add model for new terms

docs/base-logic.tex

@@ -41,7 +41,7 @@ Below, $\melt$ ranges over $\monoid$ and $i$ ranges over $\set{1,2}$.
   \term, \prop, \pred \bnfdef{}&
       \var \mid
       \sigfn(\term_1, \dots, \term_n) \mid
-      \textlog{abort}(\term) \mid
+      \textlog{abort}\; \term \mid
       () \mid
       (\term, \term) \mid
       \pi_i\; \term \mid
@@ -119,7 +119,7 @@ In writing $\vctx, x:\type$, we presuppose that $x$ is not already declared in $
 %%% empty, unit, products, sums
 \and
 	\infer{\vctx \proves \wtt\term{0}}
-        {\vctx \proves \wtt{\textlog{abort}(\term)}\type}
+        {\vctx \proves \wtt{\textlog{abort}\; \term}\type}
 \and
 	\axiom{\vctx \proves \wtt{()}{1}}
 \and

docs/model.tex

@@ -9,11 +9,13 @@ The semantic  domains are interpreted as follows:
 \[
 \begin{array}[t]{@{}l@{\ }c@{\ }l@{}}
 \Sem{\Prop} &\eqdef& \UPred(\monoid)  \\
-\Sem{\textlog{M}} &\eqdef& \monoid
+\Sem{\textlog{M}} &\eqdef& \monoid \\
+\Sem{0} &\eqdef& \Delta \emptyset \\
+\Sem{1} &\eqdef& \Delta \{ () \}
 \end{array}
 \qquad\qquad
 \begin{array}[t]{@{}l@{\ }c@{\ }l@{}}
-\Sem{1} &\eqdef& \Delta \{ () \} \\
+\Sem{\type + \type'} &\eqdef& \Sem{\type} + \Sem{\type} \\
 \Sem{\type \times \type'} &\eqdef& \Sem{\type} \times \Sem{\type} \\
 \Sem{\type \to \type'} &\eqdef& \Sem{\type} \nfn \Sem{\type} \\
 \end{array}
@@ -80,9 +82,15 @@ For every definition, we have to show all the side-conditions: The maps have to
 	\Sem{\vctx \proves \MU \var:\type. \term : \type}_\gamma &\eqdef
 	\mathit{fix}(\Lam \termB : \Sem{\type}. \Sem{\vctx, x : \type \proves \term : \type}_{\mapinsert \var \termB \gamma}) \\
   ~\\
+	\Sem{\vctx \proves \textlog{abort}\;\term : \type}_\gamma &\eqdef \mathit{abort}_{\Sem\type}(\Sem{\vctx \proves \term:0}_\gamma) \\
 	\Sem{\vctx \proves () : 1}_\gamma &\eqdef () \\
 	\Sem{\vctx \proves (\term_1, \term_2) : \type_1 \times \type_2}_\gamma &\eqdef (\Sem{\vctx \proves \term_1 : \type_1}_\gamma, \Sem{\vctx \proves \term_2 : \type_2}_\gamma) \\
-	\Sem{\vctx \proves \pi_i(\term) : \type_i}_\gamma &\eqdef \pi_i(\Sem{\vctx \proves \term : \type_1 \times \type_2}_\gamma) \\
+	\Sem{\vctx \proves \pi_i\; \term : \type_i}_\gamma &\eqdef \pi_i(\Sem{\vctx \proves \term : \type_1 \times \type_2}_\gamma) \\
+        \Sem{\vctx \proves \textlog{inj}_i\;\term : \type_1 + \type_2}_\gamma &\eqdef \mathit{inj}_i(\Sem{\vctx \proves \term : \type_i}_\gamma) \\
+        \Sem{\vctx \proves \textlog{match}\; \term \;\textlog{with}\; \Ret\textlog{inj}_1\; \var_1. \term_1 \mid \Ret\textlog{inj}_2\; \var_2. \term_2 \;\textlog{end} : \type }_\gamma &\eqdef 
+    \Sem{\vctx, \var_i:\type_i \proves \term_i : \type}_{\mapinsert{\var_i}\termB \gamma} \\
+    &\qquad \text{where $\Sem{\vctx \proves \term : \type_1 + \type_2}_\gamma = \mathit{inj}_i(\termB)$}
+    \\
   ~\\
         \Sem{ \melt : \textlog{M} }_\gamma &\eqdef \melt \\
 	\Sem{\vctx \proves \mcore\term : \textlog{M}}_\gamma &\eqdef \mcore{\Sem{\vctx \proves \term : \textlog{M}}_\gamma} \\
@@ -94,6 +102,7 @@ For every definition, we have to show all the side-conditions: The maps have to
 An environment $\vctx$ is interpreted as the set of
 finite partial functions $\rho$, with $\dom(\rho) = \dom(\vctx)$ and
 $\rho(x)\in\Sem{\vctx(x)}$.
+Above, $\mathit{fix}$ is the fixed-point on COFEs, and $\mathit{abort}_T$ is the unique function $\emptyset \to T$.
 
 \paragraph{Logical entailment.}
 We can now define \emph{semantic} logical entailment.