More "Science of Programming" and `awk`.

notes/.obsidian/app.json

@@ -1,3 +1,4 @@
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-    "c/escape-sequences.md": "07f0811b0fff14f54f78abc33f2e6606",
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-    "gawk/index.md": "0263448c8ae1ecfc0eacc4788f8402e9",
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notes/_journal/2024-02-04.md

@@ -2,10 +2,12 @@
 title: "2024-02-04"
 ---
 
-- [ ] Anki Flashcards
+- [x] Anki Flashcards
 - [x] KoL
 - [ ] Sheet Music (10 min.)
 - [ ] OGS (1 Life & Death Problem)
 - [ ] Korean (Read 1 Story)
 - [ ] Interview Prep (1 Practice Problem)
-- [ ] Log Work Hours (Max 3 hours)
+- [ ] Log Work Hours (Max 3 hours)
+
+* Today was spent primarily traveling.

notes/_journal/2024-02-05.md

@@ -0,0 +1,14 @@
+---
+title: "2024-02-04"
+---
+
+- [x] Anki Flashcards
+- [ ] KoL
+- [ ] Sheet Music (10 min.)
+- [ ] OGS (1 Life & Death Problem)
+- [ ] Korean (Read 1 Story)
+- [ ] Interview Prep (1 Practice Problem)
+- [ ] Log Work Hours (Max 3 hours)
+
+* Today was spent mostly hanging out with Brittany and Katie.
+* I spent a brief amount of time thinking about the equivalence-transformation system described by Gries.

notes/_journal/2024-02-06.md

@@ -8,6 +8,7 @@ title: "2024-02-06"
 - [ ] OGS (1 Life & Death Problem)
 - [ ] Korean (Read 1 Story)
 - [ ] Interview Prep (1 Practice Problem)
-- [ ] Log Work Hours (Max 3 hours)
+- [x] Log Work Hours (Max 3 hours)
 
-* 
+* Continued reading about `awk` regular expressions. Finished Chapter 3 of "GAWK: Effective AWK Programming".
+* Translated more notes on equivalence-transformation.

notes/_journal/2024-02-07.md

@@ -0,0 +1,13 @@
+---
+title: "2024-02-07"
+---
+
+- [x] Anki Flashcards
+- [x] KoL
+- [ ] Sheet Music (10 min.)
+- [ ] OGS (1 Life & Death Problem)
+- [ ] Korean (Read 1 Story)
+- [ ] Interview Prep (1 Practice Problem)
+- [ ] Log Work Hours (Max 3 hours)
+
+* Read section 4.1 of "GAWK: Effective AWK Programming".

notes/algorithms/sorting/index.md

@@ -14,21 +14,21 @@ Let $n \geq 0$. The **sorting problem** refers to permuting **records** $a_1, a_
 %%ANKI
 Cloze
 In the sorting problem, a "{record}" refers to {the entries being sorted}.
-Reference: Thomas H. Cormen et al., _Introduction to Algorithms_, 3rd ed (Cambridge, Mass: MIT Press, 2009).
+Reference: Thomas H. Cormen et al., *Introduction to Algorithms*, 3rd ed (Cambridge, Mass: MIT Press, 2009).
 <!--ID: 1706981319280-->
 END%%
 
 %%ANKI
 Cloze
 In the sorting problem, a "{key}" refers to {the value records are sorted by}.
-Reference: Thomas H. Cormen et al., _Introduction to Algorithms_, 3rd ed (Cambridge, Mass: MIT Press, 2009).
+Reference: Thomas H. Cormen et al., *Introduction to Algorithms*, 3rd ed (Cambridge, Mass: MIT Press, 2009).
 <!--ID: 1706981319310-->
 END%%
 
 %%ANKI
 Cloze
 In the sorting problem, "{satellite data}" refers to {the non-key values of records}.
-Reference: Thomas H. Cormen et al., _Introduction to Algorithms_, 3rd ed (Cambridge, Mass: MIT Press, 2009).
+Reference: Thomas H. Cormen et al., *Introduction to Algorithms*, 3rd ed (Cambridge, Mass: MIT Press, 2009).
 <!--ID: 1706981319317-->
 END%%
 
@@ -36,7 +36,7 @@ END%%
 Basic
 What term does Cormen et al. use to describe the record value used for sorting?
 Back: Keys.
-Reference: Thomas H. Cormen et al., _Introduction to Algorithms_, 3rd ed (Cambridge, Mass: MIT Press, 2009).
+Reference: Thomas H. Cormen et al., *Introduction to Algorithms*, 3rd ed (Cambridge, Mass: MIT Press, 2009).
 <!--ID: 1706981319324-->
 END%%
 
@@ -44,7 +44,7 @@ END%%
 Basic
 What makes a sorting algorithm stable?
 Back: "Equal" values are ordered the same in the output as they are in the input.
-Reference: Thomas H. Cormen et al., _Introduction to Algorithms_, 3rd ed (Cambridge, Mass: MIT Press, 2009).
+Reference: Thomas H. Cormen et al., *Introduction to Algorithms*, 3rd ed (Cambridge, Mass: MIT Press, 2009).
 <!--ID: 1706925787139-->
 END%%
 
@@ -52,7 +52,7 @@ END%%
 Basic
 What is an in place sorting algorithm?
 Back: One in which only a constant number of input values are ever stored outside the array.
-Reference: Thomas H. Cormen et al., _Introduction to Algorithms_, 3rd ed (Cambridge, Mass: MIT Press, 2009).
+Reference: Thomas H. Cormen et al., *Introduction to Algorithms*, 3rd ed (Cambridge, Mass: MIT Press, 2009).
 <!--ID: 1706925787146-->
 END%%
 
@@ -93,7 +93,7 @@ END%%
 
 ## References
 
-* Thomas H. Cormen et al., _Introduction to Algorithms_, 3rd ed (Cambridge, Mass: MIT Press, 2009).
+* Thomas H. Cormen et al., *Introduction to Algorithms*, 3rd ed (Cambridge, Mass: MIT Press, 2009).
 * “Kernel — Elixir v1.16.1,” accessed February 2, 2024, [https://hexdocs.pm/elixir/1.16/Kernel.html#module-structural-comparison](https://hexdocs.pm/elixir/1.16/Kernel.html#module-structural-comparison).
 
 [^structural]: [Structural Comparison](https://hexdocs.pm/elixir/1.16/Kernel.html#module-structural-comparison)

notes/algorithms/sorting/insertion-sort.md

@@ -24,7 +24,7 @@ Insertion sort works by advancing an index `i` through an array `A[1..n]` such t
 Basic
 What is insertion sort's best case runtime?
 Back: $O(n)$
-Reference: Thomas H. Cormen et al., _Introduction to Algorithms_, 3rd ed (Cambridge, Mass: MIT Press, 2009).
+Reference: Thomas H. Cormen et al., *Introduction to Algorithms*, 3rd ed (Cambridge, Mass: MIT Press, 2009).
 <!--ID: 1706925879541-->
 END%%
 
@@ -32,7 +32,7 @@ END%%
 Basic
 What input value does insertion sort perform best on?
 Back: An already sorted array.
-Reference: Thomas H. Cormen et al., _Introduction to Algorithms_, 3rd ed (Cambridge, Mass: MIT Press, 2009).
+Reference: Thomas H. Cormen et al., *Introduction to Algorithms*, 3rd ed (Cambridge, Mass: MIT Press, 2009).
 <!--ID: 1706925921544-->
 END%%
 
@@ -40,7 +40,7 @@ END%%
 Basic
 What is insertion sort's worst case runtime?
 Back: $O(n^2)$
-Reference: Thomas H. Cormen et al., _Introduction to Algorithms_, 3rd ed (Cambridge, Mass: MIT Press, 2009).
+Reference: Thomas H. Cormen et al., *Introduction to Algorithms*, 3rd ed (Cambridge, Mass: MIT Press, 2009).
 <!--ID: 1706926586947-->
 END%%
 
@@ -48,7 +48,7 @@ END%%
 Basic
 What input value does insertion sort perform worst on?
 Back: An array in reverse-sorted order.
-Reference: Thomas H. Cormen et al., _Introduction to Algorithms_, 3rd ed (Cambridge, Mass: MIT Press, 2009).
+Reference: Thomas H. Cormen et al., *Introduction to Algorithms*, 3rd ed (Cambridge, Mass: MIT Press, 2009).
 <!--ID: 1706926586951-->
 END%%
 
@@ -56,7 +56,7 @@ END%%
 Basic
 Is insertion sort in place?
 Back: Yes
-Reference: Thomas H. Cormen et al., _Introduction to Algorithms_, 3rd ed (Cambridge, Mass: MIT Press, 2009).
+Reference: Thomas H. Cormen et al., *Introduction to Algorithms*, 3rd ed (Cambridge, Mass: MIT Press, 2009).
 <!--ID: 1706926586955-->
 END%%
 
@@ -64,7 +64,7 @@ END%%
 Basic
 Is insertion sort stable?
 Back: Yes
-Reference: Thomas H. Cormen et al., _Introduction to Algorithms_, 3rd ed (Cambridge, Mass: MIT Press, 2009).
+Reference: Thomas H. Cormen et al., *Introduction to Algorithms*, 3rd ed (Cambridge, Mass: MIT Press, 2009).
 <!--ID: 1706926586959-->
 END%%
 
@@ -85,7 +85,7 @@ void insertion_sort(const int n, int A[static n]) {
 Basic
 What loop invariant is maintained in insertion sort?
 Back: `A[1..i]` is in sorted order.
-Reference: Thomas H. Cormen et al., _Introduction to Algorithms_, 3rd ed (Cambridge, Mass: MIT Press, 2009).
+Reference: Thomas H. Cormen et al., *Introduction to Algorithms*, 3rd ed (Cambridge, Mass: MIT Press, 2009).
 <!--ID: 1706927594718-->
 END%%
 
@@ -99,7 +99,7 @@ If you repeat this process for every card in the deck, your left hand will event
 Basic
 What analogy does Cormen et al. use to explain insertion sort?
 Back: Sorting a shuffled deck of playing cards.
-Reference: Thomas H. Cormen et al., _Introduction to Algorithms_, 3rd ed (Cambridge, Mass: MIT Press, 2009).
+Reference: Thomas H. Cormen et al., *Introduction to Algorithms*, 3rd ed (Cambridge, Mass: MIT Press, 2009).
 <!--ID: 1706927594729-->
 END%%
 
@@ -107,10 +107,10 @@ END%%
 Basic
 What invariant does the left hand maintain in Cormen et al.'s insertion sort analogy?
 Back: It contains all drawn cards in sorted order.
-Reference: Thomas H. Cormen et al., _Introduction to Algorithms_, 3rd ed (Cambridge, Mass: MIT Press, 2009).
+Reference: Thomas H. Cormen et al., *Introduction to Algorithms*, 3rd ed (Cambridge, Mass: MIT Press, 2009).
 <!--ID: 1706927594732-->
 END%%
 
 ## References
 
-* Thomas H. Cormen et al., _Introduction to Algorithms_, 3rd ed (Cambridge, Mass: MIT Press, 2009).
+* Thomas H. Cormen et al., *Introduction to Algorithms*, 3rd ed (Cambridge, Mass: MIT Press, 2009).

notes/c/escape-sequences.md

@@ -19,7 +19,7 @@ C has a standard for processing different escape sequences. Many languages built
 Basic
 How are C escape sequences for octal digits denoted?
 Back: As `\ooo`.
-Reference: Brian W. Kernighan and Dennis M. Ritchie, _The C Programming Language_, 2nd ed (Englewood Cliffs, N.J: Prentice Hall, 1988).
+Reference: Brian W. Kernighan and Dennis M. Ritchie, *The C Programming Language*, 2nd ed (Englewood Cliffs, N.J: Prentice Hall, 1988).
 <!--ID: 1706975891805-->
 END%%
 
@@ -27,7 +27,7 @@ END%%
 Basic
 In C, `\ooo` allows specifying how many octal digits?
 Back: One to three.
-Reference: Brian W. Kernighan and Dennis M. Ritchie, _The C Programming Language_, 2nd ed (Englewood Cliffs, N.J: Prentice Hall, 1988).
+Reference: Brian W. Kernighan and Dennis M. Ritchie, *The C Programming Language*, 2nd ed (Englewood Cliffs, N.J: Prentice Hall, 1988).
 <!--ID: 1706975891810-->
 END%%
 
@@ -59,7 +59,7 @@ END%%
 Basic
 How are C escape sequences for hexadecimal digits denoted?
 Back: As `\xhh`.
-Reference: Brian W. Kernighan and Dennis M. Ritchie, _The C Programming Language_, 2nd ed (Englewood Cliffs, N.J: Prentice Hall, 1988).
+Reference: Brian W. Kernighan and Dennis M. Ritchie, *The C Programming Language*, 2nd ed (Englewood Cliffs, N.J: Prentice Hall, 1988).
 <!--ID: 1706975891820-->
 END%%
 
@@ -67,7 +67,7 @@ END%%
 Basic
 In C, `\x` allows specifying how many hexadecimal digits?
 Back: One or more.
-Reference: Brian W. Kernighan and Dennis M. Ritchie, _The C Programming Language_, 2nd ed (Englewood Cliffs, N.J: Prentice Hall, 1988).
+Reference: Brian W. Kernighan and Dennis M. Ritchie, *The C Programming Language*, 2nd ed (Englewood Cliffs, N.J: Prentice Hall, 1988).
 <!--ID: 1706975891824-->
 END%%
 
@@ -142,7 +142,7 @@ END%%
 ## References
 
 * Arnold D. Robbins, “GAWK: Effective AWK Programming,” October 2023, [https://www.gnu.org/software/gawk/manual/gawk.pdf](https://www.gnu.org/software/gawk/manual/gawk.pdf).
-* Brian W. Kernighan and Dennis M. Ritchie, _The C Programming Language_, 2nd ed (Englewood Cliffs, N.J: Prentice Hall, 1988).
+* Brian W. Kernighan and Dennis M. Ritchie, *The C Programming Language*, 2nd ed (Englewood Cliffs, N.J: Prentice Hall, 1988).
 * Jens Gustedt, _Modern C_ (Shelter Island, NY: Manning Publications Co, 2020).
 * Mendel Cooper, “Advanced Bash-Scripting Guide,” n.d., 916.
 * Roberto Ierusalimschy, _Programming in Lua_, Fourth edition (Rio de Janeiro: Lua.org, 2016).

notes/gawk/index.md

@@ -119,12 +119,89 @@ Reference: Robbins, Arnold D. “GAWK: Effective AWK Programming,” October 202
 <!--ID: 1706822165641-->
 END%%
 
-**Targets** are specified as `$n` where `n` is a placeholder for the `n`th whitespace-separated **field**s of the input line. For example, `$1` refers to the first field of the input line. `$0` is a special target referring to the entire list of arguments, i.e. the entire line.
+`awk` reads in files in units called **records**. Each record is automatically broken up into chunks called **fields**. By default, a record corresponds to a single line. `$0` would then refer to the entire line and `$1` would refer to the first field of this line.
+
+%%ANKI
+Basic
+In `awk`, what does a "record" refer to?
+Back: The unit that input is read in.
+Reference: Robbins, Arnold D. “GAWK: Effective AWK Programming,” October 2023. [https://www.gnu.org/software/gawk/manual/gawk.pdf](https://www.gnu.org/software/gawk/manual/gawk.pdf)
+<!--ID: 1707310981378-->
+END%%
+
+%%ANKI
+Basic
+What is the default record separator?
+Back: The newline character.
+Reference: Robbins, Arnold D. “GAWK: Effective AWK Programming,” October 2023. [https://www.gnu.org/software/gawk/manual/gawk.pdf](https://www.gnu.org/software/gawk/manual/gawk.pdf)
+<!--ID: 1707310981380-->
+END%%
+
+%%ANKI
+Cloze
+The {`RS`} variable is used to change the {record separator}.
+Reference: Robbins, Arnold D. “GAWK: Effective AWK Programming,” October 2023. [https://www.gnu.org/software/gawk/manual/gawk.pdf](https://www.gnu.org/software/gawk/manual/gawk.pdf)
+<!--ID: 1707310981382-->
+END%%
+
+%%ANKI
+Cloze
+If `RS` is a string with {more than one character}, it is treated as a {regexp}.
+Reference: Robbins, Arnold D. “GAWK: Effective AWK Programming,” October 2023. [https://www.gnu.org/software/gawk/manual/gawk.pdf](https://www.gnu.org/software/gawk/manual/gawk.pdf)
+<!--ID: 1707310981384-->
+END%%
+
+%%ANKI
+Cloze
+The {`RT`} variable matches the {input characters that matched `RS`}.
+Reference: Robbins, Arnold D. “GAWK: Effective AWK Programming,” October 2023. [https://www.gnu.org/software/gawk/manual/gawk.pdf](https://www.gnu.org/software/gawk/manual/gawk.pdf)
+<!--ID: 1707310981386-->
+END%%
+
+%%ANKI
+Basic
+Barring the final record, when is `RT` always equal to `RS`?
+Back: When `RS` is a string containing a single character.
+Reference: Robbins, Arnold D. “GAWK: Effective AWK Programming,” October 2023. [https://www.gnu.org/software/gawk/manual/gawk.pdf](https://www.gnu.org/software/gawk/manual/gawk.pdf)
+<!--ID: 1707310981388-->
+END%%
+
+%%ANKI
+Basic
+What value of `RS` may `gawk` not process correctly?
+Back: A regexp with optional trailing part, e.g. `AB(XYZ)?`.
+Reference: Robbins, Arnold D. “GAWK: Effective AWK Programming,” October 2023. [https://www.gnu.org/software/gawk/manual/gawk.pdf](https://www.gnu.org/software/gawk/manual/gawk.pdf)
+<!--ID: 1707310981390-->
+END%%
+
+%%ANKI
+Basic
+What implementation detail inspires avoiding `RS = "\0"`?
+Back: Most `awk` implementations store strings internally as C-style strings?
+Reference: Robbins, Arnold D. “GAWK: Effective AWK Programming,” October 2023. [https://www.gnu.org/software/gawk/manual/gawk.pdf](https://www.gnu.org/software/gawk/manual/gawk.pdf)
+<!--ID: 1707310981392-->
+END%%
+
+%%ANKI
+Basic
+What equivalent assignment do most `awk` implementations interpret `RS = "\0"` as?
+Back: `RS = ""`
+Reference: Robbins, Arnold D. “GAWK: Effective AWK Programming,” October 2023. [https://www.gnu.org/software/gawk/manual/gawk.pdf](https://www.gnu.org/software/gawk/manual/gawk.pdf)
+<!--ID: 1707310981394-->
+END%%
+
+%%ANKI
+Basic
+In `awk`, what does a "field" refer to?
+Back: A specific part of a record.
+Reference: Robbins, Arnold D. “GAWK: Effective AWK Programming,” October 2023. [https://www.gnu.org/software/gawk/manual/gawk.pdf](https://www.gnu.org/software/gawk/manual/gawk.pdf)
+<!--ID: 1707310981395-->
+END%%
 
 %%ANKI
 Basic
 What is `$0` a placeholder for?
-Back: The entire input line.
+Back: An entire record.
 Reference: Robbins, Arnold D. “GAWK: Effective AWK Programming,” October 2023. [https://www.gnu.org/software/gawk/manual/gawk.pdf](https://www.gnu.org/software/gawk/manual/gawk.pdf)
 <!--ID: 1706823790230-->
 END%%
@@ -132,7 +209,7 @@ END%%
 %%ANKI
 Basic
 What is `$1` a placeholder for?
-Back: The first field of the input line.
+Back: The first field of a record.
 Reference: Robbins, Arnold D. “GAWK: Effective AWK Programming,” October 2023. [https://www.gnu.org/software/gawk/manual/gawk.pdf](https://www.gnu.org/software/gawk/manual/gawk.pdf)
 <!--ID: 1706823790233-->
 END%%
@@ -159,7 +236,7 @@ Describe what the following command does in in a single sentence:
 ```bash
 $ awk 'NF > 0' data
 ```
-Back: Prints every line of `data` with at least one field.
+Back: Prints every record in `data` with at least one field.
 Reference: Robbins, Arnold D. “GAWK: Effective AWK Programming,” October 2023. [https://www.gnu.org/software/gawk/manual/gawk.pdf](https://www.gnu.org/software/gawk/manual/gawk.pdf)
 <!--ID: 1706823927382-->
 END%%
@@ -170,7 +247,7 @@ Describe what the following command does in in a single sentence:
 ```bash
 $ awk 'END { print NR }' data
 ```
-Back: Prints the number of lines in `data`.
+Back: Prints the number of records in `data`.
 Reference: Robbins, Arnold D. “GAWK: Effective AWK Programming,” October 2023. [https://www.gnu.org/software/gawk/manual/gawk.pdf](https://www.gnu.org/software/gawk/manual/gawk.pdf)
 <!--ID: 1706824091124-->
 END%%
@@ -181,7 +258,7 @@ Describe what the following command does in in a single sentence:
 ```bash
 $ awk 'NR % 2 == 0' data
 ```
-Back: Prints every even-numbered line in `data`.
+Back: Prints every even-numbered record in `data`.
 Reference: Robbins, Arnold D. “GAWK: Effective AWK Programming,” October 2023. [https://www.gnu.org/software/gawk/manual/gawk.pdf](https://www.gnu.org/software/gawk/manual/gawk.pdf)
 <!--ID: 1706824091128-->
 END%%

notes/gawk/regexp.md

@@ -20,6 +20,64 @@ $ awk '$1 ~ /li/' data
 
 `awk`'s implementation of regexps are a superset of [[posix/regexp|POSIX EREs]].
 
+%%ANKI
+Basic
+What is the result of the following?
+```bash
+$ echo aaaabcd | awk '{ sub(/a+/, "<A>"); print }'
+```
+Back: `<A>bcd`
+Reference: Robbins, Arnold D. “GAWK: Effective AWK Programming,” October 2023. [https://www.gnu.org/software/gawk/manual/gawk.pdf](https://www.gnu.org/software/gawk/manual/gawk.pdf)
+<!--ID: 1707231831794-->
+END%%
+
+%%ANKI
+Cloze
+In `awk`, `/.../` is to a {regexp} constant whereas `"..."` is to a {string} constant.
+Reference: Robbins, Arnold D. “GAWK: Effective AWK Programming,” October 2023. [https://www.gnu.org/software/gawk/manual/gawk.pdf](https://www.gnu.org/software/gawk/manual/gawk.pdf)
+<!--ID: 1707232573706-->
+END%%
+
+%%ANKI
+Basic
+How are string constants processed differently from regexp constants?
+Back: The string constant is scanned twice.
+Reference: Robbins, Arnold D. “GAWK: Effective AWK Programming,” October 2023. [https://www.gnu.org/software/gawk/manual/gawk.pdf](https://www.gnu.org/software/gawk/manual/gawk.pdf)
+<!--ID: 1707232573708-->
+END%%
+
+%%ANKI
+Basic
+What term describes a regexp that isn't a regexp constant?
+Back: A dynamic regexp.
+Reference: Robbins, Arnold D. “GAWK: Effective AWK Programming,” October 2023. [https://www.gnu.org/software/gawk/manual/gawk.pdf](https://www.gnu.org/software/gawk/manual/gawk.pdf)
+<!--ID: 1707232573710-->
+END%%
+
+%%ANKI
+Basic
+How is `*` escaped in a regexp constant?
+Back: `/\*/`
+Reference: Robbins, Arnold D. “GAWK: Effective AWK Programming,” October 2023. [https://www.gnu.org/software/gawk/manual/gawk.pdf](https://www.gnu.org/software/gawk/manual/gawk.pdf)
+<!--ID: 1707232573712-->
+END%%
+
+%%ANKI
+Basic
+How is `*` escaped in a string constant (dynamic regexp)?
+Back: `"\\*"`
+Reference: Robbins, Arnold D. “GAWK: Effective AWK Programming,” October 2023. [https://www.gnu.org/software/gawk/manual/gawk.pdf](https://www.gnu.org/software/gawk/manual/gawk.pdf)
+<!--ID: 1707232573713-->
+END%%
+
+%%ANKI
+Basic
+Why is it recommended to avoid using `^`/`$` in `RS`?
+Back: These anchors match the beginning/end of a string, not of a line.
+Reference: Robbins, Arnold D. “GAWK: Effective AWK Programming,” October 2023. [https://www.gnu.org/software/gawk/manual/gawk.pdf](https://www.gnu.org/software/gawk/manual/gawk.pdf)
+<!--ID: 1707310981375-->
+END%%
+
 ## References
 
 * Robbins, Arnold D. “GAWK: Effective AWK Programming,” October 2023. [https://www.gnu.org/software/gawk/manual/gawk.pdf](https://www.gnu.org/software/gawk/manual/gawk.pdf)

notes/logic/equiv-trans.md

@@ -0,0 +1,650 @@
+---
+title: Equivalence Transformation
+TARGET DECK: Obsidian::STEM
+FILE TAGS: logic::equiv-trans
+tags:
+  - logic
+  - equiv-trans
+---
+
+## Overview
+
+**Equivalence-transformation** refers to a class of calculi for manipulating propositions derived from negation ($\neg$), conjunction ($\land$), disjunction ($\lor$), implication ($\Rightarrow$), and equality ($=$). Gries covers two in "The Science of Programming": a system of evaluation and a formal system. The system of evaluation mirrors how a computer processes instructions, at least in an abstract sense. The formal system serves as a theoretical framework for reasoning about propositions and their transformations without resorting to "lower-level" operations like substitution.
+
+%%ANKI
+Basic
+Who is the author of "The Science of Programming"?
+Back: David Gries
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1706994861286-->
+END%%
+
+%%ANKI
+Basic
+What are the constant propositions?
+Back: $T$ and $F$
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1706994861289-->
+END%%
+
+%%ANKI
+Basic
+What are the basic propositional logical operators?
+Back: $\neg$, $\land$, $\lor$, $\Rightarrow$, and $\Leftrightarrow$/$=$
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1706994861291-->
+END%%
+
+%%ANKI
+Cloze
+Gries replaces logical operator {$\Leftrightarrow$} in favor of {$=$}.
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1706994861295-->
+END%%
+
+%%ANKI
+Basic
+How does Lean define propositional equality?
+Back: Expressions `a` and `b` are propositionally equal iff `a = b` is true.
+Reference: Avigad, Jeremy. ‘Theorem Proving in Lean’, n.d.
+Tags: lean
+<!--ID: 1706994861298-->
+END%%
+
+%%ANKI
+Basic
+How does Lean define `propext`?
+Back:
+```lean
+axiom propext {a b : Prop} : (a ↔ b) → (a = b)
+```
+Reference: Avigad, Jeremy. ‘Theorem Proving in Lean’, n.d.
+Tags: lean
+<!--ID: 1706994861300-->
+END%%
+
+%%ANKI
+Basic
+What Lean theorem justifies Gries' choice of $=$ over $\Leftrightarrow$?
+Back: `propext`
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+Tags: lean
+<!--ID: 1706994861302-->
+END%%
+
+%%ANKI
+Basic
+What name is given to $\land$ operands?
+Back: Conjuncts
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1706994861304-->
+END%%
+
+%%ANKI
+Basic
+What name is given to $\lor$ operands?
+Back: Disjuncts
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1706994861306-->
+END%%
+
+%%ANKI
+Basic
+What name is given to operand $a$ in $a \Rightarrow b$?
+Back: The antecedent
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1706994861308-->
+END%%
+
+%%ANKI
+Basic
+What name is given to operand $b$ in $a \Rightarrow b$?
+Back: The consequent
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1706994861310-->
+END%%
+
+%%ANKI
+Basic
+Is $(b \land c)$ well-defined in $\{(b, T), (c, F)\}$?
+Back: Yes
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1706994861318-->
+END%%
+
+%%ANKI
+Basic
+Is $(b \lor d)$ well-defined in $\{(b, T), (c, F)\}$?
+Back: No
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1706994861320-->
+END%%
+
+%%ANKI
+Basic
+What C operator corresponds to $\neg$?
+Back: `!`
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+Tags: c
+<!--ID: 1706994861325-->
+END%%
+
+%%ANKI
+Basic
+What C operator corresponds to $\land$?
+Back: There isn't one.
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+Tags: c
+<!--ID: 1706994861327-->
+END%%
+
+%%ANKI
+Basic
+What C operator corresponds to $\lor$?
+Back: There isn't one.
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+Tags: c
+<!--ID: 1706994861329-->
+END%%
+
+%%ANKI
+Basic
+What C operator corresponds to $\Rightarrow$?
+Back: There isn't one.
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+Tags: c
+<!--ID: 1706994861331-->
+END%%
+
+%%ANKI
+Basic
+What C operator corresponds to $\Leftrightarrow$?
+Back: `==`
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+Tags: c
+<!--ID: 1706994861333-->
+END%%
+
+%%ANKI
+Basic
+What proposition represents states $\{(b, T)\}$ and $\{(c, F)\}$?
+Back: $b \lor \neg c$
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1706994861337-->
+END%%
+
+%%ANKI
+Basic
+What set of states does $a \land b$ represent?
+Back: The set containing just state $\{(a, T), (b, T)\}$.
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1706994861339-->
+END%%
+
+%%ANKI
+Basic
+What is sloppy about phrase "the states in $b \lor \neg c$"?
+Back: $b \lor \neg c$ is not a set but a representation of a set (of states).
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1706994861341-->
+END%%
+
+%%ANKI
+Basic
+What is the weakest proposition?
+Back: $T$
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1706994861348-->
+END%%
+
+%%ANKI
+Basic
+What set of states does $T$ represent?
+Back: The set of all states.
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1706994861350-->
+END%%
+
+%%ANKI
+Basic
+What is the strongest proposition?
+Back: $F$
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1706994861352-->
+END%%
+
+%%ANKI
+Basic
+What set of states does $F$ represent?
+Back: The set of no states.
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1706994861354-->
+END%%
+
+%%ANKI
+Basic
+What does a proposition *represent*?
+Back: The set of states in which it is true.
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1706994861335-->
+END%%
+
+%%ANKI
+Basic
+When is $p$ stronger than $q$?
+Back: When $p \Rightarrow q$.
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1706994861343-->
+END%%
+
+%%ANKI
+Basic
+When is $p$ weaker than $q$?
+Back: When $q \Rightarrow p$.
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1706994861346-->
+END%%
+
+%%ANKI
+Basic
+A proposition is well-defined with respect to what?
+Back: A state to evaluate against.
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1706994861316-->
+END%%
+
+%%ANKI
+Basic
+Why is $b \land c$ stronger than $b \lor c$?
+Back: The former represents a subset of the states the latter represents.
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1706994861356-->
+END%%
+
+%%ANKI
+Basic
+What is a state?
+Back: A function mapping identifiers to values.
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1706994861314-->
+END%%
+
+%%ANKI
+Basic
+What are the two calculi Gries describes equivalence-transformation with?
+Back: A formal system and a system of evaluation.
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1707251673342-->
+END%%
+
+## Equivalence Schemas
+
+A proposition is said to be a **tautology** if it evaluates to $T$ in every state it is well-defined in. We say propositions $E1$ and $E2$ are **equivalent** if $E1 = E2$ is a tautology. In this case, we say $E1 = E2$ is an **equivalence**.
+
+%%ANKI
+Basic
+What does it mean for a proposition to be a tautology?
+Back: That the proposition is true in every state it is well-defined in.
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1706994861323-->
+END%%
+
+%%ANKI
+Basic
+The term "equivalent" refers to a comparison between what two objects?
+Back: Propositions.
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1707251673345-->
+END%%
+
+%%ANKI
+Basic
+What does it mean for two propositions to be equivalent?
+Back: Given propositions $E1$ and $E2$, it means $E1 = E2$ is a tautology.
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1707251673347-->
+END%%
+
+%%ANKI
+Basic
+What is an equivalence?
+Back: Given propositions $E1$ and $E2$, tautology $E1 = E2$.
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1707251673348-->
+END%%
+
+* Commutative Laws
+	* $(E1 \land E2) = (E2 \land E1)$
+	* $(E1 \lor E2) = (E2 \lor E1)$
+	* $(E1 = E2) = (E2 = E1)$
+
+%%ANKI
+Basic
+Which of the basic logical operators do the commutative laws apply to?
+Back: $\land$, $\lor$, and $=$
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1707251673350-->
+END%%
+
+%%ANKI
+Basic
+What do the commutative laws allow us to do?
+Back: Reorder operands.
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1707251673351-->
+END%%
+
+%%ANKI
+Basic
+What is the commutative law of e.g. $\land$?
+Back: $E1 \land E2 = E2 \land E1$
+<!--ID: 1707251673353-->
+END%%
+
+* Associative Laws
+	* $E1 \land (E2 \land E3) = (E1 \land E2) \land E3$
+	* $E1 \lor (E2 \lor E3) = (E1 \lor E2) \lor E3$
+
+%%ANKI
+Basic
+Which of the basic logical operators do the associative laws apply to?
+Back: $\land$ and $\lor$
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1707251673354-->
+END%%
+
+%%ANKI
+Basic
+What do the associative laws allow us to do?
+Back: Remove parentheses.
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1707251673355-->
+END%%
+
+%%ANKI
+Basic
+What is the associative law of e.g. $\land$?
+Back: $E1 \land (E2 \land E3) = (E1 \land E2) \land E3$
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1707251673357-->
+END%%
+
+* Distributive Laws
+	* $E1 \lor (E2 \land E3) = (E1 \lor E2) \land (E1 \lor E3)$
+	* $E1 \land (E2 \lor E3) = (E1 \land E2) \lor (E1 \land E3)$
+
+%%ANKI
+Basic
+Which of the basic logical operators do the distributive laws apply to?
+Back: $\land$ and $\lor$
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1707251673358-->
+END%%
+
+%%ANKI
+Basic
+What do the distributive laws allow us to do?
+Back: "Factor" propositions.
+Reference: Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1707251673360-->
+END%%
+
+%%ANKI
+Basic
+What is the distributive law of e.g. $\land$ over $\lor$?
+Back: $E1 \land (E2 \lor E3) = (E1 \land E2) \lor (E1 \land E3)$
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1707251673361-->
+END%%
+
+* De Morgan's Laws
+	* $\neg (E1 \land E2) = \neg E1 \lor \neg E2$
+	* $\neg (E1 \lor E2) = \neg E1 \land \neg E2$
+
+%%ANKI
+Basic
+Which of the basic logical operators do De Morgan's Laws apply to?
+Back: $\land$ and $\lor$
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1707251673363-->
+END%%
+
+%%ANKI
+Basic
+What is De Morgan's Law of e.g. $\land$?
+Back: $\neg (E1 \land E2) = \neg E1 \lor \neg E2$
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1707251673364-->
+END%%
+
+* Law of Negation
+	* $\neg (\neg E1) = E1$
+
+%%ANKI
+Basic
+What does the Law of Negation say?
+Back: $\neg (\neg E1) = E1$
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1707251673365-->
+END%%
+
+* Law of the Excluded Middle
+	* $E1 \lor \neg E1 = T$
+
+%%ANKI
+Basic
+Which of the basic logical operators does the Law of the Excluded Middle apply to?
+Back: $\lor$
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1707251673367-->
+END%%
+
+%%ANKI
+Basic
+What does the Law of the Excluded Middle say?
+Back: $E1 \lor \neg E1 = T$
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1707251673368-->
+END%%
+
+%%ANKI
+Basic
+Which equivalence schema is "refuted" by sentence, "This sentence is false."
+Back: Law of the Excluded Middle
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1707251779153-->
+END%%
+
+* Law of Contradiction
+	* $E1 \land \neg E1 = F$
+
+%%ANKI
+Basic
+Which of the basic logical operators does the Law of Contradiction apply to?
+Back: $\land$
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1707251673370-->
+END%%
+
+%%ANKI
+Basic
+What does the Law of Contradiction say?
+Back: $E1 \land \neg E1 = F$
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1707251673371-->
+END%%
+
+%%ANKI
+Cloze
+The Law of {1:the Excluded Middle} is to {2:$\lor$} whereas the Law of {2:Contradiction} is to {1:$\land$}.
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1707251673373-->
+END%%
+
+Gries lists other "Laws" but they don't seem as important to note here.
+
+%%ANKI
+Basic
+How is $\Rightarrow$ written in terms of other logical operators?
+Back: $p \Rightarrow q$ is equivalent to $\neg p \lor q$.
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1706994861358-->
+END%%
+
+%%ANKI
+Basic
+How is $\Leftrightarrow$/$=$ written in terms of other logical operators?
+Back: $p \Leftrightarrow q$ is equivalent to $(p \Rightarrow q) \land (q \Rightarrow p)$.
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1706994861360-->
+END%%
+
+## Equivalence Rules
+
+* Rule of Substitution
+	* Let $P(r)$ be a predicate and $E1 = E2$ be an equivalence. Then $P(E1) = P(E2)$ is an equivalence.
+* Rule of Transitivity
+	* Let $E1 = E2$ and $E2 = E3$ be equivalences. Then $E1 = E3$ is an equivalence.
+
+%%ANKI
+Basic
+What two inference rules make up the equivalence-transformation formal system?
+Back: Substitution and transitivity.
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1707253246450-->
+END%%
+
+%%ANKI
+Basic
+What does the rule of substitution say in the system of evaluation?
+Back: Let $P(r)$ be a predicate and $E1 = E2$ be an equivalence. Then $P(E1) = P(E2)$ is an equivalence.
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1707253246452-->
+END%%
+
+%%ANKI
+Basic
+How is the rule of substitution written as an inference rule (in standard form)?
+Back:
+$$
+\begin{matrix}
+E1 = E2 \\
+\hline P(E1) = P(E2)
+\end{matrix}
+$$
+<!--ID: 1707253246454-->
+END%%
+
+%%ANKI
+Basic
+What does the rule of transitivity state in the system of evaluation?
+Back: Let $E1 = E2$ and $E2 = E3$. Then $E1 = E3$.
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1707253246455-->
+END%%
+
+%%ANKI
+Basic
+How is the rule of transitivity written as an inference rule (in standard form)?
+Back:
+$$
+\begin{matrix}
+E1 = E2, E2 = E3 \\
+\hline E1 = E3
+\end{matrix}
+$$
+<!--ID: 1707253246457-->
+END%%
+
+%%ANKI
+Cloze
+The system of evaluation has {equivalences} whereas the formal system has {theorems}.
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1707253246458-->
+END%%
+
+## Normal Forms
+
+Every proposition can be written in **disjunctive normal form** (DNF) and **conjunctive normal form** (CNF). This is evident with the use of truth tables. To write a proposition in DNF, write its corresponding truth table and $\lor$ each row that evaluates to $T$. To write the same proposition in CNF, apply $\lor$ to each row that evaluates to $F$ and negate it.
+
+$$\neg (a \Rightarrow b) \Leftrightarrow c$$
+
+It's truth table looks like
+
+$$\begin{array}{c|c|c|c|c|c}
+\neg & (a & \Rightarrow & b) & \Leftrightarrow & c \\
+\hline
+F & T & T & T & F & T \\
+F & T & T & T & T & F \\
+T & T & F & F & T & T \\
+T & T & F & F & F & F \\
+F & F & T & T & F & T \\
+F & F & T & T & T & F \\
+F & F & T & F & F & T \\
+F & F & T & F & T & F
+\end{array}$$
+
+and it's DNF looks like
+
+$$
+(a \land b \land \neg c) \lor
+(a \land \neg b \land c) \lor
+(\neg a \land b \land \neg c) \lor
+(\neg a \land \neg b \land \neg c)
+$$
+
+It's CNF results from applying De Morgan's Law to the truth table's "complement":
+
+$$
+\neg(
+  (a \land b \land c) \lor
+  (a \land \neg b \land \neg c) \lor
+  (\neg a \land b \land c) \lor
+  (\neg a \land \neg b \land c)
+)
+$$
+
+%%ANKI
+Basic
+What construct is used to prove every proposition can be written in DNF or CNF?
+Back: Truth tables
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1707311868994-->
+END%%
+
+%%ANKI
+Basic
+Where are $\land$ and $\lor$ found within a proposition in DNF?
+Back: $\lor$ separates disjuncts containing $\land$.
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1707311868998-->
+END%%
+
+%%ANKI
+Basic
+What is DNF an acronym for?
+Back: **D**isjunctive **N**ormal **F**orm.
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1707311869000-->
+END%%
+
+%%ANKI
+Basic
+What is CNF an acronym for?
+Back: **C**onjunctive **N**ormal **F**orm.
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1707311869002-->
+END%%
+
+%%ANKI
+Basic
+Where are $\land$ and $\lor$ found within a proposition in CNF?
+Back: $\land$ separates conjuncts containing $\lor$.
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1707311869003-->
+END%%
+
+## References
+
+* Avigad, Jeremy. ‘Theorem Proving in Lean’, n.d.
+* Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.

notes/logic/propositional.md

@@ -1,307 +0,0 @@
----
-title: Propositional Logic
-TARGET DECK: Obsidian::STEM
-FILE TAGS: logic::0-order
-tags:
-  - logic
-  - 0-order
----
-
-## Overview
-
-Propositional logic (or `0`-order logic) refers to the manipulation of **propositions** using the following five logical operators: $\neg$, $\land$, $\lor$, $\Rightarrow$, $\Leftrightarrow$.
-
-%%ANKI
-Basic
-Who is the author of "The Science of Programming"?
-Back: David Gries
-Reference: Gries, David. _The Science of Programming_. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
-<!--ID: 1706994861286-->
-END%%
-
-%%ANKI
-Basic
-What are the constant propositions?
-Back: $T$ and $F$
-Reference: Gries, David. _The Science of Programming_. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
-<!--ID: 1706994861289-->
-END%%
-
-%%ANKI
-Basic
-What are the five propositional logical operators?
-Back: $\neg$, $\land$, $\lor$, $\Rightarrow$, and $\Leftrightarrow$
-Reference: Gries, David. _The Science of Programming_. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
-<!--ID: 1706994861291-->
-END%%
-
-%%ANKI
-Cloze
-Gries replaces logical operator {$\Leftrightarrow$} in favor of {$=$}.
-Reference: Gries, David. _The Science of Programming_. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
-<!--ID: 1706994861295-->
-END%%
-
-%%ANKI
-Basic
-How does Lean define propositional equality?
-Back: Expressions `a` and `b` are propositionally equal iff `a = b` is true.
-Reference: Avigad, Jeremy. ‘Theorem Proving in Lean’, n.d.
-Tags: lean
-<!--ID: 1706994861298-->
-END%%
-
-%%ANKI
-Basic
-How does Lean define `propext`?
-Back:
-```lean
-axiom propext {a b : Prop} : (a ↔ b) → (a = b)
-```
-Reference: Avigad, Jeremy. ‘Theorem Proving in Lean’, n.d.
-Tags: lean
-<!--ID: 1706994861300-->
-END%%
-
-%%ANKI
-Basic
-What Lean theorem justifies Gries choice of $=$ over $\Leftrightarrow$?
-Back: `propext`
-Reference: Gries, David. _The Science of Programming_. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
-Tags: lean
-<!--ID: 1706994861302-->
-END%%
-
-%%ANKI
-Basic
-What name is given to $\land$ operands?
-Back: Conjuncts
-Reference: Gries, David. _The Science of Programming_. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
-<!--ID: 1706994861304-->
-END%%
-
-%%ANKI
-Basic
-What name is given to $\lor$ operands?
-Back: Disjuncts
-Reference: Gries, David. _The Science of Programming_. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
-<!--ID: 1706994861306-->
-END%%
-
-%%ANKI
-Basic
-What name is given to operand $a$ in $a \Rightarrow b$?
-Back: The antecedent
-Reference: Gries, David. _The Science of Programming_. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
-<!--ID: 1706994861308-->
-END%%
-
-%%ANKI
-Basic
-What name is given to operand $b$ in $a \Rightarrow b$?
-Back: The consequent
-Reference: Gries, David. _The Science of Programming_. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
-<!--ID: 1706994861310-->
-END%%
-
-%%ANKI
-Basic
-What does the evaluation model of propositional logic refer to?
-Back: An interpretation of propositional logic that associates values to identifiers.
-Reference: Gries, David. _The Science of Programming_. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
-<!--ID: 1706994861312-->
-END%%
-
-%%ANKI
-Basic
-Evaluation model. What is a state?
-Back: A function mapping identifiers to values.
-Reference: Gries, David. _The Science of Programming_. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
-<!--ID: 1706994861314-->
-END%%
-
-%%ANKI
-Basic
-What is necessary to determine if a proposition is well-defined?
-Back: A state to evaluate against.
-Reference: Gries, David. _The Science of Programming_. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
-<!--ID: 1706994861316-->
-END%%
-
-%%ANKI
-Basic
-Is $(b \land c)$ well-defined in $\{(b, T), (c, F)\}$?
-Back: Yes
-Reference: Gries, David. _The Science of Programming_. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
-<!--ID: 1706994861318-->
-END%%
-
-%%ANKI
-Basic
-Is $(b \lor d)$ well-defined in $\{(b, T), (c, F)\}$?
-Back: No
-Reference: Gries, David. _The Science of Programming_. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
-<!--ID: 1706994861320-->
-END%%
-
-%%ANKI
-Basic
-Evaluation model. What does it mean for a proposition to be a tautology?
-Back: A proposition is true in every state it is well-defined in.
-Reference: Gries, David. _The Science of Programming_. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
-<!--ID: 1706994861323-->
-END%%
-
-%%ANKI
-Basic
-What C operator corresponds to $\neg$?
-Back: `!`
-Reference: Gries, David. _The Science of Programming_. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
-Tags: c
-<!--ID: 1706994861325-->
-END%%
-
-%%ANKI
-Basic
-What C operator corresponds to $\land$?
-Back: There isn't one.
-Reference: Gries, David. _The Science of Programming_. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
-Tags: c
-<!--ID: 1706994861327-->
-END%%
-
-%%ANKI
-Basic
-What C operator corresponds to $\lor$?
-Back: There isn't one.
-Reference: Gries, David. _The Science of Programming_. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
-Tags: c
-<!--ID: 1706994861329-->
-END%%
-
-%%ANKI
-Basic
-What C operator corresponds to $\Rightarrow$?
-Back: There isn't one.
-Reference: Gries, David. _The Science of Programming_. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
-Tags: c
-<!--ID: 1706994861331-->
-END%%
-
-%%ANKI
-Basic
-What C operator corresponds to $\Leftrightarrow$?
-Back: `=`
-Reference: Gries, David. _The Science of Programming_. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
-Tags: c
-<!--ID: 1706994861333-->
-END%%
-
-%%ANKI
-Basic
-Evaluation model. What does a proposition *represent*?
-Back: The set of states in which it is true.
-Reference: Gries, David. _The Science of Programming_. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
-<!--ID: 1706994861335-->
-END%%
-
-%%ANKI
-Basic
-Evaluation model. What proposition represents states $\{(b, T)\}$ and $\{(c, F)\}$?
-Back: $b \lor \neg c$
-Reference: Gries, David. _The Science of Programming_. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
-<!--ID: 1706994861337-->
-END%%
-
-%%ANKI
-Basic
-Evaluation model. What set of states does $a \land b$ represent?
-Back: The set containing just state $\{(a, T), (b, T)\}$.
-Reference: Gries, David. _The Science of Programming_. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
-<!--ID: 1706994861339-->
-END%%
-
-%%ANKI
-Basic
-Evaluation model. What is sloppy about phrase "the states in $b \lor \neg c$"?
-Back: $b \lor \neg c$ is not a set.
-Reference: Gries, David. _The Science of Programming_. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
-<!--ID: 1706994861341-->
-END%%
-
-%%ANKI
-Basic
-When is $p$ stronger than $q$?
-Back: When $p \Rightarrow q$.
-Reference: Gries, David. _The Science of Programming_. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
-<!--ID: 1706994861343-->
-END%%
-
-%%ANKI
-Basic
-When is $p$ weaker than $q$?
-Back: When $q \Rightarrow p$.
-Reference: Gries, David. _The Science of Programming_. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
-<!--ID: 1706994861346-->
-END%%
-
-%%ANKI
-Basic
-What is the weakest proposition?
-Back: $T$
-Reference: Gries, David. _The Science of Programming_. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
-<!--ID: 1706994861348-->
-END%%
-
-%%ANKI
-Basic
-What set of states does $T$ represent?
-Back: The set of all states.
-Reference: Gries, David. _The Science of Programming_. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
-<!--ID: 1706994861350-->
-END%%
-
-%%ANKI
-Basic
-What is the strongest proposition?
-Back: $F$
-Reference: Gries, David. _The Science of Programming_. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
-<!--ID: 1706994861352-->
-END%%
-
-%%ANKI
-Basic
-What set of states does $F$ represent?
-Back: The set of no states.
-Reference: Gries, David. _The Science of Programming_. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
-<!--ID: 1706994861354-->
-END%%
-
-%%ANKI
-Basic
-Evaluation model. Why is $b \land c$ stronger than $b \lor c$?
-Back: The former represents a subset of the states the latter represents.
-Reference: Gries, David. _The Science of Programming_. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
-<!--ID: 1706994861356-->
-END%%
-
-%%ANKI
-Basic
-How is $\Rightarrow$ written in terms of other logical operators?
-Back: $p \Rightarrow q$ is equivalent to $\neg p \lor q$.
-Reference: Gries, David. _The Science of Programming_. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
-<!--ID: 1706994861358-->
-END%%
-
-%%ANKI
-Basic
-How is $\Leftrightarrow$ written in terms of other logical operators?
-Back: $p \Leftrightarrow q$ is equivalent to $(p \Rightarrow q) \land (q \Rightarrow p)$.
-Reference: Gries, David. _The Science of Programming_. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
-<!--ID: 1706994861360-->
-END%%
-
-## References
-
-* Avigad, Jeremy. ‘Theorem Proving in Lean’, n.d.
-* Gries, David. _The Science of Programming_. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.

notes/posix/regexp.md

@@ -8,7 +8,38 @@ tags:
 
 ## Overview
 
-The following ERE (**E**xtended **R**egular **E**xpression) operators were defined to achieve consistency between programs like `grep`, `sed`, and `awk`.
+The following ERE (**E**xtended **R**egular **E**xpression) operators were defined to achieve consistency between programs like `grep`, `sed`, and `awk`. In POSIX, regexps are greedy.
+
+%%ANKI
+Cloze
+Regular expressions are either {greedy} or {lazy}.
+Reference: “POSIX Basic Regular Expressions,” accessed February 4, 2024, [https://en.wikibooks.org/wiki/Regular_Expressions/POSIX_Basic_Regular_Expressions](https://en.wikibooks.org/wiki/Regular_Expressions/POSIX_Basic_Regular_Expressions).
+<!--ID: 1707231745948-->
+END%%
+
+%%ANKI
+Basic
+Are POSIX regexps greedy or lazy?
+Back: Greedy.
+Reference: Robbins, Arnold D. “GAWK: Effective AWK Programming,” October 2023. [https://www.gnu.org/software/gawk/manual/gawk.pdf](https://www.gnu.org/software/gawk/manual/gawk.pdf)
+<!--ID: 1707231745951-->
+END%%
+
+%%ANKI
+Basic
+What does it mean for a regexp to be greedy?
+Back: The regexp matches as many characters as it can.
+Reference: “POSIX Basic Regular Expressions,” accessed February 4, 2024, [https://en.wikibooks.org/wiki/Regular_Expressions/POSIX_Basic_Regular_Expressions](https://en.wikibooks.org/wiki/Regular_Expressions/POSIX_Basic_Regular_Expressions).
+<!--ID: 1707231745952-->
+END%%
+
+%%ANKI
+Basic
+What does it mean for a regexp to be lazy?
+Back: The regexp matches as few characters as it can.
+Reference: “POSIX Basic Regular Expressions,” accessed February 4, 2024, [https://en.wikibooks.org/wiki/Regular_Expressions/POSIX_Basic_Regular_Expressions](https://en.wikibooks.org/wiki/Regular_Expressions/POSIX_Basic_Regular_Expressions).
+<!--ID: 1707231745954-->
+END%%
 
 %%ANKI
 Basic
@@ -94,7 +125,7 @@ END%%
 
 %%ANKI
 Cloze
-The {`$`} operator matches {the ending position of a string}.
+The {`$$`} operator matches {the ending position of a string}.
 Reference: “POSIX Basic Regular Expressions,” accessed February 4, 2024, [https://en.wikibooks.org/wiki/Regular_Expressions/POSIX_Basic_Regular_Expressions](https://en.wikibooks.org/wiki/Regular_Expressions/POSIX_Basic_Regular_Expressions).
 <!--ID: 1707050923635-->
 END%%