dhil/phd-dissertation
1
0
Fork 0
mirror of https://github.com/dhil/phd-dissertation synced 2026-03-13 02:58:26 +00:00
Code Issues Releases Wiki Activity

Simplify example 4.1

Browse Source
This commit is contained in:
Daniel Hillerström
2020-01-29 19:52:34 +00:00
parent 539e5e6bb1
commit bbbc6bc2da
1 changed files with 5 additions and 5 deletions
Download Patch File Download Diff File Expand all files Collapse all files

10
thesis.tex
View File

@@ -1243,7 +1243,7 @@ operation in order to type check.
%
We will now show that this suspended computation fails to type check
with the above type signature. Let
$\Gamma_0 = \{\dec{fac} : \Int \to \Int \eff
$\Gamma = \{\dec{fac} : \Int \to \Int \eff
\{\dec{Div}:\Zero\}\}$. The following typing derivation shows that
the application of $\dec{fac}$ causes its effect row to be
propagated outwards.
@@ -1251,12 +1251,12 @@ operation in order to type check.
\begin{mathpar}
\inferrule*[Right={\tylab{Lam}}]
{\inferrule*[Right={\tylab{App}}]
{\typ{\emptyset;\Gamma_0,\Unit:\Record{}}{\dec{fac} : \Int \to \Int \eff \{\dec{Div}:\Zero\}}\\
\typ{\emptyset;\Gamma_0,\Unit:\Record{}}{3 : \Int}
{\typ{\emptyset;\Gamma,\Unit:\Record{}}{\dec{fac} : \Int \to \Int \eff \{\dec{Div}:\Zero\}}\\
\typ{\emptyset;\Gamma,\Unit:\Record{}}{3 : \Int}
}
{\typ{\emptyset;\Gamma_0,\Unit:\Record{}}{\dec{fac}~3 : \Int \eff \{\dec{Div}:\Zero\}}}
{\typ{\emptyset;\Gamma,\Unit:\Record{}}{\dec{fac}~3 : \Int \eff \{\dec{Div}:\Zero\}}}
}
{\typ{\emptyset;\Gamma_0}{\lambda\Unit.\dec{fac}~3} : \Unit \to \Int \eff \{\dec{Div}:\Zero\}}
{\typ{\emptyset;\Gamma}{\lambda\Unit.\dec{fac}~3} : \Unit \to \Int \eff \{\dec{Div}:\Zero\}}
\end{mathpar}
%
It follows from the typing derivation that the effect row on