💎I take the dirt that I roll in and turn it into diamonds!
I’m always putting myself through the gauntlet and learning hands-on how to do things I never knew, how to do them well, and how to put it all together.
I’ve become someone who always starts at the bottom doing the dirty work, and rises to the challenge and becomes an even more valuable member of any team I work with.
🛠I have a passion for building things, creatively and systematically.
I'm probably left-and-right brained.
I also have an affinity for improving the lives of others by creating impactful experiences - whether through design, content, product, service, or even just a simple conversation!
🔥I enjoy rallying people up through emotionally-fueled storytelling.
Knowing how to listen to their pains & struggles and understanding their perspective allows me to paint their hearts with invigorating emotions and armor their minds with a bulletproof mindset to inspire them to take action is the secret sauce of my entire skillset.
I'm not just a Full Stack Software Engineer or a Full Stack Digital Marketer..
💪I'm a Full Stack Team Player.
I’ve worked all kinds of jobs with all kinds of people and learned all kinds of skills. If we ever have a coffee together, feel free to ask me about them and i’ll tell you all the interesting growth-moments I had while I was there - you’re guaranteed an interesting conversation!
I would love to work with a team where we could dissect and understand the end-user's challenges and where I can combine and utilize my digital marketing skills and software engineering abilities to custom-tailor solutions for companies/clients so they achieve massive impact through a powerful and beautifully-designed digital presence.
🚨If you believe I can be a helpful addition to your team, I’m currently enrolled at Flatiron School's Immersive Software Engineering Bootcamp and I'll be graduating from the bootcamp April 19th!
✅Feel free to contact me via LinkedIn!
Bring to the table win-win survival strategies to ensure proactive domination. At the end of the day, going forward, a new normal that has evolved from generation X is on the runway heading towards a streamlined cloud solution. User generated content in real-time will have multiple touchpoints for offshoring.
Capitalize on low hanging fruit to identify a ballpark value added activity to beta test. Override the digital divide with additional clickthroughs from DevOps. Nanotechnology immersion along the information highway will close the loop on focusing solely on the bottom line.
Podcasting operational change management inside of workflows to establish a framework. Taking seamless key performance indicators offline to maximise the long tail. Keeping your eye on the ball while performing a deep dive on the start-up mentality to derive convergence on cross-platform integration.
Podcasting operational change management inside of workflows to establish a framework. Taking seamless key performance indicators offline to maximise the long tail. Keeping your eye on the ball while performing a deep dive on the start-up mentality to derive convergence on cross-platform integration.
Collaboratively administrate empowered markets via plug-and-play networks. Dynamically procrastinate B2C users after installed base benefits. Dramatically visualize customer directed convergence without revolutionary ROI.
Front-End & Back-End Development.
Front-End & Back-End Development.
GPA: 3.56
Apart from being a web developer, I enjoy most of my time being outdoors. In the winter, I am an avid skier and novice ice climber. During the warmer months here in Colorado, I enjoy mountain biking, free climbing, and kayaking.
When forced indoors, I follow a number of sci-fi and fantasy genre movies and television shows, I am an aspiring chef, and I spend a large amount of my free time exploring the latest technology advancements in the front-end web development world.


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| Global Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | other | (617 entries) |
| Notation Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | other | (5 entries) |
| Module Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | other | (27 entries) |
| Variable Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | other | (13 entries) |
| Library Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | other | (14 entries) |
| Lemma Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | other | (211 entries) |
| Constructor Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | other | (52 entries) |
| Axiom Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | other | (37 entries) |
| Inductive Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | other | (26 entries) |
| Section Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | other | (6 entries) |
| Definition Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | other | (226 entries) |
Global Index
A
Abs [inductive, in SearchTree]Abs [definition, in Trie]
Abs [inductive, in Redblack]
abstract [definition, in Trie]
abstraction_of_bogus_tree [lemma, in SearchTree]
AbsX [definition, in SearchTree]
Abs_T [constructor, in SearchTree]
Abs_E [constructor, in SearchTree]
Abs_three_ten [definition, in Trie]
Abs_helper [lemma, in Redblack]
Abs_T [constructor, in Redblack]
Abs_E [constructor, in Redblack]
add_edge [definition, in Color]
adj [definition, in Color]
adj_ext [lemma, in Color]
ADT [library]
ADT_SUMMARY.default [variable, in ADT]
ADT_SUMMARY.V [variable, in ADT]
ADT_SUMMARY [section, in ADT]
B
balance [definition, in Redblack]balance_relate [lemma, in Redblack]
balance_SearchTree [lemma, in Redblack]
balance_SearchTree [lemma, in Redblack]
balance_SearchTree [lemma, in Redblack]
Binom [library]
BinomQueue [module, in Binom]
BinomQueue.Abs [definition, in Binom]
BinomQueue.abs_perm [lemma, in Binom]
BinomQueue.can_relate [lemma, in Binom]
BinomQueue.carry [definition, in Binom]
BinomQueue.carry_elems [lemma, in Binom]
BinomQueue.carry_valid [lemma, in Binom]
BinomQueue.delete_max_Some_relate [lemma, in Binom]
BinomQueue.delete_max_None_relate [lemma, in Binom]
BinomQueue.delete_max_Some_priq [lemma, in Binom]
BinomQueue.delete_max [definition, in Binom]
BinomQueue.delete_max_aux [definition, in Binom]
BinomQueue.empty [definition, in Binom]
BinomQueue.empty_relate [lemma, in Binom]
BinomQueue.empty_priq [lemma, in Binom]
BinomQueue.find_max [definition, in Binom]
BinomQueue.find_max' [definition, in Binom]
BinomQueue.heap_delete_max [definition, in Binom]
BinomQueue.insert [definition, in Binom]
BinomQueue.insert_relate [lemma, in Binom]
BinomQueue.insert_priq [lemma, in Binom]
BinomQueue.join [definition, in Binom]
BinomQueue.join_elems [lemma, in Binom]
BinomQueue.join_valid [lemma, in Binom]
BinomQueue.key [definition, in Binom]
BinomQueue.Leaf [constructor, in Binom]
BinomQueue.manual_grade_for_priqueue_elems [definition, in Binom]
BinomQueue.merge [definition, in Binom]
BinomQueue.merge_relate [lemma, in Binom]
BinomQueue.merge_priq [lemma, in Binom]
BinomQueue.Node [constructor, in Binom]
BinomQueue.pow2heap [definition, in Binom]
BinomQueue.pow2heap' [definition, in Binom]
BinomQueue.priq [definition, in Binom]
BinomQueue.priqueue [definition, in Binom]
BinomQueue.priqueue_elems_ext [lemma, in Binom]
BinomQueue.priqueue_elems [inductive, in Binom]
BinomQueue.priq' [definition, in Binom]
BinomQueue.smash [definition, in Binom]
BinomQueue.smash_elems [lemma, in Binom]
BinomQueue.smash_valid [lemma, in Binom]
BinomQueue.tree [inductive, in Binom]
BinomQueue.tree_can_relate [lemma, in Binom]
BinomQueue.tree_perm [lemma, in Binom]
BinomQueue.tree_elems_ext [lemma, in Binom]
BinomQueue.tree_elems_node [constructor, in Binom]
BinomQueue.tree_elems_leaf [constructor, in Binom]
BinomQueue.tree_elems [inductive, in Binom]
BinomQueue.unzip [definition, in Binom]
Black [constructor, in Redblack]
C
can_relate [lemma, in SearchTree]cardinal_map [lemma, in Color]
check_too_clever [lemma, in SearchTree]
check_example_map [lemma, in SearchTree]
color [definition, in Color]
color [inductive, in Redblack]
Color [library]
coloring [definition, in Color]
coloring_ok [definition, in Color]
colors_of [definition, in Color]
color_correct [lemma, in Color]
color1 [definition, in Color]
combine [definition, in SearchTree]
combine [definition, in Redblack]
compute_with_StdLib_lt_dec [lemma, in Decide]
compute_with_lt_dec [lemma, in Decide]
cons_relate [lemma, in ADT]
contents [definition, in Multiset]
contents_perm [lemma, in Multiset]
contents_in [lemma, in Multiset]
contents_perm_aux [lemma, in Multiset]
create_relate [lemma, in ADT]
D
Decide [library]delete_contents [lemma, in Multiset]
domain_example_map [definition, in Color]
E
E [module, in Color]E [constructor, in SearchTree]
E [constructor, in Redblack]
elements [definition, in SearchTree]
elements [definition, in Redblack]
elements_relateX [lemma, in SearchTree]
elements_relate [lemma, in SearchTree]
elements_slow_elements [lemma, in SearchTree]
elements_relate_second_attempt [lemma, in SearchTree]
elements_relate [lemma, in SearchTree]
elements_relate [lemma, in Redblack]
elements_property [definition, in Redblack]
elements' [definition, in SearchTree]
elements' [definition, in Redblack]
empty [definition, in Trie]
empty [definition, in Multiset]
empty_tree_SearchTree [lemma, in SearchTree]
empty_tree_relate [lemma, in SearchTree]
empty_tree [definition, in SearchTree]
empty_relate [lemma, in Trie]
empty_is_trie [lemma, in Trie]
empty_tree_relate [lemma, in Redblack]
empty_tree_SearchTree [lemma, in Redblack]
empty_tree [definition, in Redblack]
eqb_reflect [lemma, in Perm]
eqlistA_Eeq_eq [lemma, in Color]
equivlistA_example [definition, in Color]
example_map [definition, in Color]
example_SearchTree_bad [lemma, in SearchTree]
example_SearchTree_good [lemma, in SearchTree]
example_map [definition, in SearchTree]
example_tree [definition, in SearchTree]
expand_range_SearchTree' [lemma, in Redblack]
Experiments [module, in Extract]
Experiments.E [definition, in Extract]
Experiments.empty_tree [definition, in Extract]
Experiments.insert [definition, in Extract]
Experiments.lookup [definition, in Extract]
Experiments.T [definition, in Extract]
Exploration1 [module, in Perm]
Exploration1.bogus_subtraction [lemma, in Perm]
Exploration1.butterfly [definition, in Perm]
Exploration1.first_le_second [definition, in Perm]
Exploration1.manual_grade_for_Permutation_properties [definition, in Perm]
Exploration1.maybe_swap_correct [lemma, in Perm]
Exploration1.maybe_swap_perm [lemma, in Perm]
Exploration1.maybe_swap_idempotent' [lemma, in Perm]
Exploration1.maybe_swap_idempotent [lemma, in Perm]
Exploration1.maybe_swap_idempotent [lemma, in Perm]
Exploration1.maybe_swap_321 [definition, in Perm]
Exploration1.maybe_swap_123 [definition, in Perm]
Exploration1.maybe_swap [definition, in Perm]
Exploration1.not_a_permutation [definition, in Perm]
Exploration1.omega_example2 [lemma, in Perm]
Exploration1.omega_example1 [lemma, in Perm]
Exploration1.omega_example1 [lemma, in Perm]
Exploration1.permut_example [definition, in Perm]
Extract [library]
F
FastEnough [module, in Trie]FastEnough.collisions [definition, in Trie]
FastEnough.collisions_pi [definition, in Trie]
FastEnough.loop [definition, in Trie]
fib [definition, in ADT]
fibish [definition, in ADT]
fibish_correct [lemma, in ADT]
fibonacci [definition, in ADT]
filter_sortE [lemma, in Color]
fold_right_rev_left [lemma, in Color]
forall_nodes [definition, in SearchTree]
Forall_nth [lemma, in Sort]
Forall_perm [lemma, in Perm]
G
G [definition, in Color]graph [definition, in Color]
H
how_many_subgoals_remaining [definition, in Redblack]I
InA_map_fst_key [lemma, in Color]InA_example [definition, in Color]
ins [definition, in Trie]
ins [definition, in Redblack]
insert [definition, in SearchTree]
insert [definition, in Trie]
insert [definition, in Sort]
insert [definition, in Redblack]
insertion_sort_correct [lemma, in Sort]
insertion_sort_correct [lemma, in Multiset]
insert_relate' [lemma, in SearchTree]
insert_SearchTree [lemma, in SearchTree]
insert_relate [lemma, in SearchTree]
insert_relate [lemma, in Trie]
insert_is_trie [lemma, in Trie]
insert_sorted' [lemma, in Sort]
insert_sorted [lemma, in Sort]
insert_perm [lemma, in Sort]
insert_is_redblack [lemma, in Redblack]
insert_relate [lemma, in Redblack]
insert_SearchTree [lemma, in Redblack]
insert_contents [lemma, in Multiset]
ins_is_redblack [lemma, in Redblack]
ins_relate [lemma, in Redblack]
ins_SearchTree [lemma, in Redblack]
ins_not_E [lemma, in Redblack]
ins_not_E [lemma, in Redblack]
ins_not_E [lemma, in Redblack]
int [axiom, in Extract]
Integers [module, in Trie]
Integers.add [definition, in Trie]
Integers.addc [definition, in Trie]
Integers.addc_correct [lemma, in Trie]
Integers.add_correct [lemma, in Trie]
Integers.compare [definition, in Trie]
Integers.compare_correct [lemma, in Trie]
Integers.comparison [inductive, in Trie]
Integers.Eq [constructor, in Trie]
Integers.Gt [constructor, in Trie]
Integers.Lt [constructor, in Trie]
Integers.positive [inductive, in Trie]
Integers.positive2nat [definition, in Trie]
Integers.positive2nat_pos [lemma, in Trie]
Integers.print_in_binary [definition, in Trie]
Integers.succ [definition, in Trie]
Integers.succ_correct [lemma, in Trie]
Integers.ten [definition, in Trie]
Integers.xH [constructor, in Trie]
Integers.xI [constructor, in Trie]
Integers.xO [constructor, in Trie]
Integers.Z [inductive, in Trie]
Integers.Zneg [constructor, in Trie]
Integers.Zpos [constructor, in Trie]
Integers.Z0 [constructor, in Trie]
_ ~ 0 [notation, in Trie]
_ ~ 1 [notation, in Trie]
IntMaps [module, in Extract]
IntMaps.total_map [definition, in Extract]
IntMaps.t_update_shadow [lemma, in Extract]
IntMaps.t_update_neq [lemma, in Extract]
IntMaps.t_update_eq [lemma, in Extract]
IntMaps.t_update [definition, in Extract]
IntMaps.t_empty [definition, in Extract]
int_ltb_reflect [lemma, in Extract]
int2Z [axiom, in Extract]
in_colors_of_1 [lemma, in Color]
In_decidable [lemma, in SearchTree]
in_perm_delete [lemma, in Multiset]
in_4_pi [definition, in Decide]
IsRB_b [constructor, in Redblack]
IsRB_r [constructor, in Redblack]
IsRB_leaf [constructor, in Redblack]
is_trie [definition, in Trie]
is_a_sorting_algorithm [definition, in Selection]
is_a_sorting_algorithm [definition, in Sort]
is_redblack_toblack [lemma, in Redblack]
is_redblack [inductive, in Redblack]
is_a_sorting_algorithm' [definition, in Multiset]
K
key [definition, in SearchTree]key [definition, in Redblack]
L
L [module, in ADT]Leaf [constructor, in Trie]
leb_reflect [lemma, in Perm]
LISTISH [module, in ADT]
LISTISH.cons [axiom, in ADT]
LISTISH.create [axiom, in ADT]
LISTISH.list [axiom, in ADT]
LISTISH.nth [axiom, in ADT]
list_delete [definition, in Multiset]
list_nat_in [definition, in Decide]
list_nat_eq_dec [definition, in Decide]
List_Priqueue.merge_relate [lemma, in Priqueue]
List_Priqueue.merge_priq [lemma, in Priqueue]
List_Priqueue.delete_max_Some_relate [lemma, in Priqueue]
List_Priqueue.delete_max_None_relate [lemma, in Priqueue]
List_Priqueue.delete_max_Some_priq [lemma, in Priqueue]
List_Priqueue.insert_relate [lemma, in Priqueue]
List_Priqueue.insert_priq [lemma, in Priqueue]
List_Priqueue.empty_relate [lemma, in Priqueue]
List_Priqueue.empty_priq [lemma, in Priqueue]
List_Priqueue.abs_perm [lemma, in Priqueue]
List_Priqueue.can_relate [lemma, in Priqueue]
List_Priqueue.Abs [definition, in Priqueue]
List_Priqueue.Abs_intro [constructor, in Priqueue]
List_Priqueue.Abs' [inductive, in Priqueue]
List_Priqueue.priq [definition, in Priqueue]
List_Priqueue.merge [definition, in Priqueue]
List_Priqueue.delete_max [definition, in Priqueue]
List_Priqueue.insert [definition, in Priqueue]
List_Priqueue.empty [definition, in Priqueue]
List_Priqueue.priqueue [definition, in Priqueue]
List_Priqueue.key [definition, in Priqueue]
List_Priqueue.select_biggest [lemma, in Priqueue]
List_Priqueue.select_biggest_aux [lemma, in Priqueue]
List_Priqueue.select_perm [lemma, in Priqueue]
List_Priqueue.select [definition, in Priqueue]
List_Priqueue [module, in Priqueue]
list2map [definition, in SearchTree]
list2map_not_in_default [lemma, in SearchTree]
list2map_app_right [lemma, in SearchTree]
list2map_app_left [lemma, in SearchTree]
look [definition, in Trie]
lookup [definition, in SearchTree]
lookup [definition, in Trie]
lookup [definition, in Redblack]
lookup_relateX [lemma, in SearchTree]
lookup_relate' [lemma, in SearchTree]
lookup_relate [lemma, in SearchTree]
lookup_relate [lemma, in Trie]
lookup_relate [lemma, in Redblack]
look_ins_other [lemma, in Trie]
look_ins_same [lemma, in Trie]
look_leaf [lemma, in Trie]
low_deg [definition, in Color]
ltb [axiom, in Extract]
ltb_reflect [lemma, in Perm]
ltb_lt [axiom, in Extract]
lt_proper [lemma, in Color]
lt_strict [lemma, in Color]
L_Abs [inductive, in ADT]
L.cons [definition, in ADT]
L.create [definition, in ADT]
L.list [definition, in ADT]
L.nth [definition, in ADT]
M
M [module, in Color]makeBlack [definition, in Redblack]
makeblack_fiddle [lemma, in Redblack]
makeBlack_relate [lemma, in Redblack]
manual_grade_for_elements_relate_informal [definition, in SearchTree]
manual_grade_for_successor_of_Z_constant_time [definition, in Trie]
manual_grade_for_permutations_vs_multiset [definition, in Multiset]
MapsTable [module, in ADT]
MapsTable.default [definition, in ADT]
MapsTable.empty [definition, in ADT]
MapsTable.gempty [lemma, in ADT]
MapsTable.get [definition, in ADT]
MapsTable.gso [lemma, in ADT]
MapsTable.gss [lemma, in ADT]
MapsTable.key [definition, in ADT]
MapsTable.set [definition, in ADT]
MapsTable.table [definition, in ADT]
MapsTable.V [definition, in ADT]
Mdomain [definition, in Color]
mk_graph [definition, in Color]
Mremove_cardinal_less [lemma, in Color]
Mremove_elements [lemma, in Color]
multiset [definition, in Multiset]
Multiset [library]
multiset_delete [definition, in Multiset]
N
naive_lookup_relateX [lemma, in SearchTree]nat2pos [definition, in Trie]
nat2pos_injective [lemma, in Trie]
nat2pos2nat [lemma, in Trie]
nearly_redblack [inductive, in Redblack]
node [definition, in Color]
Node [constructor, in Trie]
nodemap [definition, in Color]
nodes [definition, in Color]
nodeset [definition, in Color]
not_naive_lookup_relateX [lemma, in SearchTree]
not_elements_relate [lemma, in SearchTree]
no_selfloop [definition, in Color]
nrRB_b [constructor, in Redblack]
nrRB_r [constructor, in Redblack]
nth_relate [lemma, in ADT]
nth_firstn [lemma, in ADT]
O
out_of_gas [definition, in Selection]O_Abs [definition, in ADT]
P
palette [definition, in Color]Perm [library]
perm_contents [lemma, in Multiset]
pos2nat [definition, in Trie]
pos2nat_injective [lemma, in Trie]
pos2nat2pos [lemma, in Trie]
Preface [library]
PRIQUEUE [module, in Priqueue]
Priqueue [library]
PRIQUEUE.Abs [axiom, in Priqueue]
PRIQUEUE.abs_perm [axiom, in Priqueue]
PRIQUEUE.can_relate [axiom, in Priqueue]
PRIQUEUE.delete_max_Some_relate [axiom, in Priqueue]
PRIQUEUE.delete_max_Some_priq [axiom, in Priqueue]
PRIQUEUE.delete_max_None_relate [axiom, in Priqueue]
PRIQUEUE.delete_max [axiom, in Priqueue]
PRIQUEUE.empty [axiom, in Priqueue]
PRIQUEUE.empty_relate [axiom, in Priqueue]
PRIQUEUE.empty_priq [axiom, in Priqueue]
PRIQUEUE.insert [axiom, in Priqueue]
PRIQUEUE.insert_relate [axiom, in Priqueue]
PRIQUEUE.insert_priq [axiom, in Priqueue]
PRIQUEUE.key [definition, in Priqueue]
PRIQUEUE.merge [axiom, in Priqueue]
PRIQUEUE.merge_relate [axiom, in Priqueue]
PRIQUEUE.merge_priq [axiom, in Priqueue]
PRIQUEUE.priq [axiom, in Priqueue]
PRIQUEUE.priqueue [axiom, in Priqueue]
Proper_eq_key_elt [lemma, in Color]
Proper_eq_eq [lemma, in Color]
R
RatherSlow [module, in Trie]RatherSlow.collisions [definition, in Trie]
RatherSlow.collisions_pi [definition, in Trie]
RatherSlow.empty [definition, in Trie]
RatherSlow.loop [definition, in Trie]
RatherSlow.total_mapz [definition, in Trie]
RatherSlow.update [definition, in Trie]
Red [constructor, in Redblack]
Redblack [library]
reflect_example2 [definition, in Perm]
reflect_example1 [definition, in Perm]
remove_node [definition, in Color]
repeat [definition, in ADT]
repeat_step_relate [lemma, in ADT]
S
S [module, in Color]same_mod_10 [definition, in Color]
same_contents_iff_perm [lemma, in Multiset]
ScratchPad [module, in Decide]
ScratchPad.greater23 [lemma, in Decide]
ScratchPad.is_3_less_7 [definition, in Decide]
ScratchPad.left [constructor, in Decide]
ScratchPad.less37 [lemma, in Decide]
ScratchPad.lt_dec_equivalent [lemma, in Decide]
ScratchPad.lt_dec' [definition, in Decide]
ScratchPad.lt_dec [definition, in Decide]
ScratchPad.right [constructor, in Decide]
ScratchPad.sumbool [inductive, in Decide]
ScratchPad.t1 [definition, in Decide]
ScratchPad.t2 [definition, in Decide]
ScratchPad.t4 [definition, in Decide]
ScratchPad.v1a [definition, in Decide]
ScratchPad.v1b [definition, in Decide]
ScratchPad.v2a [definition, in Decide]
ScratchPad.v3 [definition, in Decide]
{ _ } + { _ } (type_scope) [notation, in Decide]
ScratchPad2 [module, in Decide]
ScratchPad2.insert [definition, in Decide]
ScratchPad2.insert_sorted [lemma, in Decide]
ScratchPad2.le_dec [definition, in Decide]
ScratchPad2.lt_dec_axiom_2 [axiom, in Decide]
ScratchPad2.lt_dec_axiom_1 [axiom, in Decide]
ScratchPad2.lt_dec [definition, in Decide]
ScratchPad2.max_with_axiom [definition, in Decide]
ScratchPad2.prove_with_max_axiom [lemma, in Decide]
ScratchPad2.sort [definition, in Decide]
ScratchPad2.sorted [inductive, in Decide]
ScratchPad2.sorted_cons [constructor, in Decide]
ScratchPad2.sorted_1 [constructor, in Decide]
ScratchPad2.sorted_nil [constructor, in Decide]
SearchTree [inductive, in SearchTree]
SearchTree [inductive, in Redblack]
SearchTree [library]
SearchTreeX [definition, in SearchTree]
SearchTree' [inductive, in SearchTree]
SearchTree' [inductive, in Redblack]
SearchTree'_le [lemma, in SearchTree]
SearchTree'_le [lemma, in Redblack]
SearchTree2 [module, in Extract]
SearchTree2.Abs [inductive, in Extract]
SearchTree2.Abs_T [constructor, in Extract]
SearchTree2.Abs_E [constructor, in Extract]
SearchTree2.combine [definition, in Extract]
SearchTree2.E [constructor, in Extract]
SearchTree2.elements [definition, in Extract]
SearchTree2.elements' [definition, in Extract]
SearchTree2.empty_tree_relate [lemma, in Extract]
SearchTree2.empty_tree [definition, in Extract]
SearchTree2.insert [definition, in Extract]
SearchTree2.insert_relate [lemma, in Extract]
SearchTree2.key [definition, in Extract]
SearchTree2.lookup [definition, in Extract]
SearchTree2.lookup_relate [lemma, in Extract]
SearchTree2.T [constructor, in Extract]
SearchTree2.tree [inductive, in Extract]
SearchTree2.TREES [section, in Extract]
SearchTree2.TREES.default [variable, in Extract]
SearchTree2.TREES.V [variable, in Extract]
SearchTree2.unrealistically_strong_can_relate [lemma, in Extract]
SectionExample1 [module, in SearchTree]
SectionExample1.empty [definition, in SearchTree]
SectionExample1.lookup [definition, in SearchTree]
SectionExample1.lookup_empty [lemma, in SearchTree]
SectionExample1.mymap [definition, in SearchTree]
SectionExample2 [module, in SearchTree]
SectionExample2.empty [definition, in SearchTree]
SectionExample2.lookup [definition, in SearchTree]
SectionExample2.lookup_empty [lemma, in SearchTree]
SectionExample2.MAPS [section, in SearchTree]
SectionExample2.MAPS.default [variable, in SearchTree]
SectionExample2.MAPS.V [variable, in SearchTree]
SectionExample2.mymap [definition, in SearchTree]
select [definition, in Selection]
Selection [library]
selection_sort_is_correct [lemma, in Selection]
selection_sort_sorted [lemma, in Selection]
selection_sort_sorted_aux [lemma, in Selection]
selection_sort_perm [lemma, in Selection]
selection_sort_correct [definition, in Selection]
selection_sort [definition, in Selection]
select_terminates [lemma, in Color]
select_smallest [lemma, in Selection]
select_smallest_aux [lemma, in Selection]
select_perm [lemma, in Selection]
selsort [definition, in Selection]
selsort_perm [lemma, in Selection]
selsort'_perm [lemma, in Selection]
singleton [definition, in Multiset]
Sin_domain [lemma, in Color]
sixlist [definition, in ADT]
slow_elements_range [lemma, in SearchTree]
slow_elements [definition, in SearchTree]
Snot_in_empty [lemma, in Color]
sort [definition, in Sort]
Sort [library]
sorted [inductive, in Selection]
sorted [inductive, in Sort]
Sorted_lt_key [lemma, in Color]
sorted_cons [constructor, in Selection]
sorted_1 [constructor, in Selection]
sorted_nil [constructor, in Selection]
sorted_sorted' [lemma, in Sort]
sorted_cons [constructor, in Sort]
sorted_1 [constructor, in Sort]
sorted_nil [constructor, in Sort]
sorted' [definition, in Sort]
sorted'_sorted [lemma, in Sort]
SortE_equivlistE_eqlistE [lemma, in Color]
sort_pi [definition, in Selection]
sort_sorted' [lemma, in Sort]
sort_sorted [lemma, in Sort]
sort_perm [lemma, in Sort]
sort_pi [definition, in Sort]
sort_specifications_equivalent [lemma, in Multiset]
sort_contents [lemma, in Multiset]
sort_pi_same_contents [definition, in Multiset]
sort_pi [definition, in Multiset]
Sort1 [module, in Extract]
Sort1.insert [definition, in Extract]
Sort1.sort [definition, in Extract]
specialize_SortA_equivlistA_eqlistA [lemma, in Color]
Sremove_cardinal_less [lemma, in Color]
Sremove_elements [lemma, in Color]
Sremove_elements [lemma, in Color]
step [definition, in ADT]
stepish [definition, in ADT]
step_relate [lemma, in ADT]
ST_intro [constructor, in SearchTree]
ST_T [constructor, in SearchTree]
ST_E [constructor, in SearchTree]
ST_intro [constructor, in Redblack]
ST_T [constructor, in Redblack]
ST_E [constructor, in Redblack]
subset_nodes_sub [lemma, in Color]
subset_nodes [definition, in Color]
T
T [constructor, in SearchTree]T [constructor, in Redblack]
TABLE [module, in ADT]
TABLE.default [axiom, in ADT]
TABLE.empty [axiom, in ADT]
TABLE.gempty [axiom, in ADT]
TABLE.get [axiom, in ADT]
TABLE.gso [axiom, in ADT]
TABLE.gss [axiom, in ADT]
TABLE.key [definition, in ADT]
TABLE.set [axiom, in ADT]
TABLE.table [axiom, in ADT]
TABLE.V [axiom, in ADT]
three_ten [definition, in Trie]
three_less_seven_2 [lemma, in Decide]
three_less_seven_1 [lemma, in Decide]
too_much_gas [definition, in Selection]
tree [inductive, in SearchTree]
tree [inductive, in Redblack]
TREES [section, in SearchTree]
TREES [section, in Redblack]
TREES.default [variable, in SearchTree]
TREES.default [variable, in Redblack]
TREES.EXAMPLES [section, in SearchTree]
TREES.EXAMPLES.v2 [variable, in SearchTree]
TREES.EXAMPLES.v4 [variable, in SearchTree]
TREES.EXAMPLES.v5 [variable, in SearchTree]
TREES.V [variable, in SearchTree]
TREES.V [variable, in Redblack]
TreeTable [module, in ADT]
TreeTable.default [definition, in ADT]
TreeTable.empty [definition, in ADT]
TreeTable.gempty [lemma, in ADT]
TreeTable.get [definition, in ADT]
TreeTable.gso [lemma, in ADT]
TreeTable.gss [lemma, in ADT]
TreeTable.key [definition, in ADT]
TreeTable.set [definition, in ADT]
TreeTable.table [definition, in ADT]
TreeTable.V [definition, in ADT]
TreeTable2 [module, in ADT]
TreeTable2.default [definition, in ADT]
TreeTable2.empty [definition, in ADT]
TreeTable2.gempty [lemma, in ADT]
TreeTable2.get [definition, in ADT]
TreeTable2.gso [lemma, in ADT]
TreeTable2.gss [lemma, in ADT]
TreeTable2.key [definition, in ADT]
TreeTable2.set [definition, in ADT]
TreeTable2.table [definition, in ADT]
TreeTable2.V [definition, in ADT]
trie [inductive, in Trie]
Trie [library]
trie_table [definition, in Trie]
T_neq_E [lemma, in Redblack]
U
undirected [definition, in Color]union [definition, in Multiset]
union_comm [lemma, in Multiset]
union_assoc [lemma, in Multiset]
unrealistically_strong_can_relate [lemma, in SearchTree]
V
value [definition, in Multiset]VerySlow [module, in Trie]
VerySlow.collisions [definition, in Trie]
VerySlow.collisions_pi [definition, in Trie]
VerySlow.loop [definition, in Trie]
W
WF [module, in Color]WP [module, in Color]
Z
Z_ltb_reflect [lemma, in Extract]Z_eqb_reflect [lemma, in Extract]
other
_ >? _ (nat_scope) [notation, in Perm]_ >=? _ (nat_scope) [notation, in Perm]
Notation Index
I
_ ~ 0 [in Trie]_ ~ 1 [in Trie]
S
{ _ } + { _ } (type_scope) [in Decide]other
_ >? _ (nat_scope) [in Perm]_ >=? _ (nat_scope) [in Perm]
Module Index
B
BinomQueue [in Binom]E
E [in Color]Experiments [in Extract]
Exploration1 [in Perm]
F
FastEnough [in Trie]I
Integers [in Trie]IntMaps [in Extract]
L
L [in ADT]LISTISH [in ADT]
List_Priqueue [in Priqueue]
M
M [in Color]MapsTable [in ADT]
P
PRIQUEUE [in Priqueue]R
RatherSlow [in Trie]S
S [in Color]ScratchPad [in Decide]
ScratchPad2 [in Decide]
SearchTree2 [in Extract]
SectionExample1 [in SearchTree]
SectionExample2 [in SearchTree]
Sort1 [in Extract]
T
TABLE [in ADT]TreeTable [in ADT]
TreeTable2 [in ADT]
V
VerySlow [in Trie]W
WF [in Color]WP [in Color]
Variable Index
A
ADT_SUMMARY.default [in ADT]ADT_SUMMARY.V [in ADT]
S
SearchTree2.TREES.default [in Extract]SearchTree2.TREES.V [in Extract]
SectionExample2.MAPS.default [in SearchTree]
SectionExample2.MAPS.V [in SearchTree]
T
TREES.default [in SearchTree]TREES.default [in Redblack]
TREES.EXAMPLES.v2 [in SearchTree]
TREES.EXAMPLES.v4 [in SearchTree]
TREES.EXAMPLES.v5 [in SearchTree]
TREES.V [in SearchTree]
TREES.V [in Redblack]
Library Index
A
ADTB
BinomC
ColorD
DecideE
ExtractM
MultisetP
PermPreface
Priqueue
R
RedblackS
SearchTreeSelection
Sort
T
TrieLemma Index
A
abstraction_of_bogus_tree [in SearchTree]Abs_helper [in Redblack]
adj_ext [in Color]
B
balance_relate [in Redblack]balance_SearchTree [in Redblack]
balance_SearchTree [in Redblack]
balance_SearchTree [in Redblack]
BinomQueue.abs_perm [in Binom]
BinomQueue.can_relate [in Binom]
BinomQueue.carry_elems [in Binom]
BinomQueue.carry_valid [in Binom]
BinomQueue.delete_max_Some_relate [in Binom]
BinomQueue.delete_max_None_relate [in Binom]
BinomQueue.delete_max_Some_priq [in Binom]
BinomQueue.empty_relate [in Binom]
BinomQueue.empty_priq [in Binom]
BinomQueue.insert_relate [in Binom]
BinomQueue.insert_priq [in Binom]
BinomQueue.join_elems [in Binom]
BinomQueue.join_valid [in Binom]
BinomQueue.merge_relate [in Binom]
BinomQueue.merge_priq [in Binom]
BinomQueue.priqueue_elems_ext [in Binom]
BinomQueue.smash_elems [in Binom]
BinomQueue.smash_valid [in Binom]
BinomQueue.tree_can_relate [in Binom]
BinomQueue.tree_perm [in Binom]
BinomQueue.tree_elems_ext [in Binom]
C
can_relate [in SearchTree]cardinal_map [in Color]
check_too_clever [in SearchTree]
check_example_map [in SearchTree]
color_correct [in Color]
compute_with_StdLib_lt_dec [in Decide]
compute_with_lt_dec [in Decide]
cons_relate [in ADT]
contents_perm [in Multiset]
contents_in [in Multiset]
contents_perm_aux [in Multiset]
create_relate [in ADT]
D
delete_contents [in Multiset]E
elements_relateX [in SearchTree]elements_relate [in SearchTree]
elements_slow_elements [in SearchTree]
elements_relate_second_attempt [in SearchTree]
elements_relate [in SearchTree]
elements_relate [in Redblack]
empty_tree_SearchTree [in SearchTree]
empty_tree_relate [in SearchTree]
empty_relate [in Trie]
empty_is_trie [in Trie]
empty_tree_relate [in Redblack]
empty_tree_SearchTree [in Redblack]
eqb_reflect [in Perm]
eqlistA_Eeq_eq [in Color]
example_SearchTree_bad [in SearchTree]
example_SearchTree_good [in SearchTree]
expand_range_SearchTree' [in Redblack]
Exploration1.bogus_subtraction [in Perm]
Exploration1.maybe_swap_correct [in Perm]
Exploration1.maybe_swap_perm [in Perm]
Exploration1.maybe_swap_idempotent' [in Perm]
Exploration1.maybe_swap_idempotent [in Perm]
Exploration1.maybe_swap_idempotent [in Perm]
Exploration1.omega_example2 [in Perm]
Exploration1.omega_example1 [in Perm]
Exploration1.omega_example1 [in Perm]
F
fibish_correct [in ADT]filter_sortE [in Color]
fold_right_rev_left [in Color]
Forall_nth [in Sort]
Forall_perm [in Perm]
I
InA_map_fst_key [in Color]insertion_sort_correct [in Sort]
insertion_sort_correct [in Multiset]
insert_relate' [in SearchTree]
insert_SearchTree [in SearchTree]
insert_relate [in SearchTree]
insert_relate [in Trie]
insert_is_trie [in Trie]
insert_sorted' [in Sort]
insert_sorted [in Sort]
insert_perm [in Sort]
insert_is_redblack [in Redblack]
insert_relate [in Redblack]
insert_SearchTree [in Redblack]
insert_contents [in Multiset]
ins_is_redblack [in Redblack]
ins_relate [in Redblack]
ins_SearchTree [in Redblack]
ins_not_E [in Redblack]
ins_not_E [in Redblack]
ins_not_E [in Redblack]
Integers.addc_correct [in Trie]
Integers.add_correct [in Trie]
Integers.compare_correct [in Trie]
Integers.positive2nat_pos [in Trie]
Integers.succ_correct [in Trie]
IntMaps.t_update_shadow [in Extract]
IntMaps.t_update_neq [in Extract]
IntMaps.t_update_eq [in Extract]
int_ltb_reflect [in Extract]
in_colors_of_1 [in Color]
In_decidable [in SearchTree]
in_perm_delete [in Multiset]
is_redblack_toblack [in Redblack]
L
leb_reflect [in Perm]List_Priqueue.merge_relate [in Priqueue]
List_Priqueue.merge_priq [in Priqueue]
List_Priqueue.delete_max_Some_relate [in Priqueue]
List_Priqueue.delete_max_None_relate [in Priqueue]
List_Priqueue.delete_max_Some_priq [in Priqueue]
List_Priqueue.insert_relate [in Priqueue]
List_Priqueue.insert_priq [in Priqueue]
List_Priqueue.empty_relate [in Priqueue]
List_Priqueue.empty_priq [in Priqueue]
List_Priqueue.abs_perm [in Priqueue]
List_Priqueue.can_relate [in Priqueue]
List_Priqueue.select_biggest [in Priqueue]
List_Priqueue.select_biggest_aux [in Priqueue]
List_Priqueue.select_perm [in Priqueue]
list2map_not_in_default [in SearchTree]
list2map_app_right [in SearchTree]
list2map_app_left [in SearchTree]
lookup_relateX [in SearchTree]
lookup_relate' [in SearchTree]
lookup_relate [in SearchTree]
lookup_relate [in Trie]
lookup_relate [in Redblack]
look_ins_other [in Trie]
look_ins_same [in Trie]
look_leaf [in Trie]
ltb_reflect [in Perm]
lt_proper [in Color]
lt_strict [in Color]
M
makeblack_fiddle [in Redblack]makeBlack_relate [in Redblack]
MapsTable.gempty [in ADT]
MapsTable.gso [in ADT]
MapsTable.gss [in ADT]
Mremove_cardinal_less [in Color]
Mremove_elements [in Color]
N
naive_lookup_relateX [in SearchTree]nat2pos_injective [in Trie]
nat2pos2nat [in Trie]
not_naive_lookup_relateX [in SearchTree]
not_elements_relate [in SearchTree]
nth_relate [in ADT]
nth_firstn [in ADT]
P
perm_contents [in Multiset]pos2nat_injective [in Trie]
pos2nat2pos [in Trie]
Proper_eq_key_elt [in Color]
Proper_eq_eq [in Color]
R
repeat_step_relate [in ADT]S
same_contents_iff_perm [in Multiset]ScratchPad.greater23 [in Decide]
ScratchPad.less37 [in Decide]
ScratchPad.lt_dec_equivalent [in Decide]
ScratchPad2.insert_sorted [in Decide]
ScratchPad2.prove_with_max_axiom [in Decide]
SearchTree'_le [in SearchTree]
SearchTree'_le [in Redblack]
SearchTree2.empty_tree_relate [in Extract]
SearchTree2.insert_relate [in Extract]
SearchTree2.lookup_relate [in Extract]
SearchTree2.unrealistically_strong_can_relate [in Extract]
SectionExample1.lookup_empty [in SearchTree]
SectionExample2.lookup_empty [in SearchTree]
selection_sort_is_correct [in Selection]
selection_sort_sorted [in Selection]
selection_sort_sorted_aux [in Selection]
selection_sort_perm [in Selection]
select_terminates [in Color]
select_smallest [in Selection]
select_smallest_aux [in Selection]
select_perm [in Selection]
selsort_perm [in Selection]
selsort'_perm [in Selection]
Sin_domain [in Color]
slow_elements_range [in SearchTree]
Snot_in_empty [in Color]
Sorted_lt_key [in Color]
sorted_sorted' [in Sort]
sorted'_sorted [in Sort]
SortE_equivlistE_eqlistE [in Color]
sort_sorted' [in Sort]
sort_sorted [in Sort]
sort_perm [in Sort]
sort_specifications_equivalent [in Multiset]
sort_contents [in Multiset]
specialize_SortA_equivlistA_eqlistA [in Color]
Sremove_cardinal_less [in Color]
Sremove_elements [in Color]
Sremove_elements [in Color]
step_relate [in ADT]
subset_nodes_sub [in Color]
T
three_less_seven_2 [in Decide]three_less_seven_1 [in Decide]
TreeTable.gempty [in ADT]
TreeTable.gso [in ADT]
TreeTable.gss [in ADT]
TreeTable2.gempty [in ADT]
TreeTable2.gso [in ADT]
TreeTable2.gss [in ADT]
T_neq_E [in Redblack]
U
union_comm [in Multiset]union_assoc [in Multiset]
unrealistically_strong_can_relate [in SearchTree]
Z
Z_ltb_reflect [in Extract]Z_eqb_reflect [in Extract]
Constructor Index
A
Abs_T [in SearchTree]Abs_E [in SearchTree]
Abs_T [in Redblack]
Abs_E [in Redblack]
B
BinomQueue.Leaf [in Binom]BinomQueue.Node [in Binom]
BinomQueue.tree_elems_node [in Binom]
BinomQueue.tree_elems_leaf [in Binom]
Black [in Redblack]
E
E [in SearchTree]E [in Redblack]
I
Integers.Eq [in Trie]Integers.Gt [in Trie]
Integers.Lt [in Trie]
Integers.xH [in Trie]
Integers.xI [in Trie]
Integers.xO [in Trie]
Integers.Zneg [in Trie]
Integers.Zpos [in Trie]
Integers.Z0 [in Trie]
IsRB_b [in Redblack]
IsRB_r [in Redblack]
IsRB_leaf [in Redblack]
L
Leaf [in Trie]List_Priqueue.Abs_intro [in Priqueue]
N
Node [in Trie]nrRB_b [in Redblack]
nrRB_r [in Redblack]
R
Red [in Redblack]S
ScratchPad.left [in Decide]ScratchPad.right [in Decide]
ScratchPad2.sorted_cons [in Decide]
ScratchPad2.sorted_1 [in Decide]
ScratchPad2.sorted_nil [in Decide]
SearchTree2.Abs_T [in Extract]
SearchTree2.Abs_E [in Extract]
SearchTree2.E [in Extract]
SearchTree2.T [in Extract]
sorted_cons [in Selection]
sorted_1 [in Selection]
sorted_nil [in Selection]
sorted_cons [in Sort]
sorted_1 [in Sort]
sorted_nil [in Sort]
ST_intro [in SearchTree]
ST_T [in SearchTree]
ST_E [in SearchTree]
ST_intro [in Redblack]
ST_T [in Redblack]
ST_E [in Redblack]
T
T [in SearchTree]T [in Redblack]
Axiom Index
I
int [in Extract]int2Z [in Extract]
L
LISTISH.cons [in ADT]LISTISH.create [in ADT]
LISTISH.list [in ADT]
LISTISH.nth [in ADT]
ltb [in Extract]
ltb_lt [in Extract]
P
PRIQUEUE.Abs [in Priqueue]PRIQUEUE.abs_perm [in Priqueue]
PRIQUEUE.can_relate [in Priqueue]
PRIQUEUE.delete_max_Some_relate [in Priqueue]
PRIQUEUE.delete_max_Some_priq [in Priqueue]
PRIQUEUE.delete_max_None_relate [in Priqueue]
PRIQUEUE.delete_max [in Priqueue]
PRIQUEUE.empty [in Priqueue]
PRIQUEUE.empty_relate [in Priqueue]
PRIQUEUE.empty_priq [in Priqueue]
PRIQUEUE.insert [in Priqueue]
PRIQUEUE.insert_relate [in Priqueue]
PRIQUEUE.insert_priq [in Priqueue]
PRIQUEUE.merge [in Priqueue]
PRIQUEUE.merge_relate [in Priqueue]
PRIQUEUE.merge_priq [in Priqueue]
PRIQUEUE.priq [in Priqueue]
PRIQUEUE.priqueue [in Priqueue]
S
ScratchPad2.lt_dec_axiom_2 [in Decide]ScratchPad2.lt_dec_axiom_1 [in Decide]
T
TABLE.default [in ADT]TABLE.empty [in ADT]
TABLE.gempty [in ADT]
TABLE.get [in ADT]
TABLE.gso [in ADT]
TABLE.gss [in ADT]
TABLE.set [in ADT]
TABLE.table [in ADT]
TABLE.V [in ADT]
Inductive Index
A
Abs [in SearchTree]Abs [in Redblack]
B
BinomQueue.priqueue_elems [in Binom]BinomQueue.tree [in Binom]
BinomQueue.tree_elems [in Binom]
C
color [in Redblack]I
Integers.comparison [in Trie]Integers.positive [in Trie]
Integers.Z [in Trie]
is_redblack [in Redblack]
L
List_Priqueue.Abs' [in Priqueue]L_Abs [in ADT]
N
nearly_redblack [in Redblack]S
ScratchPad.sumbool [in Decide]ScratchPad2.sorted [in Decide]
SearchTree [in SearchTree]
SearchTree [in Redblack]
SearchTree' [in SearchTree]
SearchTree' [in Redblack]
SearchTree2.Abs [in Extract]
SearchTree2.tree [in Extract]
sorted [in Selection]
sorted [in Sort]
T
tree [in SearchTree]tree [in Redblack]
trie [in Trie]
Section Index
A
ADT_SUMMARY [in ADT]S
SearchTree2.TREES [in Extract]SectionExample2.MAPS [in SearchTree]
T
TREES [in SearchTree]TREES [in Redblack]
TREES.EXAMPLES [in SearchTree]
Definition Index
A
Abs [in Trie]abstract [in Trie]
AbsX [in SearchTree]
Abs_three_ten [in Trie]
add_edge [in Color]
adj [in Color]
B
balance [in Redblack]BinomQueue.Abs [in Binom]
BinomQueue.carry [in Binom]
BinomQueue.delete_max [in Binom]
BinomQueue.delete_max_aux [in Binom]
BinomQueue.empty [in Binom]
BinomQueue.find_max [in Binom]
BinomQueue.find_max' [in Binom]
BinomQueue.heap_delete_max [in Binom]
BinomQueue.insert [in Binom]
BinomQueue.join [in Binom]
BinomQueue.key [in Binom]
BinomQueue.manual_grade_for_priqueue_elems [in Binom]
BinomQueue.merge [in Binom]
BinomQueue.pow2heap [in Binom]
BinomQueue.pow2heap' [in Binom]
BinomQueue.priq [in Binom]
BinomQueue.priqueue [in Binom]
BinomQueue.priq' [in Binom]
BinomQueue.smash [in Binom]
BinomQueue.unzip [in Binom]
C
color [in Color]coloring [in Color]
coloring_ok [in Color]
colors_of [in Color]
color1 [in Color]
combine [in SearchTree]
combine [in Redblack]
contents [in Multiset]
D
domain_example_map [in Color]E
elements [in SearchTree]elements [in Redblack]
elements_property [in Redblack]
elements' [in SearchTree]
elements' [in Redblack]
empty [in Trie]
empty [in Multiset]
empty_tree [in SearchTree]
empty_tree [in Redblack]
equivlistA_example [in Color]
example_map [in Color]
example_map [in SearchTree]
example_tree [in SearchTree]
Experiments.E [in Extract]
Experiments.empty_tree [in Extract]
Experiments.insert [in Extract]
Experiments.lookup [in Extract]
Experiments.T [in Extract]
Exploration1.butterfly [in Perm]
Exploration1.first_le_second [in Perm]
Exploration1.manual_grade_for_Permutation_properties [in Perm]
Exploration1.maybe_swap_321 [in Perm]
Exploration1.maybe_swap_123 [in Perm]
Exploration1.maybe_swap [in Perm]
Exploration1.not_a_permutation [in Perm]
Exploration1.permut_example [in Perm]
F
FastEnough.collisions [in Trie]FastEnough.collisions_pi [in Trie]
FastEnough.loop [in Trie]
fib [in ADT]
fibish [in ADT]
fibonacci [in ADT]
forall_nodes [in SearchTree]
G
G [in Color]graph [in Color]
H
how_many_subgoals_remaining [in Redblack]I
InA_example [in Color]ins [in Trie]
ins [in Redblack]
insert [in SearchTree]
insert [in Trie]
insert [in Sort]
insert [in Redblack]
Integers.add [in Trie]
Integers.addc [in Trie]
Integers.compare [in Trie]
Integers.positive2nat [in Trie]
Integers.print_in_binary [in Trie]
Integers.succ [in Trie]
Integers.ten [in Trie]
IntMaps.total_map [in Extract]
IntMaps.t_update [in Extract]
IntMaps.t_empty [in Extract]
in_4_pi [in Decide]
is_trie [in Trie]
is_a_sorting_algorithm [in Selection]
is_a_sorting_algorithm [in Sort]
is_a_sorting_algorithm' [in Multiset]
K
key [in SearchTree]key [in Redblack]
L
list_delete [in Multiset]list_nat_in [in Decide]
list_nat_eq_dec [in Decide]
List_Priqueue.Abs [in Priqueue]
List_Priqueue.priq [in Priqueue]
List_Priqueue.merge [in Priqueue]
List_Priqueue.delete_max [in Priqueue]
List_Priqueue.insert [in Priqueue]
List_Priqueue.empty [in Priqueue]
List_Priqueue.priqueue [in Priqueue]
List_Priqueue.key [in Priqueue]
List_Priqueue.select [in Priqueue]
list2map [in SearchTree]
look [in Trie]
lookup [in SearchTree]
lookup [in Trie]
lookup [in Redblack]
low_deg [in Color]
L.cons [in ADT]
L.create [in ADT]
L.list [in ADT]
L.nth [in ADT]
M
makeBlack [in Redblack]manual_grade_for_elements_relate_informal [in SearchTree]
manual_grade_for_successor_of_Z_constant_time [in Trie]
manual_grade_for_permutations_vs_multiset [in Multiset]
MapsTable.default [in ADT]
MapsTable.empty [in ADT]
MapsTable.get [in ADT]
MapsTable.key [in ADT]
MapsTable.set [in ADT]
MapsTable.table [in ADT]
MapsTable.V [in ADT]
Mdomain [in Color]
mk_graph [in Color]
multiset [in Multiset]
multiset_delete [in Multiset]
N
nat2pos [in Trie]node [in Color]
nodemap [in Color]
nodes [in Color]
nodeset [in Color]
no_selfloop [in Color]
O
out_of_gas [in Selection]O_Abs [in ADT]
P
palette [in Color]pos2nat [in Trie]
PRIQUEUE.key [in Priqueue]
R
RatherSlow.collisions [in Trie]RatherSlow.collisions_pi [in Trie]
RatherSlow.empty [in Trie]
RatherSlow.loop [in Trie]
RatherSlow.total_mapz [in Trie]
RatherSlow.update [in Trie]
reflect_example2 [in Perm]
reflect_example1 [in Perm]
remove_node [in Color]
repeat [in ADT]
S
same_mod_10 [in Color]ScratchPad.is_3_less_7 [in Decide]
ScratchPad.lt_dec' [in Decide]
ScratchPad.lt_dec [in Decide]
ScratchPad.t1 [in Decide]
ScratchPad.t2 [in Decide]
ScratchPad.t4 [in Decide]
ScratchPad.v1a [in Decide]
ScratchPad.v1b [in Decide]
ScratchPad.v2a [in Decide]
ScratchPad.v3 [in Decide]
ScratchPad2.insert [in Decide]
ScratchPad2.le_dec [in Decide]
ScratchPad2.lt_dec [in Decide]
ScratchPad2.max_with_axiom [in Decide]
ScratchPad2.sort [in Decide]
SearchTreeX [in SearchTree]
SearchTree2.combine [in Extract]
SearchTree2.elements [in Extract]
SearchTree2.elements' [in Extract]
SearchTree2.empty_tree [in Extract]
SearchTree2.insert [in Extract]
SearchTree2.key [in Extract]
SearchTree2.lookup [in Extract]
SectionExample1.empty [in SearchTree]
SectionExample1.lookup [in SearchTree]
SectionExample1.mymap [in SearchTree]
SectionExample2.empty [in SearchTree]
SectionExample2.lookup [in SearchTree]
SectionExample2.mymap [in SearchTree]
select [in Selection]
selection_sort_correct [in Selection]
selection_sort [in Selection]
selsort [in Selection]
singleton [in Multiset]
sixlist [in ADT]
slow_elements [in SearchTree]
sort [in Sort]
sorted' [in Sort]
sort_pi [in Selection]
sort_pi [in Sort]
sort_pi_same_contents [in Multiset]
sort_pi [in Multiset]
Sort1.insert [in Extract]
Sort1.sort [in Extract]
step [in ADT]
stepish [in ADT]
subset_nodes [in Color]
T
TABLE.key [in ADT]three_ten [in Trie]
too_much_gas [in Selection]
TreeTable.default [in ADT]
TreeTable.empty [in ADT]
TreeTable.get [in ADT]
TreeTable.key [in ADT]
TreeTable.set [in ADT]
TreeTable.table [in ADT]
TreeTable.V [in ADT]
TreeTable2.default [in ADT]
TreeTable2.empty [in ADT]
TreeTable2.get [in ADT]
TreeTable2.key [in ADT]
TreeTable2.set [in ADT]
TreeTable2.table [in ADT]
TreeTable2.V [in ADT]
trie_table [in Trie]
U
undirected [in Color]union [in Multiset]
V
value [in Multiset]VerySlow.collisions [in Trie]
VerySlow.collisions_pi [in Trie]
VerySlow.loop [in Trie]
| Global Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | other | (617 entries) |
| Notation Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | other | (5 entries) |
| Module Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | other | (27 entries) |
| Variable Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | other | (13 entries) |
| Library Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | other | (14 entries) |
| Lemma Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | other | (211 entries) |
| Constructor Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | other | (52 entries) |
| Axiom Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | other | (37 entries) |
| Inductive Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | other | (26 entries) |
| Section Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | other | (6 entries) |
| Definition Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | other | (226 entries) |
This page has been generated by coqdoc


Support
Form Authoring with XLSForms
Ona uses
XLSForm standard to allow you to author forms in XLS.
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For a full reference please use:
XLSForm.org. Also, be sure to checkout the
form gallery which provides examples you can download and modify.
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community mailing list. You can also contact our support team at:
<EMAIL_ADDRESS>API Usage
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160_Seayahh.py
class Solution:
def isTransformable(self, s: str, t: str) -> bool:
c1 = [0] * 10
c2 = [0] * 10
for c in s:
c1[int(c)] += 1
for c in t:
c2[int(c)] += 1
for i in range(10):
if c1[i] != c2[i]:
return False
def getRePair(c, s):
ans = [[0 for _ in range(10)] for _ in range(10)]
for ch in s:
d = int(ch)
c[d] -= 1
for i in range(d):
ans[d][i] += c[i]
return ans
p1 = getRePair(c1, s)
p2 = getRePair(c2, t)
for i in range(10):
for j in range(10):
if p1[i][j] < p2[i][j] :
return False
return True


Linked List, Stack, Queue
26 Jul 2018Download Jupyter/IPython Notebook here
Comparing Array and Linked List
1. Array
Fixed size, contain elements of same data type. When array is full, we need to create a new array with double the size and free the memory for former array. Insertion and deletion make almost all element moved/shifted
- Access: read/write element at any position: O(1) - best thing about array
- Insert, worst case is insert at the first position so all elements are shifted: O(n), insert at last position costs O(1)
- Remove, remove first element cost O(n) and remove last element costs O(1)
- Add, when array reaches max size, we need to copy all elements into new array: O(n), when not max size, it costs O(1)
2. Linked list
Linked list is non-consecutive nodes in memory, each node stores the actual data and the link to the next node (the address of the next node).
Good thing is that each node cost small memory and all nodes doesnt take a long chunk in memory.
Althought the total memory is a bit larger (carry a pointer every element), if data is big, carrying a pointer is not a big deal
First node: Head node, this gives access of completed list Last node: Does not point to any node. So if we want to access an element in between, we need to start to ask the first node.
- Access: O(n)
- Insert O(1), indexing (finding the node) is O(n)
Implementation:
These implementations are done individually and independent to each other
- size() - returns number of data elements in list - O(n)
- is_empty() - bool returns true if empty - O(1)
- value_at(index) - returns the value of the nth item (starting at 0 for first) O(n)
- push_front(value) - adds an item to the front of the list O(1)
- pop_front() - remove front item and return its value O(1)
- push_back(value) - adds an item at the end O(1)
- pop_back() - removes end item and returns its value O(n)
- front() - get value of front item O(1)
- back() - get value of end item O(1)
- insert(index, value) - insert value at index, so current item at that index is pointed to by new item at index O(n)
- erase(index) - removes node at given index O(n)
- search(value) - return an a list containing the indexes of every items that match the value O(n)
- reverse() - reverses the list, reverse_recursion() - reverse the list using recursion O(n)
- clear() - empty the list O(1)
- search() - search list and return the array that containt the position of the value that matched, index start at 0 O(n)
Short note on Stack and Queue
Stack and Queue are abstract data type that has different accesing protocols.
Stack: Imagine a stack of paper. The last piece put into the stack is on the top, so it is the first one to come out. This is LIFO. Adding a piece of paper is called “pushing”, and removing a piece of paper is called “popping”.
Queue: Imagine a queue at the store. The first person in line is the first person to get out of line. This is FIFO. A person getting into line is “enqueued”, and a person getting out of line is “dequeued”.
Enqueue O(1), Dequeue O(1). When implementing with linked list, enqueue (adding data) happens at tail and dequeue (removing data) happens at head. This ensure that no traversal is needed for both operation.
Priority Queue: This can be implemented using linked list, each node store a number that represent the priority of the node.
Implementation
class ListNode:
"ListNode class, each node has data and the reference to the next node"
def __init__(self, data):
self.data = data
self.next = None
class SingleLinkedList:
"class for single linked list: each node contain reference to next node"
def __init__(self):
"A LinkedList only has first node and last node "
self.head = None
self.tail = None
def size(self):
"count the number of list items"
count = 0
current_node = self.head
while current_node is not None:
count += 1
current_node = current_node.next
return count
def is_empty(self):
"check if the list is empty or not"
if self.head is None:
return True
else:
return False
def value_at(self, index):
"return the value of the nth element, index start at 0"
current_index = 0
current_node = self.head
while current_node is not None:
if current_index == index:
return current_node.data
current_index += 1
current_node = current_node.next
return "Error: Index out of range"
def push_front(self, value):
"push an item to the front of the list"
# convert data type of item to ListNode data type
if not isinstance(value, ListNode):
value = ListNode(value)
# when list is empty
if self.head is None:
self.head = value
return
# when list has one element, has to fix tail when add new element
if self.tail is None:
self.tail = self.head
self.tail.next = None
self.head = value
value.next = self.tail
return
# when list has at least 2 element
value.next = self.head
self.head = value
return
def pop_front(self):
"remove front item and return its value"
# when list is empty, return None, list remains unchanged
if self.head is None:
return None
# when list has 1 item, return head value and remove head of list
if self.tail is None:
head_value = self.head.data
self.head = None
return head_value
# when list has 2 items, return head value and remove head from list
if self.head.next is self.tail:
head_value = self.head.data
self.head = self.tail
self.head.next = None
self.tail = None
return head_value
# when list has 3 items
head_value = self.head.data
# change head position of linked list
self.head = self.head.next
return head_value
def push_back(self, item):
"add item to end of list"
# convert data type of item to ListNode data type
if not isinstance(item, ListNode):
item = ListNode(item)
# when list is empty then the value being added becomes head, otherwise it becomes
if self.head is None:
self.head = item
return
# when list has 1 item
elif self.tail is None:
self.tail = item
self.head.next = item
return
else:
self.tail.next = item
self.tail = item
return
def pop_back(self):
"removes end item and returns its value"
# edge case
# when list is empty
if self.head is None:
self.head = None
return None
# when list has 1 item, head is the last element
if self.tail is None:
head_value = self.head.data
self.head = None
return head_value
# when list has 2 items, remove tail and return it
if self.head.next is self.tail:
tail_value = self.tail.data
self.tail = None
self.head.next = None
return tail_value
# when list has at least 3 items
previous_node = None
current_node = self.head
# traverse the whole list to get the last node
while current_node.next is not None:
previous_node = current_node
current_node = current_node.next
tail_value = self.tail.data
# current_node.next is none when current_node is the last node
self.tail = previous_node
previous_node.next = None
return tail_value
def front(self):
"get value of front item"
if self.head is None:
return None
else:
return self.head.data
def back(self):
"get value of end item"
if self.tail is None:
return None
else:
return self.tail.data
def insert(self, index, value):
"insert value at index, put value at position index so current item at that index is pointed to the new item at index, index starts at 0"
success_msg = "Node inserted succesfully at index %s" % index
fail_msg = "Error: index %s out of range, unable to insert" % index
# convert value to ListNode type if not already
if not isinstance(value, ListNode):
value = ListNode(value)
# edge case: list is empty, there will be no next node
if self.head is None:
if index == 0:
self.head = value
return success_msg
else:
return fail_msg
# when list has 1 item, we have to fix tail
if self.tail is None:
# insert to head
if index == 0:
self.tail = self.head
self.head = value
value.next = self.tail
return success_msg
# insert to tail
if index == 1:
self.tail = value
self.head.next = value
return success_msg
# when list has at least 2 items, put value in the position index
current_index = 0
previous_node = None
current_node = self.head
while current_node.next is not None:
# insert to head
if index == 0:
value.next = self.head
self.head = value
return success_msg
# insert to the middle of the list
if current_index == index:
# insert new node
previous_node.next = value
value.next = current_node
return success_msg
# increment index
current_index += 1
previous_node = current_node
current_node = current_node.next
# when current_node.next is none, it mean we have traversed the whole list insert to tail
if current_node.next is None and current_index == index:
current_node.next = value
self.tail = value
return success_msg
return fail_msg
def print(self):
"outputs all value of list"
current_node = self.head
while current_node is not None:
print(current_node.data, end=' ')
current_node = current_node.next
print()
def erase(self, index):
"remove a node from the list by its position, change the referece of the node that point to them to the reference of next node from the deleted node, unrefereced data will be taken by python garbage collector"
success_msg = "Node deleted successfully at index %s" % index
fail_msg = "Error: index %s out of range, unable to delete" %index
# When list is empty
if self.head is None:
return fail_msg
# When list has 1 item
if self.tail is None:
if index == 0:
self.head = None
return success_msg
# When list has 2 items, has to remove tail
if self.head.next is self.tail:
# when erase head
if index == 0:
self.head = self.tail
self.head.next = None
self.tail = None
return success_msg
# when erase tail
if index == 1:
self.tail = None
self.head.next = None
return success_msg
return fail_msg
# when list has at least 3 items
current_index = 0
previous_node = None
current_node = self.head
while current_node is not None:
if current_index == index:
# when erase the first node
if previous_node is None: # if current_node is head
# when erase first node, the second node become the head
self.head = current_node.next
# remove the current node to free memory
current_node = None
return success_msg
# when erase last node
if current_node.next is None: # if current_node is tail
previous_node.next = None # current_node will be collected by python garbage collector
self.tail = previous_node
return success_msg
# when erase a node in the middle of the list, change reference of the node before the one being deleted
previous_node.next = current_node.next
return success_msg
current_index +=1
previous_node = current_node
current_node = current_node.next
return fail_msg
def search(self, value):
"search list and return the array that containt the position of the value that matched, index start at 0"
results = []
index = 0
current_node = self.head
while current_node is not None:
if current_node.data == value:
results.append(index)
index += 1
current_node = current_node.next
return results
def reverse(self):
"reverse the referencing order of linked list using iterative method"
previous_node = None
current_node = self.head
self.tail = self.head
while current_node is not None:
# store next node because the pointer to the next node will be change after that
next_node = current_node.next
# change pointer of each node to the previous node
current_node.next = previous_node
# shift the position of current and previous node
previous_node = current_node
current_node = next_node
# previous node is the last node, make it the head of single linked list
self.head = previous_node
def reverse_recursion(self, head):
"reverse a linked list using recursion method given the head node"
# cannot use self.head instead of head because head is updated in recursion while self.head is a fixed value, self doesn't change
self.tail = self.head
current_node = head
rest = current_node.next
if rest is None:
# rest is null when current_node is the last node of the list
self.tail = self.head
self.head = current_node
return
self.reverse_recursion(rest)
# create a reverse the link between current_node and the next node of it
current_node.next.next = current_node
# remove the the original link
current_node.next = None
def clear(self):
"empty the list, python garbage collector will clear unreferenced memory"
self.head = None
self.tail = None
Testing
# function for testing
def print_list_infor(list):
"print head,tail and the actual list"
print("Front: %s, Back: %s" % (list.front(), list.back()))
print("Actual list: ", end="")
list.print()
print()
Test size(), push_front(), is_empty()
list = SingleLinkedList()
print("Size of empty list: %s" % list.size(), end = "\n")
print("Is empty value: %s" % list.is_empty())
print()
list.push_front(2)
print_list_infor(list)
list.push_front(1)
print_list_infor(list)
print("List size: %s, actual list: " % list.size(), end = "")
list.print()
Size of empty list: 0
Is empty value: True
Front: 2, Back: None
Actual list: 2
Front: 1, Back: 2
Actual list: 1 2
List size: 2, actual list: 1 2
Test value_at()
print_list_infor(list)
print("Value at index -1: %s" % list.value_at(-1))
print("Value at index 0: %s" % list.value_at(0))
print("Value at index 1: %s" % list.value_at(1))
print("Value at index 2: %s" % list.value_at(2))
Front: 1, Back: 2
Actual list: 1 2
Value at index -1: Error: Index out of range
Value at index 0: 1
Value at index 1: 2
Value at index 2: Error: Index out of range
Test pop_front()
list.push_front(3)
print_list_infor(list)
print("Value return by pop front: %s" % list.pop_front())
print_list_infor(list)
print("Value return by pop front: %s" % list.pop_front())
print_list_infor(list)
print("Value return by pop front: %s" % list.pop_front())
print_list_infor(list)
print("Value return by pop front: %s" % list.pop_front())
print_list_infor(list)
Front: 3, Back: 2
Actual list: 3 1 2
Value return by pop front: 3
Front: 1, Back: 2
Actual list: 1 2
Value return by pop front: 1
Front: 2, Back: None
Actual list: 2
Value return by pop front: 2
Front: None, Back: None
Actual list:
Value return by pop front: None
Front: None, Back: None
Actual list:
Test push_back()
print("Actual list: ", end="")
print_list_infor(list)
list.push_back(1)
print_list_infor(list)
list.push_back(2)
print_list_infor(list)
Actual list: Front: None, Back: None
Actual list:
Front: 1, Back: None
Actual list: 1
Front: 1, Back: 2
Actual list: 1 2
Test pop_back()
list.push_back(3)
print_list_infor(list)
print("Value return by pop back: %s" % list.pop_back())
print_list_infor(list)
print("Value return by pop back: %s" % list.pop_back())
print_list_infor(list)
print("Value return by pop back: %s" % list.pop_back())
print_list_infor(list)
print("Value return by pop back: %s" % list.pop_back())
print_list_infor(list)
Front: 1, Back: 3
Actual list: 1 2 3
Value return by pop back: 3
Front: 1, Back: 2
Actual list: 1 2
Value return by pop back: 2
Front: 1, Back: None
Actual list: 1
Value return by pop back: 1
Front: None, Back: None
Actual list:
Value return by pop back: None
Front: None, Back: None
Actual list:
Test front() back()
print("Front: %s, Back: %s" % (list.front(), list.back()))
print("Actual list: ", end="")
list.print()
print()
list.push_back(3)
print("Actual list: ", end="")
list.print()
print("Front: %s, Back: %s" % (list.front(), list.back()))
print()
list.push_back(2)
print("Actual list: ", end="")
list.print()
print("Front: %s, Back: %s" % (list.front(), list.back()))
print()
list.push_back(1)
print("Actual list: ", end="")
list.print()
print("Front: %s, Back: %s" % (list.front(), list.back()))
print()
Front: None, Back: None
Actual list:
Actual list: 3
Front: 3, Back: None
Actual list: 3 2
Front: 3, Back: 2
Actual list: 3 2 1
Front: 3, Back: 1
Test insert(index,value)
list.clear()
print_list_infor(list)
print(list.insert(-1,1))
print_list_infor(list)
print(list.insert(1,1))
print_list_infor(list)
print(list.insert(0,1))
print_list_infor(list)
print(list.insert(1,2))
print_list_infor(list)
print(list.insert(0,2))
print_list_infor(list)
print(list.insert(0,3))
print_list_infor(list)
print(list.insert(2,4))
print_list_infor(list)
Front: None, Back: None
Actual list:
Error: index -1 out of range, unable to insert
Front: None, Back: None
Actual list:
Error: index 1 out of range, unable to insert
Front: None, Back: None
Actual list:
Node inserted succesfully at index 0
Front: 1, Back: None
Actual list: 1
Node inserted succesfully at index 1
Front: 1, Back: 2
Actual list: 1 2
Node inserted succesfully at index 0
Front: 2, Back: 2
Actual list: 2 1 2
Node inserted succesfully at index 0
Front: 3, Back: 2
Actual list: 3 2 1 2
Node inserted succesfully at index 2
Front: 3, Back: 2
Actual list: 3 2 4 1 2
Test erase(index)
print("Actual list: ", end="")
print_list_infor(list)
print(list.erase(1))
print_list_infor(list)
print(list.erase(0))
print_list_infor(list)
print(list.erase(3))
print_list_infor(list)
print(list.erase(2))
print_list_infor(list)
print(list.erase(0))
print_list_infor(list)
print(list.erase(0))
print_list_infor(list)
Actual list: Front: 3, Back: 2
Actual list: 3 2 4 1 2
Node deleted successfully at index 1
Front: 3, Back: 2
Actual list: 3 4 1 2
Node deleted successfully at index 0
Front: 4, Back: 2
Actual list: 4 1 2
Error: index 3 out of range, unable to delete
Front: 4, Back: 2
Actual list: 4 1 2
Node deleted successfully at index 2
Front: 4, Back: 1
Actual list: 4 1
Node deleted successfully at index 0
Front: 1, Back: None
Actual list: 1
Node deleted successfully at index 0
Front: None, Back: None
Actual list:
Test reverse(), reverse_recursion()
list.push_front(1)
list.push_front(3)
list.push_front(4)
list.push_front(5)
print_list_infor(list)
list.reverse()
print("List reversing...")
print_list_infor(list)
list.reverse_recursion(list.head)
print("List reversing...")
print_list_infor(list)
Front: 5, Back: 1
Actual list: 5 4 3 1
List reversing...
Front: 1, Back: 5
Actual list: 1 3 4 5
List reversing...
Front: 5, Back: 1
Actual list: 5 4 3 1


Allow me to introduce myself - my name is Maxwell Foley, but you can call me Max.
I am a full-stack software developer specializing in writing complex web applications in Node and React to fit the needs of my clients. Currently I am technical lead for Artifaq.IO and operate as an independent contractor.
Within the world of coding, my travels have also allowed me to dive into graphics algorithms and blockchain technology, which I research and explore on the side.
When I'm not working with code, I'm either making digital art in Photoshop and 3d rendering software, or using a beat-making program to write electronic music.
If you are looking for someone of my skillset, feel free to send me a message. I love to meet other tech lovers and work together or just chat.
I am currently technical lead and responsible for the bulk of the development of Artifaq.IO, an platform for art enthusiasts and curators alike, in MVP status as of January 2019.
Originally titled Artstamp.IO, the software began its life as a blockchain app backed by an Ethereum smart contract in which users could upload art assets to the chain and buy, sell, and trade those works. I was responsible for outlining this app's features and designing its architecture, as well as writing and implementing all the blockchain functionality.
After the peak of the ICO bubble and increasing public skepticism towards blockchain platforms, the team made a decision to shift focus and we are now solely an art platform designed to give "power to the people" by facilitating the discovery of under-explored works and breaking the hold of the existing gallery infrastructure on determining who gets seen.
The software is written entirely in Javascript, with Node as the back-end, Mongo as the database, Express for middleware, and a React front-end.
Development of Artifaq.IO is funded by Fabricatorz Foundation, whom I have worked for both as a full-time employee and independent contractor.
Created an interactive art installation conceptualized and built in 48 hours for St. Louis's Art Hack Day: Eclipse event. The installation used a NeuroSky MindWave Mobile EEG-reading headset, which was connected to my laptop via bluetooth, which ran this code and then used a projector to display an image on the wall. The idea was for the art piece to serve as a sort of impressionistic visualizer of one's mental activity, specifically how calm and/or focused the person using the headset was.
The project used node.js to communicate to the headset, and three.js to render the visuals in the browser.
A demo version where the user can use GUI sliders to simulate the EEG output is here, and the full code of the project is available on GitHub.
Working on various rendered scenes built entirely in code using volumetric raymarching rendering technique via GLSL shader language, hosted on GLSLsandbox.com.
Flashcard quiz app using the MEAN stack. Users can create sets of flashcards, upload images, edit and delete flashcards, and then quiz themselves. Heroku was used to deploy the app and Bootstrap was used for CSS. Filepicker.js was used for file uploading.
Several interactive visuals initially built in Processing then ported into P5.js for online compatibility. Try clicking and moving the mouse around to see what happens. Warning: might be too intense for slower computers.
@pseudo_frac is a now-defunct twitter bot that for a period of time generated an image from the "pseudo-fractals" algorithm above and posted it to Twitter once every 24 hours. Written in node.js and p5.js and deployed on Amazon EC2.
This was built for a project for an art class in which we were required to create a geneology of artists of the past five hundred years and find a way to visually integrate it with contemporary historical events. I developed a simple interactive page in JavaScript in which three sections of the website scroll simultaneously - a gallery of paintings, a timeline of historical events, and a horizontal timeline at the top simply for visual integration purposes. One can then click on a historic event to find the corresponding artist, or click on a handful of selected influences underneath each artist to jump to that point in the timeline.
The website you are currently reading was designed and coded by myself from scratch in HTML, CSS, and JavaScript.
Fabricatorz Foundation
Software Developer and Blockchain Engineer, Independent Contractor (April 2018 - present)
Reliv International
Contractor (November 2017 - April 2018)
Less Annoying CRM
Software Development Intern (May 2017 - August 2017)
Iowa State University
Independent Contractor (May 2015 - August 2015)
Ohio State University Department of Biomedical Informatics
Intern (May 2014 - August 2014)
Washington University in St. Louis B.F.A in Studio Art with second major in Computer Science (August 2013 - December 2017)


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--- layout: default title: Bartosz Kazimierz Papis: Skills css: list.css;skills.css;perfect-scrollbar.min.css;flash.css js: initScroll.js;perfect-scrollbar.min.js;flash.js --- {% include rightmenu.html main="skills.html" positions="PROGRAMMING;RESEARCH;TEAM LEADING;TOOLS" %}
Programming
{% include skill.html name="TDD - 4+ years of experience,Research
{% include skill.html name="Ph.D. thesis in Artificial Intelligence: State abstraction in Reinforcement Learning,Team leading
{% include skill.html name="Technical leader (8 years of experience)" %} {% include skill.html name="Certified SCRUM Master (7 years of experience)" link="https://www.scrumalliance.org/community/profile/bpapis" linkname="Scrum Alliance Profile" %} {% include skill.html name="SCRUM of SCRUMS leader (3 years of experience)" %}Tools/Libraries/Frameworks
{% include skill.html name="Qt, boost, gSoap, WCF, WPF, SCons, PyQt" %} {% include skill.html name="SQL Server, MySQL" %} {% include skill.html name="Git, SVN, CVS" %} {% include skill.html name="Emacs, Visual Studio, Eclipse, PyCharm" %} {% include skill.html name="BoostTest, NUnit, MSTest, Python’s unittest" %} {% include skill.html name="StyleCop, TeamCity, Buildbot, Trac, Jira, Confluence, MS Office" %} {% include skill.html name="ILOG, GLPK, Simone" %} {% include skill.html name="Enterprise Architect" %}


UK job growth slows as Bank of England consider rate cut
by Michael SearlesThe demand for staff from UK employers grew at its slowest rate for almost eight years in October, according to a survey revealed on Friday.
A monthly index of job vacancies from the Recruitment and Employment Confederation and accountants KPMG fell to 51.7 from 52.6 in September.
Read more: City moves for 8 November: Who’s switching jobs at Sancus BMS, Trident resources and IMG?
It is the index’s lowest level since January 2012 and highlights concerns from the Bank of England that the UK’s labour market may be losing its strength.
It comes a day after two of the Bank of England’s nine interest-rate setters voted to cut interest rates again.
The pair cited signs that the labour marker may be on the turn, despite it being one of the economy’s strong points since the Brexit vote.
The REC report released on Friday showed permanent job placements fell for an eighth consecutive month and at a faster rate than last month.
It comes as official data showed job creation was waning ahead of the previous end of October Brexit deadline.
Read more: Jobs paying below real living wage fall to seven-year low
Vice chairman at KMPG, James Stewart, said the uncertainty around Brexit and the upcoming general election on 12 December had dampened companies’ hiring plans.
“It’s not just businesses that are being cautious, however, and over October we’ve seen job-seekers become increasingly nervous about making a career change,” he said.


Computer Science and Engineering .
Electronics and Communication Engineering
Mechanical Engineering
CIVIL Engineering


With wonderful people and green meadows Ireland is a place you must visit!
| Brand Name | Type of Whiskey | Age |
|---|---|---|
| Teeling | Single Malt | 13 years |
| Teeling | Classic | 7 Years |
| Jameson | Blend | 5 years |
For additional historical information check out Ireland's Wikipedia page! The accessibility and layout of the website allows you to learn and navigate to external links.


Pride & Prejudice
England, late eighteenth century. The parents of the five Bennet sisters are anxious to successfully marry their daughters off. And so the regular life of a respectable family is turned upside down when a young gentleman - Mr. Bingley-appears in the neighbourhood... Of course, among the friends of the new neighbor is a lot of refined aristocrats who are not averse to court the charming sisters. However, it's not that simple. Headstrong Elizabeth meets Bingley's friend-the handsome and arrogant Mr. Darcy, and between them a serious confrontation breaks out, the result of which can be both love and hatred...


As you walk home, your liver makes strange scratching noises, and you topple into a wastebasket. Fliers for a sporting event adorn the bottom of your new lodging.
Examine this freely provided literature.


The T.R.C. Library is a centralized, web-based collection of pedestrian and bicycling-related materials
and documents compiled by practitioners and researchers from across the United States and abroad.
These include sample pedestrian and bicycle plans and planning tools, design guidelines, research and safety studies,
articles and white papers, case studies, and links to presentations, videos, and other web resources.


THE DUTCH MASTER A Film Review by James Berardinelli Copyright 1994 James Berardinelli
Rating (0 to 10): 7.7
Date Released: No U.S. release planned Running Length: 0:27 Rated: No MPAA Rating (Mature themes, nudity, sex, language)
Starring: Mira Sorvino, Aida Turturro Director: Susan Seidelman Producer: Jonathan Brett
THE DUTCH MASTER is a cleverly-developed, lighthearted comedy about the differences between reality and fantasy, and the hidden inhibitions uncovered by crossing that line. In one sense, there is a commonality between Susan Seidelman's Oscar-nominated short (the movie is less than 30 minutes long) and John Duigan's SIRENS - both narratives revolve around a sexually-motivated realization that forever alters the life of a female protagonist. THE DUTCH MASTER, however, is contemporary, and far funnier.
Theresa (Mira Sorvino, the daughter of actor Paul Sorvino, and co-star of AMONGST FRIENDS) is a dental hygienist engaged to be married to a real "hunk." She's basically a normal New York girl until one day when she visits an art museum and becomes fascinated by a painting depicting a 17th-century household. Fascination becomes obsession, and Theresa begins to fantasize about the lives of the people depicted on the canvas, neglecting her friends and her fiance.
With a witty script, THE DUTCH MASTER engages its audience from the outset, giving us a group of characters whose "realness" we can appreciate, if only through their down-to-earth dialogue. Director Susan Seidelman, whose full-length features include DESPERATELY SEEKING SUSAN, has chosen a perfect cast, and her method of telling this story - combining pseudo-documentary interviews with a more traditional view of events - keeps this film fresh from start to finish.
Told from a "woman's perspective," THE DUTCH MASTER nevertheless has universal appeal. Its length is both an advantage and a disadvantage - there's no fat to be trimmed, but the characters are fascinating enough to deserve more screen time and we have to leave them just as we're really getting to know them. As it is, though, there's more than enough in THE DUTCH MASTER than in many movies three times its length.
- James Berardinelli<EMAIL_ADDRESS>.
The review above was posted to the
rec.arts.movies.reviews newsgroup (de.rec.film.kritiken for German reviews).
The Internet Movie Database accepts no responsibility for the contents of the
review and has no editorial control. Unless stated otherwise, the copyright
belongs to the author.
Please direct comments/criticisms of the review to relevant newsgroups.
Broken URLs inthe reviews are the responsibility of the author.
The formatting of the review is likely to differ from the original due
to ASCII to HTML conversion.
Related links: index of all rec.arts.movies.reviews reviews


App Preferences
Notifications
Track Changes
Show a notification when the track changes to another
On Playback
Show a notification when a track starts playback
On Pause
Show a notification when the track is paused
On Stop
Show a notification when the queue is finished
Only When Focused
Show any enabled notification
but only
when you're not using the player window
Theme
Change the look of the interface
Tray
Enabled
Toggles whether Spotify Web Player for Linux should show a tray icon?
Icon
Mix-&-Match the tray icon to your DE/Icon style
Old Spotify
Green Spotify
Lime Spotify
White Spotify
Black Spotify
Close To Tray
Allows you to keep the window hidden whilst playing music and use the tray menu or application menu to quit.
The window will minimise if the tray icon is disabled
Close To Controller
Allows you to keep the window hidden without an indicator or application icon taking up space
Warning: MPRIS controllers have to raise Spotify Web Player for it to become unhidden
Show Application Menu
Toggles whether Spotify Web Player for Linux should hide the application menu
Warning! Without a tray icon, you may not be able to get into the preferences window
Start on Login
Toggles whether Spotify Web Player for Linux will start on user login
Start Hidden
Toggles whether Spotify Web Player for Linux will start minimized
Navbar
Show Browse Icon
Toggles the visibility of the browse icon on the sidebar
Show 'Your Music' Icon
Toggles the visibility of the 'Your Music' icon on the sidebar
Show Radio Icon
Toggles the visibility of the Radio icon on the sidebar
Show Follow Icon
Toggles the visibility of the follow icon on the sidebar
Show User Icon
Toggles the visibility of the user account icon on the sidebar
Show Settings Icon
Toggles the visibility of the settings icon on the sidebar
Show Sing! Icon
Toggles the visibility of the Sing! button on the sidebar
Store Album Art?
Toggles whether album art will be stored for caching
Note: Album Art will still be downloaded temporarily to /tmp for notifications (but deleted on reboot)
Album Art Cache Size
Choose the size of the Album Art that will be cached
Note: Larger images will take up more disk space over time
Large
Medium
Small
Clean Album Cache
This will remove all album art covers
Clean Me
Clean Lyric Cache
This will remove all the lyrics you have saved
Clean Me


Welcome to my awesome Docker project
José Luis Barrera Canto
Always learning to improve myself. This is the version 1.0 of this example.


Interviewing applicants who wish to join the school
Work on software projects for use by students within the school
Read more June 29th to presentMS is a 12 week coding bootcamp which imparts knowledge in javascript, ruby on rails, android to mention a few
Read more March 23rd to June 12thWent through the entire course curriculum learning different technologies along the way most prominent ones being html, css and java
Worked on my final year project which was an ecommerce platform
Read more March 2010 to December 2014Campus bay is an ecommerce platform that is exclusive to university students. The project was made during a four day period during my time at Moringa School
Drag Reader is an android app that aggregates sports rss feeds for users. The project was made during a one week period during my time at Moringa School
Naigator is a maps android application that allows users to locate goods or services located only on their route. The project was made during a four day period in my time at Moringa School
This is a website which showcases what i do, using awesome technologies such as materializecss, modernizr.js and font awesome among others. It was built gradually over my time at Moringa school


Kaiseki: The Art of Traditional Japanese Cuisine
Kaiseki refers to a traditional, multi-course Japanese dinner in which each course is small and artfully presented. Kaiseki meals are often comprised of the finest and freshest ingredients local to a particular region. As with most regional cuisines, kaiskei can be expensive.
Image credit: Kristen Boffi
Below are some examples of the types of food you may enjoy in a kaiseki experience:
| Food | Description |
|---|---|
| miso soup | A traditional, simple miso broth with tofu and seaweed |
| sashimi | Thinly sliced raw fish presented without rice or other accompaniments |
| shabu shabu | Thinly sliced raw beef, fish, or shellfish for cooking in a simple broth flavored with fresh vegetables and tofu |
| tsukemono | Preserved Japanese vegetables, or Japanese pickles |
Where to Find It
Kaiseki is most commonly served at ryokan, or traditional Japanese inns. The price point for ryokan can vary, but you can expect a similar experience at each one that includes the following:
- Simple accommodations that include tatami floors and futons that are laid out on the floor just prior to sleeping
- On-site gender-segregated bathing facilities where residents will bathe and relax upon arrival to the ryokan and prior to the meal
- Yukata, or a casual cotton kimono provided to guests to wear during their stay at the ryokan
As with many experiences of Japanese culture, etiquette is of the utmost importance when staying in a ryokan and enjoying kaiseki.


---
layout: post
title: Google Summer of Code Project
categories: []
tags: []
status: publish
type: post
published: true
meta:
blogger_blog: c13s.blogspot.com
blogger_author: djiao
blogger_6253bd7e6fe76b5f854e34389ec53677_permalink: '6065827366960100991'
_elasticsearch_indexed_on: '2008-06-24 15:46:00'
---
This summer I have been working on a Google Summer of Code project. I am trying to adding some cheminformatics functionality to cytoscape, an open source biological network visualization tool.
Here is the link to my project page on GSoC and project page on cytoscape wiki.


Job Function:
We are looking for experienced UI Developer with strong knowledge in HTML5, CSS3, JQuery, JavaScript. Candidate should have good working knowledge in creating Responsive Design and should be a good visualizer. Must be able to work closely with the members of the development team to deliver high quality web applications.
Desired Profile:
- More than 1.5 years of experience.
- Collaborate cross-functionally to deliver great user experiences.
- Requirements: Portfolio featuring comprehensive examples of product interfaces, web design, and creative branding work.
- Qualification: Any Graduate with desired skills.
Preferred Skills:
- Understanding of the capabilities and limitations of XHMTL, HTML5, javascript, CSS3 and JQuery.
- Working experience with Bootstrap and Responsive Design.
- Knowledge in SEO is an added advantage.
- A self-learner, who can keep up with latest design paradigms.
- A keen eye for good design.
- Good communication skills to work with developers and testers.


I'm a passionate and creative developer with a background in visual design and psychology. I love learning new technologies and creating great user experiences.
Need an amazing website?
I can do that
Want an app?
I can do that too!
Need help with something else?
Let's chat
I am currently available for feelance work - Let's chat.


Honors and Awards
-
2018 ACM SigHPC Dissertation Award Honorable Mention.
-
2018 Selected as an Heidelberg Laureate
Heidelberg Laureate Forum brings together Turing Laureates with young researchers.
-
2017 Selected as a Rising Star in EECS, Stanford University
-
2017 Kenichi Miura Award, UIUC
This award honors a graduate student for excellence in High Performance Computing.
-
2017 Illinois Innovation Prize Finalist, Technology Entrepreneur Center, UIUC
The prize is awarded on to the most innovative students on campus annually (with $2500 prize for finalists).
-
2016 AWARE (Accelerating Women And underRepresented Entrepreneurs) Grant Winner, UIUC Research Park
A 2500$ grant to develop a prototype for innovative ideas.
-
2012-13 Saburo Muroga Endowed Fellowship, UIUC
-
2012 Salutatorian, second highest GPA among graduating class, Bilkent University
-
2011 Erasmus Exchange Program Scholarship, Uppsala University, Sweden
-
2008-12 Bachelor of Science Full Tution-Waiver with Stipend Merit Scholarship, Bilkent University


Poll Admin
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LCase()
Syntax
Result$ = LCase(String$)Description
Returns the string converted into lower case characters.
Parameters
String$ The string to convert into lowercase.
Return value
The string converted into lowercase.
Remarks
This function also supports accent letters, so if a upper '? is found, it will be transformed into '?.
Example
Debug LCase("This is Art") ; Will display "this is art"
See Also
UCase()
Supported OS
All


It was a sunny day, I remember, as I was riding in the back of my colleague’s motorbike, in some of the fancy neighborhoods of Bangalore. I don’t even remember his full name. We called him Khan Sir. You didn’t have to have knighthood to be addressed as Sir in India. It was merely a sign of respect, a polite acknowledgement of your age, knowledge or experience.
It was about a week after our CEO told us that we were shutting down due to lack of sufficient funding. This was a perfect opportunity for the entrepreneurial-minded, and Khan Sir was one. He had an idea that he wanted to work on, to try and make a product, and eventually a company, out of it. He had always wanted to give it a shot, but the resistance that comes from comfort and a fat paycheck can be hard to battle. This was the window and the push he was secretly wishing for.
He wanted a dummy to turn his idea into a working prototype. I was willing to help, a young and naively energetic and optimistic engineer, trying to grab every opportunity that presented itself. I was waiting to fly to the US for my Master’s degree in a few months, so I had nothing to lose if this little tinkering didn’t work, and something to gain if it did.
After building an MVP, we traveled on his motorbike to pitch the idea to potential investors. That’s when I first visited some of the rich homes of the Silicon Valley of India. These were the people that made it all happen. They listened to people all day long, sifted through the pile of ideas and the list of people with ideas, and funded the ones that they thought had the potential to make it big. We sure thought we were one of them.
Those brief rounds with Khan Sir taught me more about him, his motivations and aspirations than a year working with him.
In one of the stops we made, we parked the bike right next to a dog that was sleeping on the street. Our arrival was an unwelcome change in his world. How do I know? His face told us that. Turns out animals are good at communicating non-verbal clues. At least that was my interpretation of it. I would have been pissed if somebody woke me up from my mid-day nap. I guess that tells more about me than what the dog was truly saying.
But I suppose he didn’t know, or care, that it was mid-day, or even mid-week. It’s not like he had some place he’d rather be, or something he’d rather be doing. He was right where he wanted to be, precisely when he wanted to be, doing exactly what he wanted to do. He probably also didn’t have any cultural notions about what he ought to do with his life. That seems like something only animals as smart as us could come up with, and then brood over.
Thoughts about meaning and purpose, of why we are here, consumes most of us at various points in our life. Sometimes so much that it pushes us over the edge of uncertainty and leaves us rolling down helplessly and endlessly because the answers don’t come easy. It dictates, consciously or not, things we do with our time, and hence with our lives. Different cultures and societies, as do different individuals, have different ideas about them. For some, it’s about pleasing God, or working towards a divine reward. For others, it’s about living a good life, whatever that means, a life of virtues and principles, perhaps. For some, it’s the pursuit of knowledge, and for others, it’s about finding their true potential, exploring the limits of their body and mind.
Anyway, back to the dog. There was something very peaceful about the way he was sleeping amidst all the noise around him. For a moment, I felt like trading lives with him. As I was thinking it, Khan sir interrupted my chain of thought and said something along the same lines. He said he’d have preferred to be born as a dog, so that he didn’t have to worry about building a company, or about finding meaning in life. He felt like trading lives with the dog too! The zen-like state that the dog was projecting, of being able to tune out the external noises and the internal voices and being completely immersed in what he enjoyed was enviable. It’s what we all strive to achieve, I think.
I wanted the dog’s life because I was lazy. I’d rather be sleeping than working. But for him, it was deeper than that. He was, I now realize, dealing with the dichotomy of pain and pleasure that comes from being driven. Internal drive, just like external ones, can be ruthless at times.
He had a wife and a kid. His wife was pregnant at the time with the second one and had gone to her mother’s place for six months. So he had given himself six months to work on his idea. He had saved enough to make it work, without work. It’s kind of a short deadline though, and a hard one, knowing that you got half a year to turn the abstract in your mind into something concrete in the real world, and knowing that this was one of those rare moments when things fall into place to open a narrow window of opportunity.
His passion to make an impact in the world was pushing him towards something that was hard and uncomfortable yet rewarding at the same time. He felt the agony of spending all that time away from his kid and his then-pregnant wife, of life slipping away from his hands without him being present with his loved ones, but also experienced the joy that comes from attending to the calling from within. He’d have preferred an easier life if he could, but his drive left him no choice. I learned recently that that idea or state is explained through the concept of positive liberty.
At the time, I couldn’t empathize with him. I wasn’t passionate about anything, and I didn’t have responsibilities of anyone but my own. Time, as far as I was concerned, was a perennial resource. I had the majority of my life ahead of me.
This was in the year 2013, which seems like a long time ago now. The memory of this whole episode kept coming back to me at various times, in different situations, years later.
Three years later, in 2016, when I started to become interested in outdoor activities and got into running, hiking, and biking, I remember how I couldn’t get myself to do anything during the weekends but that. The rush and excitement was irresistible. Friday evening, I hit the road, only to be back home on Sunday. Every weekend a new destination, with new people. Even my day job took a backseat for a while. I focused less on my career and more on such experiences. With this new found freedom, I thought, and read, a lot about balance and free will but at the same time felt completely helpless in the grips of the inner force that was controlling me. It occurred to me how he, or most entrepreneurs, must feel like when they invest all their precious resources – time, money, and energy – into building something, knowing well that the chances of it going anywhere good are rather slim. It’s hard to tell if it’s what you are choosing to do, or if it’s the inner voice making you do.
Today, in 2021, while sitting on a couch dragging my fingers against the iPad screen, looking for e-books in my library app, I stumbled upon a book called “How to Teach Philosophy to Your Dog - Exploring the Big Questions in Life”, by Anthony McGowan.
The title piqued my interest for two reasons: first, because of my interest in books that break down complex subjects into simple language, and second, because I was curious about how ideas from a subject, as complex and as abstract as Philosophy, could possibly be transported out of the realm of human understanding and extended to a dog’s world. The title also brought back that old memory and for a moment, my mind drifted away…wondering about that dog…
Was he still alive? What would he be doing with his life now, if he were?
Over all these years, would he have grown in some way?
Did old age teach him lessons he would tell his younger self? All those days spent sleeping, could they have been spent any better, in a more productive way?
and wondering about freedom…
Was the dog freer than us, in a way, without being constantly crippled by the worries in life?
Is free will and freedom reflected in what we do, or what we choose to do?
If it is the latter, are we choosing to do the things we do in our life, or are we merely telling ourselves that to be able to sleep at night? If we’re acting purely and solely based on our impulses, are we even exercising our freedom?
Recommended Reading
How to Teach Philosophy to Your Dog: Exploring the Big Questions in Life
Positive and Negative Liberty: Stanford Encyclopedia of Philosophy
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