eth-janishutz/eth-summaries
1
0
Fork 0
mirror of https://github.com/janishutz/eth-summaries.git synced 2026-09-10 19:15:25 +02:00
Code Issues Packages Projects Releases Wiki Activity

[FMFP] Final remarks and fixes

Browse Source
This commit is contained in:
janishutz
2026-08-06 15:10:54 +02:00
parent dad7286f10
commit 7cdba7dca9
10 changed files with 18 additions and 4 deletions
Download Patch File Download Diff File Expand all files Collapse all files
semester4/fmfp/parts/04_language-semantics/00_imp/02_properties.tex
+1 -1
View File
@@ -43,7 +43,7 @@ For Boolean Expressions
And finally for Statements:
\begin{align*}
FV(\texttt{skip}) & = \varnothing \\
FV(x := e) & = \{ x \} \cup FV(s_2) \\
FV(x := e) & = \{ x \} \cup FV(e) \\
FV(s_1; s_2) & = FV(s_1) \cup FV(s_2) \\
FV(\texttt{if}\; b\; \texttt{then} \; s_1 \; \texttt{else} \; s_2 \; \texttt{end}) & = FV(b) \cup FV(s_1) \cup FV(s_2) \\
FV(\texttt{while}\; b\; \texttt{do} \; s \; \texttt{end}) & = FV(b) \cup FV(s)
semester4/fmfp/parts/04_language-semantics/01_operational-semantics/00_big-step-semantics/06_deterministic-semantics.tex
+1 -1
View File
@@ -7,7 +7,7 @@
The full proof for this is available on the slides for Formal Methods, pages 82 - 91 (Slide Deck 3, pages 27 - 40)
In there, \bi{Induction on Derivation Trees} is used.
Similar like other induction proofs, we show that a property $P(T)$ holds for all derivation trees $T$,
Similar to other induction proofs, we show that a property $P(T)$ holds for all derivation trees $T$,
we prove that $P(T)$ holds for an arbitrary derivation tree $T$ under the assumption (the induction hypothesis) that $P(T')$ holds for all sub-trees $T'$ of $T$
This kind of induction is a special case of \bi{well-founded (Noetherian) induction}.