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diff --git a/doc/manual.tex b/doc/manual.tex index 8517206a..e83dc392 100644 --- a/doc/manual.tex +++ b/doc/manual.tex @@ -29,57 +29,80 @@ We give the Ur language definition in \LaTeX $\;$ math mode, since that is prett $\rc$ & \cd{++} \\ \\ $x$ & Normal textual identifier, not beginning with an uppercase letter \\ - $\alpha$ & Normal textual identifier, not beginning with an uppercase letter \\ - $f$ & Normal textual identifier, beginning with an uppercase letter \\ + $X$ & Normal textual identifier, beginning with an uppercase letter \\ \end{tabular} \end{center} -We often write syntax like $N, \cdots, N$ to stand for the non-terminal $N$ repeated 0 or more times. That is, the $\cdots$ symbol is not translated literally to ASCII. +We often write syntax like $e^*$ to indicate zero or more copies of $e$, $e^+$ to indicate one or more copies, and $e,^*$ and $e,^+$ to indicate multiple copies separated by commas. Another separator may be used in place of a comma. The $e$ term may be surrounded by parentheses to indicate grouping; those parentheses should not be included in the actual ASCII. \subsection{Core Syntax} \emph{Kinds} classify types and other compile-time-only entities. Each kind in the grammar is listed with a description of the sort of data it classifies. $$\begin{array}{rrcll} \textrm{Kinds} & \kappa &::=& \mt{Type} & \textrm{proper types} \\ - &&& \mid \mt{Unit} & \textrm{the trivial constructor} \\ - &&& \mid \mt{Name} & \textrm{field names} \\ - &&& \mid \kappa \to \kappa & \textrm{type-level functions} \\ - &&& \mid \{\kappa\} & \textrm{type-level records} \\ - &&& \mid (\kappa \times \cdots \times \kappa) & \textrm{type-level tuples} \\ - &&& \mid (\kappa) & \textrm{explicit precedence} \\ + &&& \mt{Unit} & \textrm{the trivial constructor} \\ + &&& \mt{Name} & \textrm{field names} \\ + &&& \kappa \to \kappa & \textrm{type-level functions} \\ + &&& \{\kappa\} & \textrm{type-level records} \\ + &&& (\kappa\times^+) & \textrm{type-level tuples} \\ + &&& (\kappa) & \textrm{explicit precedence} \\ \end{array}$$ Ur supports several different notions of functions that take types as arguments. These arguments can be either implicit, causing them to be inferred at use sites; or explicit, forcing them to be specified manually at use sites. There is a common explicitness annotation convention applied at the definitions of and in the types of such functions. $$\begin{array}{rrcll} \textrm{Explicitness} & ? &::=& :: & \textrm{explicit} \\ - &&& \mid \; ::: & \textrm{implicit} + &&& \; ::: & \textrm{implicit} \end{array}$$ \emph{Constructors} are the main class of compile-time-only data. They include proper types and are classified by kinds. $$\begin{array}{rrcll} \textrm{Constructors} & c, \tau &::=& (c) :: \kappa & \textrm{kind annotation} \\ - &&& \mid \alpha & \textrm{constructor variable} \\ + &&& x & \textrm{constructor variable} \\ \\ - &&& \mid \tau \to \tau & \textrm{function type} \\ - &&& \mid \alpha \; ? \; \kappa \to \tau & \textrm{polymorphic function type} \\ - &&& \mid \$ c & \textrm{record type} \\ + &&& \tau \to \tau & \textrm{function type} \\ + &&& x \; ? \; \kappa \to \tau & \textrm{polymorphic function type} \\ + &&& \$ c & \textrm{record type} \\ \\ - &&& \mid c \; c & \textrm{type-level function application} \\ - &&& \mid \lambda \alpha \; ? \; \kappa \Rightarrow c & \textrm{type-level function abstraction} \\ + &&& c \; c & \textrm{type-level function application} \\ + &&& \lambda x \; ? \; \kappa \Rightarrow c & \textrm{type-level function abstraction} \\ \\ - &&& \mid () & \textrm{type-level unit} \\ - &&& \mid \#f & \textrm{field name} \\ + &&& () & \textrm{type-level unit} \\ + &&& \#X & \textrm{field name} \\ \\ - &&& \mid [c = c, \cdots, c = c] & \textrm{known-length type-level record} \\ - &&& \mid c \rc c & \textrm{type-level record concatenation} \\ - &&& \mid \mt{fold} & \textrm{type-level record fold} \\ + &&& [(c = c)^*] & \textrm{known-length type-level record} \\ + &&& c \rc c & \textrm{type-level record concatenation} \\ + &&& \mt{fold} & \textrm{type-level record fold} \\ \\ - &&& \mid (c, \cdots, c) & \textrm{type-level tuple} \\ - &&& \mid c.n & \textrm{type-level tuple projection ($n \in \mathbb N^+$)} \\ + &&& (c^+) & \textrm{type-level tuple} \\ + &&& c.n & \textrm{type-level tuple projection ($n \in \mathbb N^+$)} \\ \\ - &&& \mid \lambda [c \sim c] \Rightarrow c & \textrm{guarded constructor} \\ + &&& \lambda [c \sim c] \Rightarrow c & \textrm{guarded constructor} \\ \\ - &&& \mid (c) & \textrm{explicit precedence} \\ + &&& (c) & \textrm{explicit precedence} \\ +\end{array}$$ + +Modules of the module system are described by \emph{signatures}. +$$\begin{array}{rrcll} + \textrm{Signatures} & S &::=& \mt{sig} \; s^* \; \mt{end} & \textrm{constant} \\ + &&& X & \textrm{variable} \\ + &&& \mt{functor}(X : S) : S & \textrm{functor} \\ + &&& S \; \mt{where} \; x = c & \textrm{concretizing an abstract constructor} \\ + &&& M.X & \textrm{projection from a module} \\ + \\ + \textrm{Signature items} & s &::=& \mt{con} \; x :: \kappa & \textrm{abstract constructor} \\ + &&& \mt{con} \; x :: \kappa = c & \textrm{concrete constructor} \\ + &&& \mt{datatype} \; x \; x^* = dc\mid^+ & \textrm{algebraic datatype declaration} \\ + &&& \mt{datatype} \; x = M.x & \textrm{algebraic datatype import} \\ + &&& \mt{val} \; x : \tau & \textrm{value} \\ + &&& \mt{structure} \; X : S & \textrm{sub-module} \\ + &&& \mt{signature} \; X = S & \textrm{sub-signature} \\ + &&& \mt{include} \; S & \textrm{signature inclusion} \\ + &&& \mt{constraint} \; c \sim c & \textrm{record disjointness constraint} \\ + &&& \mt{class} \; x & \textrm{abstract type class} \\ + &&& \mt{class} \; x = c & \textrm{concrete type class} \\ + \\ + \textrm{Datatype constructors} & dc &::=& X & \textrm{nullary constructor} \\ + &&& X \; \mt{of} \; \tau & \textrm{unary constructor} \\ \end{array}$$ \end{document}
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