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|
metavar ident , x ::=
{{ isa string }} {{ coq nat }} {{ hol string }} {{ ocaml string }} {{ lex [A-Z]+ }} {{ coq-equality }}
grammar
exp , e :: Exp_ ::=
| x :: :: ident
| () :: :: unit
| ( exp , exp' ) :: :: pair
| function x : type -> exp :: :: 'fun'
| exp exp' :: :: app
% | :: :: empty
type , t :: Typ_ ::=
| unit :: :: unit
| type * type' :: :: pair
| type -> type' :: :: 'fun'
E :: E_ ::= {{ isa (ident*type) list }} {{ coq list (ident*type) }} {{ hol (ident#type) list }}
| empty :: :: empty
{{ isa [] }}
{{ coq nil }}
{{ hol [] }}
| E , x : t :: :: ident
{{ isa (([[x]],[[t]])#[[E]]) }}
{{ coq (cons ([[x]],[[t]]) [[E]]) }}
{{ hol (([[x]],[[t]])::[[E]]) }}
| E , x : t , E' :: :: ident2
{{ isa ([[E']] @ ([[x]],[[t]])#[[E]]) }}
{{ coq (app [[E']] (cons ([[x]],[[t]]) [[E]])) }}
{{ hol ( [[E']] ++ ([[x]],[[t]])::[[E]] )}}
formula :: formula_ ::=
| judgement :: :: judgement
| not ( formula ) :: :: not
{{ isa ~( [[formula]] ) }}
{{ coq not([[formula]]) }}
{{ hol ~( [[formula]] ) }}
{{ ocaml not([[formula]]) }}
| x in dom ( E ) :: M :: indom
{{ isa list_ex ( \<lambda>(x',y'). [[x]]=x') [[E]] }}
{{ ocaml List.exists (fun (x',y') -> [[x]]=x') [[E]] }}
{{ coq (indom [[x]] [[E]]) }}
{{ hol (EXISTS ( \(x',y'). [[x]]=x') [[E]]) }} % TODO
terminals :: 'terminals_' ::=
| \ :: :: lambda {{ tex \lambda }}
| --> :: :: red {{ tex \longrightarrow }}
| -> :: :: arrow {{ tex \rightarrow }}
| |- :: :: turnstile {{ tex \vdash }}
| in :: :: in {{ tex \in }}
embed
{{ coq
Fixpoint indom (x:ident) (e:E) { struct e } : Prop :=
match e with
| nil => False
| cons (x',y') tl => if eq_ident x x' then True else indom x tl
end. }}
{{ isa
primrec
order :: "type => nat"
where
"order [[unit]] = 0"
| "order [[t*t']] = max (order [[t]]) (order [[t']])"
| "order [[t->t']] = max (1+order [[t]]) (order [[t']])"
}}
{{ tex
A test of some filtered embedded latex:
$Foo( [[ E,x:t |- ok ]] )$
}}
% defns
% Jin :: '' ::=
% defn
% x in dom ( E ) :: :: xinE :: xinE_ by
%
% -------------------- :: 1
% x in dom ( E )
%
% x in dom(E)
% -------------------- :: 2
% x in dom(E,x':t)
% this type system doesn't allow any shadowing
defns
Jtype :: '' ::=
defn
E |- ok :: :: Eok :: Eok_ by
----------- :: empty
empty |- ok
E |- ok
not (x in dom(E))
-------------- :: ident
E,x:t |- ok
defn
E |- e : t :: :: Eet :: Eet_ by
E,x:t,E' |- ok
--------------- :: ident
E,x:t,E' |- x:t
E |- ok
---------------- :: unit
E |- () : unit
E |- e1:t1
E |- e2:t2
------------------- :: pair
E |- (e1,e2):t1*t2
E,x:t1 |- e :t2
---------------------- :: 'fun'
E |- function x:t1 -> e : t1->t2
E |- e : t1->t2
E |- e': t1
------------------ :: app
E |- e e' : t2
>>
| let pat = exp in exp' :: :: let
pat , p :: Pat_ ::=
x :: :: ident
| _ :: :: wildcard
| () :: :: unit
| ( pat , pat' ) :: :: pair
<<
>>
|- p : t gives E'
E |- e : t
E,E' |- e' : t'
------------------------ :: let
E |- let p=e in e' : t'
defn
|- p : t gives E' :: :: Ept :: Ept_ by
----------------------- :: ident
|- x:t gives empty,x:t
----------------------- :: wildcard
|- _:t gives empty
------------------------ :: unit
|- () : unit gives empty
|- p1:t1 gives E1
|- p2:t2 gives E2
-------------------------- :: pair
|- (p1,p2):t1*t2 gives E1,E2
<<
|
