Commit c766a3f4 by Gaspard Ferey

Proposition de condition de wellformedness.

parent 6ebc8b45
 ... @@ -35,6 +35,8 @@ ... @@ -35,6 +35,8 @@ We denote $$\mathcal{T}_{\mathcal{X}}$$ the free algebra over the terms with variables in $$\mathcal{X}$$. We denote $$\mathcal{T}_{\mathcal{X}}$$ the free algebra over the terms with variables in $$\mathcal{X}$$. \end{definition} \end{definition} Note: $$\mathcal{T}_{\mathcal{\emptyset}}$$ is the set of closed terms. \begin{definition} \begin{definition} We define $$\mathfrak{R}_{\mathcal{X}}$$ the set of pairs of terms: We define $$\mathfrak{R}_{\mathcal{X}}$$ the set of pairs of terms: $\mathfrak{R}_{\mathcal{X}} \defn \{(t,u) \mid t,u \in \mathcal{T}_{\mathcal{X}}\}$ $\mathfrak{R}_{\mathcal{X}} \defn \{(t,u) \mid t,u \in \mathcal{T}_{\mathcal{X}}\}$ ... @@ -44,6 +46,7 @@ ... @@ -44,6 +46,7 @@ We denote $$Dom(\Gamma)$$ the domain of $$\Gamma$$ defines as: We denote $$Dom(\Gamma)$$ the domain of $$\Gamma$$ defines as: \begin{align*} \begin{align*} Dom(\emptyset) &\defn \emptyset \\ Dom(\emptyset) &\defn \emptyset \\ Dom(\Gamma , \mathcal{R}) &\defn Dom(\Gamma) \\ Dom(\Gamma , x : A) &\defn Dom(\Gamma) \cup \{x\} Dom(\Gamma , x : A) &\defn Dom(\Gamma) \cup \{x\} \end{align*} \end{align*} \end{definition} \end{definition} ... @@ -121,4 +124,23 @@ ... @@ -121,4 +124,23 @@ {\Gamma \vdash t: B} {\Gamma \vdash t: B} \end{rules} \end{rules} \newpage \section{A simple wellformedness condition} On could start studying a very simple wellformedness condition. \begin{rules}{A (perhaps too) simple rule for relation wellformedness}{Relation WF} \inferrule{ \Gamma \vdash A : \ttype \\ \Gamma \vdash t : A \\ \Gamma \vdash u : A } {\Gamma \vdash \wf{\{(t,u)\}}} \end{rules} \end{document} \end{document}
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