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Shifts and law of monotonicity.

c-declarations
Joshua Potter 2024-05-20 13:52:48 -06:00
parent 16ffe8d4ef
commit 06e0550b38
9 changed files with 202 additions and 16 deletions
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notes/.obsidian/plugins/obsidian-to-anki-plugin/data.json
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notes/_journal/2024-05-20.md Normal file
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---
title: "2024-05-20"
---
- [x] Anki Flashcards
- [x] KoL
- [ ] Sheet Music (10 min.)
- [ ] Go (1 Life & Death Problem)
- [ ] Korean (Read 1 Story)
* Flashcards for x86-64 [[instructions#Shift Operations|shift operations]].
* Flashcards on the [[pred-trans#Law of Monotonicity|Law of Monotonicity]].

1
notes/_journal/2024-05-19.md → notes/_journal/2024-05/2024-05-19.md
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@ -9,3 +9,4 @@ title: "2024-05-19"
- [ ] Korean (Read 1 Story)
* Flashcards on x86-64 [[instructions#Unary Operations|unary operations]] and [[instructions#Binary Operations|binary operations]].
* Struggled with getting Flutter up and running on NixOS.

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notes/encoding/integer.md
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@ -1440,7 +1440,7 @@ END%%
%%ANKI
Basic
What kinds of right shift operations are there?
Back: Logical and arithmetic
Back: Logical and arithmetic.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1707854589784-->
END%%

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@ -53,7 +53,7 @@ END%%
%%ANKI
Basic
Write pseudocode to test membership of $x$ in direct-address table `T[0:m-1]`.
Back
Back:
```c
bool membership(T, x) {
return T[x.key] != NIL;
@ -66,7 +66,7 @@ END%%
%%ANKI
Basic
Write pseudocode to insert $x$ into direct-address table `T[0:m-1]`.
Back
Back:
```c
void insert(T, x) {
T[x.key] = x;
@ -79,7 +79,7 @@ END%%
%%ANKI
Basic
Write pseudocode to delete $x$ from direct-address table `T[0:m-1]`.
Back
Back:
```c
void delete(T, x) {
T[x.key] = NIL;

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@ -297,6 +297,14 @@ Reference: Reference: Gries, David. *The Science of Programming*. Texts and Mon
<!--ID: 1715806256921-->
END%%
%%ANKI
Basic
In Gries's exposition, is the Law of the Excluded Miracle taken as an axiom or a theorem?
Back: An axiom.
Reference: Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
<!--ID: 1716227332852-->
END%%
### Distributivity of Conjunction
Given command $S$ and predicates $Q$ and $R$, $$wp(S, Q \land R) = wp(S, Q) \land wp(S, R)$$
@ -326,7 +334,7 @@ END%%
%%ANKI
Basic
Does $wp(S, Q) \land wp(S, R) \Rightarrow wp(S, Q \land R)$ hold when $S$ is nondeterministic?
Is $wp(S, Q) \land wp(S, R) \Rightarrow wp(S, Q \land R)$ true if $S$ is nondeterministic?
Back: Yes.
Reference: Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
<!--ID: 1715969047065-->
@ -334,7 +342,7 @@ END%%
%%ANKI
Basic
Does $wp(S, Q \land R) \Rightarrow wp(S, Q) \land wp(S, R)$ hold when $S$ is nondeterministic?
Is $wp(S, Q \land R) \Rightarrow wp(S, Q) \land wp(S, R)$ true if $S$ is nondeterministic?
Back: Yes.
Reference: Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
<!--ID: 1715969047067-->
@ -348,6 +356,39 @@ Reference: Reference: Gries, David. *The Science of Programming*. Texts and Mon
<!--ID: 1715969047068-->
END%%
### Law of Monotonicity
Given command $S$ and predicates $Q$ and $R$, if $Q \Rightarrow R$, then $wp(S, Q) \Rightarrow wp(S, R)$.
%%ANKI
What does the Law of Monotonicity state?
Back: Given command $S$ and predicates $Q$ and $R$, if $Q \Rightarrow R$, then $wp(S, Q) \Rightarrow wp(S, R)$.
Reference: Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
END%%
%%ANKI
Cloze
Given command $S$, the Law of Monotonicity states that if {1:$Q$} $\Rightarrow$ {2:$R$}, then {2:$wp(S, Q)$} $\Rightarrow$ {1:$wp(S, R)$}.
Reference: Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
<!--ID: 1716227332862-->
END%%
%%ANKI
Basic
In Gries's exposition, is the Law of Monotonicity taken as an axiom or a theorem?
Back: A theorem.
Reference: Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
<!--ID: 1716227332866-->
END%%
%%ANKI
Basic
Is the Law of Monotonicity true if the relevant command is nondeterministic?
Back: Yes.
Reference: Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
<!--ID: 1716227332870-->
END%%
## Bibliography
* Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.

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@ -30,7 +30,7 @@ END%%
%%ANKI
Basic
What does the Zermelo-Fraenkel alternative say about classes?
Back: It gives it no ontological status at all.
Back: It gives them no ontological status at all.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715970576763-->
END%%

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@ -418,7 +418,7 @@ For each formula $\_\_\_$ not containing $B$, the following is an axiom: $$\fora
%%ANKI
Basic
What do the subset axioms state?
Back: For each formula $\phi$ not containing $B$, the following is an axiom: $$\forall t_1, \cdots, \forall t_k, \forall c, \exists B, \forall x, (x \in B \Leftrightarrow x \in c \land \_\_\_)$$
Back: For each formula $\_\_\_$ not containing $B$, the following is an axiom: $$\forall t_1, \cdots, \forall t_k, \forall c, \exists B, \forall x, (x \in B \Leftrightarrow x \in c \land \_\_\_)$$
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1716074312858-->
END%%

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@ -1069,6 +1069,136 @@ Tags: c17
<!--ID: 1716128138046-->
END%%
### Shift Operations
| Instruction | Operands | Effect | Description |
| ----------- | -------- | ------------ | ---------------------- |
| `sal[bwlq]` | k, D | D <- D << k | Left shift |
| `shl[bwlq]` | k, D | D <- D << k | Left shift |
| `sar[bwlq]` | k, D | D <- D >> k | Arithmetic right shift |
| `shr[bwlq]` | k, D | D <- D >>> k | Logical right shift |
%%ANKI
Basic
What do instructions in the `SAL` instruction class do?
Back: Performs a left shift.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1716226827710-->
END%%
%%ANKI
Basic
What do instructions in the `SHL` instruction class do?
Back: Performs a left shift.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1716226827717-->
END%%
%%ANKI
Basic
Which instruction classes are related to left shifts?
Back: `SAL` and `SHL`.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1716226827720-->
END%%
%%ANKI
Basic
Which instruction classes are related to right shifts?
Back: `SAR` and `SHR`.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1716226827723-->
END%%
%%ANKI
Basic
What do instructions in the `SAR` instruction class do?
Back: Performs an arithmetic right shift.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1716226827725-->
END%%
%%ANKI
Basic
What do instructions in the `SHR` instruction class do?
Back: Performs a logical right shift.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1716226827729-->
END%%
%%ANKI
Basic
What distinguishes the `SAR` and `SHR` instruction classes?
Back: The former is arithmetic whereas the latter is logical.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1716226827732-->
END%%
%%ANKI
Basic
What distinguishes the `SAL` and `SHL` instruction classes?
Back: N/A.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1716226827736-->
END%%
%%ANKI
Basic
Which register are shift operations limited to?
Back: `%cl`
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1716226827740-->
END%%
%%ANKI
Basic
How many lower-order bits of `%cl` does e.g. `salb` look at?
Back: $3$
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1716226827744-->
END%%
%%ANKI
Basic
What can the source of a shift operation be?
Back: An immediate or the `%cl` register.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1716226827748-->
END%%
%%ANKI
Basic
What can the destination of a shift operation be?
Back: A register or memory location.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1716226827752-->
END%%
%%ANKI
Basic
How many lower-order bits of `%cl` does e.g. `salw` look at?
Back: $4$
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1716226827756-->
END%%
%%ANKI
Basic
How many lower-order bits of `%cl` does e.g. `sall` look at?
Back: $5$
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1716226827760-->
END%%
%%ANKI
Basic
How many lower-order bits of `%cl` does e.g. `salq` look at?
Back: $6$
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1716226827764-->
END%%
## Bibliography
* Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.