Skip to content
Toggle navigation
P
Projects
G
Groups
S
Snippets
Help
Mark Cohen
/
thesis
This project
Loading...
Sign in
Toggle navigation
Go to a project
Project
Repository
Merge Requests
0
Pipelines
Members
Activity
Graph
Charts
Create a new issue
Jobs
Commits
Issue Boards
Files
Commits
Branches
Tags
Contributors
Graph
Compare
Charts
Commit
7d3f4f9c
authored
May 27, 2019
by
Mark Cohen
Browse files
Options
Browse Files
Download
Email Patches
Plain Diff
Paper: inference rules WIP
parent
9b75f0b4
Hide whitespace changes
Inline
Side-by-side
Showing
1 changed file
with
83 additions
and
8 deletions
final/main.tex
final/main.tex
View file @
7d3f4f9c
...
...
@@ -25,6 +25,15 @@
% judgment form
\usepackage
{
ebproof
}
% turnstile alias
\newcommand
{
\proves
}{
\vdash
}
% function arrow alias
\newcommand
{
\arrow
}{
\to
}
% backslash alias
\newcommand
{
\bs
}{
\,
\backslash
\,
}
\title
{
[TITLE]
}
\author
{
Mark Cohen, Adam Shaw
}
\date
{
5 June 2019
}
...
...
@@ -32,13 +41,79 @@
\begin{document}
\maketitle
\[
\begin
{
array
}{
cl
}
\textbf
{
PRED
}
&
{
\begin
{
prooftree
}
\Hypo
{
A
\vdash
e ::
(
x ::
\tau
)
.
\rho
\mapsto
(
\lambda
x
_
\tau
.
\bar
{
e
}
)
}
\Infer
1
{
A,
(
x ::
\tau
\mapsto
x
_
\tau
)
\vdash
e ::
\rho
\mapsto
\bar
{
e
}}
\end
{
prooftree
}}
\\
\end
{
array
}
\]
\newpage
\begin{table}
\renewcommand
{
\arraystretch
}{
3.5
}
\[
\begin
{
array
}{
r c
}
\textbf
{
TAUT
}
&
{
\begin
{
prooftree
}
\Infer
0
{
A,
(
x ::
\sigma
\bs
\bar
{
x
}
)
\proves
x ::
\sigma
\bs
\bar
{
x
}}
\end
{
prooftree
}}
\\
\textbf
{
TAUT
-
INST
}
&
{
\begin
{
prooftree
}
\Infer
0
{
A,
(
x ::
_
i
\sigma
\bs
\bar
{
x
}
)
\proves
x ::
\sigma
\bs
\bar
{
x
}}
\end
{
prooftree
}}
\\
\textbf
{
GEN
}
&
{
\begin
{
prooftree
}
\Hypo
{
\alpha
\text
{
not free in
}
A
}
\Hypo
{
A
\proves
e ::
\sigma
\bs
\bar
{
e
}}
\Infer
2
{
A
\proves
e ::
\forall
\alpha
.
\sigma
\bs
\bar
{
e
}}
\end
{
prooftree
}}
\\
\textbf
{
SPEC
}
&
{
\begin
{
prooftree
}
\Hypo
{
A
\proves
e ::
\forall
\alpha
.
\sigma
\bs
\bar
{
e
}}
\Infer
1
{
A
\proves
e ::
\left
[
\alpha
\backslash
\tau
\right
]
\sigma
\bs
\bar
{
e
}}
\end
{
prooftree
}}
\\
\textbf
{
ABS
}
&
{
\begin
{
prooftree
}
\Hypo
{
A,
(
x ::
\tau
'
\bs
x
)
\proves
e ::
\tau
\bs
\bar
{
e
}}
\Infer
1
{
A
\proves
(
\lambda
x . e
)
::
(
\tau
'
\arrow
\tau
)
\bs
(
\lambda
x .
\bar
{
e
}
)
}
\end
{
prooftree
}}
\\
\textbf
{
APP
}
&
{
\begin
{
prooftree
}
\Hypo
{
A
\proves
e ::
(
\tau
'
\arrow
\tau
)
\bs
\bar
{
e
}}
\Hypo
{
A
\proves
e' ::
\tau
'
\bs
\bar
{
e
}
'
}
\Infer
2
{
A
\proves
(
e
\;
e'
)
::
\tau
\bs
(
\bar
{
e
}
\;
\bar
{
e
}
'
)
}
\end
{
prooftree
}}
\\
\textbf
{
LETREC
}
&
{
\begin
{
prooftree
}
\Hypo
{
A,
(
x ::
\alpha
\bs
x
)
\proves
e ::
\sigma
\bs
\bar
{
e
}}
\Hypo
{
A,
(
x ::
\sigma
\bs
x
)
\proves
e' ::
\tau
\bs
\bar
{
e
}
'
}
\Infer
2
{
A
\proves
(
\textbf
{
let
}
x
=
e
\textbf
{
in
}
e'
)
::
\tau
\bs
(
\textbf
{
let
}
x
=
\bar
{
e
}
\textbf
{
in
}
\bar
{
e
}
'
)
}
\end
{
prooftree
}}
\\
\textbf
{
OVER
}
&
{
\begin
{
prooftree
}
\Hypo
{
A,
(
x ::
_
o
\sigma
)
\proves
e' ::
\tau
\bs
\bar
{
e
}
'
}
\Infer
1
{
A
\proves
(
\textbf
{
over
}
x ::
\sigma
\textbf
{
in
}
e'
)
::
\tau
\bs
\bar
{
e
}
'
}
\end
{
prooftree
}}
\\
\textbf
{
INST
}
&
{
\begin
{
prooftree
}
\Hypo
{
(
x ::
_
o
\sigma
)
\in
A
}
\Hypo
{
A,
(
x ::
_
i
\sigma
\bs
x
_
\sigma
)
\proves
e ::
\sigma
\bs
\bar
{
e
}}
\Hypo
{
A,
(
x ::
_
i
\sigma
\bs
x
_
\sigma
)
\proves
e' ::
\tau
\bs
\bar
{
e
}
'
}
\Infer
3
{
A
\proves
(
\textbf
{
inst
}
x ::
\sigma
=
e
\textbf
{
in
}
e'
)
::
\tau
\bs
(
\textbf
{
let
}
x
_
\sigma
=
\bar
{
e
}
\textbf
{
in
}
\bar
{
e
}
'
)
}
\end
{
prooftree
}}
\\
% TODO: INST-PRED
\textbf
{
REL
}
&
{
\begin
{
prooftree
}
\Hypo
{
(
x ::
_
o
\sigma
)
\in
A
}
\Hypo
{
A
\proves
e ::
(
x ::
\tau
)
.
\rho
\bs
\bar
{
e
}}
\Hypo
{
A
\proves
x ::
\tau
\bs
\bar
{
e
}
'
}
\Infer
3
{
A
\proves
e ::
\rho
\bs
(
\bar
{
e
}
\;
\bar
{
e
}
'
)
}
\end
{
prooftree
}}
\\
\end
{
array
}
\]
\end{table}
% \begin{align*}
% \Phi(\forall \alpha . \sigma) &= \Phi(\sigma) \\
% \Phi((x :: \tau) . \rho) &= \Phi(\rho) \\
% \Phi((x :: \tau) . \tau') &= ((x :: \tau), \tau') \\
% \end{align*}
\end{document}
Write
Preview
Markdown
is supported
0%
Try again
or
attach a new file
Attach a file
Cancel
You are about to add
0
people
to the discussion. Proceed with caution.
Finish editing this message first!
Cancel
Please
register
or
sign in
to comment