107 lines
2.6 KiB
Typst
107 lines
2.6 KiB
Typst
#import "@preview/codly:1.3.0": *
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#import "@preview/codly-languages:0.1.1": *
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#import "@preview/catppuccin:1.0.1": catppuccin, flavors
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#show: codly-init.with()
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#show: catppuccin.with(flavors.latte)
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#codly(languages: codly-languages)
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= Exercise 01
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#let question(body) = block(
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fill: luma(240),
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inset: 8pt,
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radius: 4pt
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)[
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#body
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]
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== 01 Grundbegriffe
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=== Task a
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#question[
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Wie lang (in Terminalsymbolen) ist der kürzeste Satz in MicroJava, der mindestens ein Tilde (“∼”)
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enthält? Geben Sie ein Beispiel für einen Satz dieser Länge an. Der Satz muss nur syntaktisch korrekt
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(entspricht der Grammatik) sein, nicht semantisch (hält alle Kontextbedingungen der Sprache ein). Bei-
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spielsweise ist x = x + 1, ohne x zuvor zu definieren, eine syntaktisch korrekte Zuweisung, semantisch
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korrekt ist sie aber nicht.
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]
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```java
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x[~1]++;
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```
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The statement above contains the following tokens:
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- x (iden, terminal)
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- "\[" (literal, terminal)
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- "~" (literall, terminal)
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- 1 (number, terminal)
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- "\]" (literal, terminal)
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- "++" (literal, terminal)
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- ";" (literal, terminal)
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To sum it up the statement has a `~` and has a terminal symbol count of 7.
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=== Task b
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#question[
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Sind die Nonterminalsymbole Statement und ActPars rekursiv? Wenn ja, geben Sie alle Rekursionen-
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arten an (Transitivität: direkt, indirekt; Orientierung: links, rechts, zentral). Beispiele für Rekursionsarten
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sind direkt zentralrekursiv, indirekt linksrekursiv, . . . Pro NT kann es mehrere Rekursionsarten geben.
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Geben Sie bei indirekten Rekursionen einen möglichen Pfad an (Beispiel: Factor ist indirekt zentralre-
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kursiv über Factor -> Expr -> Term -> Factor).
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]
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==== Statement
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The relevant Productions for the Statement Symbol are:
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```
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Statement = Designator ( Assignop Expr | ActPars | "++" | "--" ) ";"
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| "if" "(" Condition ")" Statement [ "else" Statement ]
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| "while" "(" Condition ")" Statement
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| "break" ";"
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| "return" [ Expr ] ";"
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| "read" "(" Designator ")" ";"
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| "print" "(" Expr [ "," number ] ")" ";"
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| Block
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| ";".
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Block = "{" { Statement } "}".
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```
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We have the following Recursions:
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- line 2: Statement is directly central recursive
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- line 3: Statement is directly right recursive
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- line 8: Block is indirectly central recursive
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==== ActPars
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The relevant Productions for the ActPars Symbol are:
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```
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ActPars = "(" [ Expr { "," Expr } ] ")".
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Expr = [ "–" ] Term { Addop Term }.
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Term = Factor { Mulop Factor }.
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Factor = Designator [ ActPars ]
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| number
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| charConst
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| "new" ident [ "[" Expr "]" ]
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| "(" Expr ")".
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```
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We have the following Recursion:
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- line 1: Factor is indirectly central recursive
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=== Task c
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