diff --git a/docs/constructions.tex b/docs/constructions.tex index 0afec08f23bf5c15dd0e03a70f1cfb10c8cfc8ac..3dcc198e95937bc06d2b6628c438c0420d6012ec 100644 --- a/docs/constructions.tex +++ b/docs/constructions.tex @@ -6,11 +6,11 @@ Given some COFE $\cofe$, we define $\agm(\cofe)$ as follows: \begin{align*} - \monoid \eqdef{}& \setComp{(c, V) \in (\mathbb{N} \to T) \times \pset{\mathbb{N}}}{ \All n, m. n \geq m \Ra n \in V \Ra m \in V } \\ + \monoid \eqdef{}& \recordComp{c : \mathbb{N} \to T , V : \pset{\mathbb{N}}}{ \All n, m. n \geq m \Ra n \in V \Ra m \in V } \\ & \text{quotiented by} \\ - (c_1, V_1) \equiv (c_1, V_2) \eqdef{}& V_1 = V_2 \land \All n. n \in V_1 \Ra c_1(n) \nequiv{n} c_2(n) \\ - (c_1, V_1) \nequiv{n} (c_1, V_2) \eqdef{}& (\All m \leq n. m \in V_1 \Lra m \in V_2) \land (\All m \leq n. m \in V_1 \Ra c_1(m) \nequiv{m} c_2(m)) \\ - \mval_n \eqdef{}& \setComp{(c, V) \in \monoid}{ n \in V \land \All m \leq n. c(n) \nequiv{m} c(m) } \\ + \melt \equiv \meltB \eqdef{}& \melt.V = \meltB.V \land \All n. n \in \melt.V \Ra \melt.c(n) \nequiv{n} \meltB.c(n) \\ + \melt \nequiv{n} \meltB \eqdef{}& (\All m \leq n. m \in \melt.V \Lra m \in \meltB.V) \land (\All m \leq n. m \in \melt.V \Ra \melt.c(m) \nequiv{m} \meltB.c(m)) \\ + \mval_n \eqdef{}& \setComp{\melt \in \monoid}{ n \in \melt.V \land \All m \leq n. \melt.c(n) \nequiv{m} \melt.c(m) } \\ \mcore\melt \eqdef{}& \melt \\ \melt \mtimes \meltB \eqdef{}& (\melt.c, \setComp{n}{n \in \melt.V \land n \in \meltB.V_2 \land \melt \nequiv{n} \meltB }) \\ \melt \mdiv \meltB \eqdef{}& \melt \\ diff --git a/docs/iris.sty b/docs/iris.sty index 3cfdedd633b3e8943cebac298c05ff2e3738883d..31f53a06609a1347f5923cdbac2ccd2ed88fc3c7 100644 --- a/docs/iris.sty +++ b/docs/iris.sty @@ -59,6 +59,7 @@ \newcommand*\setComp[2]{\left\{#1\spac\middle|\spac#2\right\}} \newcommand*\set[1]{\left\{#1\right\}} \newcommand*\record[1]{\left\{\spac#1\spac\right\}} +\newcommand*\recordComp[2]{\left\{\spac#1\spac\middle|\spac#2\spac\right\}} \newenvironment{inbox}[1][]{ \begin{array}[#1]{@{}l@{}}