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Fix typos in operational semantics for "Loop" command

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In section 13.3, the type of Loop is defined as:

    Loop : forall a, a -> (a -> cmd (outcome a)) -> cmd a

However, the operational semantics provided in sections 14.1 and 18.1
invoke the loop body function using "Again(i)" (type "outcome a").
They should instead use simply "i" (type "a").

Changing to "f(i)" also matches the StepLoop formalizations in
SeparationLogic.v and ConcurrentSeparationLogic.v, which invoke simply
"body init" (rather than "body (Again init)").
This commit is contained in:
Matthew Dempsky 2020-09-24 11:43:41 -07:00
parent e32105c142
commit bd92c1cbb3
1 changed files with 2 additions and 2 deletions
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frap_book.tex
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@ -3703,7 +3703,7 @@ $$\infer{\smallstep{(h, x \leftarrow c_1; c_2(x))}{(h', x \leftarrow c'_1; c_2(x
} }
\quad \infer{\smallstep{(h, x \leftarrow \mt{Return} \; v; c(x))}{(h, c(v))}}{}$$ \quad \infer{\smallstep{(h, x \leftarrow \mt{Return} \; v; c(x))}{(h, c(v))}}{}$$
$$\infer{\smallstep{(h, \mt{Loop} \; i \; f)}{(h, x \leftarrow f(\mt{Again}(i)); \mt{match} \; x \; \mt{with} \; \mt{Done}(a) \Rightarrow \mt{Return} \; a \mid \mt{Again}(a) \Rightarrow \mt{Loop} \; a \; f)}}{}$$ $$\infer{\smallstep{(h, \mt{Loop} \; i \; f)}{(h, x \leftarrow f(i); \mt{match} \; x \; \mt{with} \; \mt{Done}(a) \Rightarrow \mt{Return} \; a \mid \mt{Again}(a) \Rightarrow \mt{Loop} \; a \; f)}}{}$$
$$\infer{\smallstep{(h, \mt{Read} \; a)}{(h, \mt{Return} \; v)}}{ $$\infer{\smallstep{(h, \mt{Read} \; a)}{(h, \mt{Return} \; v)}}{
\msel{h}{a} = v \msel{h}{a} = v
@ -4753,7 +4753,7 @@ $$\infer{\smallstep{(h, l, x \leftarrow c_1; c_2(x))}{(h', l', x \leftarrow c'_1
} }
\quad \infer{\smallstep{(h, l, x \leftarrow \mt{Return} \; v; c_2(x))}{(h, k, c_2(v))}}{}$$ \quad \infer{\smallstep{(h, l, x \leftarrow \mt{Return} \; v; c_2(x))}{(h, k, c_2(v))}}{}$$
$$\infer{\smallstep{(h, l, \mt{Loop} \; i \; f)}{(h, l, x \leftarrow f(\mt{Again}(i)); \mt{match} \; x \; \mt{with} \; \mt{Done}(a) \Rightarrow \mt{Return} \; a \mid \mt{Again}(a) \Rightarrow \mt{Loop} \; a \; f)}}{}$$ $$\infer{\smallstep{(h, l, \mt{Loop} \; i \; f)}{(h, l, x \leftarrow f(i); \mt{match} \; x \; \mt{with} \; \mt{Done}(a) \Rightarrow \mt{Return} \; a \mid \mt{Again}(a) \Rightarrow \mt{Loop} \; a \; f)}}{}$$
$$\infer{\smallstep{(h, l, \mt{Read} \; a)}{(h, l, \mt{Return} \; v)}}{ $$\infer{\smallstep{(h, l, \mt{Read} \; a)}{(h, l, \mt{Return} \; v)}}{
\msel{h}{a} = v \msel{h}{a} = v