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|
embed {{ tex-preamble
\newcommand{\coderef}[2]{\ghcfile{#1}:\texttt{#2}%
}
\newcommand{\keyword}[1]{\textbf{#1} }
\newcommand{\labeledjudge}[1]{\vdash_{\!\!\mathsf{#1} } }
}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Metavariables %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
metavar x ::= {{ com Term-level variable names }}
metavar alpha {{ tex \alpha }}, beta {{ tex \beta }} ::=
{{ com Type-level variable names }}
metavar N ::= {{ com Type-level constructor names }}
metavar K ::= {{ com Term-level data constructor names }}
indexvar i, j, kk {{ tex k }} ::= {{ com Indices to be used in lists }}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Syntax %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
grammar
lit {{ tex \textsf{lit} }} :: 'Literal_' ::=
{{ com Literals, \coderef{basicTypes/Literal.lhs}{Literal} }}
z :: 'Name_' ::= {{ com Term or type name }}
| alpha :: :: Type {{ com Type-level name }}
| x :: :: Term {{ com Term-level name }}
n, m :: 'Var_' ::= {{ com Variable names, \coderef{basicTypes/Var.lhs}{Var} }}
| z _ t :: :: IdOrTyVar {{ com Name, labeled with type/kind }}
{{ tex {[[z]]}^{[[t]]} }}
vars :: 'Vars_' ::= {{ com List of variables }}
| </ ni // , // i /> :: :: List
| fv ( t ) :: M :: fv
{{ tex \textit{fv}([[t]]) }}
| empty :: M :: empty
e, u :: 'Expr_' ::= {{ com Expressions, \coderef{coreSyn/CoreSyn.lhs}{Expr} }}
| n :: :: Var {{ com Variable }}
| lit :: :: Lit {{ com Literal }}
| e1 e2 :: :: App {{ com Application }}
| \ n . e :: :: Lam {{ com Abstraction }}
| let binding in e :: :: Let {{ com Variable binding }}
| case e as n return t of </ alti // | // i /> :: :: Case {{ com Pattern match }}
| e |> g :: :: Cast {{ com Cast }}
| e { tick } :: :: Tick {{ com Internal note }}
{{ tex {[[e]]}_{\{[[tick]]\} } }}
| t :: :: Type {{ com Type }}
| g :: :: Coercion {{ com Coercion }}
| e [ n |-> t ] :: M :: TySubst {{ com Type substitution }}
binding :: 'Bind_' ::= {{ com Let-bindings, \coderef{coreSyn/CoreSyn.lhs}{Bind} }}
| n = e :: :: NonRec {{ com Non-recursive binding }}
| rec </ ni = ei // and // i /> :: :: Rec {{ com Recursive binding }}
alt :: 'Alt_' ::= {{ com Case alternative, \coderef{coreSyn/CoreSyn.lhs}{Alt} }}
| Kp </ ni // i /> -> e :: :: Alt {{ com Constructor applied to fresh names }}
tick :: 'Tickish_' ::= {{ com Internal notes, \coderef{coreSyn/CoreSyn.lhs}{Tickish} }}
Kp {{ tex \mathbb{K} }} :: 'AltCon_' ::= {{ com Constructors used in patterns, \coderef{coreSyn/CoreSyn.lhs}{AltCon} }}
| K :: :: DataAlt {{ com Data constructor }}
| lit :: :: LitAlt {{ com Literal (such as an integer or character) }}
| _ :: :: DEFAULT {{ com Wildcard }}
program :: 'CoreProgram_' ::= {{ com A System FC program, \coderef{coreSyn/CoreSyn.lhs}{CoreProgram} }}
| </ bindingi // i /> :: :: CoreProgram {{ com List of bindings }}
%% TYPES %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
t {{ tex \tau }}, k {{ tex \kappa }}, s {{ tex \sigma }}
:: 'Type_' ::= {{ com Types/kinds, \coderef{types/TypeRep.lhs}{Type} }}
| n :: :: TyVarTy {{ com Variable }}
| t1 t2 :: :: AppTy {{ com Application }}
| T </ ti // i /> :: :: TyConApp {{ com Application of type constructor }}
| t1 -> t2 :: :: FunTy {{ com Function }}
| forall n . t :: :: ForAllTy {{ com Polymorphism }}
| lit :: :: LitTy {{ com Type-level literal }}
| tyConKind T :: M :: tyConKind {{ com \coderef{types/TyCon.lhs}{tyConKind} }}
| t1 ~# k t2 :: M :: unliftedEq {{ com Metanotation for coercion types }}
{{ tex [[t1]] \mathop{\sim_{\#}^{[[k]]} } [[t2]] }}
| literalType t :: M :: literalType {{ com \coderef{basicTypes/Literal.lhs}{literalType} }}
| ( t ) :: M :: parens {{ com Parentheses }}
| t [ n |-> s ] :: M :: TySubst {{ com Type substitution }}
| subst ( k ) :: M :: TySubstList {{ com Type substitution list }}
| t subst :: M :: TySubstListPost {{ com Type substitution list }}
| dataConRepType K :: M :: dataConRepType {{ com Type of DataCon }}
%% COERCIONS %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
g {{ tex \gamma }} :: 'Coercion_' ::= {{ com Coercions, \coderef{types/Coercion.lhs}{Coercion} }}
| < t > :: :: Refl {{ com Reflexivity }}
{{ tex \langle [[t]] \rangle }}
| T </ gi // i /> :: :: TyConAppCo {{ com Type constructor application }}
| g1 g2 :: :: AppCo {{ com Application }}
| forall n . g :: :: ForAllCo {{ com Polymorphism }}
| n :: :: CoVarCo {{ com Variable }}
| C ind </ gj // j /> :: :: AxiomInstCo {{ com Axiom application }}
| t1 ==>! t2 :: :: UnsafeCo {{ com Unsafe coercion }}
| sym g :: :: SymCo {{ com Symmetry }}
| g1 ; g2 :: :: TransCo {{ com Transitivity }}
| nth i g :: :: NthCo {{ com Projection (0-indexed) }}
{{ tex \textsf{nth}_{[[i]]}\,[[g]] }}
| LorR g :: :: LRCo {{ com Left/right projection }}
| g t :: :: InstCo {{ com Type application }}
| ( g ) :: M :: Parens {{ com Parentheses }}
LorR :: 'LeftOrRight_' ::= {{ com left or right deconstructor, \coderef{types/Coercion.lhs}{LeftOrRight} }}
| Left :: :: CLeft {{ com Left projection }}
| Right :: :: CRight {{ com Right projection }}
C :: 'CoAxiom_' ::= {{ com Axioms, \coderef{types/TyCon.lhs}{CoAxiom} }}
| T </ axBranchi // ; // i /> :: :: CoAxiom {{ com Axiom }}
| ( C ) :: M :: Parens {{ com Parentheses }}
axBranch, b :: 'CoAxBranch_' ::= {{ com Axiom branches, \coderef{types/TyCon.lhs}{CoAxBranch} }}
| forall </ ni // i /> . ( </ tj // j /> ~> s ) :: :: CoAxBranch {{ com Axiom branch }}
| ( </ axBranchi // i /> ) [ ind ] :: M :: lookup {{ com List lookup }}
%% TYCONS %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
T :: 'TyCon_' ::= {{ com Type constructors, \coderef{types/TyCon.lhs}{TyCon} }}
| ( -> ) :: :: FunTyCon {{ com Arrow }}
% the following also includes TupleTyCon, SynTyCon
| N _ k :: :: AlgTyCon {{ com Named tycon: algebraic, tuples, and synonyms }}
{{ tex {[[N]]}^{[[k]]} }}
| H :: :: PrimTyCon {{ com Primitive tycon }}
| ' K :: :: PromotedDataCon {{ com Promoted data constructor }}
| ' T :: :: PromotedTyCon {{ com Promoted type constructor }}
| dataConTyCon K :: M :: dataConTyCon {{ com TyCon extracted from DataCon }}
H :: 'PrimTyCon_' ::= {{ com Primitive type constructors, \coderef{prelude/TysPrim.lhs}{} }}
| Int# :: :: intPrimTyCon {{ com Unboxed Int }}
| ( ~# ) :: :: eqPrimTyCon {{ com Unboxed equality }}
| BOX :: :: superKindTyCon {{ com Sort of kinds }}
| * :: :: liftedTypeKindTyCon {{ com Kind of lifted types }}
| # :: :: unliftedTypeKindTyCon {{ com Kind of unlifted types }}
| OpenKind :: :: openTypeKindTyCon {{ com Either $*$ or $\#$ }}
| Constraint :: :: constraintTyCon {{ com Constraint }}
%% CONTEXTS %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
G {{ tex \Gamma }} :: 'LintM_Bindings_' ::= {{ com List of bindings, \coderef{coreSyn/CoreLint.lhs}{LintM} }}
| n :: :: Binding {{ com Single binding }}
| </ Gi // , // i /> :: :: Concat {{ com Context concatenation }}
| vars_of binding :: M :: VarsOf {{ com \coderef{coreSyn/CoreSyn.lhs}{bindersOf} }}
%% UTILITY %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
B {{ tex \mathbb{B} }} :: 'Bool_' ::= {{ com Booleans in metatheory }}
| false :: :: False
| true :: :: True
kinded_types {{ tex \overline{(\sigma_i : \kappa_i)}^i }} :: 'Kinded_Types_' ::= {{ com List of types with kinds }}
| </ ( si : ki ) // , // i /> :: :: List
| empty :: M :: empty
subst :: 'Subst_' ::= {{ com List of type substitutions }}
| [ n |-> t ] :: :: Mapping
| </ substi // i /> :: :: List
ind :: 'Ind_' ::= {{ com Indices, numbers }}
| i :: :: index
| length </ ti // i /> :: M :: length_t
| length </ axBranchi // i /> :: M :: length_axBranch
| tyConArity T :: M :: tyConArity
| ind - 1 :: M :: decrement
| -1 :: M :: minusOne
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Terminals %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
terminals :: 'terminals_' ::=
| \ :: :: lambda {{ tex \lambda }}
| let :: :: let {{ tex \keyword{let} }}
| in :: :: key_in {{ tex \keyword{in} }}
| rec :: :: rec {{ tex \keyword{rec} }}
| and :: :: key_and {{ tex \keyword{and} }}
| case :: :: case {{ tex \keyword{case} }}
| of :: :: of {{ tex \keyword{of} }}
| -> :: :: arrow {{ tex \to }}
| |> :: :: cast {{ tex \triangleright }}
| forall :: :: forall {{ tex {\forall}\! }}
| ==>! :: :: unsafe
{{ tex \twoheadrightarrow\!\!\!\!\!\! \raisebox{-.3ex}{!} \,\,\,\,\, }}
| sym :: :: sym {{ tex \textsf{sym} }}
| ; :: :: trans {{ tex \fatsemi }}
| Left :: :: Left {{ tex \textsf{left} }}
| Right :: :: Right {{ tex \textsf{right} }}
| _ :: :: wildcard {{ tex \text{\textvisiblespace} }}
| BOX :: :: BOX {{ tex \Box }}
| Int# :: :: int_hash {{ tex {\textsf{Int} }_{\#} }}
| ~# :: :: eq_hash {{ tex \mathop{ {\sim}_{\#} } }}
| OpenKind :: :: OpenKind {{ tex \textsf{OpenKind} }}
| ok :: :: ok {{ tex \textsf{ ok} }}
| no_duplicates :: :: no_duplicates {{ tex \textsf{no\_duplicates } }}
| vars_of :: :: vars_of {{ tex \textsf{vars\_of } }}
| not :: :: not {{ tex \neg }}
| isUnLiftedTyCon :: :: isUnLiftenTyCon {{ tex \textsf{isUnLiftedTyCon} }}
| false :: :: false {{ tex \textsf{false} }}
| true :: :: true {{ tex \textsf{true} }}
| \/ :: :: or {{ tex \vee }}
| /\ :: :: and {{ tex \mathop{\wedge} }}
| elt :: :: elt {{ tex \in }}
| /= :: :: neq {{ tex \neq }}
| literalType :: :: literalType {{ tex \textsf{literalType} }}
| |-> :: :: mapsto {{ tex \mapsto }}
| <- :: :: assignment {{ tex \leftarrow }}
| @ :: :: marker {{ tex }}
| inits :: :: inits {{ tex \textsf{inits} }}
| ~> :: :: squigarrow {{ tex \rightsquigarrow }}
| tyConKind :: :: tyConKind {{ tex \mathop{\textsf{tyConKind} } }}
| empty :: :: empty {{ tex \cdot }}
| length :: :: length {{ tex \mathsf{length} }}
| <: :: :: subkind {{ tex \mathop{ {<} {:}\, } }}
| ~ :: :: eq {{ tex \sim }}
| tyConArity :: :: tyConArity {{ tex \textsf{tyConArity} }}
| dataConTyCon :: :: dataConTyCon {{ tex \textsf{dataConTyCon} }}
| dataConRepType :: :: dataConRepType {{ tex \textsf{dataConRepType} }}
| isNewTyCon :: :: isNewTyCon {{ tex \textsf{isNewTyCon} }}
| Constraint :: :: Constraint {{ tex \textsf{Constraint} }}
| no_conflict :: :: no_conflict {{ tex \textsf{no\_conflict} }}
| apart :: :: apart {{ tex \textsf{apart} }}
| unify :: :: unify {{ tex \textsf{unify} }}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Formulae %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
formula :: 'formula_' ::=
| judgement :: :: judgement
| formula1 ... formulai :: :: dots
| G1 = G2 :: :: context_rewrite
| t1 = t2 :: :: type_rewrite
| t1 /= t2 :: :: type_inequality
| e1 /=e e2 :: :: expr_inequality
{{ tex [[e1]] \neq [[e2]] }}
| 0 <= ind1 < ind2 :: :: in_bounds
{{ tex 0 \leq [[ind1]] < [[ind2]] }}
| g1 = g2 :: :: co_rewrite
| no_duplicates </ zi // i /> :: :: no_duplicates_name
| no_duplicates </ bindingi // i /> :: :: no_duplicates_binding
| not formula :: :: not
| isUnLiftedTyCon T :: :: isUnLiftedTyCon
| formula1 /\ formula2 :: :: and
| formula1 \/ formula2 :: :: or
| ( formula ) :: :: parens
| n elt G :: :: context_inclusion
| vars1 = vars2 :: :: vars_rewrite
| </ Gi @ // i /> = inits ( </ nj // j /> ) :: :: context_folding
| </ substi @ // i /> = inits ( </ [ nj |-> tj ] // j /> ) :: :: subst_folding
| ind1 = ind2 :: :: eq_ind
| ind1 < ind2 :: :: lt
| G |- tylit lit : k :: :: lintTyLit
{{ tex [[G]] \labeledjudge{tylit} [[lit]] : [[k]] }}
| isNewTyCon T :: :: isNewTyCon
| k1 elt { </ ki // , // i /> } :: :: kind_elt
| e is_a_type :: :: is_a_type
{{ tex \exists \tau \text{ s.t.~} [[e]] = \tau }}
| t is_a_coercion :: :: is_a_coercion
{{ tex \exists \tau_1, \tau_2, \kappa \text{ s.t.~} [[t]] =
\tau_1 \mathop{ {\sim}_{\#}^{\kappa} } \tau_2 }}
| axBranch1 = axBranch2 :: :: branch_rewrite
| C1 = C2 :: :: axiom_rewrite
| apart ( </ ti // i /> , </ sj // j /> ) :: :: apart
| unify ( </ ti // i /> , </ sj // j /> ) = subst :: :: unify
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Subrules and Parsing %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
parsing
TyCon_FunTyCon right Type_AppTy
TyCon_PrimTyCon right Type_AppTy
TyCon_AlgTyCon right Type_AppTy
TyCon_PromotedDataCon right Type_AppTy
TyCon_PromotedTyCon right Type_AppTy
TyCon_FunTyCon right Coercion_AppCo
TyCon_PrimTyCon right Coercion_AppCo
TyCon_AlgTyCon right Coercion_AppCo
TyCon_PromotedDataCon right Coercion_AppCo
TyCon_PromotedTyCon right Coercion_AppCo
Subst_Mapping <= Type_TySubstList
Subst_List <= Type_TySubstList
Subst_Mapping <= Type_TySubstListPost
|
