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November 10, 2025 21:56
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| \documentclass{article} | |
| \usepackage{amsmath} | |
| \usepackage{amssymb} | |
| \usepackage{simplebnf} | |
| \def\colon{:} | |
| \def\tyvar{\alpha} | |
| \def\clsname{C} | |
| \def\method{m} | |
| \def\termvar{x} | |
| \def\instvar{\iota} | |
| \def\tycon{\chi} | |
| \def\kindnt{\kappa} | |
| \def\typent{\tau} | |
| \def\karrow{\Rrightarrow} | |
| \def\defenv{\Delta} | |
| \begin{document} | |
| \begin{center} | |
| \begin{bnf}( | |
| relation-sym-map = | |
| { | |
| {::=} = {\ensuremath{\Coloneqq}}, | |
| {:in:} = {}, | |
| }, | |
| ) | |
| $\tyvar$ : type variable :in: | |
| ;; | |
| $\instvar$ : instance variable :in: | |
| ;; | |
| $\clsname$ : class name :in: | |
| ;; | |
| $\tycon$ : type constructor :in: | |
| ;; | |
| $\termvar$ : term variable :in: | |
| ;; | |
| $\method$ : method name :in: | |
| ;; | |
| \end{bnf} | |
| \bigskip | |
| \begin{bnf} | |
| $p$ : programs ::= | |
| | $d_1;\dots;d_n;e$ : ($n\ge0$) | |
| ;; | |
| $d$ : declarations ::= | |
| | $\mathbf{type}\ \theta \Rightarrow \tyvar \colon \kindnt = \tau$ : type declaration | |
| | $\mathbf{type}\ \clsname = c$ : class declaration | |
| | $\mathbf{type}\ \iota = i$ : instance declaration | |
| ;; | |
| $c$ : class expressions ::= | |
| | $\theta \Rightarrow \langle \method\colon\tau\rangle$ | |
| ;; | |
| $i$ : instance expressions ::= | |
| | $\theta \Rightarrow \clsname (\tycon\ \tau)\ \langle \method=e\rangle$ | |
| ;; | |
| $\typent$ : types ::= | |
| | $\tyvar$ : type variable | |
| | $\forall\tyvar\colon \kindnt.\typent$ : universal type | |
| | $\typent\rightarrow\typent$ : function type | |
| | $\tycon\ \typent$ : type application | |
| | $\theta\Rightarrow\typent$ : constrained type | |
| | $\typent\Leftarrow\instvar$ : instance supply | |
| ;; | |
| $\theta$ : constraints ::= | |
| | $\clsname\ \typent\ \mathbf{as}\ \instvar$ | |
| ;; | |
| $e$ : expressions ::= | |
| | $\termvar$ : variable | |
| | $\instvar.\method$ : method access | |
| | $\lambda \termvar \colon \typent . e$ : abstraction | |
| | $\Lambda \termvar \colon \kindnt. e$ : type abstraction | |
| | $e\ e$ : application | |
| | $e\ [e]$ : type application | |
| | $e \Leftarrow \instvar$ : instance supply | |
| ;; | |
| $\kindnt$ : kinds ::= | |
| | $\star$ : type | |
| | $\mathcal{I}$ : instance | |
| | $\mathcal{C}$ : constraint | |
| | $\kindnt\karrow\kindnt$ : type function | |
| ;; | |
| \end{bnf} | |
| \end{center} | |
| \end{document} |
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