2024-04-29 13:29:03 +00:00
|
|
|
|
---
|
|
|
|
|
|
title: Assertions
|
|
|
|
|
|
TARGET DECK: Obsidian::STEM
|
|
|
|
|
|
FILE TAGS: programming::assertions
|
|
|
|
|
|
tags:
|
|
|
|
|
|
- assertions
|
|
|
|
|
|
- programming
|
|
|
|
|
|
---
|
|
|
|
|
|
|
|
|
|
|
|
## Overview
|
|
|
|
|
|
|
2024-04-29 20:47:33 +00:00
|
|
|
|
Define $\{Q\}\; S\; \{R\}$ as the predicate:
|
|
|
|
|
|
|
|
|
|
|
|
> If execution of $S$ is begun in a state satisfying $Q$, then it is guaranteed to terminate in a finite amount of time in a state satisfying $R$.
|
|
|
|
|
|
|
|
|
|
|
|
%%ANKI
|
|
|
|
|
|
Basic
|
|
|
|
|
|
*What* is $Q$ in predicate $\{Q\}\; S\; \{R\}$?
|
|
|
|
|
|
Back: A predicate.
|
|
|
|
|
|
Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
|
|
|
|
|
|
<!--ID: 1714420640219-->
|
|
|
|
|
|
END%%
|
|
|
|
|
|
|
|
|
|
|
|
%%ANKI
|
|
|
|
|
|
Basic
|
|
|
|
|
|
What name is given to $Q$ in $\{Q\}\; S\; \{R\}$?
|
|
|
|
|
|
Back: The precondition of $S$.
|
|
|
|
|
|
Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
|
|
|
|
|
|
<!--ID: 1714420640222-->
|
|
|
|
|
|
END%%
|
|
|
|
|
|
|
|
|
|
|
|
%%ANKI
|
|
|
|
|
|
Basic
|
|
|
|
|
|
*What* is $R$ in predicate $\{Q\}\; S\; \{R\}$?
|
|
|
|
|
|
Back: A predicate.
|
|
|
|
|
|
Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
|
|
|
|
|
|
<!--ID: 1714420640224-->
|
|
|
|
|
|
END%%
|
|
|
|
|
|
|
|
|
|
|
|
%%ANKI
|
|
|
|
|
|
Basic
|
|
|
|
|
|
What name is given to $R$ in $\{Q\}\; S\; \{R\}$?
|
|
|
|
|
|
Back: The postcondition of $S$.
|
|
|
|
|
|
Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
|
|
|
|
|
|
<!--ID: 1714420640226-->
|
|
|
|
|
|
END%%
|
|
|
|
|
|
|
|
|
|
|
|
%%ANKI
|
|
|
|
|
|
Basic
|
|
|
|
|
|
*What* is $S$ in predicate $\{Q\}\; S\; \{R\}$?
|
|
|
|
|
|
Back: A program (a sequence of statements).
|
|
|
|
|
|
Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
|
|
|
|
|
|
<!--ID: 1714420640227-->
|
|
|
|
|
|
END%%
|
|
|
|
|
|
|
|
|
|
|
|
%%ANKI
|
|
|
|
|
|
Basic
|
|
|
|
|
|
What is the antecedent of $\{Q\}\; S\; \{R\}$ in English?
|
|
|
|
|
|
Back: $S$ is executed in a state satisfying $Q$.
|
|
|
|
|
|
Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
|
|
|
|
|
|
<!--ID: 1714420640229-->
|
|
|
|
|
|
END%%
|
|
|
|
|
|
|
|
|
|
|
|
%%ANKI
|
|
|
|
|
|
Basic
|
|
|
|
|
|
What is the consequenct of $\{Q\}\; S\; \{R\}$ in English?
|
|
|
|
|
|
Back: $S$ terminates in a finite amount of time in a state satisfying $R$.
|
|
|
|
|
|
Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
|
|
|
|
|
|
<!--ID: 1714420640231-->
|
|
|
|
|
|
END%%
|
|
|
|
|
|
|
|
|
|
|
|
%%ANKI
|
|
|
|
|
|
Basic
|
|
|
|
|
|
How is $\{Q\}\; S\; \{R\}$ defined?
|
|
|
|
|
|
Back: If $S$ is executed in a state satisfying $Q$, it terminates in a finite amount of time in a state satisfying $R$.
|
|
|
|
|
|
Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
|
|
|
|
|
|
<!--ID: 1714420640232-->
|
|
|
|
|
|
END%%
|
|
|
|
|
|
|
|
|
|
|
|
%%ANKI
|
|
|
|
|
|
Basic
|
|
|
|
|
|
How is $\{x = X \land y = Y\}\; swap\; \{x = Y \land y = X\}$ rewritten without free identifiers?
|
|
|
|
|
|
Back: $\forall x, y, X, Y, \{x = X \land y = Y\}\; swap\; \{x = Y \land y = X\}$
|
|
|
|
|
|
Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
|
|
|
|
|
|
<!--ID: 1714420640234-->
|
|
|
|
|
|
END%%
|
|
|
|
|
|
|
|
|
|
|
|
%%ANKI
|
|
|
|
|
|
Basic
|
|
|
|
|
|
What name is given to $X$ in e.g. $\{x = X\}\; S\; \{y = Y\}$?
|
|
|
|
|
|
Back: The initial value of $x$.
|
|
|
|
|
|
Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
|
|
|
|
|
|
<!--ID: 1714420640235-->
|
|
|
|
|
|
END%%
|
|
|
|
|
|
|
|
|
|
|
|
%%ANKI
|
|
|
|
|
|
Basic
|
|
|
|
|
|
How is $\{Q\}\; S\; \{R\}$ augmented so that $x$ has initial value $X$?
|
|
|
|
|
|
Back: $\{Q \land x = X\}\; S\; \{R\}$
|
|
|
|
|
|
Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
|
|
|
|
|
|
<!--ID: 1714420640237-->
|
|
|
|
|
|
END%%
|
|
|
|
|
|
|
|
|
|
|
|
%%ANKI
|
|
|
|
|
|
Basic
|
|
|
|
|
|
What name is given to $Y$ in e.g. $\{x = X\}\; S\; \{y = Y\}$?
|
|
|
|
|
|
Back: The final value of $y$.
|
|
|
|
|
|
Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
|
|
|
|
|
|
<!--ID: 1714420640238-->
|
|
|
|
|
|
END%%
|
|
|
|
|
|
|
|
|
|
|
|
%%ANKI
|
|
|
|
|
|
Basic
|
|
|
|
|
|
How is $\{Q\}\; S\; \{R\}$ augmented so that $y$ has final value $X$?
|
|
|
|
|
|
Back: $\{Q\}\; S\; \{R \land y = X\}$
|
|
|
|
|
|
Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
|
|
|
|
|
|
<!--ID: 1714420640240-->
|
|
|
|
|
|
END%%
|
|
|
|
|
|
|
|
|
|
|
|
%%ANKI
|
|
|
|
|
|
Basic
|
|
|
|
|
|
How is $\{Q\}\; S\; \{R\}$ augmented so that $y$ has initial value $X$?
|
|
|
|
|
|
Back: $\{Q \land y = X\}\; S\; \{R\}$
|
|
|
|
|
|
Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
|
|
|
|
|
|
<!--ID: 1714420640241-->
|
|
|
|
|
|
END%%
|
2024-04-29 13:29:03 +00:00
|
|
|
|
|
|
|
|
|
|
## Bibliography
|
|
|
|
|
|
|
|
|
|
|
|
* Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
|
