Module voile::check::expr

$$ \newcommand{\xx}[0]{\texttt{x}} \newcommand{\istype}[0]{\vdash_\texttt{t}} \newcommand{\Gistype}[0]{\Gamma \istype} \newcommand{\tyck}[0]{\vdash_\texttt{c}} \newcommand{\Gtyck}[0]{\Gamma \tyck} \newcommand{\infer}[0]{\vdash_\texttt{i}} \newcommand{\Ginfer}[0]{\Gamma \infer} \newcommand{\subtype}[0]{\vdash_{<:}} \newcommand{\Gsubtype}[0]{\Gamma \subtype} \newcommand{\ty}[0]{\textsf{Type}} \newcommand{\Sum}[0]{\texttt{Sum}\ } \newcommand{\merge}[0]{\texttt{merge}} \newcommand{\inst}[0]{\texttt{inst}} \newcommand{\ctor}[0]{\texttt{cons}\ } \newcommand{\app}[0]{\texttt{app}} \newcommand{\first}[0]{\texttt{first}} \newcommand{\second}[0]{\texttt{second}} \Gistype a \Rightarrow o \quad \Ginfer a \Rightarrow o \quad \Gtyck a:m \Rightarrow o $$ Expression/Type relevant checking.

Functions

check	$$ \newcommand{\xx}[0]{\texttt{x}} \newcommand{\istype}[0]{\vdash_\texttt{t}} \newcommand{\Gistype}[0]{\Gamma \istype} \newcommand{\tyck}[0]{\vdash_\texttt{c}} \newcommand{\Gtyck}[0]{\Gamma \tyck} \newcommand{\infer}[0]{\vdash_\texttt{i}} \newcommand{\Ginfer}[0]{\Gamma \infer} \newcommand{\subtype}[0]{\vdash_{<:}} \newcommand{\Gsubtype}[0]{\Gamma \subtype} \newcommand{\ty}[0]{\textsf{Type}} \newcommand{\Sum}[0]{\texttt{Sum}\ } \newcommand{\merge}[0]{\texttt{merge}} \newcommand{\eval}[0]{\texttt{eval}} \newcommand{\inst}[0]{\texttt{inst}} \newcommand{\first}[0]{\texttt{first}} \newcommand{\second}[0]{\texttt{second}} \newcommand{\ctor}[0]{\texttt{Cons}\ } \newcommand{\app}[0]{\texttt{app}} \cfrac{\Gtyck a:o \Rightarrow n \quad \Gamma,n:o \tyck b:\inst(C, n) \Rightarrow m} {\Gtyck a, b : \Sigma\ C \Rightarrow n, m} \\ \space \\ \space \cfrac{\Gamma,[\xx]:o \tyck a:\app(n, [\xx])} {\Gtyck \lambda \xx.a :\Pi o. \lang n \rang \Rightarrow \lambda \lang n \rang} \\ \space \\ \space \cfrac{\Gtyck a:o \Rightarrow n \quad \Gistype c \Rightarrow m} {\Gtyck a:o+m \Rightarrow n} \\ \space \\ \space \cfrac{}{\Gtyck `\ctor:\Pi o. \lang n \rang \Rightarrow \lambda \lang n \rang} \\ \space \\ \space \cfrac{\Gistype a \Rightarrow n \quad \Gamma, [\xx]:n \istype b \Rightarrow m} {\Gtyck (\Sigma \xx:a.b):\ty \Rightarrow \Sigma n. \lang m \rang} \\ \space \\ \space \cfrac{\Gistype a \Rightarrow n \quad \Gamma, [\xx]:n \istype b \Rightarrow m} {\Gtyck (\Pi \xx:a.b):\ty \Rightarrow \Pi n. \lang m \rang} \\ \space \\ \space \cfrac{\Ginfer a \Rightarrow n \quad \Gsubtype n <: m} {\Gtyck a:m \Rightarrow \eval(a)} $$ Abstract Term -> Core Term under an expected type.
check_subtype	Check if subtype is a subtype of supertype.
check_type	$$ \newcommand{\xx}\[0\]{\texttt{x}} \newcommand{\istype}\[0\]{\vdash_\texttt{t}} \newcommand{\Gistype}\[0\]{\Gamma \istype} \newcommand{\tyck}\[0\]{\vdash_\texttt{c}} \newcommand{\Gtyck}\[0\]{\Gamma \tyck} \newcommand{\infer}\[0\]{\vdash_\texttt{i}} \newcommand{\Ginfer}\[0\]{\Gamma \infer} \newcommand{\subtype}\[0\]{\vdash_{<:}} \newcommand{\Gsubtype}\[0\]{\Gamma \subtype} \newcommand{\ty}\[0\]{\textsf{Type}} \newcommand{\Sum}\[0\]{\texttt{Sum}\ } \newcommand{\merge}\[0\]{\texttt{merge}} \newcommand{\eval}\[0\]{\texttt{eval}} \newcommand{\inst}\[0\]{\texttt{inst}} \newcommand{\first}\[0\]{\texttt{first}} \newcommand{\second}\[0\]{\texttt{second}} \newcommand{\ctor}\[0\]{\texttt{Cons}\ } \newcommand{\app}\[0\]{\texttt{app}} \cfrac{}{\Gistype \ty \Rightarrow \ty} \quad \cfrac{}{\Gistype \bot \Rightarrow \Sum ()} \\ \space \\ \space \cfrac{\Gistype a \Rightarrow n \quad \Gamma, [\xx]:n \istype b \Rightarrow m} {\Gistype \Sigma \xx:a.b \Rightarrow \Sigma n. \lang m \rang} \\ \space \\ \space \cfrac{\Gistype a \Rightarrow n \quad \Gamma, [\xx]:n \istype b \Rightarrow m} {\Gistype \Pi \xx:a.b \Rightarrow \Pi n. \lang m \rang} \\ \space \\ \space \cfrac{\Gistype a \Rightarrow \Sum S_1 \quad \Gistype b \Rightarrow \Sum S_2} {\Gistype a+b \Rightarrow \Sum \merge(S_1, S_2)} $$ Check if an expression is a valid type expression.
check_variant_or_cons
infer	$$ \newcommand{\xx}[0]{\texttt{x}} \newcommand{\istype}[0]{\vdash_\texttt{t}} \newcommand{\Gistype}[0]{\Gamma \istype} \newcommand{\tyck}[0]{\vdash_\texttt{c}} \newcommand{\Gtyck}[0]{\Gamma \tyck} \newcommand{\infer}[0]{\vdash_\texttt{i}} \newcommand{\Ginfer}[0]{\Gamma \infer} \newcommand{\subtype}[0]{\vdash_{<:}} \newcommand{\Gsubtype}[0]{\Gamma \subtype} \newcommand{\ty}[0]{\textsf{Type}} \newcommand{\Sum}[0]{\texttt{Sum}\ } \newcommand{\merge}[0]{\texttt{merge}} \newcommand{\eval}[0]{\texttt{eval}} \newcommand{\inst}[0]{\texttt{inst}} \newcommand{\first}[0]{\texttt{first}} \newcommand{\second}[0]{\texttt{second}} \newcommand{\ctor}[0]{\texttt{Cons}\ } \newcommand{\app}[0]{\texttt{app}} \cfrac{\Gamma(\xx) = o}{\Ginfer \xx \Rightarrow o} \quad \cfrac{}{\Ginfer \ty \Rightarrow \ty} \\ \space \\ \space \cfrac{\Ginfer a \Rightarrow \Sigma n. \lang m \rang} {\Ginfer a\ .1 \Rightarrow n} \\ \space \\ \space \cfrac{\Ginfer a \Rightarrow n \quad \Ginfer b \Rightarrow m} {\Ginfer a,b \Rightarrow \Sigma n. \lang m \rang} \\ \space \\ \space \cfrac{\Gistype a \Rightarrow o}{\Ginfer `\ctor a \Rightarrow \ty} \\ \space \\ \space \cfrac{\Ginfer a \Rightarrow o}{\Ginfer \ctor a \Rightarrow \sum (`\ctor o, ())} \\ \space \\ \space \cfrac{\Ginfer a \Rightarrow \Pi o. \lang n \rang \quad \Gtyck b:o \Rightarrow m} {\Ginfer a \ b \Rightarrow \inst(n, m)} \\ \space \\ \space \cfrac{\Gistype a \Rightarrow \Sum S_1 \quad \Gistype b \Rightarrow \Sum S_2} {\Ginfer a+b \Rightarrow \ty} \\ \space \\ \space \cfrac{\Ginfer a \Rightarrow \Sigma n. \lang m \rang} {\Ginfer a\ .2 \Rightarrow \inst(m, \first(a))} $$ Infer type of a value.