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Lambda calculus, hashing, financing.

c-declarations
Joshua Potter 2024-06-29 09:59:48 -06:00
parent 87ca0829b2
commit 42fc08e4c1
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---
title: "2024-06-29"
---
- [ ] Anki Flashcards
- [x] KoL
- [x] OGS
- [ ] Sheet Music (10 min.)
- [ ] Korean (Read 1 Story)

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* Notes on [[beta-reduction#Normal Form|β-normal forms]].
* Very basic notes on [[ars|abstract rewriting systems]].
* Additional set theory definitions ([[functions#Restrictions|restrictions]] and [[functions#Images|images]]).
* Additional set theory definitions ([[functions#Restrictions|restrictions]] and [[functions#Images|images]]).
* Read chapters 2 ("Methodology") and 3 ("Properties") of "An Introduction to Ontology".

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---
title: "2024-06-23"
---
- [x] Anki Flashcards
- [x] KoL
- [x] OGS
- [ ] Sheet Music (10 min.)
- [ ] Korean (Read 1 Story)
* Read chapter 4 ("Numbers") of "An Introduction to Ontology".
* Notes on [[financing]] rounds.
* Additional notes on hash tables with [[closed-addressing#Chaining|chaining]] and independent uniform hashing.

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---
title: "2024-06-24"
---
- [x] Anki Flashcards
- [x] KoL
- [x] OGS
- [ ] Sheet Music (10 min.)
- [ ] Korean (Read 1 Story)
* Further reading on possible worlds in "An Introduction to Ontology".

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---
title: "2024-06-25"
---
- [x] Anki Flashcards
- [x] KoL
- [x] OGS
- [ ] Sheet Music (10 min.)
- [ ] Korean (Read 1 Story)
* Finished transcribing notes on chapter 1 of "Venture Deals".

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---
title: "2024-06-26"
---
- [x] Anki Flashcards
- [x] KoL
- [x] OGS
- [ ] Sheet Music (10 min.)
- [ ] Korean (Read 1 Story)
* Prove basic theorems on functions (chapter 3 of "Elements of Set Theory").
* Notes on substitution being well defined with respect to $\beta$-reductions.
* Finished chapter 5 ("Possible Worlds") of "An Introduction to Ontology".

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---
title: "2024-06-27"
---
- [x] Anki Flashcards
- [x] KoL
- [x] OGS
- [ ] Sheet Music (10 min.)
- [ ] Korean (Read 1 Story)
* Read chapter 6 "Space" in "An Introduction to Ontology."

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---
title: "2024-06-28"
---
- [x] Anki Flashcards
- [x] KoL
- [x] OGS
- [ ] Sheet Music (10 min.)
- [ ] Korean (Read 1 Story)
* Notes on the [[beta-reduction#Church-Rosser Theorem|Church-Rosser theorem]] and [[ars#Confluence|confluence]] in general.
* Read chapter 7 "Time" and chapter 8 "Mereology" of "An Introduction to Ontology".

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@ -391,7 +391,7 @@ END%%
For any sets $A$, $B$, and $C$, $$\begin{align*} A \times (B \cap C) & = (A \times B) \cap (A \times C) \\ A \times (B \cup C) & = (A \times B) \cup (A \times C) \\ A \times (B - C) & = (A \times B) - (A \times C) \end{align*}$$
%%ANKI
Basic
Which algebra of sets operators is the Cartesian product distributive over?
Which of the algebra of sets operators does the Cartesian product distributive over?
Back: $\cap$, $\cup$, and $-$
Reference: “Cartesian Product,” in _Wikipedia_, April 17, 2024, [https://en.wikipedia.org/w/index.php?title=Cartesian_product&oldid=1219343305](https://en.wikipedia.org/w/index.php?title=Cartesian_product&oldid=1219343305).
<!--ID: 1718069881718-->

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@ -147,6 +147,78 @@ Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (
<!--ID: 1718759188281-->
END%%
%%ANKI
Basic
What is the worst-case behavior of hashing with chaining?
Back: All keys hash to the same slot.
Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
<!--ID: 1719174576856-->
END%%
%%ANKI
Basic
What is the load factor of a hash table in which all $n$ keys hash to one of $m$ slots?
Back: $n / m$ (the load factor is a property of the table, not the distribution of keys)
Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
<!--ID: 1719174576860-->
END%%
%%ANKI
Basic
In a hash table with chaining and independent uniform hashing, what is the average *unsuccessful* search runtime?
Back: Given load factor $\alpha$, $\Theta(1 + \alpha)$.
Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
<!--ID: 1719174576864-->
END%%
%%ANKI
Basic
In a hash table with chaining and independent uniform hash function $h$, *which* elements are examined in an unsuccessful search for element $x$?
Back: All the elements in slot $h(x.key)$.
Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
<!--ID: 1719176493045-->
END%%
%%ANKI
Basic
In a hash table with chaining and independent uniform hashing, what is the average *successful* search runtime?
Back: Given load factor $\alpha$, $\Theta(1 + \alpha)$.
Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
<!--ID: 1719176493050-->
END%%
%%ANKI
Basic
In a hash table with chaining and independent uniform hash function $h$, *which* elements are examined in a successful search for element $x$?
Back: $x$ and the elements preceding $x$ in slot $h(x.key)$.
Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
<!--ID: 1719176797748-->
END%%
%%ANKI
Basic
In a hash table with chaining and independent uniform hashing, what is the average seach runtime?
Back: Given load factor $\alpha$, $\Theta(1 + \alpha)$.
Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
<!--ID: 1719176797752-->
END%%
%%ANKI
Basic
In a hash table with chaining and independent uniform hashing, *when* is the average runtime of search $O(1)$?
Back: When the number of entries is at most proportional to the number of slots in the table.
Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
<!--ID: 1719176797756-->
END%%
%%ANKI
Basic
Suppose $n$ is at most proportional to $m$. How is this denoted in complexity notation?
Back: $n = O(m)$
Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
<!--ID: 1719176797760-->
END%%
## Bibliography
* “Hash Tables: Open vs Closed Addressing | Programming.Guide,” accessed June 12, 2024, [https://programming.guide/hash-tables-open-vs-closed-addressing.html](https://programming.guide/hash-tables-open-vs-closed-addressing.html).

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@ -137,11 +137,13 @@ Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (
<!--ID: 1716307180980-->
END%%
## Load Factor
Consider hash table $T$ with $m$ slots that stores $n$ entries. Then the **load factor** $\alpha$ for $T$ is defined to be $n / m$, i.e. the average number of entries that map to the same slot.
%%ANKI
Basic
The load factor is a ratio of what two numbers?
The load factor of a hash table is a ratio of what two numbers?
Back: The number of entries in the table to the number of slots stored in the table.
Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
<!--ID: 1718759188190-->
@ -201,6 +203,8 @@ END%%
An **independent uniform hash function** is the ideal theoretical abstraction. For each possible input $k$ in universe $U$, an output $h(k)$ is produced randomly and independently chosen from range $\{0, 1, \ldots, m - 1\}$. Once a value $h(k)$ is chosen, each subsequent call to $h$ with the same input $k$ yields the same output $h(k)$.
Independent uniform hashing is **universal**, meaning the chance of any two distinct keys colliding is at most $1 / m$.
%%ANKI
Basic
What is considered the ideal (though only theoretical) hash function?
@ -241,6 +245,22 @@ Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (
<!--ID: 1718197741555-->
END%%
%%ANKI
Basic
What is uniform hashing?
Back: Any given element is equally likely to hash into any slot.
Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
<!--ID: 1719174576842-->
END%%
%%ANKI
Basic
What is independent hashing?
Back: The slot an element hashes to is independent of where other elements hash to.
Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
<!--ID: 1719174576848-->
END%%
## Bibliography
* Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).

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@ -59,7 +59,7 @@ END%%
%%ANKI
Basic
*Why* is the theoretical maximum load factor of open addressing unbounded?
*Why* is the theoretical maximum load factor of open addressing bounded?
Back: An open addressing hash table can only store as many entries as slots.
Reference: “Hash Tables: Open vs Closed Addressing | Programming.Guide,” accessed June 12, 2024, [https://programming.guide/hash-tables-open-vs-closed-addressing.html](https://programming.guide/hash-tables-open-vs-closed-addressing.html).
<!--ID: 1718759188176-->

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@ -404,12 +404,12 @@ Reference: Hindley, J Roger, and Jonathan P Seldin. “Lambda-Calculus and Combi
<!--ID: 1717855810802-->
END%%
For $\lambda$-terms $M$, $M'$, $N$, and $N'$, and variable $x$, $$M \equiv_\alpha M' \land N \equiv_\alpha N' \Rightarrow [N/x]M \equiv_\alpha [N'/x]M'$$
Substitution is well-defined with respect to $\alpha$-conversion. That is, if $M \equiv_\alpha M'$ and $N \equiv N'$, then $$[N/x]M \equiv_\alpha [N'/x]M'$$
%%ANKI
Basic
The proof of which implication shows "substitution is well-behaved w.r.t. $\alpha$-conversion"?
Back: $P \equiv_\alpha P' \land M \equiv_\alpha M' \Rightarrow [P/x]M \equiv_\alpha [P'/x]M'$
The proof of which implication shows substitution is well-behaved w.r.t. $\alpha$-conversion?
Back: $M \equiv_\alpha M' \land N \equiv_\alpha N' \Rightarrow [N/x]M \equiv_\alpha [N'/x]M'$
Reference: Hindley, J Roger, and Jonathan P Seldin. “Lambda-Calculus and Combinators, an Introduction,” n.d. [https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf](https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf).
<!--ID: 1718422973129-->
END%%
@ -417,7 +417,7 @@ END%%
%%ANKI
Basic
What does Hindley et al. mean by "substitution is well-behaved w.r.t. $\alpha$-conversion"?
Back: $\alpha$-converting substitution inputs yields congruent outputs.
Back: Substitution then $\alpha$-conversion is congruent to $\alpha$-conversion then substitution.
Reference: Hindley, J Roger, and Jonathan P Seldin. “Lambda-Calculus and Combinators, an Introduction,” n.d. [https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf](https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf).
<!--ID: 1718422973135-->
END%%
@ -431,12 +431,28 @@ END%%
%%ANKI
Basic
What does Hindley et al. say the following implication says about substitution? $$M \equiv_\alpha M' \land N \equiv_\alpha N' \Rightarrow [N/x]M \equiv_\alpha [N'/x]M'$$
Back: It is well-defined with respect to $\alpha$-conversion.
How does Hindley et al. describe the following implication? $$M \equiv_\alpha M' \land N \equiv_\alpha N' \Rightarrow [N/x]M \equiv_\alpha [N'/x]M'$$
Back: As "substitution is well-defined with respect to $\alpha$-conversion."
Reference: Hindley, J Roger, and Jonathan P Seldin. “Lambda-Calculus and Combinators, an Introduction,” n.d. [https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf](https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf).
<!--ID: 1718422981125-->
END%%
%%ANKI
Basic
Suppose $P \equiv_\alpha Q$. How do $FV(P)$ and $FV(Q)$ relate to one another?
Back: $FV(P) = FV(Q)$
Reference: Hindley, J Roger, and Jonathan P Seldin. “Lambda-Calculus and Combinators, an Introduction,” n.d. [https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf](https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf).
<!--ID: 1719406791439-->
END%%
%%ANKI
Basic
*Why* is this implication true: $P \equiv_\alpha Q \Rightarrow FV(P) = FV(Q)$
Back: $\alpha$-conversions do not modify free variables in any way.
Reference: Hindley, J Roger, and Jonathan P Seldin. “Lambda-Calculus and Combinators, an Introduction,” n.d. [https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf](https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf).
<!--ID: 1719406791443-->
END%%
## Simultaneous Substitution
Substitution can be generalized in the natural way to define simultaneous substitution $$[N_1/x_1, N_2/x_2, \ldots, N_n/x_n]M$$ for $n \geq 2$. As in [[equiv-trans#Substitution|equivalence-transformation]], simultaneous substitution is different from sequential substitution.

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END%%
%%ANKI
Basic
*Why* isn't $(\lambda x. x) \,\triangleright_{1\beta}\, (\lambda x. x)$ true?
Back: No $\beta$-redex was replaced with its contractum.
Reference: Hindley, J Roger, and Jonathan P Seldin. “Lambda-Calculus and Combinators, an Introduction,” n.d. [https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf](https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf).
<!--ID: 1719143537493-->
END%%
%%ANKI
Basic
Given $\lambda$-term $P$, is $P \,\triangleright_{1\beta}\, P$ true?
Back: No.
Back: Not necessarily.
Reference: Hindley, J Roger, and Jonathan P Seldin. “Lambda-Calculus and Combinators, an Introduction,” n.d. [https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf](https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf).
<!--ID: 1718475424855-->
END%%
%%ANKI
Basic
Given $\lambda$-term $P$, *why* isn't $P \,\triangleright_{1\beta}\, P$ true?
Back: Replacing a $\beta$-redex in $P$ with its contractum cannot again yield $P$ again.
Given $\lambda$-term $P$, when is $P \,\triangleright_{1\beta}\, P$ true?
Back: When substituting a $\beta$-redex in $P$ with its contractum yields $P$ again.
Reference: Hindley, J Roger, and Jonathan P Seldin. “Lambda-Calculus and Combinators, an Introduction,” n.d. [https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf](https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf).
<!--ID: 1718475424857-->
END%%
@ -167,6 +175,39 @@ Reference: Hindley, J Roger, and Jonathan P Seldin. “Lambda-Calculus and Combi
<!--ID: 1718475424868-->
END%%
Substitution is well-defined with respect to $\beta$-reduction. That is, if $M \,\triangleright_\beta\, M'$ and $N \,\triangleright_\beta\, N'$, then $$[N/x]M \,\triangleright_\beta\, [N'/x]M'$$
%%ANKI
Basic
The proof of which implication shows "substitution is well-behaved w.r.t. $\beta$-reduction"?
Back: $M \,\triangleright_\beta\, M' \land N \,\triangleright_\beta\, N' \Rightarrow [N/x]M \,\triangleright_\beta\, [N'/x]M'$
Reference: Hindley, J Roger, and Jonathan P Seldin. “Lambda-Calculus and Combinators, an Introduction,” n.d. [https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf](https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf).
<!--ID: 1719406791418-->
END%%
%%ANKI
Basic
What does Hindley et al. mean by "substitution is well-behaved w.r.t. $\beta$-conversion"?
Back: Substitution then $\beta$-reduction is congruent to $\beta$-reduction then substitution.
Reference: Hindley, J Roger, and Jonathan P Seldin. “Lambda-Calculus and Combinators, an Introduction,” n.d. [https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf](https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf).
<!--ID: 1719406791421-->
END%%
%%ANKI
Cloze
{$M \,\triangleright_\beta\, M' \land N \,\triangleright_\beta\, N'$} $\Rightarrow [N/x]M \,\triangleright_\beta\, [N'/x]M'$
Reference: Hindley, J Roger, and Jonathan P Seldin. “Lambda-Calculus and Combinators, an Introduction,” n.d. [https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf](https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf).
<!--ID: 1719406791424-->
END%%
%%ANKI
Basic
How does Hindley et al. describe the following implication? $$M \,\triangleright_\beta\, M' \land N \,\triangleright_\beta\, N' \Rightarrow [N/x]M \,\triangleright_\beta\, [N'/x]M'$$
Back: As "substitution is well-defined with respect to $\beta$-reduction."
Reference: Hindley, J Roger, and Jonathan P Seldin. “Lambda-Calculus and Combinators, an Introduction,” n.d. [https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf](https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf).
<!--ID: 1719406791427-->
END%%
## Normal Form
A term $Q$ which contains no $\beta$-redexes is called a **$\beta$-normal form** (or a **term in $\beta$-normal form** or just a **$\beta$-nf**). The class of all $\beta$-normal forms is called $\beta$-nf or $\lambda\beta$-nf. If a term $P$ $\beta$-reduces to a term $Q$ in $\beta$-nf, then $Q$ is called a **$\beta$-normal form of $P$**.
@ -298,6 +339,142 @@ Reference: Hindley, J Roger, and Jonathan P Seldin. “Lambda-Calculus and Combi
<!--ID: 1719103644325-->
END%%
%%ANKI
Basic
Let $P \,\triangleright_\beta\, Q$. How do $FV(P)$ and $FV(Q)$ relate to one another?
Back: $FV(Q) \subseteq FV(P)$
Reference: Hindley, J Roger, and Jonathan P Seldin. “Lambda-Calculus and Combinators, an Introduction,” n.d. [https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf](https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf).
<!--ID: 1719406791430-->
END%%
%%ANKI
Basic
Suppose $P \,\triangleright_\beta\, Q$. When is $FV(Q) \subset FV(P)$ true?
Back: When replacing a $\beta$-redex with its contractum removes a free variable.
Reference: Hindley, J Roger, and Jonathan P Seldin. “Lambda-Calculus and Combinators, an Introduction,” n.d. [https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf](https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf).
<!--ID: 1719406791433-->
END%%
%%ANKI
Basic
$\beta$-reduction "loses" free variable $N$ when it contains what $\beta$-redex?
Back: If $x \not\in FV(M)$, then $(\lambda x. M)N$.
Reference: Hindley, J Roger, and Jonathan P Seldin. “Lambda-Calculus and Combinators, an Introduction,” n.d. [https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf](https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf).
<!--ID: 1719406791436-->
END%%
## Church-Rosser Theorem
If $P \,\triangleright_\beta\, M$ and $P \,\triangleright_\beta\, N$, then there exists a term $T$ such that $M \,\triangleright_\beta\, T$ and $N \,\triangleright_\beta\, T$.
As an immediate corollary, if $P$ has a $\beta$-normal form then it it is unique modulo $\equiv_\alpha$.
%%ANKI
Basic
According to Hindley et al., what is the most quoted theorem in $\lambda$-calculus?
Back: The Church-Rosser theorem.
Reference: Hindley, J Roger, and Jonathan P Seldin. “Lambda-Calculus and Combinators, an Introduction,” n.d. [https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf](https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf).
<!--ID: 1719577152587-->
END%%
%%ANKI
Basic
The Church-Rosser theorem is related to which greek-prefixed concept?
Back: $\beta$-reductions.
Reference: Hindley, J Roger, and Jonathan P Seldin. “Lambda-Calculus and Combinators, an Introduction,” n.d. [https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf](https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf).
<!--ID: 1719577152591-->
END%%
%%ANKI
Basic
What does the Church-Rosser theorem state in terms of $\triangleright_\beta$?
Back: If $P \,\triangleright_\beta\, M$ and $P \,\triangleright_\beta\, N$, then there exists a term $T$ such that $M \,\triangleright_\beta\, T$ and $N \,\triangleright_\beta\, T$.
Reference: Hindley, J Roger, and Jonathan P Seldin. “Lambda-Calculus and Combinators, an Introduction,” n.d. [https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf](https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf).
<!--ID: 1719577152594-->
END%%
%%ANKI
Basic
When does a $\lambda$-term have zero $\beta$-normal forms (modulo $\equiv_\alpha$)?
Back: When its $\beta$-reductions fail to simplify.
Reference: Hindley, J Roger, and Jonathan P Seldin. “Lambda-Calculus and Combinators, an Introduction,” n.d. [https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf](https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf).
<!--ID: 1719577152597-->
END%%
%%ANKI
Basic
When does a $\lambda$-term have one $\beta$-normal form (modulo $\equiv_\alpha$)?
Back: When its $\beta$-reductions simplify to a point of containing no $\beta$-redexes.
Reference: Hindley, J Roger, and Jonathan P Seldin. “Lambda-Calculus and Combinators, an Introduction,” n.d. [https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf](https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf).
<!--ID: 1719577152601-->
END%%
%%ANKI
Basic
When does a $\lambda$-term have two $\beta$-normal form (modulo $\equiv_\alpha$)?
Back: N/A.
Reference: Hindley, J Roger, and Jonathan P Seldin. “Lambda-Calculus and Combinators, an Introduction,” n.d. [https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf](https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf).
<!--ID: 1719577152604-->
END%%
%%ANKI
Basic
What theorem is used to prove uniqueness of $\beta$-normal forms?
Back: The Church-Rosser theorem.
Reference: Hindley, J Roger, and Jonathan P Seldin. “Lambda-Calculus and Combinators, an Introduction,” n.d. [https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf](https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf).
<!--ID: 1719577152607-->
END%%
%%ANKI
Basic
If a $\lambda$-term has $\beta$-normal forms $P$ and $Q$, what can be said about $P$ and $Q$?
Back: $P \equiv_\alpha Q$
Reference: Hindley, J Roger, and Jonathan P Seldin. “Lambda-Calculus and Combinators, an Introduction,” n.d. [https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf](https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf).
<!--ID: 1719577152610-->
END%%
%%ANKI
Basic
What does the Church-Rosser theorem state in terms of confluence?
Back: $\beta$-reduction is confluent.
Reference: Hindley, J Roger, and Jonathan P Seldin. “Lambda-Calculus and Combinators, an Introduction,” n.d. [https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf](https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf).
<!--ID: 1719577152613-->
END%%
%%ANKI
Basic
The following diagram is a representation of what theorem?
![[church-rosser.png]]
Back: The Church-Rosser theorem for $\triangleright_\beta$.
Reference: Hindley, J Roger, and Jonathan P Seldin. “Lambda-Calculus and Combinators, an Introduction,” n.d. [https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf](https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf).
<!--ID: 1719577152616-->
END%%
%%ANKI
Basic
According to Hindley et al., what is the most important application of the Church-Rosser theorem?
Back: Showing computations in $\lambda$-calculus produce congruent results.
Reference: Hindley, J Roger, and Jonathan P Seldin. “Lambda-Calculus and Combinators, an Introduction,” n.d. [https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf](https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf).
<!--ID: 1719577152620-->
END%%
%%ANKI
Basic
For a given $\lambda$-term $P$, how many $\beta$-normal forms does $P$ have?
Back: Zero or one.
Reference: Hindley, J Roger, and Jonathan P Seldin. “Lambda-Calculus and Combinators, an Introduction,” n.d. [https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf](https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf).
<!--ID: 1719577152623-->
END%%
%%ANKI
Basic
In the following Church-Rosser diagram, what do the arrows represent?
![[church-rosser.png]]
Back: $\beta$-reductions.
Reference: Hindley, J Roger, and Jonathan P Seldin. “Lambda-Calculus and Combinators, an Introduction,” n.d. [https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf](https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf).
<!--ID: 1719577152627-->
END%%
## Bibliography
* Hindley, J Roger, and Jonathan P Seldin. “Lambda-Calculus and Combinators, an Introduction,” n.d. [https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf](https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf).

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notes/logic/quantification.md
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%%ANKI
Basic
How is $\exists x : S, P(x)$ written in terms of counting quantification?
Back: $\exists^{\geq 1} x : S, P(x)$
Back: $\exists^{\geq 1}\, x : S, P(x)$
Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
<!--ID: 1707494832056-->
END%%
@ -153,7 +153,7 @@ END%%
%%ANKI
Basic
How is $\forall x : S, P(x)$ written in terms of counting quantification?
Back: Assuming $S$ has $k$ members, $\exists^{= k} x : S, P(x)$
Back: Assuming $S$ has $k$ members, $\exists^{= k}\, x : S, P(x)$
Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
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END%%

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---
title: callPackage
TARGET DECK: Obsidian::STEM
FILE TAGS: nix
tags:
- nix
---
## Overview
We first examine `lib.makeOverridable`. It's implementation isn't too important but understanding how it's used is. We adapt the example found in [nixpkgs](https://github.com/NixOS/nixpkgs/blob/56df668386ac83c5bcddf9849c645cf0d25706d7/lib/customisation.nix#L77):
```nix
nix-repl> x = {a, b}: { example = a + b; }
nix-repl> y = lib.makeOverridable x { a = 1; b = 2; }
nix-repl> y
{ override = «lambda»; overrideDerivation = «lambda»; example = 3; }
nix-repl> y.override { a = 10; }
{ override = «lambda»; overrideDerivation = «lambda»; example = 12; }
```
`lib.makeOverridable` is an example of partial function application. Notice `y` still contains the result (`example`) of evaluating `x`. We can re-run the computation with a different value (in this case `a`) by invoking `y.override`.
%%ANKI
Basic
What is the result of the following?
```nix
x = {a, b}: { example = a + b; }
lib.functionArgs x
```
Back: `{ a = false; b = false; }`
Reference: Yin, Ryan. “NixOS and Flakes Book.” Nix, February 1, 2024. [https://github.com/ryan4yin/nixos-and-flakes-book](https://github.com/ryan4yin/nixos-and-flakes-book)
<!--ID: 1706828138583-->
END%%
%%ANKI
Basic
What does each boolean returned by `lib.functionArgs` indicate?
Back: Whether the associated attribute has a default value.
Reference: Yin, Ryan. “NixOS and Flakes Book.” Nix, February 1, 2024. [https://github.com/ryan4yin/nixos-and-flakes-book](https://github.com/ryan4yin/nixos-and-flakes-book)
<!--ID: 1706828138588-->
END%%
%%ANKI
Basic
What additional attributes is included in the set returned by `lib.makeOverridable`?
Back: `override` and `overrideDerivation`.
Reference: Yin, Ryan. “NixOS and Flakes Book.” Nix, February 1, 2024. [https://github.com/ryan4yin/nixos-and-flakes-book](https://github.com/ryan4yin/nixos-and-flakes-book)
<!--ID: 1706828138590-->
END%%
%%ANKI
Basic
What is the value of `y.example` in the following?
```nix
x = {a, b}: { example = a + b; }
y = lib.makeOverridable x { a = 1; b = 2; }
```
Back: `3`
Reference: Yin, Ryan. “NixOS and Flakes Book.” Nix, February 1, 2024. [https://github.com/ryan4yin/nixos-and-flakes-book](https://github.com/ryan4yin/nixos-and-flakes-book)
<!--ID: 1706828225233-->
END%%
%%ANKI
Basic
What is the value of `(y.override { a = 10; }).example` in the following?
```nix
x = {a, b}: { example = a + b; }
y = lib.makeOverridable x { a = 1; b = 2; }
```
Back: `12`
Reference: Yin, Ryan. “NixOS and Flakes Book.” Nix, February 1, 2024. [https://github.com/ryan4yin/nixos-and-flakes-book](https://github.com/ryan4yin/nixos-and-flakes-book)
<!--ID: 1706828225236-->
END%%
Now we can understand how `pkgs.callPackage` works. The following is a simplification of the [actual implementation](https://github.com/NixOS/nixpkgs/blob/56df668386ac83c5bcddf9849c645cf0d25706d7/lib/customisation.nix#L153):
```nix
callPackageWith = autoArgs: fn: args:
let
f = if isFunction fn then fn else import fn;
fargs = functionArgs f;
allArgs = intersectArgs fargs autoArgs // args;
in
lib.makeOverridable f allArgs
callPackage = callPackageWith pkgs;
```
%%ANKI
Basic
What two functions is `callPackage` implemented on top of?
Back: `callPackageWith` and `makeOverridable`.
Reference: Yin, Ryan. “NixOS and Flakes Book.” Nix, February 1, 2024. [https://github.com/ryan4yin/nixos-and-flakes-book](https://github.com/ryan4yin/nixos-and-flakes-book)
<!--ID: 1706828138592-->
END%%
%%ANKI
Basic
What is the purpose of `callPackage`?
Back: It calls package functions with arguments automatically supplied if not overridden.
Reference: Yin, Ryan. “NixOS and Flakes Book.” Nix, February 1, 2024. [https://github.com/ryan4yin/nixos-and-flakes-book](https://github.com/ryan4yin/nixos-and-flakes-book)
<!--ID: 1706828138594-->
END%%
%%ANKI
Basic
What attribute must be invoked in `callPackage`'s return value to override arguments?
Back: `override`
Reference: Yin, Ryan. “NixOS and Flakes Book.” Nix, February 1, 2024. [https://github.com/ryan4yin/nixos-and-flakes-book](https://github.com/ryan4yin/nixos-and-flakes-book)
<!--ID: 1706828225240-->
END%%
## Bibliography
* Yin, Ryan. “NixOS and Flakes Book.” Nix, February 1, 2024. [https://github.com/ryan4yin/nixos-and-flakes-book](https://github.com/ryan4yin/nixos-and-flakes-book)

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---
title: Nix
tags:
- nix
---

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END%%
## Confluence
**Confluence** is the property by which two different terms can be further reduced to one common term. That is to say, confluence is a property of rewriting systems describing which terms in such a system can be rewritten in more than one way.
%%ANKI
Basic
What is confluence?
Back: A property by which two different terms can be further reduced to one common term.
Reference: “Confluence (Abstract Rewriting),” in _Wikipedia_, May 22, 2024, [https://en.wikipedia.org/w/index.php?title=Confluence](https://en.wikipedia.org/w/index.php?title=Confluence_(abstract_rewriting)&oldid=1225041322).
<!--ID: 1719578045810-->
END%%
%%ANKI
Basic
How might $(11 + 9) \times (2 + 4)$ be reduced to demonstrate confluence?
Back: As $20 \times (2 + 4)$ and as $(11 + 9) \times 6$.
Reference: “Confluence (Abstract Rewriting),” in _Wikipedia_, May 22, 2024, [https://en.wikipedia.org/w/index.php?title=Confluence](https://en.wikipedia.org/w/index.php?title=Confluence_(abstract_rewriting)&oldid=1225041322).
<!--ID: 1719578045839-->
END%%
%%ANKI
Basic
How might $(\lambda x. (\lambda y. yx)z)v$ be reduced to demonstrate confluence?
Back: As $(\lambda y.yv)z$ and as $(\lambda x. zx)v$.
Reference: “Confluence (Abstract Rewriting),” in _Wikipedia_, May 22, 2024, [https://en.wikipedia.org/w/index.php?title=Confluence](https://en.wikipedia.org/w/index.php?title=Confluence_(abstract_rewriting)&oldid=1225041322).
<!--ID: 1719578045843-->
END%%
## Bibliography
* “Canonical Form,” in _Wikipedia_, January 7, 2024, [https://en.wikipedia.org/w/index.php?title=Canonical_form](https://en.wikipedia.org/w/index.php?title=Canonical_form&oldid=1194093963).
* “Confluence (Abstract Rewriting),” in _Wikipedia_, May 22, 2024, [https://en.wikipedia.org/w/index.php?title=Confluence](https://en.wikipedia.org/w/index.php?title=Confluence_(abstract_rewriting)&oldid=1225041322).
* Normal Form,” in _Wikipedia_, April 27, 2024, [https://en.wikipedia.org/w/index.php?title=Normal_form](https://en.wikipedia.org/w/index.php?title=Normal_form_(abstract_rewriting)&oldid=1221094193).

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%%ANKI
Basic
How is the inverse of set $F$ defined in set-builder notation?
Back: $F^{-1} = \{\langle u, v \rangle \mid vFu\}$\
Back: $F^{-1} = \{\langle u, v \rangle \mid vFu\}$
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1719016770752-->
END%%
@ -633,6 +633,29 @@ Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Pre
<!--ID: 1719103644293-->
END%%
%%ANKI
Basic
Given set $F$, what does $\mathop{\text{dom}}F^{-1}$ evaluate to?
Back: $\mathop{\text{ran}}F$
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1719398756549-->
END%%
%%ANKI
Basic
Given set $F$, what does $\mathop{\text{ran}}F^{-1}$ evaluate to?
Back: $\mathop{\text{dom}}F$
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1719398756554-->
END%%
%%ANKI
Cloze
For any set $F$, {1:$F$} is {2:single-valued} iff {2:$F^{-1}$} is {1:single-rooted}.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1719398756558-->
END%%
## Compositions
Let $F$ and $G$ be arbitrary sets. The **composition** of $F$ and $G$ is the set $$F \circ G = \{\langle u, v \rangle \mid \exists t, uGt \land tFv \}$$
@ -716,6 +739,67 @@ Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Pre
<!--ID: 1719103644296-->
END%%
%%ANKI
Cloze
Let $F$ be {a function}. If $t \in$ {$\mathop{\text{ran}}F$}, then $F(F^{-1}(t)) = t$.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1719398756562-->
END%%
%%ANKI
Cloze
Let $F$ be {an injection}. If $t \in$ {$\mathop{\text{dom}}F$}, then $F^{-1}(F(t)) = t$.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1719398756565-->
END%%
%%ANKI
Basic
If $F$ is a relation and $G$ is a function, is $F \circ G$ a function?
Back: Not necessarily.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1719406791406-->
END%%
%%ANKI
Basic
If $F$ is a function and $G$ is a relation, is $F \circ G$ a function?
Back: Not necessarily.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1719406791410-->
END%%
%%ANKI
Basic
If $F$ is a function and $G$ is a function, is $F \circ G$ a function?
Back: Yes.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1719406791413-->
END%%
%%ANKI
Basic
Let $F$ and $G$ be functions. How is $\mathop{\text{dom}}(F \circ G)$ defined using set-builder notation?
Back: $\{x \in \mathop{\text{dom}}G \mid G(x) \in \mathop{\text{dom}}F\}$
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1719406791415-->
END%%
%%ANKI
Cloze
For any sets $F$ and $G$, {$(F \circ G)^{-1}$} $=$ {$G^{-1} \circ F^{-1}$}.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1719666552283-->
END%%
%%ANKI
Basic
How might you explain $(F \circ G)^{-1} = G^{-1} \circ F^{-1}$ in plain English?
Back: The opposite of applying $G$ then $F$ is to undo $F$ then $G$.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1719666552291-->
END%%
## Restrictions
Let $F$ and $A$ be arbitrary sets. The **restriction of $F$ to $A$** is the set $$F \restriction A = \{\langle u, v \rangle \mid uFv \land u \in A\}$$

2
notes/set/index.md
View File

@ -400,7 +400,7 @@ For any sets $a$ and $b$, there exists a set whose members are those sets belong
%%ANKI
Basic
What does the union axiom (preliminary form) state?
Back: For any sets $a$ and $b$, there exists a set whose members are all in either $a$ or $b$.
Back: For any sets $a$ and $b$, there exists a set whose members are all in either $a$ or $b$ (or both).
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715688034333-->
END%%

433
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@ -0,0 +1,433 @@
---
title: Financing
TARGET DECK: Obsidian::H&SS
FILE TAGS: startups::financing
tags:
- financing
- startups
---
## Overview
Financing rounds roughly follow the given naming scheme:
* Early-stage companies:
* Series Pre-Seed
* Series Seed
* Series A
* Mid-stage companies:
* Series B
* Series C
* Late-stage companies:
* Series D
* ...
Financing rounds with numerical suffices (e.g. Series B-1) usually refer to situations where the same investors, on the same terms, invest additional money.
%%ANKI
Basic
What name is given to the earliest financing round?
Back: Series Pre-Seed.
Reference: Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.
<!--ID: 1719151112996-->
END%%
%%ANKI
Cloze
The Series {Seed} round follows the Series {Pre-Seed} round.
Reference: Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.
<!--ID: 1719151113006-->
END%%
%%ANKI
Cloze
The Series {A} round follows the Series {Seed} round.
Reference: Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.
<!--ID: 1719151113010-->
END%%
%%ANKI
Basic
What two financing rounds can follow a Series B round?
Back: A "Series B-1" or "Series C".
Reference: Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.
<!--ID: 1719151159514-->
END%%
%%ANKI
Basic
When does a Series A round transition to a Series A-1 round?
Back: When the same investors, on the same terms, invest additional money.
Reference: Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.
<!--ID: 1719151113015-->
END%%
%%ANKI
Basic
When does a Series A round transition to a Series B round?
Back: When new investors or new terms are applied to a new investment.
Reference: Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.
<!--ID: 1719151113019-->
END%%
%%ANKI
Basic
When does a Series A-2 round transition to a Series B round?
Back: When new investors or new terms are applied to a new investment.
Reference: Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.
<!--ID: 1719151113024-->
END%%
%%ANKI
Basic
When does a Series A-2 round transition to a Series B-1 round?
Back: N/A.
Reference: Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.
<!--ID: 1719151113030-->
END%%
%%ANKI
Basic
What financing rounds are considered "early-stage"?
Back: Series Pre-Seed, Seed, and A.
Reference: Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.
<!--ID: 1719151113034-->
END%%
%%ANKI
Basic
What financing rounds are considered "mid-stage"?
Back: Series B and C.
Reference: Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.
<!--ID: 1719151113039-->
END%%
%%ANKI
Basic
What financing rounds are considered "late-stage"?
Back: Series D and after.
Reference: Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.
<!--ID: 1719151113045-->
END%%
A **party round** refers to a financing round with many investors that make relatively small investments.
%%ANKI
Cloze
A {party round} is a {round of financing with many investors making small investments}.
Reference: Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.
<!--ID: 1719360934653-->
END%%
%%ANKI
Basic
Why are party rounds discouraged?
Back: You have many VCs but none committed in any meaningful way.
Reference: Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.
<!--ID: 1719360934657-->
END%%
%%ANKI
Basic
Why aren't VCs usually meaningfully committed in a party round?
Back: Their investment is likely much smaller relative to what they'd normally invest.
Reference: Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.
<!--ID: 1719360934661-->
END%%
%%ANKI
Basic
What is the primary motivation behind having a party round?
Back: You can potentially have many fancy names associated with your company.
Reference: Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.
<!--ID: 1719360934665-->
END%%
## Venture Capitalists
A **venture capitalist** (VC) is an investor who provides capital to companies in exchange for an equity stake on behalf of a firm. A firm comprises of the following roles (in order of seniority):
* **Managing director** (MD) or **general partner** (GP). The VCs that make the final investment decisions and sit on the boards of directors of the companies they invest in.
* **Principal** or **director**. Junior deal professionals looking to become managing directors.
* **Associate**. Work for one or more deal partners, usually a managing director.
* **Analyst**. Individuals with similar responsibilites as the associate, though usually less deal-centric.
%%ANKI
Basic
What is VC short for?
Back: **V**enture **c**apitalist.
Reference: Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.
<!--ID: 1718878788273-->
END%%
%%ANKI
Basic
What ambiguity does the term "VC" introduce?
Back: It may refer to a VC firm or an individual of said firm.
Reference: Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.
<!--ID: 1718878788303-->
END%%
%%ANKI
Cloze
Typically VCs provide {capital} in exchange for {equity}.
Reference: Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.
<!--ID: 1718878788311-->
END%%
%%ANKI
Basic
How is a "venture capitalist" defined?
Back: An investor who provides capital to companies, on behalf of a firm, in exchange for equity.
Reference: Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.
<!--ID: 1718878788328-->
END%%
%%ANKI
Basic
What form of capital does a VC typically work in?
Back: Cash flow.
Reference: Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.
<!--ID: 1718878788334-->
END%%
%%ANKI
Basic
Within a VC firm, what does MD stand for?
Back: **M**anaging **d**irector.
Reference: Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.
<!--ID: 1718878788338-->
END%%
%%ANKI
Basic
Within a VC firm, what does GP stand for?
Back: **G**eneral **p**artner.
Reference: Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.
<!--ID: 1718878788342-->
END%%
%%ANKI
Basic
With respect to a VC firm, what does a "managing director" refer to?
Back: A senior VC, generally responsible for making final investment decisions.
Reference: Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.
<!--ID: 1718879311552-->
END%%
%%ANKI
Basic
With respect to a VC firm, what does a "general partner" refer to?
Back: A senior VC, generally responsible for making final investment decisions.
Reference: Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.
<!--ID: 1718878788345-->
END%%
%%ANKI
Cloze
A {general partner} is also known as a {managing director}.
Reference: Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.
<!--ID: 1718878788348-->
END%%
%%ANKI
Cloze
The {principal/director} role follows the {MD/GP} role in seniority.
Reference: Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.
<!--ID: 1718878788353-->
END%%
%%ANKI
Basic
With respect to a VC firm, what does a "principal" refer to?
Back: A VC working their way up to becoming a GP.
Reference: Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.
<!--ID: 1718878788357-->
END%%
%%ANKI
Basic
With respect to a VC firm, what does a "director" refer to?
Back: A VC working their way up to becoming an MD.
Reference: Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.
<!--ID: 1718879311558-->
END%%
%%ANKI
Cloze
A {principal} is also known as a {director}.
Reference: Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.
<!--ID: 1718878788361-->
END%%
%%ANKI
Basic
What types of VCs are grouped under term "deal partner"?
Back: GPs and principals.
Reference: Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.
<!--ID: 1718878788368-->
END%%
%%ANKI
Basic
What distinguishes VCs from angel investors?
Back: The former use a pool of investors' money. The latter uses their own money.
Reference: Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.
<!--ID: 1718879311563-->
END%%
%%ANKI
Cloze
The {associate} role follows the {principal/director} role in seniority.
Reference: Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.
<!--ID: 1718879311566-->
END%%
%%ANKI
Cloze
The {analyst} role follows the {associate} role in seniority.
Reference: Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.
<!--ID: 1718879311572-->
END%%
%%ANKI
Basic
How are analysts and associates typically distinguished?
Back: The latter are usually more deal-centric than the former.
Reference: Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.
<!--ID: 1718879311577-->
END%%
%%ANKI
Basic
What role is a recent college graduate likely given at a VC firm?
Back: Analyst.
Reference: Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.
<!--ID: 1718879311581-->
END%%
%%ANKI
Basic
With respect to a VC firm, what does an "associate" refer to?
Back: An employee usually working directly for one or more deal managers.
Reference: Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.
<!--ID: 1718879311586-->
END%%
%%ANKI
Basic
With respect to a VC firm, what does an "analyst" refer to?
Back: An employee working on general functions for the firm.
Reference: Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.
<!--ID: 1718879311590-->
END%%
While some VCs invest alone, many invest with other VCs. A collection of investors is called a **syndicate**. Most syndicates have a **lead investor** usually responsible for taking the role of negotiating terms on behalf of the entire syndicate.
%%ANKI
Cloze
A {syndicate} is a {collection of investors}.
Reference: Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.
<!--ID: 1719360934669-->
END%%
%%ANKI
Basic
A syndicate collectively refers to which kind of investors?
Back: *Anyone* that ends up purchasing equity in a financing.
Reference: Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.
<!--ID: 1719360934673-->
END%%
%%ANKI
Basic
A "lead investor" is considered the lead of what?
Back: A syndicate.
Reference: Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.
<!--ID: 1719360934678-->
END%%
%%ANKI
Basic
What is the usual responsibility of a lead investor?
Back: Negotiating terms on behalf of the syndicate.
Reference: Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.
<!--ID: 1719360934682-->
END%%
%%ANKI
Basic
*Why* do entrepreneurs want a lead investor?
Back: To limit the number of negotiations to just those with the lead.
Reference: Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.
<!--ID: 1719360934687-->
END%%
%%ANKI
Basic
How many lead investors can a syndicate have?
Back: There is no limit.
Reference: Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.
<!--ID: 1719360934693-->
END%%
## Angel Investors
**Angels** are usually high-net-worth individuals that invest in a company. They must qualify as an **accredited investor** or have an appropriate exemption to invest. Angel investors that make many small investments to companies are called **super angels**.
%%ANKI
Cloze
An {angel} is a shorthand term for an {angel investor}.
Reference: Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.
<!--ID: 1719360934700-->
END%%
%%ANKI
Cloze
Angels must be {accredited}, as defined by the SEC.
Reference: Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.
<!--ID: 1719360934706-->
END%%
%%ANKI
Basic
What distinguishes an angel and VC's funding source?
Back: The former use their own money. The latter uses a group of investors' money.
Reference: Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.
<!--ID: 1719360934711-->
END%%
%%ANKI
Basic
What is a super angel?
Back: Angel investors that make many small investments to companies.
Reference: Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.
<!--ID: 1719360934716-->
END%%
%%ANKI
Cloze
{Angel}s become {super angel}s become {micro} VCs.
Reference: Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.
<!--ID: 1719360934720-->
END%%
%%ANKI
Basic
VCs have a fiduciary reponsibility to whom?
Back: Investors of the VC.
Reference: Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.
<!--ID: 1719360934724-->
END%%
%%ANKI
Basic
At what point does a super angel become a VC?
Back: When they accept money from others to raise a fund.
Reference: Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.
<!--ID: 1719360934730-->
END%%
## Bibliography
* Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.

190
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@ -1,190 +0,0 @@
---
title: Venture Capitalist
TARGET DECK: Obsidian::H&SS
FILE TAGS: startups::vc
tags:
- startups
---
## Overview
A **venture capitalist** (VC) is an investor who provides capital to companies in exchange for an equity stake on behalf of a firm. A firm comprises of the following roles (in order of seniority):
* **Managing director** (MD) or **general partner** (GP). The VCs that make the final investment decisions and sit on the boards of directors of the companies they invest in.
* **Principal** or **director**. Junior deal professionals looking to become managing directors.
* **Associate**. Work for one or more deal partners, usually a managing director.
* **Analyst**. Individuals with similar responsibilites as the associate, though usually less deal-centric.
%%ANKI
Basic
What is VC short for?
Back: **V**enture **c**apitalist.
Reference: Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.
<!--ID: 1718878788273-->
END%%
%%ANKI
Basic
What ambiguity does the term "VC" introduce?
Back: It may refer to a VC firm or an individual of said firm.
Reference: Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.
<!--ID: 1718878788303-->
END%%
%%ANKI
Cloze
Typically VCs provide {capital} in exchange for {equity}.
Reference: Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.
<!--ID: 1718878788311-->
END%%
%%ANKI
Basic
How is a "venture capitalist" defined?
Back: An investor who provides capital to companies, on behalf of a firm, in exchange for equity.
Reference: Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.
<!--ID: 1718878788328-->
END%%
%%ANKI
Basic
What form of capital does a VC typically work in?
Back: Cash flow.
Reference: Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.
<!--ID: 1718878788334-->
END%%
%%ANKI
Basic
Within a VC firm, what does MD stand for?
Back: **M**anaging **d**irector.
Reference: Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.
<!--ID: 1718878788338-->
END%%
%%ANKI
Basic
Within a VC firm, what does GP stand for?
Back: **G**eneral **p**artner.
Reference: Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.
<!--ID: 1718878788342-->
END%%
%%ANKI
Basic
With respect to a VC firm, what does a "managing director" refer to?
Back: A senior VC, generally responsible for making final investment decisions.
Reference: Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.
<!--ID: 1718879311552-->
END%%
%%ANKI
Basic
With respect to a VC firm, what does a "general partner" refer to?
Back: A senior VC, generally responsible for making final investment decisions.
Reference: Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.
<!--ID: 1718878788345-->
END%%
%%ANKI
Cloze
A {general partner} is also known as a {managing director}.
Reference: Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.
<!--ID: 1718878788348-->
END%%
%%ANKI
Cloze
The {principal/director} role follows the {MD/GP} role in seniority.
Reference: Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.
<!--ID: 1718878788353-->
END%%
%%ANKI
Basic
With respect to a VC firm, what does a "principal" refer to?
Back: A VC working their way up to becoming a GP.
Reference: Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.
<!--ID: 1718878788357-->
END%%
%%ANKI
Basic
With respect to a VC firm, what does a "director" refer to?
Back: A VC working their way up to becoming an MD.
Reference: Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.
<!--ID: 1718879311558-->
END%%
%%ANKI
Cloze
A {principal} is also known as a {director}.
Reference: Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.
<!--ID: 1718878788361-->
END%%
%%ANKI
Basic
What types of VCs are grouped under term "deal partner"?
Back: GPs and principals.
Reference: Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.
<!--ID: 1718878788368-->
END%%
%%ANKI
Basic
What distinguishes VCs from angel investors?
Back: The former use a pool of investors' money. The latter uses their own money.
Reference: Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.
<!--ID: 1718879311563-->
END%%
%%ANKI
Cloze
The {associate} role follows the {principal/director} role in seniority.
Reference: Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.
<!--ID: 1718879311566-->
END%%
%%ANKI
Cloze
The {analyst} role follows the {associate} role in seniority.
Reference: Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.
<!--ID: 1718879311572-->
END%%
%%ANKI
Basic
How are analysts and associates typically distinguished?
Back: The latter are usually more deal-centric than the former.
Reference: Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.
<!--ID: 1718879311577-->
END%%
%%ANKI
Basic
What role is a recent college graduate likely given at a VC firm?
Back: Analyst.
Reference: Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.
<!--ID: 1718879311581-->
END%%
%%ANKI
Basic
With respect to a VC firm, what does an "associate" refer to?
Back: An employee usually working directly for one or more deal managers.
Reference: Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.
<!--ID: 1718879311586-->
END%%
%%ANKI
Basic
With respect to a VC firm, what does an "analyst" refer to?
Back: An employee working on general functions for the firm.
Reference: Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.
<!--ID: 1718879311590-->
END%%
## Bibliography
* Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.