From 939fd9d78dea9ca768753028ef3f5d0f8bba629b Mon Sep 17 00:00:00 2001
From: pimjager <pim@pimjager.nl>
Date: Mon, 13 Jun 2016 22:23:53 +0200
Subject: [PATCH] Added inferenece formulas, need some explaination and
formatting
---
deliverables/report/sem.tex | 103 ++++++++++++++++++++++++++++++++++++
1 file changed, 103 insertions(+)
diff --git a/deliverables/report/sem.tex b/deliverables/report/sem.tex
index 3687777..6b49e68 100644
--- a/deliverables/report/sem.tex
+++ b/deliverables/report/sem.tex
@@ -261,3 +261,106 @@ determined and are shown below.
\infer[\emptyset]
{\Gamma \vdash [] \Rightarrow (\Gamma, \star_0, \alpha, [])}{}
\end{equation}
+
+\paragraph{If statements}
+balbal de if en else mzelfed type, jwz statements hebben he tupen wat ze
+returnen.
+\begin{equation}
+ \infer[If]
+ {\Gamma \vdash \underline{\textrm{if }} e
+ \underline{\textrm{ then }} s_1
+ \underline{\textrm{ else }} s_2
+ \Rightarrow
+ (\Gamma^\star, \star, \tau_e^\star, \underline{\textrm{if }} e'
+ \underline{\textrm{ then }} s_1'
+ \underline{\textrm{ else }} s_2')
+ }
+ {\Gamma \vdash e \Rightarrow (\Gamma^{\star_1}, \star_1, \tau_1, e')
+ &\tau_1 \unif \textrm{Bool} = \star_2
+ &\Gamma^{\star_2\cdot \star_1} \vdash s_1 \Rightarrow
+ (\Gamma^{\star_3}, \star_3, \tau_t, s_1')
+ &\Gamma^{\star_3} \vdash s_2 \Rightarrow
+ (\Gamma^{\star_4}, \star_4, \tau_e, s_2')
+ &\tau_t \unif \tau_e = \star_5
+ }
+\end{equation}
+
+\paragraph{While statements}
+\begin{equation}
+ \infer[While]
+ {\Gamma \vdash \underline{\textrm{while }} e \textrm{ } s
+ \Rightarrow
+ (\Gamma^\star, \star, \tau_s^\star,
+ \underline{\textrm{while }} e' \textrm{ } s_1')
+ }
+ {\Gamma \vdash e \Rightarrow (\Gamma^{\star_1}, \star_1, \tau_1, e')
+ &\tau_1 \unif \textrm{Bool} = \star_2
+ &\Gamma^{\star_2\cdot \star_1} \vdash s \Rightarrow
+ (\Gamma^{\star_3}, \star_3, \tau_t, s')
+ &\star = \star_3 \cdot \star_2 \cdot \star_1
+ }
+\end{equation}
+
+\paragraph{Assignment statement}
+blabla unapfs, en extenden van Gamma
+\begin{equation}
+ \infer[Ass]
+ {\Gamma \vdash \textit{id.fs}^* \underline{=} e \Rightarrow
+ (\Gamma^\star.k:\tau_r^\star, \star, \textrm{Void},
+ \textit{id.fs}^* \underline{=} e')
+ }
+ {\Gamma(\textit{id}) = \lfloor \tau_e \rfloor
+ &\Gamma \vdash e \Rightarrow (\Gamma^{\star_1}, \star_1, \tau_g, e')
+ &\texttt{fold unapfs } \tau_g \textit{reverse fs} = \tau^r
+ &\tau_e \unif \tau_g = \star_2
+ &\star = \star_2 \cdot \star_1
+ }
+\end{equation}
+
+\paragraph{Function Statements}
+Blabl, praktisch gelijk aan function call, behalve dat ze altijd Void als
+type hebben.
+
+\begin{equation} \label{eq:inferStmtApp0}
+ \infer[Stmt App 0]
+ {\Gamma \vdash \textit{id}().\textit{fs}^* \Rightarrow
+ ((\Gamma^\star, \star, \textrm{Void},
+ \textit{id}().\textit{fs}^*)}
+ {\Gamma(id) = \lfloor \tau^e \rfloor
+ &\texttt{fold apfs } \tau \textit{ fs}^* = \tau^r
+ }
+\end{equation}
+
+\begin{equation} \label{eq:inferAppN}
+ \infer[Stmt AppN]
+ {\Gamma \vdash \textit{id}(e^*).\textit{fs}^* \Rightarrow
+ ((\Gamma^\star, \star, \textrm{Void},
+ \textit{id}({e^*}').\textit{fs}^*)}
+ {\Gamma(id) = \lfloor \tau^e \rfloor
+ &\Gamma \vdash e^* \Rightarrow
+ (\Gamma^{\star_1}, \star_1, \tau^*, {e^*}')
+ &(\texttt{fold } (\rightarrow) \texttt{ } \alpha \texttt{ } \tau^*)
+ \unif \tau^e = \star_2
+ &\star = \star_2 \cdot \star_1
+ &\texttt{fold apfs } \tau \textit{ fs}^* = \tau^e
+ }
+\end{equation}
+
+\paragraph{Return statements}
+blabla, verschil tussen wel en niet iets returnen
+
+\begin{equation}
+ \infer[Return \emptyset]
+ {\Gamma \vdash \underline{\textrm{return}} \Rightarrow
+ (\Gamma, \star_0, \textrm{Void}, \underline{\textrm{return}})
+ }
+ {}
+\end{equation}
+
+\begin{equation}
+ \infer[Return]
+ {\Gamma \vdash \underline{\textrm{return }} e \Rightarrow
+ (\Gamma^\star, \star, \tau, \underline{\textrm{return }} e')
+ }
+ {\Gamma \vdash e \Rightarrow (\Gamma^\star, \star, \tau, e')}
+\end{equation}
\ No newline at end of file
--
2.20.1