f t -> 
+            if validRev vtd
+            then Py.BinOp Py.GreaterThanEq e f
+            else Py.BinOp Py.LessThan e t
+        Random -> Py.BoolLiteral True
+
+traverserStep :: String -> ValidTraverserData -> Py.PyStmt
+traverserStep s vtd =
+    case validBounds vtd of
+        Range _ _ -> Py.Assign (Py.VarPat s) $ Py.BinOp op (Py.Var s) (Py.IntLiteral 1)
+            where op = if validRev vtd then Py.Subtract else Py.Add
+        Random -> traverserRandom s $ validList vtd
+
+traverserRandom :: String -> String -> Py.PyStmt
+traverserRandom s l = 
+    Py.Assign (Py.VarPat s) $ Py.FunctionCall (Py.Var "random.randrange")
+        [Py.FunctionCall (Py.Var "len") [Py.Var l]]
+
+hasVar :: String -> Py.PyPat -> Bool
+hasVar s (Py.VarPat s') = s == s'
+hasVar s (Py.TuplePat ps) = any (hasVar s) ps
+hasVar s _ = False
+
+substituteVariable :: String -> Py.PyExpr -> Py.PyExpr -> Py.PyExpr
+substituteVariable s e (Py.BinOp o l r) =
+    Py.BinOp o (substituteVariable s e l) (substituteVariable s e r)
+substituteVariable s e (Py.ListLiteral es) = 
+    Py.ListLiteral $ map (substituteVariable s e) es
+substituteVariable s e (Py.DictLiteral es) =
+    Py.DictLiteral $
+        map (first (substituteVariable s e) . second (substituteVariable s e)) es
+substituteVariable s e (Py.Lambda ps e') =
+    Py.Lambda ps $ if any (hasVar s) ps then substituteVariable s e e' else e'
+substituteVariable s e (Py.Var s')
+    | s == s' = e
+    | otherwise = Py.Var s'
+substituteVariable s e (Py.TupleLiteral es) =
+    Py.TupleLiteral $ map (substituteVariable s e) es
+substituteVariable s e (Py.FunctionCall e' es) =
+    Py.FunctionCall (substituteVariable s e e') $
+        map (substituteVariable s e) es
+substituteVariable s e (Py.Access e' es) =
+    Py.Access (substituteVariable s e e') $
+        map (substituteVariable s e) es
+substituteVariable s e (Py.Ternary i t e') =
+    Py.Ternary (substituteVariable s e i) (substituteVariable s e t)
+        (substituteVariable s e e')
+substituteVariable s e (Py.Member e' m) =
+    Py.Member (substituteVariable s e e') m
+substituteVariable s e (Py.In e1 e2) =
+    Py.In (substituteVariable s e e1) (substituteVariable s e e2)
+substituteVariable s e (Py.NotIn e1 e2) =
+    Py.NotIn (substituteVariable s e e1) (substituteVariable s e e2)
+substituteVariable s e (Py.Slice f t) =
+    Py.Slice (substituteVariable s e <$> f) (substituteVariable s e <$> t)
+
+translateExpr :: Expr -> Translator Py.PyExpr
+translateExpr (TraverserCall "pop" [Var s]) = do
+    l <- validList <$> requireTraverser s
+    return $ Py.FunctionCall (Py.Member (Py.Var l) "pop") [Py.Var s]
+translateExpr (TraverserCall "pos" [Var s]) = do
+    requireTraverser s
+    return $ Py.Var s
+translateExpr (TraverserCall "at" [Var s]) = do
+    l <- validList <$> requireTraverser s
+    return $ Py.Access (Py.Var l) [Py.Var s]
+translateExpr (TraverserCall "at" [Var s, IntLiteral i]) = do
+    vtd <- requireTraverser s
+    return $ Py.Access (Py.Var $ validList vtd)
+        [traverserIncrement (validRev vtd) (Py.IntLiteral i) (Py.Var s)]
+translateExpr (TraverserCall "step" [Var s]) = do
+    vtd <- requireTraverser s
+    emitStatement $ traverserStep s vtd
+    return $ Py.IntLiteral 0
+translateExpr (TraverserCall "canstep" [Var s]) = do
+    vtd <- requireTraverser s
+    return $
+        traverserValid
+            (traverserIncrement (validRev vtd) (Py.IntLiteral 1) (Py.Var s)) vtd
+translateExpr (TraverserCall "valid" [Var s]) = do
+    vtd <- requireTraverser s
+    return $ traverserValid (Py.Var s) vtd
+translateExpr (TraverserCall "subset" [Var s1, Var s2]) = do
+    l1 <- validList <$> requireTraverser s1
+    l2 <- validList <$> requireTraverser s2
+    if l1 == l2
+    then return $ Py.Access (Py.Var l1) [Py.Slice (Just $ Py.Var s1) (Just $ Py.Var s2)]
+    else fail "Incompatible traversers!"
+translateExpr (TraverserCall "bisect" [Var s, Lambda [x] e]) = do
+    vtd <- requireTraverser s
+    newTemp <- freshTemp
+    lambdaExpr <- translateExpr e
+    let access = Py.Access (Py.Var $ validList vtd) [Py.Var s]
+    let translated = substituteVariable x access lambdaExpr
+    let append s = Py.FunctionCall (Py.Member (Py.Var s) "append") [ access ]
+    let bisectStmt = Py.FunctionDef newTemp []
+         [ Py.Nonlocal [s]
+         , Py.Assign (Py.VarPat "l") (Py.ListLiteral [])
+         , Py.Assign (Py.VarPat "r") (Py.ListLiteral [])
+         , Py.While (traverserValid (Py.Var s) vtd)
+            [ Py.IfElse translated
+                [ Py.Standalone $ append "l" ]
+                []
+                (Just [ Py.Standalone $ append "r" ])
+            , traverserStep s vtd
+            ]
+         , Py.Return $ Py.TupleLiteral [Py.Var "l", Py.Var "r"]
+         ]
+    emitStatement bisectStmt
+    return $ Py.FunctionCall (Py.Var newTemp) []
+translateExpr (TraverserCall _ _) = fail "Invalid traverser operation"
+translateExpr (FunctionCall f ps) = do
+    pes <- mapM translateExpr ps
+    return $ Py.FunctionCall (Py.Var f) pes 
+translateExpr (BinOp o l r) =
+    Py.BinOp (translateOp o) <$> translateExpr l <*> translateExpr r
+translateExpr (Lambda ps e) =
+    Py.Lambda (map Py.VarPat ps) <$> translateExpr e
+translateExpr (Var s) = return $ Py.Var s
+translateExpr (IntLiteral i) = return $ Py.IntLiteral i
+translateExpr (BoolLiteral b) = return $ Py.BoolLiteral b
+translateExpr (ListLiteral es) = Py.ListLiteral <$> mapM translateExpr es
+translateExpr (TupleLiteral es) = Py.TupleLiteral <$> mapM translateExpr es
+
+applyOption :: TraverserData -> (String, Py.PyExpr) -> Maybe TraverserData
+applyOption td ("list", Py.Var s) =
+    return $ td { list = Just s }
+applyOption td ("span", Py.TupleLiteral [f, t]) =
+    return $ td { bounds = Just $ Range f t }
+applyOption td ("random", Py.BoolLiteral True) =
+    return $ td { bounds = Just Random }
+applyOption td ("reverse", Py.BoolLiteral b) =
+    return $ td { rev = b }
+applyOption td _ = Nothing
+
+translateOption :: (String, Expr) -> Translator (String, Py.PyExpr)
+translateOption (s, e) = (,) s <$> translateExpr e
+
+defaultTraverser :: TraverserData
+defaultTraverser =
+    TraverserData { list = Nothing, bounds = Nothing, rev = False }
+
+translateBranch :: Branch -> Translator (Py.PyExpr, [Py.PyStmt])
+translateBranch (e, s) = (,) <$> translateExpr e <*>
+    (concat <$> mapM (withdrawStatements . translateStmt) s)
+
+translateStmt :: Stmt -> Translator Py.PyStmt
+translateStmt (IfElse i els e) = uncurry Py.IfElse
+    <$> (translateBranch i) <*> (mapM translateBranch els) <*> convertElse e
+    where
+        convertElse [] = return Nothing
+        convertElse es = Just . concat <$>
+            mapM (withdrawStatements . translateStmt) es
+translateStmt (While b) = uncurry Py.While <$> translateBranch b
+translateStmt (Traverser s os) =
+    foldlM applyOption defaultTraverser <$> mapM translateOption os >>= saveTraverser 
+    where
+        saveTraverser :: Maybe TraverserData -> Translator Py.PyStmt
+        saveTraverser (Just (td@TraverserData { list = Just l, bounds = Just bs})) =
+            putTraverser s vtd $> translateInitialBounds s vtd
+            where
+                vtd = ValidTraverserData
+                    { validList = l
+                    , validBounds = bs
+                    , validRev = rev td
+                    }
+        saveTraverser Nothing = fail "Invalid traverser (!)"
+translateStmt (Let p e) = Py.Assign <$> translatePat p <*> translateExpr e
+translateStmt (Return e) = Py.Return <$> translateExpr e
+translateStmt (Standalone e) = Py.Standalone <$> translateExpr e
+
+translateInitialBounds :: String -> ValidTraverserData -> Py.PyStmt
+translateInitialBounds s vtd =
+    case (validBounds vtd, validRev vtd) of
+        (Random, _) -> traverserRandom s $ validList vtd
+        (Range l _, False) -> Py.Assign (Py.VarPat s) l
+        (Range _ r, True) -> Py.Assign (Py.VarPat s) r
+
+translatePat :: Pat -> Translator Py.PyPat
+translatePat (VarPat s) = clearTraverser s $> Py.VarPat s
+translatePat (TuplePat ts) = Py.TuplePat <$> mapM translatePat ts
+
+translateOp :: Op -> Py.PyBinOp
+translateOp Add = Py.Add
+translateOp Subtract = Py.Subtract
+translateOp Multiply = Py.Multiply
+translateOp Divide = Py.Divide
+translateOp LessThan = Py.LessThan
+translateOp LessThanEqual = Py.LessThanEq
+translateOp GreaterThan = Py.GreaterThan
+translateOp GreaterThanEqual = Py.GreaterThanEq
+translateOp Equal = Py.Equal
+translateOp NotEqual = Py.NotEqual
+translateOp And = Py.And
+translateOp Or = Py.Or
+
+translateFunction :: Function -> [Py.PyStmt]
+translateFunction (Function m s ps ss) = return $ Py.FunctionDef s ps $
+    [ Py.Standalone $ Py.FunctionCall (Py.Member (Py.Var p) "sort") []
+        | p <- take 1 ps, m == Sorted ] ++ stmts
+    where
+        stmts = concat $ evalState
+            (mapM (withdrawStatements . translateStmt) ss) (Map.empty, [], 0)
+
+translate :: Prog -> [Py.PyStmt]
+translate (Prog fs) =
+    (Py.FromImport "bisect" ["bisect"]) :
+    (Py.Import "random") : concatMap translateFunction fs

code/cs325-langs/src/LanguageTwo.hs

@@ -0,0 +1,198 @@
+module LanguageTwo where
+import qualified PythonAst as Py
+import qualified CommonParsing as P
+import Data.Char
+import Data.Functor
+import Text.Parsec
+import Text.Parsec.Char
+import Text.Parsec.Combinator
+
+{- Data Types -}
+data Op
+    = Add
+    | Subtract
+    | Multiply
+    | Divide
+    | Equal
+    | NotEqual
+    | And
+    | Or
+
+data Expr
+    = IntLiteral Int
+    | BinOp Op Expr Expr
+    | Var String
+    | Length Expr
+
+data Stmt
+    = IfElse Expr Stmt (Maybe Stmt)
+    | Assign String Expr
+    | Block [Stmt]
+
+data Prog = Prog Expr [Stmt] [Stmt]
+
+{- Parser -}
+type Parser = Parsec String ()
+
+parseVar :: Parser String
+parseVar = P.var [ "if", "else", "state", "effect", "combine" ]
+
+parseLength :: Parser Expr
+parseLength = Length <$> P.surround '|' '|' parseExpr
+
+parseParenthesized :: Parser Expr
+parseParenthesized = P.surround '(' ')' parseExpr
+
+parseBasic :: Parser Expr
+parseBasic = choice
+    [ IntLiteral <$> P.int
+    , Var <$> parseVar
+    , parseLength
+    , parseParenthesized
+    ]
+
+
+parseExpr :: Parser Expr
+parseExpr = P.precedence BinOp parseBasic
+    [ P.op "*" Multiply <|> P.op "/" Divide
+    , P.op "+" Add <|> P.op "-" Subtract
+    , P.op "==" Equal <|> P.op "!=" NotEqual
+    , P.op "&&" And
+    , try $ P.op "||" Or
+    ]
+
+parseIf :: Parser Stmt
+parseIf = do
+    P.kwIf >> spaces
+    c <- parseParenthesized
+    t <- parseStmt <* spaces
+    e <- (Just <$> (P.kwElse >> spaces *> parseStmt)) <|> return Nothing
+    return $ IfElse c t e
+
+parseBlockStmts :: Parser [Stmt]
+parseBlockStmts = P.surround '{' '}' (many parseStmt)
+
+parseBlock :: Parser Stmt
+parseBlock = Block <$> parseBlockStmts
+
+parseAssign :: Parser Stmt
+parseAssign = Assign <$>
+    (parseVar <* char '=' <* spaces) <*>
+    parseExpr <* (char ';' >> spaces)
+
+parseStmt :: Parser Stmt
+parseStmt = choice
+    [ parseIf
+    , parseAssign
+    , parseBlock
+    ]
+
+parseProgram :: Parser Prog
+parseProgram = do
+    state <- P.kwState >> spaces *> parseExpr <* char ';' <* spaces
+    effect <- P.kwEffect >> spaces *> parseBlockStmts <* spaces
+    combined <- P.kwCombine >> spaces *> parseBlockStmts <* spaces
+    return $ Prog state effect combined
+
+parse :: String -> String -> Either ParseError Prog
+parse = runParser parseProgram ()
+
+{- Translation -}
+baseFunction :: Py.PyExpr -> [Py.PyStmt] -> [Py.PyStmt] -> Py.PyStmt
+baseFunction s e c = Py.FunctionDef "prog" ["xs"] $
+    [Py.IfElse
+        (Py.BinOp Py.LessThan
+            (Py.FunctionCall (Py.Var "len") [Py.Var "xs"])
+            (Py.IntLiteral 2))
+        [Py.Return $ Py.Tuple [s, Py.Var "xs"]]
+        []
+        Nothing
+    , Py.Assign (Py.VarPat "leng")
+        (Py.BinOp Py.FloorDiv
+            (Py.FunctionCall (Py.Var "len") [Py.Var "xs"]) 
+            (Py.IntLiteral 2))
+    , Py.Assign (Py.VarPat "left")
+        (Py.Access
+            (Py.Var "xs") 
+            [Py.Slice Nothing $ Just (Py.Var "leng")])
+    , Py.Assign (Py.VarPat "right")
+        (Py.Access
+            (Py.Var "xs") 
+            [Py.Slice (Just (Py.Var "leng")) Nothing])
+    , Py.Assign (Py.TuplePat [Py.VarPat "ls", Py.VarPat "left"])
+        (Py.FunctionCall (Py.Var "prog") [Py.Var "left"])
+    , Py.Assign (Py.TuplePat [Py.VarPat "rs", Py.VarPat "right"])
+        (Py.FunctionCall (Py.Var "prog") [Py.Var "right"])
+    , Py.Standalone $
+        Py.FunctionCall (Py.Member (Py.Var "left") "reverse") []
+    , Py.Standalone $
+        Py.FunctionCall (Py.Member (Py.Var "right") "reverse") []
+    , Py.Assign (Py.VarPat "state") s
+    , Py.Assign (Py.VarPat "source") (Py.IntLiteral 0)
+    , Py.Assign (Py.VarPat "total") (Py.ListLiteral [])
+    , Py.While
+        (Py.BinOp Py.And
+            (Py.BinOp Py.NotEqual (Py.Var "left") (Py.ListLiteral []))
+            (Py.BinOp Py.NotEqual (Py.Var "right") (Py.ListLiteral []))) $
+        [ Py.IfElse
+            (Py.BinOp Py.LessThanEq
+                (Py.Access (Py.Var "left") [Py.IntLiteral $ -1])
+                (Py.Access (Py.Var "right") [Py.IntLiteral $ -1]))
+            [ Py.Standalone $
+                Py.FunctionCall (Py.Member (Py.Var "total") "append")
+                    [Py.FunctionCall (Py.Member (Py.Var "left") "pop") []]
+            , Py.Assign (Py.VarPat "source") (Py.IntLiteral 1)
+            ]
+            [] $
+            Just
+            [ Py.Standalone $
+                Py.FunctionCall (Py.Member (Py.Var "total") "append")
+                    [Py.FunctionCall (Py.Member (Py.Var "right") "pop") []]
+            , Py.Assign (Py.VarPat "source") (Py.IntLiteral 2)
+            ]
+        ] ++ e
+    ] ++ c ++
+    [ Py.Standalone $ Py.FunctionCall (Py.Member (Py.Var "left") "reverse") []
+    , Py.Standalone $ Py.FunctionCall (Py.Member (Py.Var "right") "reverse") []
+    , Py.Return $ Py.Tuple
+        [ Py.Var "state"
+        , foldl (Py.BinOp Py.Add) (Py.Var "total") [Py.Var "left", Py.Var "right"]
+        ]
+    ]
+
+translateExpr :: Expr -> Py.PyExpr
+translateExpr (IntLiteral i) = Py.IntLiteral i
+translateExpr (BinOp op l r) =
+    Py.BinOp (translateOp op) (translateExpr l) (translateExpr r)
+translateExpr (Var s)
+    | s == "SOURCE" = Py.Var "source"
+    | s == "LEFT" = Py.Var "left"
+    | s == "RIGHT" = Py.Var "right"
+    | s == "STATE" = Py.Var "state"
+    | s == "LSTATE" = Py.Var "ls"
+    | s == "RSTATE" = Py.Var "rs"
+    | s == "L" = Py.IntLiteral 1
+    | s == "R" = Py.IntLiteral 2
+    | otherwise = Py.Var s
+translateExpr (Length e) = Py.FunctionCall (Py.Var "len") [translateExpr e]
+
+translateOp :: Op -> Py.PyBinOp
+translateOp Add = Py.Add
+translateOp Subtract = Py.Subtract
+translateOp Multiply = Py.Multiply
+translateOp Divide = Py.Divide
+translateOp Equal = Py.Equal
+translateOp NotEqual = Py.NotEqual
+translateOp And = Py.And
+translateOp Or = Py.Or
+
+translateStmt :: Stmt -> [Py.PyStmt]
+translateStmt (IfElse c t e) =
+    [Py.IfElse (translateExpr c) (translateStmt t) [] (translateStmt <$> e)]
+translateStmt (Assign "STATE" e) = [Py.Assign (Py.VarPat "state") (translateExpr e)]
+translateStmt (Assign v e) = [Py.Assign (Py.VarPat v) (translateExpr e)]
+translateStmt (Block s) = concatMap translateStmt s
+
+translate :: Prog -> [Py.PyStmt]
+translate (Prog s e c) =
+    [baseFunction (translateExpr s) (concatMap translateStmt e) (concatMap translateStmt c)]

code/cs325-langs/src/PythonAst.hs

@@ -0,0 +1,52 @@
+module PythonAst where
+
+data PyBinOp
+    = Add
+    | Subtract
+    | Multiply
+    | Divide
+    | FloorDiv
+    | LessThan
+    | LessThanEq
+    | GreaterThan
+    | GreaterThanEq 
+    | Equal
+    | NotEqual
+    | And
+    | Or
+
+data PyExpr
+    = BinOp PyBinOp PyExpr PyExpr
+    | IntLiteral Int
+    | StrLiteral String
+    | BoolLiteral Bool
+    | ListLiteral [PyExpr]
+    | DictLiteral [(PyExpr, PyExpr)]
+    | Lambda [PyPat] PyExpr
+    | Var String
+    | TupleLiteral [PyExpr]
+    | FunctionCall PyExpr [PyExpr]
+    | Access PyExpr [PyExpr]
+    | Ternary PyExpr PyExpr PyExpr
+    | Member PyExpr String
+    | In PyExpr PyExpr
+    | NotIn PyExpr PyExpr
+    | Slice (Maybe PyExpr) (Maybe PyExpr)
+
+data PyPat
+    = VarPat String
+    | IgnorePat
+    | TuplePat [PyPat]
+    | AccessPat PyExpr [PyExpr]
+
+data PyStmt
+    = Assign PyPat PyExpr
+    | IfElse PyExpr [PyStmt] [(PyExpr, [PyStmt])] (Maybe [PyStmt])
+    | While PyExpr [PyStmt]
+    | For PyPat PyExpr [PyStmt]
+    | FunctionDef String [String] [PyStmt]
+    | Return PyExpr
+    | Standalone PyExpr
+    | Import String
+    | FromImport String [String]
+    | Nonlocal [String]

code/cs325-langs/src/PythonGen.hs

@@ -0,0 +1,142 @@
+module PythonGen where
+import PythonAst
+import Data.List
+import Data.Bifunctor
+import Data.Maybe
+
+indent :: String -> String
+indent = ("    " ++)
+
+stmtBlock :: [PyStmt] -> [String]
+stmtBlock = concatMap translateStmt
+
+block :: String -> [String] -> [String]
+block s ss = (s ++ ":") : map indent ss
+
+prefix :: String -> PyExpr -> [PyStmt] -> [String]
+prefix s e sts = block (s ++ " " ++ translateExpr e) $ stmtBlock sts
+
+if_ :: PyExpr -> [PyStmt] -> [String]
+if_ = prefix "if"
+
+elif :: PyExpr -> [PyStmt] -> [String]
+elif = prefix "elif"
+
+else_ :: [PyStmt] -> [String]
+else_ = block "else" . stmtBlock
+
+while :: PyExpr -> [PyStmt] -> [String]
+while = prefix "while"
+
+parenth :: String -> String
+parenth s = "(" ++ s ++ ")"
+
+translateStmt :: PyStmt -> [String]
+translateStmt (Assign p e) = [translatePat p ++ " = " ++ translateExpr e]
+translateStmt (IfElse i t es e) =
+    if_ i t ++ concatMap (uncurry elif) es ++ maybe [] else_ e
+translateStmt (While c t) = while c t
+translateStmt (For x in_ b) = block head body
+    where
+        head = "for " ++ translatePat x ++ " in " ++ translateExpr in_
+        body = stmtBlock b
+translateStmt (FunctionDef s ps b) = block head body
+    where
+        head = "def " ++ s ++ "(" ++ intercalate "," ps ++ ")"
+        body = stmtBlock b
+translateStmt (Return e) = ["return " ++ translateExpr e]
+translateStmt (Standalone e) = [translateExpr e]
+translateStmt (Import s) = ["import " ++ s]
+translateStmt (FromImport s ss) =
+    ["from " ++ s ++ " import " ++ intercalate "," ss]
+translateStmt (Nonlocal vs) = 
+    ["nonlocal " ++ intercalate "," vs]
+
+precedence :: PyBinOp -> Int
+precedence Add = 3
+precedence Subtract = 3
+precedence Multiply = 4
+precedence Divide = 4
+precedence FloorDiv = 4
+precedence LessThan = 2
+precedence LessThanEq = 2
+precedence GreaterThan = 2
+precedence GreaterThanEq = 2
+precedence Equal = 2
+precedence NotEqual = 2
+precedence And = 1
+precedence Or = 0
+
+opString :: PyBinOp -> String
+opString Add = "+"
+opString Subtract = "-"
+opString Multiply = "*"
+opString Divide = "/"
+opString FloorDiv = "//"
+opString LessThan = "<"
+opString LessThanEq = "<="
+opString GreaterThan = ">"
+opString GreaterThanEq = ">="
+opString Equal = "=="
+opString NotEqual = "!="
+opString And = " and "
+opString Or = " or "
+
+translateOp :: PyBinOp -> PyBinOp -> PyExpr -> String
+translateOp o o' =
+    if precedence o > precedence o'
+    then parenth . translateExpr
+    else translateExpr
+
+dictMapping :: PyExpr -> PyExpr -> String
+dictMapping f t = translateExpr f ++ ": " ++ translateExpr t
+
+list :: String -> String -> [PyExpr] -> String
+list o c es = o ++ intercalate ", " (map translateExpr es) ++ c
+
+translateExpr :: PyExpr -> String
+translateExpr (BinOp o l@(BinOp o1 _ _) r@(BinOp o2 _ _)) =
+    translateOp o o1 l ++ opString o ++ translateOp o o2 r
+translateExpr (BinOp o l@(BinOp o1 _ _) r) =
+    translateOp o o1 l ++ opString o ++ translateExpr r
+translateExpr (BinOp o l r@(BinOp o2 _ _)) =
+    translateExpr l ++ opString o ++ translateOp o o2 r
+translateExpr (BinOp o l r) =
+    translateExpr l ++ opString o ++ translateExpr r
+translateExpr (IntLiteral i) = show i
+translateExpr (StrLiteral s) = "\"" ++ s ++ "\""
+translateExpr (BoolLiteral b) = if b then "true" else "false"
+translateExpr (ListLiteral l) = list "[" "]" l
+translateExpr (DictLiteral l) =
+    "{" ++ intercalate ", " (map (uncurry dictMapping) l) ++ "}"
+translateExpr (Lambda ps e) = parenth (head ++ ": " ++ body)
+    where
+        head = "lambda " ++ intercalate ", " (map translatePat ps)
+        body = translateExpr e
+translateExpr (Var s) = s
+translateExpr (TupleLiteral es) = list "(" ")" es
+translateExpr (FunctionCall f ps) = translateExpr f ++ list "(" ")" ps
+translateExpr (Access (Var s) e) = s ++ list "[" "]" e
+translateExpr (Access e@Access{} i) = translateExpr e ++ list "[" "]" i
+translateExpr (Access e i) = "(" ++ translateExpr e ++ ")" ++ list "[" "]" i
+translateExpr (Ternary c t e) =
+    translateExpr t ++ " if " ++ translateExpr c ++ " else " ++ translateExpr e
+translateExpr (Member (Var s) m) = s ++ "." ++ m
+translateExpr (Member e@Member{} m) = translateExpr e ++ "." ++ m
+translateExpr (Member e m) = "(" ++ translateExpr e ++ ")." ++ m
+translateExpr (In m c) =
+    "(" ++ translateExpr m ++ ") in (" ++ translateExpr c ++ ")"
+translateExpr (NotIn m c) =
+    "(" ++ translateExpr m ++ ") not in (" ++ translateExpr c ++ ")"
+translateExpr (Slice l r) =
+    maybe [] (parenth . translateExpr) l ++ ":" ++ maybe [] (parenth . translateExpr) r
+
+translatePat :: PyPat -> String
+translatePat (VarPat s) = s
+translatePat IgnorePat = "_"
+translatePat (TuplePat ps) =
+    "(" ++ intercalate "," (map translatePat ps) ++ ")"
+translatePat (AccessPat e es) = translateExpr (Access e es)
+
+translate :: [PyStmt] -> String
+translate = intercalate "\n" . concatMap translateStmt

content/_index.md

@@ -2,5 +2,5 @@
 title: Daniel's Blog
 ---
 ## Hello!
-Welcome to my blog. Here, I write abour various subjects, including (but not limited to)
+Welcome to my blog. Here, I write about various subjects, including (but not limited to)
 functional programming, compiler development, programming language theory, and occasionally video games. I hope you find something useful here!

content/blog/00_cs325_languages_hw1.md

@@ -0,0 +1,511 @@
+---
+title: A Language for an Assignment - Homework 1
+date: 2019-12-27T23:27:09-08:00
+tags: ["Haskell", "Python", "Algorithms"]
+---
+
+On a rainy Oregon day, I was walking between classes with a group of friends.
+We were discussing the various ways to obfuscate solutions to the weekly
+homework assignments in our Algorithms course: replace every `if` with
+a ternary expression, use single variable names, put everything on one line.
+I said:
+
+> The
+{{< sidenote "right" "chad-note" "chad" >}}
+This is in reference to a meme, <a href="https://knowyourmeme.com/memes/virgin-vs-chad">Virgin vs Chad</a>.
+A "chad" characteristic is masculine or "alpha" to the point of absurdity.
+{{< /sidenote >}} move would be to make your own, different language for every homework assignment.
+
+It was required of us to use
+{{< sidenote "left" "python-note" "Python" >}}
+A friend suggested making a Haskell program
+that generates Python-based interpreters for languages. While that would be truly
+absurd, I'll leave <em>this</em> challenge for another day.
+{{< /sidenote >}} for our solutions, so that was the first limitation on this challenge.
+Someone suggested to write the languages in Haskell, since that's what we used
+in our Programming Languages class. So the final goal ended up:
+
+* For each of the 10 homework assignments in CS325 - Analysis of Algorithms,
+* Create a Haskell program that translates a language into,
+* A valid Python program that works (nearly) out of the box and passes all the test cases.
+
+It may not be worth it to create a whole
+{{< sidenote "right" "general-purpose-note" "general-purpose" >}}
+A general purpose language is one that's designed to be used in various
+domains. For instance, C++ is a general-purpose language because it can
+be used for embedded systems, GUI programs, and pretty much anything else.
+This is in contrast to a domain-specific language, such as Game Maker Language,
+which is aimed at a much narrower set of uses.
+{{< /sidenote >}} language for each problem,
+but nowhere in the challenge did we say that it had to be general-purpose. In
+fact, some interesting design thinking can go into designing a domain-specific
+language for a particular assignment. So let's jump right into it, and make
+a language for the first homework assignment.
+
+### Homework 1
+There are two problems in Homework 1. Here they are, verbatim:
+
+{{< codelines "text" "cs325-langs/hws/hw1.txt" 32 38 >}}
+
+And the second:
+
+{{< codelines "text" "cs325-langs/hws/hw1.txt" 47 68 >}}
+
+We want to make a language __specifically__ for these two tasks (one of which
+is split into many tasks). What common things can we isolate? I see two:
+
+First, __all the problems deal with lists__. This may seem like a trivial observation,
+but these two problems are the __only__ thing we use our language for. We have
+list access,
+{{< sidenote "right" "filterting-note" "list filtering" >}}
+Quickselect is a variation on quicksort, which itself
+finds all the "lesser" and "greater" elements in the input array.
+{{< /sidenote >}} and list creation. That should serve as a good base!
+
+If you squint a little bit, __all the problems are recursive with the same base case__.
+Consider the first few lines of `search`, implemented naively:
+
+```Python
+def search(xs, k):
+    if xs == []:
+        return false
+```
+
+How about `sorted`? Take a look:
+
+```Python
+def sorted(xs):
+    if xs == []:
+        return []
+```
+
+I'm sure you see the picture. But it will take some real mental gymnastics to twist the
+rest of the problems into this shape. What about `qselect`, for instance? There's two
+cases for what it may return:
+
+* `None` or equivalent if the index is out of bounds (we give it `4` an a list `[1, 2]`).
+* A number if `qselect` worked.
+
+The test cases never provide a concrete example of what should be returned from
+`qselect` in the first case, so we'll interpret it like
+{{< sidenote "right" "undefined-note" "undefined behavior" >}}
+For a quick sidenote about undefined behavior, check out how
+C++ optimizes the <a href="https://godbolt.org/z/3skK9j">Collatz Conjecture function</a>.
+Clang doesn't know whether or not the function will terminate (whether the Collatz Conjecture
+function terminates is an <a href="https://en.wikipedia.org/wiki/Collatz_conjecture">unsolved problem</a>),
+but functions that don't terminate are undefined behavior. There's only one other way the function
+returns, and that's with "1". Thus, clang optimizes the entire function to a single "return 1" call.
+{{< /sidenote >}} in C++:
+we can do whatever we want. So, let's allow it to return `[]` in the `None` case.
+This makes this base case valid:
+
+```Python
+def qselect(xs, k):
+    if xs == []:
+        return []
+```
+
+"Oh yeah, now it's all coming together." With one more observation (which will come
+from a piece I haven't yet shown you!), we'll be able to generalize this base case.
+
+The observation is this section in the assignment:
+
+{{< codelines "text" "cs325-langs/hws/hw1.txt" 83 98 >}}
+
+The real key is the part about "returning the `[]` where x should be inserted". It so
+happens that when the list given to the function is empty, the number should be inserted
+precisely into that list. Thus:
+
+```Python
+def _search(xs, k):
+    if xs == []:
+        return xs
+```
+
+The same works for `qselect`:
+
+```Python
+def qselect(xs, k):
+    if xs == []:
+        return xs
+```
+
+And for sorted, too:
+
+```Python
+def sorted(xs):
+    if xs == []:
+        return xs
+```
+
+There are some functions that are exceptions, though:
+
+```Python
+def insert(xs, k):
+    # We can't return early here!
+    # If we do, we'll never insert anything.
+```
+
+Also:
+
+```Python
+def search(xs, k):
+    # We have to return true or false, never
+    # an empty list.
+```
+
+So, whenever we __don't__ return a list, we don't want to add a special case.
+We arrive at the following common base case: __whenever a function returns a list, if its first argument
+is the empty list, the first argument is immediately returned__.
+
+We've largely exhasuted the conclusiosn we can draw from these problems. Let's get to designing a language.
+
+### A Silly Language
+Let's start by visualizing our goals. Without base cases, the solution to `_search`
+would be something like this:
+
+{{< codelines "text" "cs325-langs/sols/hw1.lang" 11 14 >}}
+
+Here we have an __`if`-expression__. It has to have an `else`, and evaluates to the value
+of the chosen branch. That is, `if true then 0 else 1` evaluates to `0`, while
+`if false then 0 else 1` evaluates to `1`. Otherwise, we follow the binary tree search
+algorithm faithfully.
+
+Using this definition of `_search`, we can define `search` pretty easily:
+
+{{< codelines "text" "cs325-langs/sols/hw1.lang" 17 17 >}}
+
+Let's use Haskell's `(++)` operator for concatentation. This will help us understand
+when the user is operating on lists, and when they're not. With this, `sorted` becomes:
+
+{{< codelines "text" "cs325-langs/sols/hw1.lang" 16 16 >}}
+
+Let's go for `qselect` now. We'll introduce a very silly language feature for this
+problem:
+{{< sidenote "right" "selector-note" "list selectors" >}}
+You've probably never heard of list selectors, and for a good reason:
+this is a <em>terrible</em> language feature. I'll go in more detail
+later, but I wanted to make this clear right away.
+{{< /sidenote >}}. We observe that `qselect` aims to partition the list into
+other lists. We thus add the following pieces of syntax:
+
+```
+~xs -> {
+    pivot <- xs[rand]!
+    left <- xs[#0 <= pivot]
+    ...
+} -> ...
+```
+
+There are three new things here.
+
+1. The actual "list selector": `~xs -> { .. } -> ...`. Between the curly braces
+are branches which select parts of the list and assign them to new variables.
+Thus, `pivot <- xs[rand]!` assigns the element at a random index to the variable `pivot`.
+the `!` at the end means "after taking this out of `xs`, delete it from `xs`". The
+syntax {{< sidenote "right" "curly-note" "starts with \"~\"" >}}
+An observant reader will note that there's no need for the "xs" after the "~".
+The idea was to add a special case syntax to reference the "selected list", but
+I ended up not bothering. So in fact, this part of the syntax is useless.
+{{< /sidenote >}} to make it easier to parse.
+2. The `rand` list access syntax. `xs[rand]` is a special case that picks a random
+element from `xs`.
+3. The `xs[#0 <= pivot]` syntax. This is another special case that selects all elements
+from `xs` that match the given predicate (where `#0` is replaced with each element in `xs`).
+
+The big part of qselect is to not evaluate `right` unless you have to. So, we shouldn't
+eagerly evaluate the list selector. We also don't want something like `right[|right|-1]` to evaluate
+`right` twice. So we settle on
+{{< sidenote "right" "lazy-note" "lazy evaluation" >}}
+Lazy evaluation means only evaluating an expression when we need to. Thus,
+although we might encounter the expression for <code>right</code>, we
+only evaluate it when the time comes. Lazy evaluation, at least
+the way that Haskell has it, is more specific: an expression is evaluated only
+once, or not at all.
+{{</ sidenote >}}.
+Ah, but the `!` marker introduces
+{{< sidenote "left" "side-effect-note" "side effects" >}}
+A side effect is a term frequently used when talking about functional programming.
+Evaluating the expression <code>xs[rand]!</code> doesn't just get a random element,
+it also changes <em>something else</em>. In this case, that something else is 
+the <code>xs</code> list.
+{{< /sidenote >}}. So we can't just evaluate these things all willy-nilly.
+So, let's make it so that each expression in the selector list requires the ones above it. Thus,
+`left` will require `pivot`, and `right` will require `left` and `pivot`. So,
+lazily evaluated, ordered expressions. The whole `qselect` becomes:
+
+{{< codelines "text" "cs325-langs/sols/hw1.lang" 1 9 >}}
+
+We've now figured out all the language constructs. Let's start working on
+some implementation!
+
+#### Implementation
+It would be silly of me to explain every detail of creating a language in Haskell
+in this post; this is neither the purpose of the post, nor is it plausible
+to do this without covering monads, parser combinators, grammars, abstract syntax
+trees, and more. So, instead, I'll discuss the _interesting_ parts of the
+implementation. 
+
+##### Temporary Variables
+Our language is expression-based, yes. A function is a single,
+arbitrarily complex expression (involving `if/else`, list
+selectors, and more). So it would make sense to translate
+a function to a single, arbitrarily complex Python expression.
+However, the way we've designed our language makes it
+not-so-suitable for converting to a single expression! For
+instance, consider `xs[rand]`. We need to compute the list,
+get its length, generate a random number, and then access
+the corresponding element in the list. We use the list
+here twice, and simply repeating the expression would not
+be very smart: we'd be evaluating twice. So instead,
+we'll use a variable, assign the list to that variable,
+and then access that variable multiple times.
+
+To be extra safe, let's use a fresh temporary variable
+every time we need to store something. The simplest
+way is to simply maintain a counter of how many temporary
+variables we've already used, and generate a new variable
+by prepending the word "temp" to that number. We start
+with `temp0`, then `temp1`, and so on. To keep a counter,
+we can use a state monad:
+
+{{< codelines "Haskell" "cs325-langs/src/LanguageOne.hs" 230 230 >}}
+
+Don't worry about the `Map.Map String [String]`, we'll get to that in a bit.
+For now, all we have to worry about is the second element of the tuple,
+the integer counting how many temporary variables we've used. We can
+get the current temporary variable as follows:
+
+{{< codelines "Haskell" "cs325-langs/src/LanguageOne.hs" 232 235 >}}
+
+We can also get a fresh temporary variable like this:
+
+{{< codelines "Haskell" "cs325-langs/src/LanguageOne.hs" 237 240 >}}
+
+Now, the
+{{< sidenote "left" "code-note" "code" >}}
+Since we are translating an expression, we must have the result of
+the translation yield an Python expression we can use in generating
+larger Python expressions. However, as we've seen, we occasionally
+have to use statements. Thus, the <code>translateExpr</code> function
+returns a <code>Translator ([Py.PyStmt], Py.PyExpr)</code>.
+{{< /sidenote >}}for generating a random list access looks like
+{{< sidenote "right" "ast-note" "this:" >}}
+The <code>Py.*</code> constructors are a part of a Python AST module I quickly
+threw together. I won't showcase it here, but you can always look at the
+source code for the blog (which includes this project)
+<a href="https://dev.danilafe.com/Web-Projects/blog-static">here</a>.
+{{< /sidenote >}}
+
+{{< codelines "Haskell" "cs325-langs/src/LanguageOne.hs" 325 330 >}}
+
+##### Implementing "lazy evaluation"
+Lazy evaluation in functional programs usually arises from
+{{< sidenote "right" "graph-note" "graph reduction" >}}
+Graph reduction, more specifically the <em>Spineless,
+Tagless G-machine</em> is at the core of the Glasgow Haskell
+Compiler (GHC). Simon Peyton Jones' earlier book,
+<em>Implementing Functional Languages: a tutorial</em>
+details an earlier version of the G-machine.
+{{< /sidenote >}}. However, Python is neither
+functional nor graph-based, and we only lazily
+evaluate list selectors. Thus, we'll have to do
+some work to get our lazy evaluation to work as we desire.
+Here's what I came up with:
+
+1. It's difficult to insert Python statements where they are
+needed: we'd have to figure out in which scope each variable
+has already been declared, and in which scope it's yet
+to be assigned. 
+2. Instead, we can use a Python dictionary, called `cache`,
+and store computed versions of each variable in the cache.
+3. It's pretty difficult to check if a variable
+is in the cache, compute it if not, and then return the
+result of the computation, in one expression. This is
+true, unless that single expression is a function call, and we have a dedicated
+function that takes no arguments, computes the expression if needed,
+and uses the cache otherwise. We choose this route.
+4. We have already promised that we'd evaluate all the selected
+variables above a given variable before evaluating the variable
+itself. So, each function will first call (and therefore
+{{< sidenote "right" "force-note" "force" >}}
+Forcing, in this case, comes from the context of lazy evaluation. To
+force a variable or an expression is to tell the program to compute its
+value, even though it may have been putting it off.
+{{< /sidenote >}}) the functions
+generated for variables declared above the function's own variable.
+5. To keep track of all of this, we use the already-existing state monad
+as a reader monad (that is, we clear the changes we make to the monad
+after we're done translating the list selector). This is where the `Map.Map String [String]`
+comes from.
+
+The `Map.Map String [String]` keeps track of variables that will be lazily computed,
+and also of the dependencies of each variable (the variables that need
+to be access before the variable itself). We compute such a map for
+each selector as follows: 
+
+{{< codelines "Haskell" "cs325-langs/src/LanguageOne.hs" 298 298 >}}
+
+We update the existing map using `Map.union`:
+
+{{< codelines "Haskell" "cs325-langs/src/LanguageOne.hs" 299 299 >}}
+
+And, after we're done generating expressions in the body of this selector,
+we clear it to its previous value `vs`:
+
+{{< codelines "Haskell" "cs325-langs/src/LanguageOne.hs" 302 302 >}}
+
+We generate a single selector as follows:
+
+{{< codelines "Haskell" "cs325-langs/src/LanguageOne.hs" 268 281 >}}
+
+This generates a function definition statement, which we will examine in
+generated Python code later on.
+
+Solving the problem this way also introduces another gotcha: sometimes,
+a variable is produced by a function call, and other times the variable
+is just a Python variable. We write this as follows:
+
+{{< codelines "Haskell" "cs325-langs/src/LanguageOne.hs" 283 288 >}}
+
+##### Special Case Insertion
+This is a silly language for a single homework assignment. I'm not
+planning to implement Hindley-Milner type inference, or anything
+of that sort. For the purpose of this language, things will be
+either a list, or not a list. And as long as a function __can__ return
+a list, it can also return the list from its base case. Thus,
+that's all we will try to figure out. The checking code is so
+short that we can include the whole snippet at once:
+
+{{< codelines "Haskell" "cs325-langs/src/LanguageOne.hs" 219 227 >}}
+
+`mergePossibleType`
+{{< sidenote "right" "bool-identity-note" "figures out" >}}
+An observant reader will note that this is just a logical
+OR function. It's not, however, good practice to use
+booleans for types that have two constructors with no arguments.
+Check out this <a href="https://programming-elm.com/blog/2019-05-20-solving-the-boolean-identity-crisis-part-1/">
+Elm-based article</a> about this, which the author calls the
+Boolean Identity Crisis.
+{{< /sidenote >}}, given two possible types for an
+expression, the final type for the expression.
+
+There's only one real trick to this. Sometimes, like in
+`_search`, the only time we return something _known_ to be a list, that
+something is `xs`. Since we're making a list manipulation language,
+let's __assume the first argument to the function is a list__, and
+__use this information to determine expression types__. We guess
+types in a very basic manner otherwise: If you use the concatenation
+operator, or a list literal, then obviously we're working on a list.
+If you're returning the first argument of the function, that's also
+a list. Otherwise, it could be anything.
+
+My Haskell linter actually suggested a pretty clever way of writing
+the whole "add a base case if this function returns a list" code.
+Check it out:
+
+{{< codelines "Haskell" "cs325-langs/src/LanguageOne.hs" 260 266 >}}
+
+Specifically, look at the line with `let fastReturn = ...`. It
+uses a list comprehension: we take a parameter `p` from the list of
+parameter `ps`, but only produce the statements for the base case
+if the possible type computed using `p` is `List`.
+
+### The Output
+What kind of beast have we created? Take a look for yourself:
+```Python
+def qselect(xs,k):
+    if xs==[]:
+        return xs
+    cache = {}
+    def pivot():
+        if ("pivot") not in (cache):
+            cache["pivot"] = xs.pop(0)
+        return cache["pivot"]
+    def left():
+        def temp2(arg):
+            out = []
+            for arg0 in arg:
+                if arg0<=pivot():
+                    out.append(arg0)
+            return out
+        pivot()
+        if ("left") not in (cache):
+            cache["left"] = temp2(xs)
+        return cache["left"]
+    def right():
+        def temp3(arg):
+            out = []
+            for arg0 in arg:
+                if arg0>pivot():
+                    out.append(arg0)
+            return out
+        left()
+        pivot()
+        if ("right") not in (cache):
+            cache["right"] = temp3(xs)
+        return cache["right"]
+    if k>(len(left())+1):
+        temp4 = qselect(right(), k-len(left())-1)
+    else:
+        if k==(len(left())+1):
+            temp5 = [pivot()]
+        else:
+            temp5 = qselect(left(), k)
+        temp4 = temp5
+    return temp4
+def _search(xs,k):
+    if xs==[]:
+        return xs
+    if xs[1]==k:
+        temp6 = xs
+    else:
+        if xs[1]>k:
+            temp8 = _search(xs[0], k)
+        else:
+            temp8 = _search(xs[2], k)
+        temp6 = temp8
+    return temp6
+def sorted(xs):
+    if xs==[]:
+        return xs
+    return sorted(xs[0])+[xs[1]]+sorted(xs[2])
+def search(xs,k):
+    return len(_search(xs, k))!=0
+def insert(xs,k):
+    return _insert(k, _search(xs, k))
+def _insert(k,xs):
+    if k==[]:
+        return k
+    if len(xs)==0:
+        temp16 = xs
+        temp16.append([])
+        temp17 = temp16
+        temp17.append(k)
+        temp18 = temp17
+        temp18.append([])
+        temp15 = temp18
+    else:
+        temp15 = xs
+    return temp15
+```
+It's...horrible! All the `tempX` variables, __three layers of nested function declarations__, hardcoded cache access. This is not something you'd ever want to write.
+Even to get this code, I had to come up with hacks __in a language I created__.
+The first is the hack is to make the `qselect` function use the `xs == []` base
+case. This doesn't happen by default, because `qselect` doesn't return a list!
+To "fix" this, I made `qselect` return the number it found, wrapped in a
+list literal. This is not up to spec, and would require another function
+to unwrap this list.
+
+While `qselect` was struggling with not having the base case, `insert` had
+a base case it didn't need: `insert` shouldn't return the list itself
+when it's empty, it should insert into it! However, when we use the `<<`
+list insertion operator, the language infers `insert` to be a list-returning
+function itself, inserting into an empty list will always fail. So, we
+make a function `_insert`, which __takes the arguments in reverse__.
+The base case will still be generated, but the first argument (against
+which the base case is checked) will be a number, so the `k == []` check
+will always fail.
+
+That concludes this post. I'll be working on more solutions to homework
+assignments in self-made languages, so keep an eye out!

content/blog/01_cs325_languages_hw2.md

@@ -0,0 +1,218 @@
+---
+title: A Language for an Assignment - Homework 2
+date: 2019-12-30T20:05:10-08:00
+tags: ["Haskell", "Python", "Algorithms"]
+---
+
+After the madness of the
+[language for homework 1]({{< relref "00_cs325_languages_hw1.md" >}}),
+the solution to the second homework offers a moment of respite.
+Let's get right into the problems, shall we?
+
+### Homework 2
+Besides some free-response questions, the homework contains
+two problems. The first:
+
+{{< codelines "text" "cs325-langs/hws/hw2.txt" 29 34 >}}
+
+And the second:
+
+{{< codelines "text" "cs325-langs/hws/hw2.txt" 36 44 >}}
+
+At first glance, it's not obvious why these problems are good for
+us. However, there's one key observation: __`num_inversions` can be implemented
+using a slightly-modified `mergesort`__. The trick is to maintain a counter
+of inversions in every recursive call to `mergesort`, updating
+it every time we take an element from the
+{{< sidenote "right" "right-note" "right list" >}}
+If this nomenclature is not clear to you, recall that
+mergesort divides a list into two smaller lists. The
+"right list" refers to the second of the two, because
+if you visualize the original list as a rectangle, and cut
+it in half (vertically, down the middle), then the second list
+(from the left) is on the right.
+{{< /sidenote >}} while there are still elements in the
+{{< sidenote "left" "left-note" "left list" >}}
+Why this is the case is left as an exercise to the reader.
+{{< /sidenote >}}.
+When we return from the call,
+we add up the number of inversions from running `num_inversions`
+on the smaller lists, and the number of inversions that we counted
+as I described. We then return both the total number
+of inversions and the sorted list. 
+
+So, we either perform the standard mergesort, or we perform mergesort
+with additional steps added on. The additional steps can be divided into
+three general categories:
+
+1. __Initialization__: We create / set some initial state. This state
+doesn't depend on the lists or anything else.
+2. __Effect__: Each time that an element is moved from one of the two smaller
+lists into the output list, we may change the state in some way (create
+an effect).
+3. __Combination__: The final state, and the results of the two
+sub-problem states, are combined into the output of the function.
+
+This is all very abstract. In the concrete case of inversions,
+these steps are as follows:
+
+1. __Initializtion__: The initial state, which is just the counter, is set to 0.
+2. __Effect__: Each time an element is moved, if it comes from the right list,
+the number of inversions is updated.
+3. __Combination__: We update the state, simply adding the left and right
+inversion counts.
+
+We can make a language out of this!
+
+### A Language
+Again, let's start by visualizing what the solution will look like. How about this:
+
+{{< rawblock "cs325-langs/sols/hw2.lang" >}}
+
+We divide the code into the same three steps that we described above. The first
+section is the initial state. Since it doesn't depend on anything, we expect
+it to be some kind of literal, like an integer. Next, we have the effect section,
+which has access to the variables below:
+
+* `STATE`, to manipulate or check the current state.
+* `LEFT` and `RIGHT`, to access the two lists being merged.
+* `L` and `R`, constants that are used to compare against the `SOURCE` variable.
+* `SOURCE`, to denote which list a number came from. 
+* `LSTATE` and `RSTATE`, to denote the final states from the two subproblems.
+
+We use an `if`-statement to check if the element that was popped came
+from the right list (by checking `SOURCE == R`). If it did, we increment the counter
+(state) by the proper amount. In the combine step, which has access to the
+same variables, we simply increment the state by the counters from the left
+and right solutions, stored in `LSTATE` and `RSTATE`. That's it!
+
+#### Implementation
+The implementation is not tricky at all. We don't need to use monads like we did last
+time, and nor do we have to perform any fancy Python nested function declarations.
+
+To keep with the Python convention of lowercase variables, we'll translate the
+uppercase "global" variables to lowercase. We'll do it like so:
+
+{{< codelines "Haskell" "cs325-langs/src/LanguageTwo.hs" 167 176 >}}
+
+Note that we translated `L` and `R` to integer literals. We'll indicate the source of
+each element with an integer, since there's no real point to representing it with
+a string or a variable. We'll need to be aware of this when we implement the actual, generic
+mergesort code. Let's do that now:
+
+{{< codelines "Haskell" "cs325-langs/src/LanguageTwo.hs" 101 161 >}}
+
+This is probably the ugliest part of this assignment: we handwrote a Python
+AST in Haskell that implements mergesort with our augmentations. Note that
+this is a function, which takes a `Py.PyExpr` (the initial state expression),
+and two lists of `Py.PyStmt`, which are the "effect" and "combination" code,
+respectively. We simply splice them into our regular mergesort function.
+The translation is otherwise pretty trivial, so there's no real reason
+to show it here.
+
+### The Output
+What's the output of our solution to `num_inversions`? Take a look for yourself:
+
+```Python
+def prog(xs):
+    if len(xs)<2:
+        return (0, xs)
+    leng = len(xs)//2
+    left = xs[:(leng)]
+    right = xs[(leng):]
+    (ls,left) = prog(left)
+    (rs,right) = prog(right)
+    left.reverse()
+    right.reverse()
+    state = 0
+    source = 0
+    total = []
+    while (left!=[])and(right!=[]):
+        if left[-1]<=right[-1]:
+            total.append(left.pop())
+            source = 1
+        else:
+            total.append(right.pop())
+            source = 2
+        if source==2:
+            state = state+len(left)
+    state = state+ls+rs
+    left.reverse()
+    right.reverse()
+    return (state, total+left+right)
+```
+
+Honestly, that's pretty clean. As clean as `left.reverse()` to allow for \\(O(1)\\) pop is.
+What's really clean, however, is the implementation of mergesort in our language.
+It goes as follows:
+
+```
+state 0;
+effect {}
+combine {}
+```
+
+To implement mergesort in our language, which describes mergesort variants, all
+we have to do is not specify any additional behavior. Cool, huh?
+
+That's the end of this post. If you liked this one (and the previous one!),
+keep an eye out for more!
+
+### Appendix (Missing Homework Question)
+I should not view homework assignments on a small-screen device. There __was__ a third problem
+on homework 2:
+
+{{< codelines "text" "cs325-langs/hws/hw2.txt" 46 65 >}}
+
+This is not a mergesort variant, and adding support for it into our second language
+will prevent us from making it the neat specialized
+{{< sidenote "right" "dsl-note" "DSL" >}}
+DSL is a shortened form of "domain specific language", which was briefly
+described in another sidenote while solving homework 1.
+{{< /sidenote >}} that was just saw. We'll do something else, instead:
+we'll use the language we defined in homework 1 to solve this
+problem:
+
+```
+empty() = [0, 0];
+longest(xs) =
+    if |xs| != 0
+    then _longest(longest(xs[0]), longest(xs[2]))
+    else empty();
+_longest(l, r) = [max(l[0], r[0]) + 1, max(l[0]+r[0], max(l[1], r[1]))];
+```
+
+{{< sidenote "right" "terrible-note" "This is quite terrible." >}}
+This is probably true with any program written in our first
+language.
+{{< /sidenote >}} In these 6 lines of code, there are two hacks
+to work around the peculiarities of the language.
+
+At each recursive call, we want to keep track of both the depth
+of the tree and the existing longest path. This is because
+the longest path could be found either somewhere down
+a subtree, or from combining the largest depths of
+two subtrees. To return two values from a function in Python,
+we'd use a tuple. Here, we use a list.
+
+Alarm bells should be going off here. There's no reason why we should
+ever return an empty list from the recursive call: at the very least, we
+want to return `[0,0]`. But placing such a list literal in a function
+will trigger the special case insertion. So, we have to hide this literal
+from the compiler. Fortunately, that's not too hard to do - the compiler
+is pretty halfhearted in its inference of types. Simply putting
+the literal behind a constant function (`empty`) does the trick.
+
+The program uses the subproblem depths multiple times in the
+final computation. We thus probably want to assign these values
+to names so we don't have to perform any repeated work. Since
+the only two mechanisms for
+{{< sidenote "right" "binding-note" "binding variables" >}}
+To bind a variable means to assign a value to it.
+{{< /sidenote >}} in this language are function calls
+and list selectors, we use a helper function `_longest`,
+which takes two subproblem solutions an combines them
+into a new solution. It's pretty obvious that `_longest`
+returns a list, so the compiler will try insert a base
+case. Fortunately, subproblem solutions are always
+lists of two numbers, so this doesn't affect us too much.

content/blog/02_cs325_languages_hw3.md

@@ -0,0 +1,295 @@
+---
+title: A Language for an Assignment - Homework 3
+date: 2020-01-02T22:17:43-08:00
+tags: ["Haskell", "Python", "Algorithms"]
+draft: true
+---
+
+It rained in Sunriver on New Year's Eve, and it continued to rain
+for the next couple of days. So, instead of going skiing as planned,
+to the dismay of my family and friends, I spent the majority of
+those days working on the third language for homework 3. It
+was quite the language, too - the homework has three problems, each of
+which has a solution independent of the others. I invite you
+to join me in my descent into madness as we construct another language.
+
+### Homework 3
+Let's take a look at the three homework problems. The first two are
+related, but are solved using a different technique:
+
+{{< codelines "text" "cs325-langs/hws/hw3.txt" 18 30 >}}
+
+This problem requires us to find the `k` numbers closest to some
+query (which I will call `n`) from a list `xs`. The list isn't sorted, and the
+problem must run in linear time. Sorting the list would require
+the standard
+{{< sidenote "right" "n-note" "\(O(n\log n)\) time." >}}
+The \(n\) in this expression is not the same as the query <code>n</code>,
+but rather the length of the list. In fact, I have not yet assigned
+the length of the input <code>xs</code> to any variable. If we say that
+\(m\) is a number that denotes that length, the proper expression
+for the complexity is \(O(m \log m)\).
+{{< /sidenote >}} Thus, we have to take another route, which should
+already be familiar: quickselect. Using quickselect, we can find the `k`th
+closest number, and then collect all the numbers that are closer than the `kth`
+closest number. So, we need a language that:
+
+* Supports quickselect (and thus, list partitioning and recursion).
+* Supports iteration, {{< sidenote "left" "iteration-note" "multiple times." >}}
+Why would we need to iterate multiple times? Note that we could have a list
+of numbers that are all the same, <code>[1,1,1,1,1]</code>. Then, we'll need
+to know how many of the numbers <em>equally close</em> as the <code>k</code>th
+element we need to include, which will require another pass through the list.
+{{< /sidenote >}}
+
+That's a good start. Let's take a look at the second problem:
+
+{{< codelines "text" "cs325-langs/hws/hw3.txt" 33 47 >}}
+
+This problem really is easier. We have to find the position of _the_ closest
+element, and then try expand towards either the left or right, depending on
+which end is better. This expansion will take several steps, and will
+likely require a way to "look" at a given part of the list. So let's add two more
+rules. We need a language that also:
+
+* Supports looping control flow, such as `while`.
+* {{< sidenote "right" "view-note" "Allows for a \"view\" into the list" >}}
+We could, of course, simply use list indexing. But then, we'd just be making
+a simple imperative language, and that's boring. So let's play around
+with our design a little, and experimentally add such a "list view" component.
+{{< /sidenote >}}
+(like an abstraction over indexing).
+
+This is shaping up to be a fun language. Let's take a look at the last problem:
+{{< codelines "text" "cs325-langs/hws/hw3.txt" 50 64 >}}
+
+This problem requires more iterations of a list. We have several
+{{< sidenote "right" "cursor-note" "\"cursors\"" >}}
+I always make the language before I write the post, since a lot of
+design decisions change mid-implementation. I realize now that
+"cursors" would've been a better name for this language feature,
+but alas, it is too late.
+{{< /sidenote >}} looking into the list, and depending if the values
+at each of the cursors add up, we do or do not add a new tuple to a list. So,
+two more requirements:
+
+* The "cursors" must be able to interact.
+* The language can represent {{< sidenote "left" "tuple-note" "tuples." >}}
+We could, of course, hack some other way to return a list of tuples, but
+it turns out tuples are pretty simple to implement, and help make for nicer
+programming in our language.
+{{< /sidenote >}}
+
+I think we've gathered what we want from the homework. Let's move on to the
+language!
+
+### A Language
+As is now usual, let's envision a solution to the problems in our language. There
+are actually quite a lot of functions to look at, so let's see them one by one.
+First, let's look at `qselect`.
+
+{{< codelines "text" "cs325-langs/sols/hw3.lang" 1 19 >}}
+
+After the early return, the first interesting part of the language is the
+use of what I have decided to call a __list traverser__. The list
+traverser is a __generalization of a list index__. Whenever we use a list
+index variable, we generally use the following operations:
+
+* __Initialize__: we set the list index to some initial value, such as 0.
+* __Step__: If we're walking the list from left to right, we increment the index.
+If we're walking the list from right to left, we decrement the index.
+* __Validity Check__: We check if the index is still valid (that is, we haven't
+gone past the edge of the list).
+* __Access__: Get the element the cursor is pointing to.
+
+A {{< sidenote "right" "cpp-note" "traverser declaration" >}}
+A fun fact is that we've just rediscovered C++
+<a href="http://www.cplusplus.com/reference/iterator/">iterators</a>. C++
+containers and their iterators provide us with the operations I described:
+
+We can initialize an iterator like <code>auto it = list.begin()</code>. We
+can step the iterator using <code>it++</code>. We can check its validity
+using <code>it != list.end()</code>, and access what it's pointing to using
+<code>*it</code>. While C++ uses templates and inheritance for this,
+we define a language feature specifically for lists.
+
+{{< /sidenote >}} describes these operations. The declartion for the `bisector`
+traverser creates a "cursor" over the list `xs`, that goes between the 0th
+and last elements of `xs`. The declaration for the `pivot` traverser creates
+a "cursor" over the list `xs` that jumps around random locations in the list.
+
+The next interesting part of the language is a __traverser macro__. This thing,
+that looks like a function call (but isn't), performs an operation on the
+cursor. For instance, `pop!` removes the element at the cursor from the list,
+whereas `bisect!` categorizes the remaining elements in the cursor's list
+into two lists, using a boolean-returning lambda (written in Java syntax).
+
+Note that this implementation of `qselect` takes a function `c`, which it
+uses to judge the actual value of the number. This is because our `qselect`
+won't be finding _the_ smallest number, but the number with the smallest difference
+with `n`. `n` will be factored in via the function.
+
+Next up, let's take a look at the function that uses `qselect`, `closestUnsorted`:
+
+{{< codelines "text" "cs325-langs/sols/hw3.lang" 21 46 >}}
+
+Like we discussed, it finds the `k`th closest element (calling it `min`),
+and counts how many elements that are __equal__ need to be included,
+by setting the number to `k` at first, and subtracting 1 for every number
+it encounters that's closer than `min`. Notice that we use the `valid!` and
+`step!` macros, which implement the opertions we described above. Notice
+that the user doesn't deal with adding and subtracting numbers, and doing
+comparisons. All they have to do is ask "am I still good to iterate?"
+
+Next, let's take a look at `closestSorted`, which will require more
+traverser macros.
+
+{{< codelines "text" "cs325-langs/sols/hw3.lang" 48 70 >}}
+
+The first new macro is `canstep!`. This macro just verifies that
+the traverser can make another step. We need this for the "reverse" iterator,
+which indicates the lower bound of the range of numbers we want to return,
+because `subset!` (which itself is just Python's slice, like `xs[a:b]`), uses an inclusive bottom
+index, and thus, we can't afford to step it before knowing that we can, and that
+it's a better choice after the step.
+
+Similarly, we have the `at!(t, i)` macro, which looks at the
+traverser `t`, with offset `i`.
+
+We have two loops. The first loop runs as long as we can expand the range in both
+directions, and picks the better direction at each iteration. The second loop
+runs as long as we still want more numbers, but have already hit the edge
+of the list on the left or on the right.
+
+Finally, let's look at the solution to `xyz`:
+
+{{< codelines "text" "cs325-langs/sols/hw3.lang" 72 95 >}}
+
+I won't go in depth, but notice that the expression in the `span` part
+of the `traverser` declaration can access another traverser. We treat
+as a feature the fact that this expression isn't immediately evaluated at the place
+of the traverser declaration. Rather, every time that a comparison for a traverser
+operation is performed, this expression is re-evaluated. This allows us to put
+dynamic bounds on traversers `y` and `z`, one of which must not exceed the other.
+
+This is more than enough to work with. Let's move on to the implementation.
+
+#### Implementation
+Again, let's not go too far into the details of implementing the language from scratch.
+Instead, let's take a look into specific parts of the language that deserve attention.
+
+##### Revenge of the State Monad
+Our previous language was, indeed, a respite from complexity. Translation was
+straightforward, and the resulting expressions and statements were plugged straight
+into a handwritten AST. We cannot get away with this here; the language is powerful
+enough to implement three list-based problems, which comes at the cost of increased 
+complexity.
+
+We need, once again, to generate temporary variables. We also need to keep track of
+which variables are traversers, and the properties of these traversers, throughout
+each function of the language. We thus fall back to using `Control.Monad.State`:
+
+{{< todo >}}Code for Translator Monad{{< /todo >}}
+
+There's one part of the state tuple that we haven't yet explained: the list of
+statements.
+
+##### Generating Statements
+Recall that our translation function for expressions in the first homework had the type:
+
+```Haskell
+translateExpr :: Expr -> Translator ([Py.PyStmt], Py.PyExpr)
+```
+
+We then had to use `do`-notation, and explicitly concatenate lists
+of emitted statements. In this language, I took an alternative route: I made
+the statements part of the state. They are thus implicitly generated and
+stored in the monad, and expression generators don't have to worry about
+concatenating them. When the program is ready to use the generated statements
+(say, when an `if`-statement needs to use the statements emitted by the condition
+expression), we retrieve them from the monad:
+
+{{< todo >}}Code for getting statements{{< /todo >}}
+
+##### Validating Traverser Declarations
+We declare two separate types that hold traverser data. The first is a kind of "draft"
+type, `TraverserData`. This record holds all possible configurations of a traverser
+that occur as the program is iterating through the various `key: value` pairs in
+the declaration. For instance, at the very beginning of processing a traverser declaration,
+our program will use a "default" `TraverserData`, with all fields set to `Nothing` or
+their default value. This value will then be modified by the first key/value pair,
+changing, for instance, the list that the traverser operates on. This new modified
+`TraverserData` will then be modified by the next key/value pair, and so on. This
+is, effectively, a fold operation.
+
+{{< todo >}}Code for TraverserData{{< /todo >}}
+{{< todo >}}Maybe sidenote about fold?{{< /todo >}}
+
+The data may not have all the required fields until the very end, and its type
+reflects that: `Maybe String` here, `Maybe TraverserBounds` there. We don't
+want to deal with unwrapping the `Maybe a` values every time we use the traverser,
+especially if we've done so before. So, we define a `ValidTraverserData` record,
+that does not have `Maybe` arguments, and thus, has all the required data. At the
+end of a traverser declaration, we attempt to translate a `TraverserData` into
+a `ValidTraverserData`, invoking `fail` if we can't, and storing the `ValidTraverserData`
+into the state otherwise. Then, every time we retrieve a traverser from the state,
+it's guaranteed to be valid, and we have to spend no extra work unpacking it. We
+define a lookup monadic operation like this:
+
+{{< todo >}}Code for getting ValidTraverserData{{< /todo >}}
+
+##### Compiling Macros
+I didn't call them macros for no reason. Clearly, we don't want to generate
+code that
+{{< sidenote "right" "increment-note" "calls functions only to increment an index." >}}
+In fact, there's no easy way to do this at all. Python's integers (if we choose to
+represent our traversers using integers), are immutable. Furthermore, unlike C++,
+where passing by reference allows a function to change its parameters "outside"
+the call, Python offers no way to reassign a different value to a variable given
+to a function.
+<br><br>
+For an example use of C++'s pass-by-reference mechanic, consider <code>std::swap</code>:
+it's a function, but it modifies the two variables given to it. There's no
+way to generically implement such a function in Python.
+{{< /sidenote >}} We also can't allow arbitrary expressions to serve as traversers:
+our translator keeps some context about which variables are traversers, what their
+bounds are, and how they behave. Thus, __calls to traverser macros are very much macros__:
+they operate on AST nodes, and __require__ that their first argument is a variable,
+named like the traverser. We use the `requireTraverser` monadic operation
+to get the traverser associated with the given variable name, and then perform
+the operation as intended. The `at!(t)` operation is straightforward:
+
+{{< todo >}}Code for at!{{< /todo >}}
+
+The `at!(t,i)` is less so, since it deals with the intricacies of accessing
+the list at either a positive of negative offset, depending on the direction
+of the traverser. We implement a function to properly generate an expression for the offset:
+
+{{< todo >}}Code for traverserIncrement{{< /todo >}}
+
+We then implement `at!(t,i)` as follows:
+
+{{< todo >}}Code for at!{{< /todo >}}
+
+The most complicated macro is `bisect!`. It must be able to step the traverser,
+and also return a tuple of two lists that the bisection yields. We also
+prefer that it didn't pollute the environment with extra variables. To
+achieve this, we want `bisect!` to be a function call. We want this
+function to implement the iteration and list construction.
+
+`bisect!`, by definition, takes a lambda. This lambda, in our language, is declared
+in the lexical scope in which `bisect!` is called. Thus, to guarantee correct translation,
+we must do one of two things:
+
+1. Translate 1-to-1, and create a lambda, passing it to a fixed `bisect` function declared
+elsewhere.
+2. Translate to a nested function declaration, inlining the lambda.
+
+{{< todo >}}Maybe sidenote about inline?{{< /todo >}}
+
+Since I quite like the idea of inlining a lambda, let's settle for that. To do this,
+we pull a fresh temporary variable and declare a function, into which we place
+the traverser iteration code, as well as the body of the lambda, with the variable
+substituted for the list access expression. Here's the code:
+
+{{< todo >}}Code for bisect!{{< /todo >}}

content/blog/09_compiler_polymorphism.md

@@ -0,0 +1,65 @@
+---
+title: Compiling a Functional Language Using C++, Part 9 - Polymorphism
+date: 2019-12-09T23:26:46-08:00
+tags: ["C and C++", "Functional Languages", "Compilers"]
+draft: true
+---
+
+Last time, we wrote some pretty interesting programs in our little language.
+We successfully expressed arithmetic and recursion. But there's one thing
+that we cannot express in our language without further changes: an `if` statement.
+
+Suppose we didn't want to add a special `if/else` expression into our language.
+Thanks to lazy evaluation, we can express it using a function:
+
+```
+defn if c t e = {
+    case c of {
+        True -> { t }
+        False -> { e }
+    }
+}
+```
+
+But an issue still remains: so far, our compiler remains __monomorphic__. That
+is, a particular function can only have one possible type for each one of its
+arguments. With our current setup, something like this
+{{< sidenote "right" "if-note" "would not work:" >}}
+In a polymorphically typed language, the inner <code>if</code> would just evaluate to
+<code>False</code>, and the whole expression to 3.
+{{< /sidenote >}}
+
+```
+if (if True False True) 11 3
+```
+
+This is because, for this to work, both of the following would need to hold (borrowing
+some of our notation from the [typechecking]({{< relref "03_compiler_typechecking.md" >}}) post):
+
+$$
+\\text{if} : \\text{Int} \\rightarrow \\text{Int}
+$$
+$$
+\\text{if} : \\text{Bool} \\rightarrow \\text{Bool}
+$$
+
+But using our rules so far, such a thing is impossible, since there is no way for
+\\(\text{Int}\\) to be unified with \\(\text{Bool}\\). We need a more powerful
+set of rules to describe our program's types. One such set of rules is
+the [Hindley-Milner type system](https://en.wikipedia.org/wiki/Hindley%E2%80%93Milner_type_system),
+which we have previously alluded to. In fact, the rules we came up
+with were already very close to Hindley-Milner, with the exception of two:
+__generalization__ and __instantiation__. Instantiation first:
+
+$$
+\frac
+{\\Gamma \\vdash e : \\sigma \\quad \\sigma' \\sqsubseteq \\sigma}
+{\\Gamma \\vdash e : \\sigma'}
+$$
+
+Next, generalization:
+$$
+\frac
+{\\Gamma \\vdash e : \\sigma \\quad \\alpha \\not \\in \\text{free}(\\Gamma)}
+{\\Gamma \\vdash e : \\forall a . \\sigma}
+$$

content/blog/sidenotes.md

@@ -10,7 +10,7 @@ I found that __sidenotes__ were a feature that I didn't even know I needed.
 A lot of my writing seems to use small parenthesized remarks (like this), which,
 although it doesn't break the flow in a grammatical sense, lengthens the
 sentence, and makes it harder to follow. Since I do my best to write content
-to help explain stuff (like the [compiler series]({{ relref "00_compiler_intro.md" }})),
+to help explain stuff (like the [compiler series]({{< relref "00_compiler_intro.md" >}})),
 making sentences __more__ difficult to understand is a no-go.
 
 So, what do they look like?

themes/vanilla/assets/scss/sidenotes.scss

@@ -1,7 +1,9 @@
 @import "style.scss";
 
-$sidenote-width: 350px;
+$sidenote-width: 30rem;
-$sidenote-offset: 15px;
+$sidenote-offset: 1.5rem;
+$sidenote-padding: 1rem;
+$sidenote-highlight-border-width: .2rem;
 
 .sidenote {
     &:hover {
@@ -11,15 +13,16 @@ $sidenote-offset: 15px;
         }
 
         .sidenote-content {
-            border: 2px dashed;
+            border: $sidenote-highlight-border-width dashed;
-            padding: 9px;
+            padding: $sidenote-padding -
+                ($sidenote-highlight-border-width - $standard-border-width);
             border-color: $primary-color;
         }
     }
 }
 
 .sidenote-label {
-    border-bottom: 2px solid $primary-color;
+    border-bottom: .2rem solid $primary-color;
 }
 
 .sidenote-checkbox {
@@ -30,7 +33,7 @@ $sidenote-offset: 15px;
     display: block;
     position: absolute;
     width: $sidenote-width;
-    margin-top: -1.5em;
+    margin-top: -1.5rem;
 
     &.sidenote-right {
         right: 0;
@@ -45,8 +48,8 @@ $sidenote-offset: 15px;
     @media screen and
         (max-width: $container-width + 2 * ($sidenote-width + 2 * $sidenote-offset)) {
         position: static;
-        margin-top: 10px;
+        margin-top: 1rem;
-        margin-bottom: 10px;
+        margin-bottom: 1rem;
         width: 100%;
         display: none;
 
@@ -55,16 +58,16 @@ $sidenote-offset: 15px;
         }
 
         &.sidenote-left {
-            margin-left: 0px;
+            margin-left: 0rem;
         }
 
         &.sidenote-right {
-            margin-right: 0px;
+            margin-right: 0rem;
         }
     }
 
     @include bordered-block;
-    padding: 10px;
+    padding: $sidenote-padding;
     box-sizing: border-box;
     text-align: left;
 }

themes/vanilla/assets/scss/style.scss

@@ -1,24 +1,28 @@
-$container-width: 800px;
+$container-width: 50rem;
+$standard-border-width: .075rem;
+
 $primary-color: #36e281;
 $primary-color-dark: darken($primary-color, 10%);
 $code-color: #f0f0f0;
 $code-color-dark: darken($code-color, 10%);
 $border-color: #bfbfbf;
+
 $font-heading: "Lora", serif;
 $font-body: "Raleway", serif;
 $font-code: "Inconsolata", monospace;
-$standard-border: 1px solid $border-color;
+
+$standard-border: $standard-border-width solid $border-color;
 
 @mixin bordered-block {
     border: $standard-border;
-    border-radius: 2px;
+    border-radius: .2rem;
 }
 
 body {
   font-family: $font-body;
-  font-size: 1.0em;
+  font-size: 1.0rem;
   line-height: 1.5;
-  margin-bottom: 1em;
+  margin-bottom: 1rem;
   text-align: justify;
 }
 
@@ -27,8 +31,8 @@ main {
 }
 
 h1, h2, h3, h4, h5, h6 {
-  margin-bottom: .1em;
+  margin-bottom: .1rem;
-  margin-top: .5em;
+  margin-top: .5rem;
   font-family: $font-heading;
   font-weight: normal;
   text-align: left;
@@ -49,7 +53,7 @@ code {
 
 pre code {
     display: block;
-    padding: 0.5em;
+    padding: 0.5rem;
     overflow-x: auto;
     background-color: $code-color;
 }
@@ -61,12 +65,12 @@ pre code {
   box-sizing: border-box;
 
   @media screen and (max-width: $container-width){
-    padding: 0em 1em 0em 1em;
+    padding: 0rem 1rem 0rem 1rem;
   }
 }
 
 .button, input[type="submit"] {
-  padding: 0.5em;
+  padding: 0.5rem;
   background-color: $primary-color;
   border: none;
   color: white;
@@ -87,7 +91,7 @@ pre code {
 nav {
   background-color: $primary-color;
   width: 100%;
-  margin: 1em 0px 1em 0px;
+  margin: 1rem 0rem 1rem 0rem;
 }
 
 nav a {
@@ -110,7 +114,7 @@ nav a {
 }
 
 .post-content {
-  margin-top: .5em;
+  margin-top: .5rem;
 }
 
 h1 {

themes/vanilla/layouts/partials/head.html

@@ -6,9 +6,11 @@
     <link href="https://fonts.googleapis.com/css?family=Inconsolata|Lora|Raleway" rel="stylesheet">
     <link rel="stylesheet" href="//cdnjs.cloudflare.com/ajax/libs/normalize/5.0.0/normalize.min.css">
     {{ $style := resources.Get "scss/style.scss" | resources.ToCSS | resources.Minify }}
-    {{ $sidenotes:= resources.Get "scss/sidenotes.scss" | resources.ToCSS | resources.Minify }}
+    {{ $sidenotes := resources.Get "scss/sidenotes.scss" | resources.ToCSS | resources.Minify }}
+    {{ $icon := resources.Get "img/favicon.png" }}
     <link rel="stylesheet" href="{{ $style.Permalink }}">
     <link rel="stylesheet" href="{{ $sidenotes.Permalink }}">
+    <link rel="icon" type="image/png" href="{{ $icon.Permalink }}">
 
     <script src='https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js?config=TeX-MML-AM_CHTML' async></script>
     {{ template "_internal/google_analytics.html" . }}

themes/vanilla/layouts/shortcodes/numberedsidenote

@@ -0,0 +1,9 @@
+{{ .Page.Scratch.Add "numbernote-id" 1 }}
+{{ $id := .Page.Scratch.Get "numbernote-id" }}
+<span class="sidenote">
+<label class="sidenote-label" for="numbernote-{{ $id }}">({{ $id }})</label>
+<input class="sidenote-checkbox" type="checkbox" id="numbernote-{{ $id }}"></input>
+<span class="sidenote-content sidenote-{{ .Get 0 }}">
+{{ .Inner }}
+</span>
+</span>