diff options
Diffstat (limited to 'language')
| -rw-r--r-- | language/Makefile | 26 | ||||
| -rw-r--r-- | language/l2.ott | 2392 |
2 files changed, 2418 insertions, 0 deletions
diff --git a/language/Makefile b/language/Makefile new file mode 100644 index 00000000..6576e3d8 --- /dev/null +++ b/language/Makefile @@ -0,0 +1,26 @@ +#OTTLIB=/Users/sowens/ott/hol +OTTLIB=$(dir $(shell which ott))../hol + +all: l2.pdf + +l2.pdf: l2.tex + pdflatex l2.tex + +l2Theory.uo: l2Script.sml + Holmake --qof -I $(OTTLIB) l2Theory.uo + +l2.tex ../src/ast.ml l2Script.sml: l2.ott + ott -ocaml_include_terminals true -o l2.tex -o l2.ml -o l2Script.sml -picky_multiple_parses true l2.ott + + #rm -f ../src/ast.ml +# chmod a-w ../src/ast.ml + +l2.lem: l2.ott + ott -o l2.lem -picky_multiple_parses true l2.ott + + +clean: + rm -rf *~ + -rm -rf *.uo *.ui l2Theory.sig l2Theory.sml l2.tex l2Script.sml l2.aux l2.log l2.dvi l2.ps l2_unwrapped.tex .HOLMK +#l2.sys l2 library/lib_cache + diff --git a/language/l2.ott b/language/l2.ott new file mode 100644 index 00000000..309ab7ec --- /dev/null +++ b/language/l2.ott @@ -0,0 +1,2392 @@ +indexvar n , i , j , k ::= + {{ phantom }} + {{ com Index variables for meta-lists }} + +metavar num ::= + {{ phantom }} + {{ lex numeric }} + {{ ocaml terminal * int }} + {{ hol num }} + {{ lem (terminal * num) }} + {{ com Numeric literals }} + +% metavar nat ::= +% {{ phantom }} +% {{ lex numeric }} +% {{ ocaml int }} +% {{ hol num }} +% {{ lem num }} +% {{ com Internal literal numbers }} + +metavar hex ::= + {{ phantom }} + {{ lex numeric }} + {{ ocaml terminal * string }} + {{ lem (terminal * string) }} + {{ com Bit vector literal, specified by C-style hex number }} + +metavar bin ::= + {{ phantom }} + {{ lex numeric }} + {{ ocaml terminal * string }} + {{ lem (terminal * string) }} + {{ com Bit vector literal, specified by C-style binary number }} + +metavar string ::= + {{ phantom }} + {{ ocaml terminal * Ulib.UTF8.t }} + {{ lem (terminal * string) }} + {{ hol string }} + {{ com String literals }} + +metavar regexp ::= + {{ phantom }} + {{ ocaml terminal * string }} + {{ lem (terminal * string) }} + {{ hol string }} + {{ com Regular expresions, as a string literal }} + +embed +{{ ocaml + +type text = Ulib.Text.t + +type l = + | Unknown + | Trans of string * l option + | Range of Lexing.position * Lexing.position + +exception Parse_error_locn of l * string + +type ml_comment = + | Chars of Ulib.Text.t + | Comment of ml_comment list + +type lex_skip = + | Com of ml_comment + | Ws of Ulib.Text.t + | Nl + +type lex_skips = lex_skip list option + +let pp_lex_skips ppf sk = + match sk with + | None -> () + | Some(sks) -> + List.iter + (fun sk -> + match sk with + | Com(ml_comment) -> + (* TODO: fix? *) + Format.fprintf ppf "(**)" + | Ws(r) -> + Format.fprintf ppf "%s" (Ulib.Text.to_string r) + | Nl -> Format.fprintf ppf "\\n") + sks + +let combine_lex_skips s1 s2 = + match (s1,s2) with + | (None,_) -> s2 + | (_,None) -> s1 + | (Some(s1),Some(s2)) -> Some(s2@s1) + +type terminal = lex_skips + +}} + +embed +{{ lem +open Pmap +open Pervasives + +type l = + | Unknown + | Trans of string * option l + | Range of num * num + +type lex_skip = + | Com of string + | Ws of string + | Nl + +type lex_skips = option (list lex_skip) +type terminal = lex_skips + +val disjoint : forall 'a . set 'a -> set 'a -> bool +let disjoint s1 s2 = + let diff = s1 inter s2 in + diff = Pervasives.empty + +val disjoint_all : forall 'a. list (set 'a) -> bool +let rec disjoint_all ls = match ls with + | [] -> true + | [a] -> true + | a::b::rs -> (disjoint a b) && (disjoint_all (b::rs)) +end + +val duplicates : forall 'a. list 'a -> list 'a + +val union_map : forall 'a 'b. map 'a 'b -> map 'a 'b -> map 'a 'b + +val set_from_list : forall 'a. list 'a -> set 'a + +val subst : forall 'a. list 'a -> list 'a -> bool + +}} + +metavar x , y , z ::= + {{ ocaml terminal * text }} + {{ lem terminal * string }} + {{ hol string }} + {{ com Variables }} + {{ ocamlvar "[[x]]" }} + {{ lemvar "[[x]]" }} + +metavar ix ::= + {{ lex alphanum }} + {{ ocaml terminal * text }} + {{ lem terminal * string }} + {{ hol string }} + {{ com Variables }} + {{ ocamlvar "[[ix]]" }} + {{ lemvar "[[ix]]" }} + + + +grammar + +l :: '' ::= {{ phantom }} + {{ ocaml l }} + {{ lem l }} + {{ hol unit }} + {{ com Source locations }} + | :: :: Unknown + {{ ocaml Unknown }} + {{ lem Unknown }} + {{ hol () }} + +x_l {{ tex \ottnt{x}^{l} }} , y_l {{ tex \ottnt{y}^{l} }} , z_l {{ tex \ottnt{z}^{l} }} , name :: '' ::= + {{ com Location-annotated names }} + | x l :: :: X_l + | ( ix ) l :: :: PreX_l + {{ com Remove infix status }} + +ix_l {{ tex \ottnt{ix}^{l} }} :: '' ::= + {{ com Location-annotated infix names }} + | ix l :: :: SymX_l + | ` x ` l :: :: InX_l + {{ com Add infix status }} + +embed +{{ ocaml +let xl_to_l = function + | X_l(_,l) -> l + | PreX_l(_,_,_,l) -> l + +let ixl_to_l = function + | SymX_l(_,l) -> l + | InX_l(_,_,_,l) -> l +}} +{{ lem + +(*let xl_to_l = function + | X_l(_,l) -> l + | PreX_l(_,_,l) -> l +end + +let ixl_to_l = function + | SymX_l(_,l) -> l + | InX_l(_,_,_,l) -> l +end*) + +}} + +grammar + +a {{ tex \alpha }} :: '' ::= + {{ ocaml terminal * text }} + {{ lem terminal * string }} + {{ hol string }} + {{ com Type variables }} + | ' x :: :: A + {{ hol [[x]] }} + {{ ocaml [[x]] }} + {{ lem [[x]] }} + +a_l {{ tex \alpha^{l} }} :: '' ::= + {{ com Location-annotated type variables }} + | a l :: :: A_l + +N :: '' ::= + {{ ocaml terminal * text }} + {{ lem terminal * string }} + {{ hol string }} + {{ com numeric variables }} + | ' ' x :: :: N + {{ hol [[x]] }} + {{ ocaml [[x]] }} + {{ lem [[x]] }} + +N_l {{ tex N^{l} }} :: '' ::= + {{ com Location-annotated numeric variables }} + | N l :: :: N_l + + +EN :: '' ::= + {{ ocaml terminal * text }} + {{ lem terminal * string }} + {{ hol string }} + {{ com endianness variables }} + | ' ' ' x :: :: EN + {{ hol [[x]] }} + {{ ocaml [[x]] }} + {{ lem [[x]] }} + +EN_l {{ tex EN^{l} }} :: '' ::= + {{ com Location-annotated endianness variables }} + | EN l :: :: EN_l + + +id :: '' ::= + {{ com Not-very-long identifers }} + | x_l :: :: Id + +tnv :: '' ::= + {{ com Union of type variables and nexp type variables, without locations }} + | a :: :: Av + | N :: :: Nv + | EN :: :: ENv + +tnvar {{ tex tnvar^{l} }} :: '' ::= + {{ com Union of type variables and nexp type variables, with locations }} + | a_l :: :: Avl + | N_l :: :: Nvl + | EN_l :: :: ENvl + +tnvs :: '' ::= {{ phantom }} + {{ hol tnv list }} + {{ ocaml tnv list }} + {{ lem list tnv }} + {{ com Type variable lists }} + | tnv1 .. tnvn :: :: Tvars + {{ hol [[tnv1..tnvn]] }} + {{ ocaml [[tnv1..tnvn]] }} + {{ lem [[tnv1..tnvn]] }} + +tnvars {{ tex tnvars^{l} }} :: '' ::= {{ phantom }} + {{ hol tnvar list }} + {{ ocaml tnvar list }} + {{ lem list tnvar }} + {{ com Type variable lists }} + | tnvar1 .. tnvarn :: :: tnvars_l + {{ hol [[tnvar1..tnvarn]] }} + {{ ocaml [[tnvar1..tnvarn]] }} + {{ lem [[tnvar1..tnvarn]] }} + +base_kind_aux :: 'BK_' ::= + {{ com base kinds}} + | Type :: :: type + | Nat :: :: nat + | Endian :: :: endian + +base_kind :: '' ::= + {{ com location-annotated base kinds }} + | base_kind_aux l :: :: Base_kind_l + +kind_aux :: 'K_' ::= + {{ com kinds}} + | base_kind1 -> ... -> base_kindn :: :: kind +% we'll never use ...-> Nat + +kind :: '' ::= + {{ com location-annotated kinds}} + | kind_aux l :: :: Kind_l + + +nexp_aux :: 'Nexp_' ::= + {{ com Numerical expressions for specifying vector lengths and indexes}} + | N :: :: var + | num :: :: constant + | nexp1 * nexp2 :: :: times {{ com must be linear after normalisation... }} + | nexp1 + nexp2 :: :: sum + | 2 ^ nexp :: :: exp + | ( nexp ) :: S :: paren {{ icho [[nexp]] }} + +nexp :: '' ::= + {{ com Location-annotated vector lengths }} + | nexp_aux l :: :: Length_l + + +end_aux :: 'End_' ::= + {{ com Numerical expressions for specifying vector lengths and indexes}} + | EN :: :: var + | inc :: :: inc + | dec :: :: dec + | ( end ) :: S :: paren {{ icho [[end]] }} + +end :: '' ::= + {{ com Location-annotated vector lengths }} + | end_aux l :: :: End_l + + + +typ_aux :: 'Typ_' ::= + {{ com Constructors (of all kinds, not just Type) }} + | _ :: :: wild + {{ com Unspecified type }} + | a_l :: :: var + {{ com Type variables }} + | typ1 -> typ2 :: :: fn + {{ com Function types -- first-order only}} +% TODO: build first-order restriction into AST or just into type rules? + | typ1 * .... * typn :: :: tup + {{ com Tuple types }} + | nexp :: :: nexps + {{ com here to permit applications to nexps, otherwise not accepted }} + | id typ1 .. typn :: :: app + {{ com Type applications }} + | ( typ ) + :: S :: paren {{ icho [[typ]] }} + +% plus more for l-value/r-value pairs, as introduced by the L3 'compound' declarations ... ref typ + +typ_sugar :: 'TypSugar_' ::= + {{ com library types and syntactic sugar }} +% boring base types: + | bool :: :: bool + | bit :: :: bit +% experimentally trying with two distinct types there... + | nat :: :: nat + | string :: :: string +% finite subranges of nat + | enum nexp1 nexp2 end :: :: enum {{ com type of the natural numbers from [[nexp2]] to [[nexp2]]+[[nexp1]]-1, ordered according to [[end]] }} + | [ nexp ] :: :: enum1 {{ com sugar for \texttt{enum nexp 0 inc} }} + | [ nexp : nexp' ] :: :: enum2 {{ com sugar for \texttt{enum (nexp'-nexp+1) nexp inc} or \texttt{enum (nexp-nexp'+1) nexp' dec} }} +% total maps or vectors + | enummap nexp1 nexp2 end typ :: :: enummap +% probably some sugar for enummap types, using [ ] similarly to enums: + | typ [ nexp ] :: :: enummap2 + | typ [ nexp : nexp' ] :: :: enummap3 +% ...so bit [ nexp ] etc is just an instance of that + | list typ :: :: list + | set typ :: :: set + + + +typ :: '' ::= + {{ com Location-annotated types }} + | typ_aux l :: :: Typ_l + +parsing + +Typ_tup <= Typ_tup +Typ_fn right Typ_fn +Typ_fn <= Typ_tup +%Typ_fn right Typ_app1 +%Typ_tup right Typ_app1 + +grammar + +nexp_constraint_aux :: '' ::= + {{ com Whether a vector is bounded or fixed size }} + | nexp = nexp' :: :: fixed + | nexp >= nexp' :: :: bounded_ge + | nexp '<=' nexp' :: :: bounded_le + | nexp 'IN' { num1 , ... , numn } :: :: ad_hoc_nat_set_bounded + +% Note only constants in a finite-set-bound, as we don't think we need +% anything more + +nexp_constraint :: '' ::= + {{ com Location-annotated nexp range }} + | nexp_constraint_aux l :: :: range_l + + +typquant :: 'TQ_' ::= + | forall tnvar1 .. tnvarn . nexp_constraint1 , .. , nexp_constrainti => :: :: Ts +%TODO add sugar here for no constraints and no constraints-or-tnvars +% | forall tnvar1 ... tnvarn . typ :: S :: Ts_no_constraint +% +% | typ :: S :: Ts_no_forall + +typschm :: 'TS_' ::= + {{ com Type schemes }} + | typquant typ :: :: Ts + + +grammar +ctor_def :: '' ::= + {{ com Datatype definition clauses }} + | x_l : typschm :: :: Cte +% but we could get away with disallowing constraints in typschm, we +% think - if it's useful to do that + + +enumeration_flag_opt :: 'Enum_' ::= + | :: :: empty + | enum :: :: enum + +tdefbody :: 'Te_' ::= + {{ com Type definition bodies }} + | typschm :: :: abbrev + {{ com Type abbreviations }} + | typquant <| x_l1 : typ1 ; ... ; x_ln : typn semi_opt |> :: :: record + {{ com Record types }} + | enumeration_flag_opt '|' ctor_def1 '|' ... '|' ctor_defn :: :: variant + {{ com Variant types }} + +naming_scheme_opt {{ tex \ottnt{name}^{?} }} :: 'Name_sect_' ::= + {{ com Optional variable-naming-scheme specification for variables of defined type }} + | :: :: none + | [ name = regexp ] :: :: name + +td :: '' ::= + {{ com Type definitions }} + | type x_l : kind naming_scheme_opt = tdefbody :: :: Td +% | enumeration x_l naming_scheme_opt = tdefbody :: :: Td2 +% the enumeration is sugar for something that uses an enum flag, where the type system will restrict the tdefbody to be a simple enum... + + + +%... | x_l tnvars naming_scheme_opt = texp :: S :: Td + + +% eg t 'a ''n 'b [name="a*"] = ('a * 'b * (enum 0 ''n)) +% slightly odd that we don't currently allow constraints there + + + + +grammar + +lit_aux :: 'L_' ::= + {{ com Literal constants }} + | true :: :: true + | false :: :: false + | num :: :: num + | hex :: :: hex + {{ com hex and bin are constant bit vectors, entered as C-style hex or binaries }} + | bin :: :: bin + | string :: :: string + | ( ) :: :: unit + | bitzero :: :: zero + {{ com bitzero and bitone are constant bits, if commonly used we will consider overloading 0 and 1 }} + | bitone :: :: one + +lit :: '' ::= + | lit_aux l :: :: Lit_l + {{ com Location-annotated literal constants }} + +semi_opt {{ tex \ottnt{;}^{?} }} :: 'semi_' ::= {{ phantom }} + {{ ocaml terminal * bool }} + {{ lem (terminal * bool) }} + {{ hol bool }} + {{ com Optional semi-colons }} + | :: :: no + {{ hol F }} + {{ ocaml false }} + {{ lem false }} + | ';' :: :: yes + {{ hol T }} + {{ ocaml true }} + {{ lem true }} + + +pat_aux :: 'P_' ::= + {{ com Patterns }} + | _ :: :: wild + {{ com Wildcards }} + | ( pat as x_l ) :: :: as + {{ com Named patterns }} + | ( pat : typ ) :: :: typ + {{ com Typed patterns }} + | id pat1 .. patn :: :: app + {{ com Single variable and constructor patterns }} + | <| fpat1 ; ... ; fpatn semi_opt |> :: :: record + {{ com Record patterns }} +%Patterns for vectors + + | [| pat1 ; .. ; patn semi_opt |] :: :: vector + {{ com Vector patterns }} + + | [| pat1 .. patn |] :: :: vectorC + {{ com Concatenated vector patterns }} + + | ( pat1 , .... , patn ) :: :: tup + {{ com Tuple patterns }} + | [ pat1 ; .. ; patn semi_opt ] :: :: list + {{ com List patterns }} + | ( pat ) :: :: paren + | pat1 '::' pat2 :: :: cons + {{ com Cons patterns }} + | x_l '+' num :: :: num_add + {{ com constant addition patterns }} + | lit :: :: lit + {{ com Literal constant patterns }} + +pat :: '' ::= + {{ com Location-annotated patterns }} + | pat_aux l :: :: Pat_l + +fpat :: '' ::= + {{ com Field patterns }} + | id = pat l :: :: Fpat + +parsing +P_app <= P_app +P_app <= P_as + +grammar + +bar_opt {{ tex \ottkw{|}^{?} }} :: 'bar_' ::= {{ phantom }} + {{ ocaml terminal * bool }} + {{ lem (terminal * bool) }} + {{ hol bool }} + {{ com Optional bars }} + | :: :: no + {{ hol F }} + {{ ocaml false }} + {{ lem false }} + | '|' :: :: yes + {{ hol T }} + {{ ocaml true }} + {{ lem true }} + +exp_aux :: '' ::= + {{ com Expressions }} + | id :: :: Ident + {{ com Identifiers }} + | N :: :: Nvar + {{ com nexp var, has type num }} + | exp1 exp2 :: :: App + {{ com Function applications }} + | exp1 ix_l exp2 :: :: Infix + {{ com Infix applications }} + | <| fexps |> :: :: Record + {{ com Records }} + | <| exp with fexps |> :: :: Recup + {{ com Functional update for records }} + | exp . id :: :: Field + {{ com Field projection for records }} + +%Expressions for creating and accessing vectors + | [| exp1 ; .. ; expn semi_opt |] :: :: Vector + {{ com Vector instantiation }} + + | exp .( nexp ) :: :: VAccess + {{ com Vector access }} + +% PS '..' or . . ? + | exp .( nexp1 '..' nexp2 ) :: :: VAccessR + {{ com Subvector extraction }} + + +% map : forall 'x 'y ''N. ('x -> 'y) -> vector ''N 'x -> vector ''N 'y +% zip : forall 'x 'y ''N. vector ''N 'x -> vector ''N 'y -> vector ''N ('x*'y) +% foldl : forall 'x 'y ''N. ('x 'y -> 'y) -> vector ''N 'x -> 'y -> 'y +% foldr : forall 'x 'y ''N. ('x 'y -> 'y) -> 'y -> vector ''N 'x -> 'y +% foldmap : forall 'x 'y 'z ''N. ((x,y) -> (x,z)) -> x -> vector ''N y -> vector ''N z +%(or unzip) + +% and maybe with nice syntax + + | match exp with bar_opt pexp1 '|' ... '|' pexpn l end :: :: Case + {{ com Pattern matching expressions }} + | ( exp : typ ) :: :: Typed + {{ com Type-annotated expressions }} + | let letbind in exp :: :: Let + {{ com Let expressions }} + | ( exp1 , .... , expn ) :: :: Tup + {{ com Tuples }} + | [ exp1 ; .. ; expn semi_opt ] :: :: Elist + {{ com Lists }} + | ( exp ) :: :: Paren + | begin exp end :: :: Begin + {{ com Alternate syntax for $\ottnt(exp)$ }} + | if exp1 then exp2 else exp3 :: :: If + {{ com Conditionals }} + | exp1 '::' exp2 :: :: Cons + {{ com Cons expressions }} + | lit :: :: Lit + {{ com Literal constants }} + +exp :: '' ::= + {{ com Location-annotated expressions }} + | exp_aux l :: :: Expr_l + +fexp :: '' ::= + {{ com Field-expressions }} + | id = exp l :: :: Fexp + +fexps :: '' ::= + {{ com Field-expression lists }} + | fexp1 ; ... ; fexpn semi_opt l :: :: Fexps + +pexp :: '' ::= + {{ com Pattern matches }} + | pat -> exp l :: :: Patexp + +psexp :: '' ::= + {{ com Multi-pattern matches }} + | pat1 ... patn -> exp l :: :: Patsexp + +tannot_opt {{ tex \ottnt{tannot}^? }} :: 'Typ_annot_' ::= + {{ com Optional type annotations }} + | :: :: none + | : typ :: :: some + +funcl_aux :: '' ::= + {{ com Function clauses }} + | x_l pat1 ... patn tannot_opt = exp :: :: Funcl + +letbind_aux :: '' ::= + {{ com Let bindings }} + | pat tannot_opt = exp :: :: Let_val + {{ com Value bindings }} + | funcl_aux :: :: Let_fun + {{ com Function bindings }} + +letbind :: '' ::= + {{ com Location-annotated let bindings }} + | letbind_aux l :: :: Letbind + +funcl :: '' ::= + {{ com Location-annotated function clauses }} + | funcl_aux l :: :: Rec_l + +parsing + +P_app right Let_val + +%P_app <= Fun + +%Fun right App +%Function right App +Case right App +Let right App + +%Fun <= Field +%Function <= Field +App <= Field +Case <= Field +Let <= Field + +App left App + +grammar + + + +val_def :: '' ::= + {{ com Value definitions }} + | let letbind :: :: Let_def + {{ com Non-recursive value definitions }} + | let rec funcl1 and ... and funcln :: :: Let_rec + {{ com Recursive function definitions }} + +val_spec :: '' ::= + {{ com Value type specifications }} + | val x_l : typschm :: :: Val_spec + +def_aux :: '' ::= + {{ com Top-level definitions }} + | type td1 and ... and tdn :: :: Type_def + {{ com Type definitions }} + | val_def :: :: Val_def + {{ com Value definitions }} + | val_spec :: :: Spec_def + {{ com Top-level type constraints }} + +def :: '' ::= + {{ com Location-annotated definitions }} + | def_aux l :: :: Def_l + +semisemi_opt {{ tex \ottkw{;;}^? }} :: 'semisemi_' ::= {{ phantom }} + {{ ocaml terminal * bool }} + {{ lem (terminal * bool) }} + {{ hol bool }} + {{ com Optional double-semi-colon }} + | :: :: no + {{ hol F }} + {{ ocaml false }} + {{ lem false }} + | ;; :: :: yes + {{ hol T }} + {{ ocaml true }} + {{ lem true }} + +defs :: '' ::= + {{ com Definition sequences }} + | def1 semisemi_opt1 .. defn semisemi_optn :: :: Defs + + +grammar + + +p :: 'Path_' ::= + {{ com Unique paths }} + | x1 . .. xn . x :: :: def + | __list :: :: list + {{ tex \ottkw{\_\_list} }} + | __bool :: :: bool + {{ tex \ottkw{\_\_bool} }} + | __num :: :: num + {{ tex \ottkw{\_\_num} }} + | __set :: :: set + {{ tex \ottkw{\_\_set} }} + | __string :: :: string + {{ tex \ottkw{\_\_string} }} + | __unit :: :: unit + {{ tex \ottkw{\_\_unit} }} + | __bit :: :: bit + {{ tex \ottkw{\_\_bit} }} + | __vector :: :: vector + {{ tex \ottkw{\_\_vector} }} +%TODO morally, delete the above - but what are the __ things for? +% cleaner to declare early in the library? + +t_subst {{ tex \ensuremath{\sigma} }} :: '' ::= {{ phantom }} + {{ hol (a # t) list }} + {{ lem list (tnv * t) }} + {{ com Type variable substitutions }} + | { tnv1 |-> t1 .. tnvn |-> tn } :: :: T_subst + {{ ocaml (assert false) }} + {{ lem ([[tnv1 t1 .. tnvn tn]]) }} + {{ hol ([[tnv1 t1 .. tnvn tn]]) }} + +t , u :: 'T_' ::= + {{ com Internal types }} + | a :: :: var + | t1 -> t2 :: :: fn + | t1 * .... * tn :: :: tup + | p t_args :: :: app + | ne :: :: len + | t_subst ( t ) :: M :: subst_app + {{ com Multiple substitutions }} + {{ ocaml (assert false) }} + {{ hol (t_subst_t [[t_subst]] [[t]]) }} + {{ lem (t_subst_t [[t_subst]] [[t]]) }} + | t_subst ( tnv ) :: M :: var_subst_app + {{ com Single variable substitution }} + {{ ocaml (assert false) }} + {{ hol (t_subst_tnv [[t_subst]] [[tnv]]) }} + {{ lem (t_subst_tnv [[t_subst]] [[tnv]]) }} + | curry ( t_multi , t ) :: M :: multifn + {{ com Curried, multiple argument functions }} + {{ ocaml (assert false) }} + {{ hol (FOLDR T_fn [[t]] [[t_multi]]) }} + {{ lem (List.fold_right T_fn [[t_multi]] [[t]]) }} + +ne :: 'Ne_' ::= + {{ com internal numeric expressions }} + | N :: :: var + | nat :: :: const + | ne1 * ne2 :: :: mult + | ne1 + ne2 :: :: add + | ( - ne ) :: :: unary + | normalize ( ne ) :: M :: normalize + {{ ocaml (assert false) }} + {{ hol ARB }} + {{ lem (normalize [[ne]] ) }} + | ne1 + ... + nen :: M :: addmany + {{ ocaml (assert false) }} + {{ hol ARB }} + {{ lem (sumation_nes [[ne1...nen]]) }} + | bitlength ( bin ) :: M :: cbin + {{ ocaml (asssert false) }} + {{ hol ARB }} + {{ lem (blength [[bin]]) }} + | bitlength ( hex ) :: M :: chex + {{ ocaml (assert false) }} + {{ hol ARB }} + {{ lem (hlength [[hex]]) }} + | length ( pat1 ... patn ) :: M :: cpat + {{ ocaml (assert false) }} + {{ hol ARB }} + {{ lem (Ne_const (List.length [[pat1...patn]])) }} + | length ( exp1 ... expn ) :: M :: cexp + {{ hol ARB }} + {{ ocaml (assert false) }} + {{ lem (Ne_const (List.length [[exp1...expn]])) }} + +t_args :: '' ::= + {{ com Lists of types }} + | t1 .. tn :: :: T_args + | t_subst ( t_args ) :: M :: T_args_subst_app + {{ com Multiple substitutions }} + {{ ocaml (assert false) }} + {{ hol (t_subst_t_args [[t_subst]] [[t_args]]) }} + {{ lem (t_subst_t_args [[t_subst]] [[t_args]]) }} + +t_multi :: '' ::= {{ phantom }} + {{ hol t list }} + {{ ocaml t list }} + {{ lem list t }} + {{ com Lists of types }} + | ( t1 * .. * tn ) :: :: T_multi + {{ hol [[t1..tn]] }} + {{ lem [[t1..tn]] }} + | t_subst ( t_multi ) :: M :: T_multi_subst_app + {{ com Multiple substitutions }} + {{ ocaml (assert false) }} + {{ hol (MAP (t_subst_t [[t_subst]]) [[t_multi]]) }} + {{ lem (List.map (t_subst_t [[t_subst]]) [[t_multi]]) }} + +nec :: '' ::= + {{ com Numeric expression constraints }} + | ne < nec :: :: lessthan + | ne = nec :: :: eq + | ne <= nec :: :: lteq + | ne :: :: base + +parsing +T_fn right T_fn +T_tup <= T_multi + +embed +{{ lem + +val t_subst_t : list (tnv * t) -> t -> t +val t_subst_tnv : list (tnv * t) -> tnv -> t +val ftv_t : t -> list tnv +val ftv_tm : list t -> list tnv +val ftv_s : list (p*tnv) -> list tnv +val compatible_overlap : list (x*t) -> bool + +(*TODO Should this normalize following the implementation? And blength and hlength need a means of implementation*) +let normalize n = n + +let blength (_,bit) = Ne_const 8 +let hlength (_,bit) = Ne_const 8 + +let rec sumation_nes nes = match nes with + | [ a; b] -> Ne_add a b + | x :: y -> Ne_add x (sumation_nes y) +end + +}} + +grammar + + +names :: '' ::= {{ phantom }} + {{ hol x set }} + {{ lem set x }} + {{ ocaml Set.Make(String).t }} + {{ com Sets of names }} + | { x1 , .. , xn } :: :: Names + {{ hol (LIST_TO_SET [[x1..xn]]) }} + {{ lem (set_from_list [[x1..xn]]) }} + +semC {{ tex \ensuremath{\mathcal{C} } }} :: '' ::= + {{ hol (p#tnv) list }} + {{ lem list (p*tnv) }} +% {{ com Typeclass constraint lists }} +% | ( p1 tnv1 ) .. ( pn tnvn ) :: :: SemC_concrete +% {{ hol ([[p1 tnv1..pn tnvn]]) }} +% {{ lem ([[p1 tnv1..pn tnvn]]) }} + +env_tag :: '' ::= + {{ com Tags for the (non-constructor) value descriptions }} +% | method :: :: method +% {{ com Bound to a method }} + | val :: :: spec + {{ com Specified with val }} + | let :: :: def + {{ com Defined with let or indreln }} + +v_desc :: 'V_' ::= + {{ com Value descriptions }} + | < forall tnvs . t_multi -> p , ( x of names ) > :: :: constr + {{ com Constructors }} + | < forall tnvs . semC => t , env_tag > :: :: val + {{ com Values }} + +f_desc :: 'F_' ::= + | < forall tnvs . p -> t , ( x of names ) > :: :: field + {{ com Fields }} + +embed +{{ hol +load "fmaptreeTheory"; +val _ = + Hol_datatype + `env_body = <| env_p : x|->p; env_f : x|->f_desc; env_v : x|->v_desc |>`; + +val _ = Define ` + env_union e1 e2 = + let i1 = item e1 in + let m1 = map e1 in + let i2 = item e2 in + let m2 = map e2 in + FTNode <| env_p:=FUNION i1.env_p i2.env_p; + env_f:=FUNION i1.env_f i2.env_f; + env_v:=FUNION i1.env_v i2.env_v |> + (FUNION m1 m2)`; +}} +{{ lem +type env = + | EnvEmp + | Env of (map x env) * (map x p) * (map x f_desc) * (map x v_desc) + +val env_union : env -> env -> env +let env_union e1 e2 = + match (e1,e2) with + | (EnvEmp,e2) -> e2 + | (e1,EnvEmp) -> e1 + | ((Env Em1 Ep1 Ef1 Ev1),(Env Em2 Ep2 Ef2 Ev2)) -> + Env(union_map Em1 Em2) (union_map Ep1 Ep2) (union_map Ef1 Ef2) (union_map Ev1 Ev2) +end + +}} + +grammar + +xs :: '' ::= {{ phantom }} + {{ hol string list }} + {{ lem list string }} + | x1 .. xn :: :: Xs + {{ hol [[x1..xn]] }} + {{ lem [[x1..xn]] }} + +%TODO: no clue what the following are: +S_c {{ tex {\ensuremath{ {\Sigma}^{\mathcal{C} } } } }} :: '' ::= {{ phantom }} + {{ hol (p#t) list }} + {{ lem list (p*t) }} + {{ com Typeclass constraints }} + | { ( p1 t1 ) , .. , ( pn tn ) } :: :: S_concrete + {{ hol [[p1 t1 .. pn tn]] }} + {{ lem [[p1 t1 .. pn tn]] }} + | S_c1 union .. union S_cn :: M :: S_union + {{ hol (FLAT [[S_c1..S_cn]]) }} + {{ lem (List.flatten [[S_c1..S_cn]]) }} + {{ ocaml assert false }} + +S_N {{ tex { \ensuremath{ {\Sigma}^{\mathcal{N} } } } }} :: '' ::= {{ phantom }} + {{ hol nec list }} + {{ lem list nec }} + {{ com nexp constraint lists }} + | { nec1 , .. , necn } :: :: Sn_concrete + {{ hol [[nec1 .. necn]] }} + {{ lem [[nec1 .. necn]] }} + | S_N1 union .. union S_Nn :: M :: SN_union + {{ hol (FLAT [[S_N1..S_Nn]]) }} + {{ lem (List.flatten [[S_N1..S_Nn]]) }} + {{ ocaml assert false }} + + +E :: '' ::= {{ phantom }} + {{ hol ((string,env_body) fmaptree) }} + + +%TODO: simplify by removing E_m throughout? And E_p?? + {{ lem env }} + {{ com Environments }} + | < E_m , E_p , E_f , E_x > :: :: E + {{ hol (FTNode <|env_p:=[[E_p]]; env_f:=[[E_f]]; env_v:=[[E_x]]|> ([[E_m]])) }} + {{ lem (Env [[E_m]] [[E_p]] [[E_f]] [[E_x]]) }} + | E1 u+ E2 :: M :: E_union + {{ hol (env_union [[E1]] [[E2]]) }} + {{ lem (env_union [[E1]] [[E2]]) }} + {{ ocaml assert false }} + | empty :: M :: E_empty + {{ hol (FTNode <|env_p:=FEMPTY; env_f:=FEMPTY; env_v:=FEMPTY|> FEMPTY) }} + {{ lem EnvEmp }} + {{ ocaml assert false }} + +E_x {{ tex \ottnt{E}^{\textsc{x} } }} :: 'E_x_' ::= {{ phantom }} + {{ hol (x|-> v_desc) }} + {{ lem map x v_desc }} + {{ com Value environments }} + | { x1 |-> v_desc1 , .. , xn |-> v_descn } :: :: concrete + {{ hol (FOLDR (\(k1,k2) E. E |+ (k1,k2)) FEMPTY [[x1 v_desc1 .. xn v_descn]]) }} + {{ lem (List.fold_right (fun (x,v) m -> Pmap.add x v m) [[x1 v_desc1 .. xn v_descn]] Pmap.empty) }} + | E_x1 u+ .. u+ E_xn :: M :: union + {{ hol (FOLDR FUNION FEMPTY [[E_x1..E_xn]]) }} + {{ lem (List.fold_right union_map [[E_x1..E_xn]] Pmap.empty) }} + {{ ocaml (assert false) }} + +E_f {{ tex \ottnt{E}^{\textsc{f} } }} :: 'E_f_' ::= {{ phantom }} + {{ hol (x |-> f_desc) }} + {{ lem map x f_desc }} + {{ com Field environments }} + | { x1 |-> f_desc1 , .. , xn |-> f_descn } :: :: concrete + {{ hol (FOLDR (\x E. E |+ x) FEMPTY [[x1 f_desc1 .. xn f_descn]]) }} + {{ lem (List.fold_right (fun (x,f) m -> Pmap.add x f m) [[x1 f_desc1 .. xn f_descn]] Pmap.empty) }} + | E_f1 u+ .. u+ E_fn :: M :: union + {{ hol (FOLDR FUNION FEMPTY [[E_f1..E_fn]]) }} + {{ lem (List.fold_right union_map [[E_f1..E_fn]] Pmap.empty) }} + {{ ocaml (assert false) }} + +E_m {{ tex \ottnt{E}^{\textsc{m} } }} :: 'E_m_' ::= {{ phantom }} + {{ hol (string |-> (string,env_body) fmaptree) }} + {{ lem map x env }} +% {{ com Module environments }} +% | { x1 |-> E1 , .. , xn |-> En } :: :: concrete +% {{ hol (FOLDR (\x E. E |+ x) FEMPTY [[x1 E1 .. xn En]]) }} +% {{ lem (List.fold_right (fun (x,e) m -> Pmap.add x e m) [[x1 E1 .. xn En]] Pmap.empty) }} +% +% _p {{ tex \ottnt{E}^{\textsc{p} } }} :: 'E_p_' ::= {{ phantom }} +% {{ hol (x |-> p) }} +% {{ lem map x p }} +% {{ com Path environments }} +% | { x1 |-> p1 , .. , xn |-> pn } :: :: concrete +% {{ hol (FOLDR (\x E. E |+ x) FEMPTY [[x1 p1 .. xn pn]]) }} +% {{ lem (List.fold_right (fun (x,p) m -> Pmap.add x p m) [[x1 p1 .. xn pn]] Pmap.empty) }} +% | E_p1 u+ .. u+ E_pn :: M :: union +% {{ hol (FOLDR FUNION FEMPTY [[E_p1..E_pn]]) }} +% {{ lem (List.fold_right union_map [[E_p1..E_pn]] Pmap.empty) }} +% +% {{ ocaml (assert false) }} + E_l {{ tex \ottnt{E}^{\textsc{l} } }} :: 'E_l_' ::= {{ phantom }} + {{ hol (x |-> t) }} + {{ lem map x t }} + {{ com Lexical bindings }} + | { x1 |-> t1 , .. , xn |-> tn } :: :: concrete + {{ hol (FOLDR (\x E. E |+ x) FEMPTY [[x1 t1 .. xn tn]]) }} + {{ lem (List.fold_right (fun (x,t) m -> Pmap.add x t m) [[x1 t1 .. xn tn]] Pmap.empty) }} + | E_l1 u+ .. u+ E_ln :: M :: union + {{ hol (FOLDR FUNION FEMPTY [[E_l1..E_ln]]) }} + {{ lem (List.fold_right union_map [[E_l1..E_ln]] Pmap.empty) }} + {{ ocaml (assert false) }} + +tc_abbrev :: 'Tc_abbrev_' ::= {{ phantom }} + {{ hol t option }} + {{ lem option t }} + {{ ocaml t option }} + {{ com Type abbreviations }} + | . t :: :: some + {{ hol (SOME [[t]]) }} + {{ lem (Some [[t]]) }} + | :: :: none + {{ hol NONE }} + {{ lem None }} + +tc_def :: '' ::= + {{ com Type and class constructor definitions }} + | tnvs tc_abbrev :: :: Tc_def + {{ com Type constructors }} + +TD {{ tex \ensuremath{\Delta} }} :: 'TD_' ::= {{ phantom }} + {{ hol p |-> tc_def }} + {{ lem map p tc_def }} + {{ com Type constructor definitions }} + | { p1 |-> tc_def1 , .. , pn |-> tc_defn } :: :: concrete + {{ hol (FOLDR (\x E. E |+ x) FEMPTY [[p1 tc_def1 .. pn tc_defn]]) }} + {{ lem (List.fold_right (fun (p,t) m -> Pmap.add p t m) [[p1 tc_def1 .. pn tc_defn]] Pmap.empty) }} + {{ ocaml (assert false) }} + | TD1 u+ TD2 :: M :: union + {{ hol (FUNION [[TD1]] [[TD2]]) }} + {{ lem (union_map [[TD1]] [[TD2]]) }} + {{ ocaml (assert false) }} + + + +D :: 'D_' ::= {{ phantom }} + {{ hol ((p |-> tc_def) # (p |-> x list) # (inst list)) }} + {{ lem tdefs}} + {{ com Global type definition store }} + | < TD , TC , I > :: :: concrete + {{ hol ([[TD]], [[TC]], [[I]]) }} + {{ lem (D [[TD]] [[TC]] [[I]]) }} + | D1 u+ D2 :: M :: union + {{ hol (case ([[D1]],[[D2]]) of ((x1,x2,x3),(y1,y2,y3)) => (FUNION x1 y1, FUNION x2 y2, x3 ++ y3)) }} + {{ lem (union_tcdefs [[D1]] [[D2]]) }} + {{ ocaml (assert false) }} + | empty :: M :: empty + {{ hol (FEMPTY, FEMPTY, []) }} + {{ lem DEmp }} + {{ ocaml assert false }} + +parsing +E_union left E_union + +embed +{{ lem +type tdefs = + | DEmp + | D of (map p tc_def) * (map p (list x)) * (set inst) + +val union_tcdefs : tdefs -> tdefs -> tdefs + +}} + +grammar + +terminals :: '' ::= + | >= :: :: geq + {{ tex \ensuremath{\geq} }} + {{ com \texttt{>=} }} + | '<=' :: :: leq + {{ tex \ensuremath{\leq} }} + {{ com \texttt{<=} }} + | -> :: :: arrow + {{ tex \ensuremath{\rightarrow} }} + {{ com \texttt{->} }} + | ==> :: :: Longrightarrow + {{ tex \ensuremath{\Longrightarrow} }} + {{ com \texttt{==>} }} + | <| :: :: startrec + {{ tex \ensuremath{\langle|} }} + {{ com \texttt{<|} }} + | |> :: :: endrec + {{ tex \ensuremath{|\rangle} }} + {{ com \texttt{|>} }} + | inter :: :: inter + {{ tex \ensuremath{\cap} }} + | union :: :: union + {{ tex \ensuremath{\cup} }} + | u+ :: :: uplus + {{ tex \ensuremath{\uplus} }} + | NOTIN :: :: notin + {{ tex \ensuremath{\not\in} }} + | SUBSET :: :: subset + {{ tex \ensuremath{\subset} }} + | NOTEQ :: :: noteq + {{ tex \ensuremath{\not=} }} + | emptyset :: :: emptyset + {{ tex \ensuremath{\emptyset} }} + | < :: :: lt + {{ tex \ensuremath{\langle} }} + | > :: :: gt + {{ tex \ensuremath{\rangle} }} + | |- :: :: vdash + {{ tex \ensuremath{\vdash} }} + | ' :: :: quote + {{ tex \mbox{'} }} + | |-> :: :: mapsto + {{ tex \ensuremath{\mapsto} }} + | gives :: :: gives + {{ tex \ensuremath{\triangleright} }} + | ~> :: :: leadsto + {{ tex \ensuremath{\leadsto} }} + | => :: :: Rightarrow + {{ tex \ensuremath{\Rightarrow} }} + | -- :: :: dashdash + {{ tex \mbox{--} }} + | empty :: :: empty + {{ tex \ensuremath{\epsilon} }} + + +formula :: formula_ ::= + | judgement :: :: judgement + + | formula1 .. formulan :: :: dots + +% | E_m ( x ) gives E :: :: lookup_m +% {{ com Module lookup }} +% {{ hol (FLOOKUP [[E_m]] [[x]] = SOME [[E]]) }} +% {{ lem (Pmap.find [[x]] [[E_m]]) = [[E]] }} +% +% | E_p ( x ) gives p :: :: lookup_p +% {{ com Path lookup }} +% {{ hol (FLOOKUP [[E_p]] [[x]] = SOME [[p]]) }} +% {{ lem Pmap.find [[x]] [[E_p]] = [[p]] }} + + | E_f ( x ) gives f_desc :: :: lookup_f + {{ com Field lookup }} + {{ hol (FLOOKUP [[E_f]] [[x]] = SOME [[f_desc]]) }} + {{ lem Pmap.find [[x]] [[E_f]] = [[f_desc]] }} + + | E_x ( x ) gives v_desc :: :: lookup_v + {{ com Value lookup }} + {{ hol (FLOOKUP [[E_x]] [[x]] = SOME [[v_desc]]) }} + {{ lem Pmap.find [[x]] [[E_x]] = [[v_desc]] }} + + | E_l ( x ) gives t :: :: lookup_l + {{ com Lexical binding lookup }} + {{ hol (FLOOKUP [[E_l]] [[x]] = SOME [[t]]) }} + {{ lem Pmap.find [[x]] [[E_l]] = [[t]] }} + +% | TD ( p ) gives tc_def :: :: lookup_tc +% {{ com Type constructor lookup }} +% {{ hol (FLOOKUP [[TD]] [[p]] = SOME [[tc_def]]) }} +% {{ lem Pmap.find [[p]] [[TD]] = [[tc_def]] }} +% +% | TC ( p ) gives xs :: :: lookup_class +% {{ com Type constructor lookup }} +% {{ hol (FLOOKUP [[TC]] [[p]] = SOME [[xs]]) }} +% {{ lem Pmap.find [[p]] [[TC]] = [[xs]] }} + + | dom ( E_m1 ) inter dom ( E_m2 ) = emptyset :: :: E_m_disjoint + {{ hol (DISJOINT (FDOM [[E_m1]]) (FDOM [[E_m2]])) }} + {{ lem disjoint (Pmap.domain [[E_m1]]) (Pmap.domain [[E_m2]]) }} + + | dom ( E_x1 ) inter dom ( E_x2 ) = emptyset :: :: E_x_disjoint + {{ hol (DISJOINT (FDOM [[E_x1]]) (FDOM [[E_x2]])) }} + {{ lem disjoint (Pmap.domain [[E_x1]]) (Pmap.domain [[E_x2]]) }} + + | dom ( E_f1 ) inter dom ( E_f2 ) = emptyset :: :: E_f_disjoint + {{ hol (DISJOINT (FDOM [[E_f1]]) (FDOM [[E_f2]])) }} + {{ lem disjoint (Pmap.domain [[E_f1]]) (Pmap.domain [[E_f2]]) }} + +% | dom ( E_p1 ) inter dom ( E_p2 ) = emptyset :: :: E_p_disjoint +% {{ hol (DISJOINT (FDOM [[E_p1]]) (FDOM [[E_p2]])) }} +% {{ lem disjoint (Pmap.domain [[E_p1]]) (Pmap.domain [[E_p2]]) }} +% + | disjoint doms ( E_l1 , .... , E_ln ) :: :: E_l_disjoint + {{ hol (FOLDR (\E b. case b of NONE => NONE | SOME s => if DISJOINT (FDOM +E) s then SOME (FDOM E UNION s) else NONE) (SOME {}) [[E_l1....E_ln]] <> NONE) }} + {{ lem disjoint_all (List.map Pmap.domain [[E_l1 .... E_ln]]) }} + {{ com Pairwise disjoint domains }} + + | disjoint doms ( E_x1 , .... , E_xn ) :: :: E_x_disjoint_many + {{ hol (FOLDR (\E b. case b of NONE => NONE | SOME s => if DISJOINT (FDOM +E) s then SOME (FDOM E UNION s) else NONE) (SOME {}) [[E_x1....E_xn]] <> NONE) }} + {{ lem disjoint_all (List.map Pmap.domain [[E_x1 .... E_xn]]) }} + {{ com Pairwise disjoint domains }} + + | compatible overlap ( x1 |-> t1 , .. , xn |-> tn ) :: :: E_l_compat + {{ hol (!__n __m. MEM __m [[x1 t1 .. xn tn]] /\ MEM __n [[x1 t1..xn tn]] /\ (FST __m = FST __n) ==> (SND __m = SND __n)) }} + {{ lem (compatible_overlap [[x1 t1 .. xn tn]]) }} + {{ com $(\ottnt{x}_i = \ottnt{x}_j) \ensuremath{\Longrightarrow} (\ottnt{t}_i = \ottnt{t}_j)$ }} + + | duplicates ( tnvs ) = emptyset :: :: no_dups_tnvs + {{ hol (ALL_DISTINCT [[tnvs]]) }} + {{ lem (duplicates [[tnvs]]) = [ ] }} + + | duplicates ( x1 , .. , xn ) = emptyset :: :: no_dups + {{ hol (ALL_DISTINCT [[x1..xn]]) }} + {{ lem (duplicates [[x1..xn]]) = [ ] }} + + | x NOTIN dom ( E_l ) :: :: notin_dom_l + {{ hol ([[x]] NOTIN FDOM [[E_l]]) }} + {{ lem Pervasives.not (Pmap.mem [[x]] [[E_l]]) }} + + | x NOTIN dom ( E_x ) :: :: notin_dom_v + {{ hol ([[x]] NOTIN FDOM [[E_x]]) }} + {{ lem Pervasives.not (Pmap.mem [[x]] [[E_x]]) }} + + | x NOTIN dom ( E_f ) :: :: notin_dom_f + {{ hol ([[x]] NOTIN FDOM [[E_f]]) }} + {{ lem Pervasives.not (Pmap.mem [[x]] [[E_f]]) }} + +% | p NOTIN dom ( TC ) :: :: notin_dom_tc +% {{ hol ([[p]] NOTIN FDOM [[TC]]) }} +% {{ lem Pervasives.not (Pmap.mem [[p]] [[TC]]) }} + + | p NOTIN dom ( TD ) :: :: notin_dom_td + {{ hol ([[p]] NOTIN FDOM [[TD]]) }} + {{ lem Pervasives.not (Pmap.mem [[p]] [[TD]]) }} + + | FV ( t ) SUBSET tnvs :: :: FV_t + {{ com Free type variables }} + {{ hol (LIST_TO_SET (ftv_t [[t]]) SUBSET LIST_TO_SET [[tnvs]]) }} + {{ lem subst (ftv_t [[t]]) [[tnvs]] }} + + | FV ( t_multi ) SUBSET tnvs :: :: FV_t_multi + {{ com Free type variables }} + {{ hol (LIST_TO_SET (FLAT (MAP ftv_t [[t_multi]])) SUBSET LIST_TO_SET [[tnvs]]) }} + {{ lem subst (ftv_tm [[t_multi]]) [[tnvs]] }} + + | FV ( semC ) SUBSET tnvs :: :: FV_semC + {{ com Free type variables }} + {{ hol (LIST_TO_SET (MAP SND [[semC]]) SUBSET LIST_TO_SET [[tnvs]]) }} + {{ lem subst (ftv_s [[semC]]) [[tnvs]] }} + + | inst 'IN' I :: :: inst_in + {{ hol (MEM [[inst]] [[I]]) }} + {{ lem ([[inst]] IN [[I]]) }} + + | ( p t ) NOTIN I :: :: notin_I + {{ hol (~?__semC__. MEM (Inst __semC__ [[p]] [[t]]) [[I]]) }} + {{ lem (Pervasives.not ((Inst [] [[p]] [[t]]) IN [[I]])) }} + + | E_l1 = E_l2 :: :: E_l_eqn + {{ ichl ([[E_l1]] = [[E_l2]]) }} + + | E_x1 = E_x2 :: :: E_x_eqn + {{ ichl ([[E_x1]] = [[E_x2]]) }} + + | E_f1 = E_f2 :: :: E_f_eqn + {{ ichl ([[E_f1]] = [[E_f2]]) }} + + | E1 = E2 :: :: E_eqn + {{ ichl ([[E1]] = [[E2]]) }} + + | TD1 = TD2 :: :: TD_eqn + {{ ichl ([[TD1]] = [[TD2]]) }} + + | TC1 = TC2 :: :: TC_eqn + {{ ichl ([[TC1]] = [[TC2]]) }} + + | I1 = I2 :: :: I_eqn + {{ ichl ([[I1]] = [[I2]]) }} + + | names1 = names2 :: :: names_eq + {{ ichl ([[names1]] = [[names2]]) }} + + | t1 = t2 :: :: t_eq + {{ ichl ([[t1]] = [[t2]]) }} + + | t_subst1 = t_subst2 :: :: t_subst_eq + {{ ichl ([[t_subst1]] = [[t_subst2]]) }} + + | p1 = p2 :: :: p_eq + {{ ichl ([[p1]] = [[p2]]) }} + + | xs1 = xs2 :: :: xs_eq + {{ ichl ([[xs1]] = [[xs2]]) }} + + | tnvs1 = tnvs2 :: :: tnvs_eq + {{ ichl ([[tnvs1]] = [[tnvs2]]) }} + +% Substitutions and freevars are not correctly generated for the OCaml ast.ml +%substitutions +%multiple t a :: t_subst +% +%freevars +%t a :: ftv + +%% % +%% % +%% % defns +%% % convert_tnvars :: '' ::= +%% % +%% % defn +%% % tnvars ~> tnvs :: :: convert_tnvars :: convert_tnvars_ +%% % by +%% % +%% % :convert_tnvar: tnvar1 ~> tnv1 .. :convert_tnvar: tnvarn ~> tnvn +%% % ------------------------------------------------------------ :: none +%% % tnvar1 .. tnvarn ~> tnv1 .. tnvn +%% % +%% % defn +%% % tnvar ~> tnv :: :: convert_tnvar :: convert_tnvar_ +%% % by +%% % +%% % ----------------------------------------------------------- :: a +%% % a l ~> a +%% % +%% % ---------------------------------------------------------- :: N +%% % N l ~> N +%% % +%% % +%% % defns +%% % look_m :: '' ::= +%% % +%% % defn +%% % E1 ( x_l1 .. x_ln ) gives E2 :: :: look_m :: look_m_ +%% % {{ com Name path lookup }} +%% % by +%% % +%% % ------------------------------------------------------------ :: none +%% % E() gives E +%% % +%% % E_m(x) gives E1 +%% % E1(</y_li//i/>) gives E2 +%% % ------------------------------------------------------------ :: some +%% % <E_m,E_p,E_f,E_x>(x l </y_li//i/>) gives E2 +%% % +%% % defns +%% % look_m_id :: '' ::= +%% % +%% % defn +%% % E1 ( id ) gives E2 :: :: look_m_id :: look_m_id_ +%% % {{ com Module identifier lookup }} +%% % by +%% % +%% % E1(</y_li//i/> x l1) gives E2 +%% % ------------------------------------------------------------ :: all +%% % E1(</y_li.//i/> x l1 l2) gives E2 +%% % +%% % defns +%% % look_tc :: '' ::= +%% % +%% % defn +%% % E ( id ) gives p :: :: look_tc :: look_tc_ +%% % {{ com Path identifier lookup }} +%% % by +%% % +%% % E(</y_li//i/>) gives <E_m,E_p,E_f,E_x> +%% % E_p(x) gives p +%% % ------------------------------------------------------------ :: all +%% % E(</y_li.//i/> x l1 l2) gives p +%% % +%% % +%% % defns +%% % check_t :: '' ::= +%% % +%% % defn +%% % TD |- t ok :: :: check_t :: check_t_ +%% % {{ com Well-formed types }} +%% % by +%% % +%% % ------------------------------------------------------------ :: var +%% % TD |- a ok +%% % +%% % TD |- t1 ok +%% % TD |- t2 ok +%% % ------------------------------------------------------------ :: fn +%% % TD |- t1 -> t2 ok +%% % +%% % TD |- t1 ok .... TD |- tn ok +%% % ------------------------------------------------------------ :: tup +%% % TD |- t1 * .... * tn ok +%% % +%% % TD(p) gives tnv1..tnvn tc_abbrev +%% % TD,tnv1 |- t1 ok .. TD,tnvn |- tn ok +%% % ------------------------------------------------------------ :: app +%% % TD |- p t1 .. tn ok +%% % +%% % +%% % defn +%% % TD , tnv |- t ok :: :: check_tlen :: check_tlen_ +%% % {{ com Well-formed type/nexps matching the application type variable }} +%% % by +%% % +%% % TD |- t ok +%% % ------------------------------------------------------------ :: t +%% % TD,a |- t ok +%% % +%% % ------------------------------------------------------------ :: len +%% % TD,N |- ne ok +%% % +%% % %TODO type equality isn't right; neither is type conversion +%% % +%% % defns +%% % teq :: '' ::= +%% % +%% % defn +%% % TD |- t1 = t2 :: :: teq :: teq_ +%% % {{ com Type equality }} +%% % by +%% % +%% % TD |- t ok +%% % ------------------------------------------------------------ :: refl +%% % TD |- t = t +%% % +%% % TD |- t2 = t1 +%% % ------------------------------------------------------------ :: sym +%% % TD |- t1 = t2 +%% % +%% % TD |- t1 = t2 +%% % TD |- t2 = t3 +%% % ------------------------------------------------------------ :: trans +%% % TD |- t1 = t3 +%% % +%% % TD |- t1 = t3 +%% % TD |- t2 = t4 +%% % ------------------------------------------------------------ :: arrow +%% % TD |- t1 -> t2 = t3 -> t4 +%% % +%% % TD |- t1 = u1 .... TD |- tn = un +%% % ------------------------------------------------------------ :: tup +%% % TD |- t1*....*tn = u1*....*un +%% % +%% % TD(p) gives a1..an +%% % TD |- t1 = u1 .. TD |- tn = un +%% % ------------------------------------------------------------ :: app +%% % TD |- p t1 .. tn = p u1 .. un +%% % +%% % TD(p) gives a1..an . u +%% % ------------------------------------------------------------ :: expand +%% % TD |- p t1 .. tn = {a1|->t1..an|->tn}(u) +%% % +%% % ne = normalize (ne') +%% % ---------------------------------------------------------- :: nexp +%% % TD |- ne = ne' +%% % +%% % +%% % defns +%% % convert_typ :: '' ::= +%% % +%% % defn +%% % TD , E |- typ ~> t :: :: convert_typ :: convert_typ_ +%% % {{ com Convert source types to internal types }} +%% % by +%% % +%% % % TODO : Can't allow things like type t = _, but it's useful to have things +%% % % like f (x : (_, int)) = snd x +%% % %TD |- t ok +%% % %------------------------------------------------------------ :: wild +%% % %TD,E |- _ l ~> t +%% % +%% % ------------------------------------------------------------ :: var +%% % TD,E |- a l' l ~> a +%% % +%% % TD,E |- typ1 ~> t1 +%% % TD,E |- typ2 ~> t2 +%% % ------------------------------------------------------------ :: fn +%% % TD,E |- typ1->typ2 l ~> t1->t2 +%% % +%% % TD,E |- typ1 ~> t1 .... TD,E |- typn ~> tn +%% % ------------------------------------------------------------ :: tup +%% % TD,E |- typ1 * .... * typn l ~> t1 * .... * tn +%% % +%% % TD,E |- typ1 ~> t1 .. TD,E |- typn ~> tn +%% % E(id) gives p +%% % TD(p) gives a1..an tc_abbrev +%% % ------------------------------------------------------------ :: app +%% % TD,E |- id typ1 .. typn l ~> p t1 .. tn +%% % +%% % |- nexp ~> ne +%% % ------------------------------------------------------------ :: nexp +%% % TD,E |- nexp ~> ne +%% % +%% % TD,E |- typ ~> t +%% % ------------------------------------------------------------ :: paren +%% % TD,E |- (typ) l ~> t +%% % +%% % +%% % TD,E |- typ ~> t1 +%% % TD |- t1 = t2 +%% % ------------------------------------------------------------ :: eq +%% % TD,E |- typ ~> t2 +%% % +%% % defn +%% % |- nexp ~> ne :: :: convert_nexp :: convert_nexp_ +%% % {{ com Convert and normalize numeric expressions }} +%% % by +%% % +%% % ------------------------------------------------------------ :: var +%% % |- N l ~> N +%% % +%% % ------------------------------------------------------------ :: num +%% % |- num l ~> nat +%% % +%% % |- nexp1 ~> ne1 +%% % |- nexp2 ~> ne2 +%% % ------------------------------------------------------------ :: mult +%% % |- nexp1 * nexp2 l ~> ne1 * ne2 +%% % +%% % |- nexp1 ~> ne1 +%% % |- nexp2 ~> ne2 +%% % ----------------------------------------------------------- :: add +%% % |- nexp1 + nexp2 l ~> :Ne_add: ne1 + ne2 +%% % +%% % defns +%% % convert_typs :: '' ::= +%% % +%% % defn +%% % TD , E |- typs ~> t_multi :: :: convert_typs :: convert_typs_ by +%% % +%% % TD,E |- typ1 ~> t1 .. TD,E |- typn ~> tn +%% % ------------------------------------------------------------ :: all +%% % TD,E |- typ1 * .. * typn ~> (t1 * .. * tn) +%% % +%% % defns +%% % check_lit :: '' ::= +%% % +%% % defn +%% % |- lit : t :: :: check_lit :: check_lit_ +%% % {{ com Typing literal constants }} +%% % by +%% % +%% % ------------------------------------------------------------ :: true +%% % |- true l : __bool +%% % +%% % ------------------------------------------------------------ :: false +%% % |- false l : __bool +%% % +%% % ------------------------------------------------------------ :: num +%% % |- num l : __num +%% % +%% % nat = bitlength(hex) +%% % ------------------------------------------------------------ :: hex +%% % |- hex l : __vector nat __bit +%% % +%% % nat = bitlength(bin) +%% % ------------------------------------------------------------ :: bin +%% % |- bin l : __vector nat __bit +%% % +%% % ------------------------------------------------------------ :: string +%% % |- string l : __string +%% % +%% % ------------------------------------------------------------ :: unit +%% % |- () l : __unit +%% % +%% % ------------------------------------------------------------ :: bitzero +%% % |- bitzero l : __bit +%% % +%% % ------------------------------------------------------------ :: bitone +%% % |- bitone l : __bit +%% % +%% % +%% % defns +%% % inst_field :: '' ::= +%% % +%% % defn +%% % TD , E |- field id : p t_args -> t gives ( x of names ) :: :: inst_field :: inst_field_ +%% % {{ com Field typing (also returns canonical field names) }} +%% % by +%% % +%% % E(</x_li//i/>) gives <E_m,E_p,E_f,E_x> +%% % E_f(y) gives <forall tnv1..tnvn. p -> t, (z of names)> +%% % TD |- t1 ok .. TD |- tn ok +%% % ------------------------------------------------------------ :: all +%% % TD,E |- field </x_li.//i/> y l1 l2: p t1 .. tn -> {tnv1|->t1..tnvn|->tn}(t) gives (z of names) +%% % +%% % defns +%% % inst_ctor :: '' ::= +%% % +%% % defn +%% % TD , E |- ctor id : t_multi -> p t_args gives ( x of names ) :: :: inst_ctor :: inst_ctor_ +%% % {{ com Data constructor typing (also returns canonical constructor names) }} +%% % by +%% % +%% % E(</x_li//i/>) gives <E_m,E_p,E_f,E_x> +%% % E_x(y) gives <forall tnv1..tnvn. t_multi -> p, (z of names)> +%% % TD |- t1 ok .. TD |- tn ok +%% % ------------------------------------------------------------ :: all +%% % TD,E |- ctor </x_li.//i/> y l1 l2 : {tnv1|->t1..tnvn|->tn}(t_multi) -> p t1 .. tn gives (z of names) +%% % +%% % defns +%% % inst_val :: '' ::= +%% % +%% % defn +%% % TD , E |- val id : t gives S_c :: :: inst_val :: inst_val_ +%% % {{ com Typing top-level bindings, collecting typeclass constraints }} +%% % by +%% % +%% % E(</x_li//i/>) gives <E_m,E_p,E_f,E_x> +%% % E_x(y) gives <forall tnv1..tnvn. (p1 tnv'1) .. (pi tnv'i) => t,env_tag> +%% % TD |- t1 ok .. TD |- tn ok +%% % t_subst = {tnv1|->t1..tnvn|->tn} +%% % ------------------------------------------------------------ :: all +%% % TD, E |- val </x_li.//i/> y l1 l2 : t_subst(t) gives {(p1 t_subst(tnv'1)), .. , (pi t_subst(tnv'i))} +%% % +%% % defns +%% % not_ctor :: '' ::= +%% % +%% % defn +%% % E , E_l |- x not ctor :: :: not_ctor :: not_ctor_ +%% % {{ com $\ottnt{v}$ is not bound to a data constructor }} +%% % by +%% % +%% % E_l(x) gives t +%% % ------------------------------------------------------------ :: val +%% % E,E_l |- x not ctor +%% % +%% % x NOTIN dom(E_x) +%% % ------------------------------------------------------------ :: unbound +%% % <E_m,E_p,E_f,E_x>,E_l |- x not ctor +%% % +%% % E_x(x) gives <forall tnv1..tnvn. (p1 tnv'1)..(pi tnv'i) => t,env_tag> +%% % ------------------------------------------------------------ :: bound +%% % <E_m,E_p,E_f,E_x>,E_l |- x not ctor +%% % +%% % defns +%% % not_shadowed :: '' ::= +%% % +%% % defn +%% % E_l |- id not shadowed :: :: not_shadowed :: not_shadowed_ +%% % {{ com $\ottnt{id}$ is not lexically shadowed }} +%% % by +%% % +%% % x NOTIN dom(E_l) +%% % ------------------------------------------------------------ :: sing +%% % E_l |- x l1 l2 not shadowed +%% % +%% % ------------------------------------------------------------ :: multi +%% % E_l |- x_l1. .. x_ln.y_l.z_l l not shadowed +%% % +%% % +%% % defns +%% % check_pat :: '' ::= +%% % +%% % defn +%% % TD , E , E_l1 |- pat : t gives E_l2 :: :: check_pat :: check_pat_ +%% % {{ com Typing patterns, building their binding environment }} +%% % by +%% % +%% % :check_pat_aux: TD,E,E_l1 |- pat_aux : t gives E_l2 +%% % ------------------------------------------------------------ :: all +%% % TD,E,E_l1 |- pat_aux l : t gives E_l2 +%% % +%% % defn +%% % TD , E , E_l1 |- pat_aux : t gives E_l2 :: :: check_pat_aux :: check_pat_aux_ +%% % {{ com Typing patterns, building their binding environment }} +%% % by +%% % +%% % TD |- t ok +%% % ------------------------------------------------------------ :: wild +%% % TD,E,E_l |- _ : t gives {} +%% % +%% % TD,E,E_l1 |- pat : t gives E_l2 +%% % x NOTIN dom(E_l2) +%% % ------------------------------------------------------------ :: as +%% % TD,E,E_l1 |- (pat as x l) : t gives E_l2 u+ {x|->t} +%% % +%% % TD,E,E_l1 |- pat : t gives E_l2 +%% % TD,E |- typ ~> t +%% % ------------------------------------------------------------ :: typ +%% % TD,E,E_l1 |- (pat : typ) : t gives E_l2 +%% % +%% % TD,E |- ctor id : (t1*..*tn) -> p t_args gives (x of names) +%% % E_l |- id not shadowed +%% % TD,E,E_l |- pat1 : t1 gives E_l1 .. TD,E,E_l |- patn : tn gives E_ln +%% % disjoint doms(E_l1,..,E_ln) +%% % ------------------------------------------------------------ :: ident_constr +%% % TD,E,E_l |- id pat1 .. patn : p t_args gives E_l1 u+ .. u+ E_ln +%% % +%% % TD |- t ok +%% % E,E_l |- x not ctor +%% % ------------------------------------------------------------ :: var +%% % TD,E,E_l |- x l1 l2 : t gives {x|->t} +%% % +%% % </TD,E |- field idi : p t_args -> ti gives (xi of names) // i /> +%% % </TD,E,E_l |- pati : ti gives E_li//i/> +%% % disjoint doms(</E_li//i/>) +%% % duplicates(</xi//i/>) = emptyset +%% % ------------------------------------------------------------ :: record +%% % TD,E,E_l |- <| </idi = pati li//i/> semi_opt |> : p t_args gives u+ </E_li//i/> +%% % +%% % TD,E,E_l |- pat1 : t gives E_l1 ... TD,E,E_l |- patn : t gives E_ln +%% % disjoint doms(E_l1 , ... , E_ln) +%% % length(pat1 ... patn) = nat +%% % ----------------------------------------------------------- :: vector +%% % TD,E,E_l |- [| pat1 ; ... ; patn semi_opt |] : __vector nat t gives E_l1 u+ ... u+ E_ln +%% % +%% % TD,E,E_l |- pat1 : __vector ne1 t gives E_l1 ... TD,E,E_l |- patn : __vector nen t gives E_ln +%% % disjoint doms(E_l1 , ... , E_ln) +%% % ne' = ne1 + ... + nen +%% % ----------------------------------------------------------- :: vectorConcat +%% % TD,E,E_l |- [| pat1 ... patn |] : __vector ne' t gives E_l1 u+ ... u+ E_ln +%% % +%% % +%% % TD,E,E_l |- pat1 : t1 gives E_l1 .... TD,E,E_l |- patn : tn gives E_ln +%% % disjoint doms(E_l1,....,E_ln) +%% % ------------------------------------------------------------ :: tup +%% % TD,E,E_l |- (pat1, ...., patn) : t1 * .... * tn gives E_l1 u+ .... u+ E_ln +%% % +%% % TD |- t ok +%% % TD,E,E_l |- pat1 : t gives E_l1 .. TD,E,E_l |- patn : t gives E_ln +%% % disjoint doms(E_l1,..,E_ln) +%% % ------------------------------------------------------------ :: list +%% % TD,E,E_l |- [pat1; ..; patn semi_opt] : __list t gives E_l1 u+ .. u+ E_ln +%% % +%% % TD,E,E_l1 |- pat : t gives E_l2 +%% % ------------------------------------------------------------ :: paren +%% % TD,E,E_l1 |- (pat) : t gives E_l2 +%% % +%% % TD,E,E_l1 |- pat1 : t gives E_l2 +%% % TD,E,E_l1 |- pat2 : __list t gives E_l3 +%% % disjoint doms(E_l2,E_l3) +%% % ------------------------------------------------------------ :: cons +%% % TD,E,E_l1 |- pat1 :: pat2 : __list t gives E_l2 u+ E_l3 +%% % +%% % |- lit : t +%% % ------------------------------------------------------------ :: lit +%% % TD,E,E_l |- lit : t gives {} +%% % +%% % E,E_l |- x not ctor +%% % ------------------------------------------------------------ :: num_add +%% % TD,E,E_l |- x l + num : __num gives {x|->__num} +%% % +%% % +%% % defns +%% % id_field :: '' ::= +%% % +%% % defn +%% % E |- id field :: :: id_field :: id_field_ +%% % {{ com Check that the identifier is a permissible field identifier }} +%% % by +%% % +%% % E_f(x) gives f_desc +%% % ------------------------------------------------------------ :: empty +%% % <E_m,E_p,E_f,E_x> |- x l1 l2 field +%% % +%% % +%% % E_m(x) gives E +%% % x NOTIN dom(E_f) +%% % E |- </y_li.//i/> z_l l2 field +%% % ------------------------------------------------------------ :: cons +%% % <E_m,E_p,E_f,E_x> |- x l1.</y_li.//i/> z_l l2 field +%% % +%% % defns +%% % id_value :: '' ::= +%% % +%% % defn +%% % E |- id value :: :: id_value :: id_value_ +%% % {{ com Check that the identifier is a permissible value identifier }} +%% % by +%% % +%% % E_x(x) gives v_desc +%% % ------------------------------------------------------------ :: empty +%% % <E_m,E_p,E_f,E_x> |- x l1 l2 value +%% % +%% % +%% % E_m(x) gives E +%% % x NOTIN dom(E_x) +%% % E |- </y_li.//i/> z_l l2 value +%% % ------------------------------------------------------------ :: cons +%% % <E_m,E_p,E_f,E_x> |- x l1.</y_li.//i/> z_l l2 value +%% % +%% % defns +%% % check_exp :: '' ::= +%% % +%% % defn +%% % TD , E , E_l |- exp : t gives S_c , S_N :: :: check_exp :: check_exp_ +%% % {{ com Typing expressions, collecting typeclass and index constraints }} +%% % by +%% % +%% % :check_exp_aux: TD,E,E_l |- exp_aux : t gives S_c,S_N +%% % ------------------------------------------------------------ :: all +%% % TD,E,E_l |- exp_aux l : t gives S_c,S_N +%% % +%% % defn +%% % TD , E , E_l |- exp_aux : t gives S_c , S_N :: :: check_exp_aux :: check_exp_aux_ +%% % {{ com Typing expressions, collecting typeclass and index constraints }} +%% % by +%% % +%% % E_l(x) gives t +%% % ------------------------------------------------------------ :: var +%% % TD,E,E_l |- x l1 l2 : t gives {},{} +%% % +%% % %TODO KG Add check that N is in scope +%% % ------------------------------------------------------------ :: nvar +%% % TD,E,E_l |- N : __num gives {},{} +%% % +%% % E_l |- id not shadowed +%% % E |- id value +%% % TD,E |- ctor id : t_multi -> p t_args gives (x of names) +%% % ------------------------------------------------------------ :: ctor +%% % TD,E,E_l |- id : curry(t_multi, p t_args) gives {},{} +%% % +%% % E_l |- id not shadowed +%% % E |- id value +%% % TD, E |- val id : t gives S_c +%% % ------------------------------------------------------------ :: val +%% % TD,E,E_l |- id : t gives S_c,{} +%% % +%% % +%% % TD,E,E_l |- pat1 : t1 gives E_l1 ... TD,E,E_l |- patn : tn gives E_ln +%% % TD,E,E_l u+ E_l1 u+ ... u+ E_ln |- exp : u gives S_c,S_N +%% % disjoint doms(E_l1,...,E_ln) +%% % ------------------------------------------------------------ :: fn +%% % TD,E,E_l |- fun pat1 ... patn -> exp l : curry((t1*...*tn), u) gives S_c,S_N +%% % +%% % %TODO: the various patterns might want to use different specifications for vector length (i.e. 32 in one and 8+n+8 in another) +%% % % So should be pati : t gives E_li,S_Ni +%% % </TD,E,E_l |- pati : t gives E_li//i/> +%% % </TD,E,E_l u+ E_li |- expi : u gives S_ci, S_Ni//i/> +%% % ------------------------------------------------------------ :: function +%% % TD,E,E_l |- function bar_opt </pati -> expi li//i/> end : t -> u gives </S_ci//i/> , </S_Ni//i/> +%% % +%% % %TODO t1 and t1 should be t1 and t'1 so that constraints from any vectors can be extracted and added to S_N +%% % TD,E,E_l |- exp1 : t1 -> t2 gives S_c1,S_N1 +%% % TD,E,E_l |- exp2 : t1 gives S_c2,S_N2 +%% % ------------------------------------------------------------ :: app +%% % TD,E,E_l |- exp1 exp2 : t2 gives S_c1 union S_c2, S_N1 union S_N2 +%% % +%% % %TODO t1 and t1 should be t1 and t'1 so that constraints from any vectors can be extracted and added to S_N +%% % % Same for t2 +%% % :check_exp_aux: TD,E,E_l |- (ix) : t1 -> t2 -> t3 gives S_c1,S_N1 +%% % TD,E,E_l |- exp1 : t1 gives S_c2,S_N2 +%% % TD,E,E_l |- exp2 : t2 gives S_c3,S_N3 +%% % ------------------------------------------------------------ :: infix_app1 +%% % TD,E,E_l |- exp1 ix l exp2 : t3 gives S_c1 union S_c2 union S_c3,S_N1 union S_N2 union S_N3 +%% % +%% % %TODO, see above todo +%% % :check_exp_aux: TD,E,E_l |- x : t1 -> t2 -> t3 gives S_c1,S_N1 +%% % TD,E,E_l |- exp1 : t1 gives S_c2,S_N2 +%% % TD,E,E_l |- exp2 : t2 gives S_c3,S_N3 +%% % ------------------------------------------------------------ :: infix_app2 +%% % TD,E,E_l |- exp1 `x` l exp2 : t3 gives S_c1 union S_c2 union S_c3,S_N1 union S_N2 union S_N3 +%% % +%% % %TODO, see above todo, with regard to t_args +%% % </TD,E |- field idi : p t_args -> ti gives (xi of names)//i/> +%% % </TD,E,E_l |- expi : ti gives S_ci,S_Ni//i/> +%% % duplicates(</xi//i/>) = emptyset +%% % names = {</xi//i/>} +%% % ------------------------------------------------------------ :: record +%% % TD,E,E_l |- <| </idi = expi li//i/> semi_opt l |> : p t_args gives </S_ci//i/>,</S_Ni//i/> +%% % +%% % %TODO, see above todo, with regard to t_args +%% % </TD,E |- field idi : p t_args -> ti gives (xi of names)//i/> +%% % </TD,E,E_l |- expi : ti gives S_ci,S_Ni//i/> +%% % duplicates(</xi//i/>) = emptyset +%% % TD,E,E_l |- exp : p t_args gives S_c',S_N' +%% % ------------------------------------------------------------ :: recup +%% % TD,E,E_l |- <| exp with </idi = expi li//i/> semi_opt l |> : p t_args gives S_c' union </S_ci//i/>,S_N' union </S_Ni//i/> +%% % +%% % TD,E,E_l |- exp1 : t gives S_c1,S_N1 ... TD,E,E_l |- expn : t gives S_cn,S_Nn +%% % length(exp1 ... expn) = nat +%% % ------------------------------------------------------------ :: vector +%% % TD,E,E_l |- [| exp1 ; ... ; expn semi_opt |] : __vector nat t gives S_c1 union ... union S_cn, S_N1 union ... union S_Nn +%% % +%% % TD,E,E_l |- exp : __vector ne' t gives S_c,S_N +%% % |- nexp ~> ne +%% % ------------------------------------------------------------- :: vectorget +%% % TD,E,E_l |- exp .( nexp ) : t gives S_c,S_N union {ne<ne'} +%% % +%% % TD,E,E_l |- exp : __vector ne' t gives S_c,S_N +%% % |- nexp1 ~> ne1 +%% % |- nexp2 ~> ne2 +%% % ne = :Ne_add: ne2 + (- ne1) +%% % ------------------------------------------------------------- :: vectorsub +%% % TD,E,E_l |- exp .( nexp1 .. nexp2 ) : __vector ne t gives S_c,S_N union {ne1 < ne2 < ne'} +%% % +%% % E |- id field +%% % TD,E |- field id : p t_args -> t gives (x of names) +%% % TD,E,E_l |- exp : p t_args gives S_c,S_N +%% % ------------------------------------------------------------ :: field +%% % TD,E,E_l |- exp.id : t gives S_c,S_N +%% % +%% % </TD,E,E_l |- pati : t gives E_li//i/> +%% % </TD,E,E_l u+ E_li |- expi : u gives S_ci,S_Ni//i/> +%% % TD,E,E_l |- exp : t gives S_c',S_N' +%% % ------------------------------------------------------------ :: case +%% % TD,E,E_l |- match exp with bar_opt </pati -> expi li//i/> l end : u gives S_c' union </S_ci//i/>,S_N' union </S_Ni//i/> +%% % +%% % TD,E,E_l |- exp : t gives S_c,S_N +%% % TD,E |- typ ~> t +%% % ------------------------------------------------------------ :: typed +%% % TD,E,E_l |- (exp : typ) : t gives S_c,S_N +%% % +%% % %KATHYCOMMENT: where does E_l1 come from? +%% % TD,E,E_l1 |- letbind gives E_l2, S_c1,S_N1 +%% % TD,E,E_l1 u+ E_l2 |- exp : t gives S_c2,S_N2 +%% % ------------------------------------------------------------ :: let +%% % TD,E,E_l |- let letbind in exp : t gives S_c1 union S_c2,S_N1 union S_N2 +%% % +%% % TD,E,E_l |- exp1 : t1 gives S_c1,S_N1 .... TD,E,E_l |- expn : tn gives S_cn,S_Nn +%% % ------------------------------------------------------------ :: tup +%% % TD,E,E_l |- (exp1, ...., expn) : t1 * .... * tn gives S_c1 union .... union S_cn,S_N1 union .... union S_Nn +%% % +%% % TD |- t ok +%% % TD,E,E_l |- exp1 : t gives S_c1,S_N1 .. TD,E,E_l |- expn : t gives S_cn,S_Nn +%% % ------------------------------------------------------------ :: list +%% % TD,E,E_l |- [exp1; ..; expn semi_opt] : __list t gives S_c1 union .. union S_cn, S_N1 union .. union S_Nn +%% % +%% % TD,E,E_l |- exp : t gives S_c,S_N +%% % ------------------------------------------------------------ :: paren +%% % TD,E,E_l |- (exp) : t gives S_c,S_N +%% % +%% % TD,E,E_l |- exp : t gives S_c,S_N +%% % ------------------------------------------------------------ :: begin +%% % TD,E,E_l |- begin exp end : t gives S_c,S_N +%% % +%% % %TODO t might need different index constraints +%% % TD,E,E_l |- exp1 : __bool gives S_c1,S_N1 +%% % TD,E,E_l |- exp2 : t gives S_c2,S_N2 +%% % TD,E,E_l |- exp3 : t gives S_c3,S_N3 +%% % ------------------------------------------------------------ :: if +%% % TD,E,E_l |- if exp1 then exp2 else exp3 : t gives S_c1 union S_c2 union S_c3,S_N1 union S_N2 union S_N3 +%% % +%% % %TODO t might need different index constraints +%% % TD,E,E_l |- exp1 : t gives S_c1,S_N1 +%% % TD,E,E_l |- exp2 : __list t gives S_c2,S_N2 +%% % ------------------------------------------------------------ :: cons +%% % TD,E,E_l |- exp1 :: exp2 : __list t gives S_c1 union S_c2,S_N1 union S_N2 +%% % +%% % |- lit : t +%% % ------------------------------------------------------------ :: lit +%% % TD,E,E_l |- lit : t gives {},{} +%% % +%% % % TODO: should require that each xi actually appears free in exp1 +%% % </TD |- ti ok//i/> +%% % TD,E,E_l u+ {</xi|->ti//i/>} |- exp1 : t gives S_c1,S_N1 +%% % TD,E,E_l u+ {</xi|->ti//i/>} |- exp2 : __bool gives S_c2,S_N2 +%% % disjoint doms(E_l, {</xi|->ti//i/>}) +%% % E = <E_m,E_p,E_f,E_x> +%% % </xi NOTIN dom(E_x)//i/> +%% % ------------------------------------------------------------ :: set_comp +%% % TD,E,E_l |- { exp1 | exp2 } : __set t gives S_c1 union S_c2,S_N1 union S_N2 +%% % +%% % TD,E,E_l1 |- </qbindi//i/> gives E_l2,S_c1 +%% % TD,E,E_l1 u+ E_l2 |- exp1 : t gives S_c2,S_N2 +%% % TD,E,E_l1 u+ E_l2 |- exp2 : __bool gives S_c3,S_N3 +%% % ------------------------------------------------------------ :: set_comp_binding +%% % TD,E,E_l1 |- { exp1 | forall </qbindi//i/> | exp2 } : __set t gives S_c1 union S_c2 union S_c3,S_N2 union S_N3 +%% % +%% % TD |- t ok +%% % TD,E,E_l |- exp1 : t gives S_c1,S_N1 .. TD,E,E_l |- expn : t gives S_cn,S_Nn +%% % ------------------------------------------------------------ :: set +%% % TD,E,E_l |- { exp1; ..; expn semi_opt } : __set t gives S_c1 union .. union S_cn,S_N1 union .. union S_Nn +%% % +%% % TD,E,E_l1 |- </qbindi//i/> gives E_l2,S_c1 +%% % TD,E,E_l1 u+ E_l2 |- exp : __bool gives S_c2,S_N2 +%% % ------------------------------------------------------------ :: quant +%% % TD,E,E_l1 |- q </qbindi//i/> . exp : __bool gives S_c1 union S_c2,S_N2 +%% % +%% % TD,E,E_l1 |- list </qbindi//i/> gives E_l2,S_c1 +%% % TD,E,E_l1 u+ E_l2 |- exp1 : t gives S_c2,S_N2 +%% % TD,E,E_l1 u+ E_l2 |- exp2 : __bool gives S_c3,S_N3 +%% % ------------------------------------------------------------ :: list_comp_binding +%% % TD,E,E_l1 |- [ exp1 | forall </qbindi//i/> | exp2 ] : __list t gives S_c1 union S_c2 union S_c3,S_N2 union S_N3 +%% % +%% % defn +%% % TD , E , E_l1 |- qbind1 .. qbindn gives E_l2 , S_c :: :: check_listquant_binding +%% % :: check_listquant_binding_ +%% % {{ com Build the environment for quantifier bindings, collecting typeclass constraints }} +%% % by +%% % +%% % ------------------------------------------------------------ :: empty +%% % TD,E,E_l |- gives {},{} +%% % +%% % TD |- t ok +%% % TD,E,E_l1 u+ {x |-> t} |- </qbindi//i/> gives E_l2,S_c1 +%% % disjoint doms({x |-> t}, E_l2) +%% % ------------------------------------------------------------ :: var +%% % TD,E,E_l1 |- x l </qbindi//i/> gives {x |-> t} u+ E_l2,S_c1 +%% % +%% % TD,E,E_l1 |- pat : t gives E_l3 +%% % TD,E,E_l1 |- exp : __set t gives S_c1,S_N1 +%% % TD,E,E_l1 u+ E_l3 |- </qbindi//i/> gives E_l2,S_c2 +%% % disjoint doms(E_l3, E_l2) +%% % ------------------------------------------------------------ :: restr +%% % TD,E,E_l1 |- (pat IN exp) </qbindi//i/> gives E_l2 u+ E_l3,S_c1 union S_c2 +%% % +%% % TD,E,E_l1 |- pat : t gives E_l3 +%% % TD,E,E_l1 |- exp : __list t gives S_c1,S_N1 +%% % TD,E,E_l1 u+ E_l3 |- </qbindi//i/> gives E_l2,S_c2 +%% % disjoint doms(E_l3, E_l2) +%% % ------------------------------------------------------------ :: list_restr +%% % TD,E,E_l1 |- (pat MEM exp) </qbindi//i/> gives E_l2 u+ E_l3,S_c1 union S_c2 +%% % +%% % defn +%% % TD , E , E_l1 |- list qbind1 .. qbindn gives E_l2 , S_c :: :: check_quant_binding :: check_quant_binding_ +%% % {{ com Build the environment for quantifier bindings, collecting typeclass constraints }} +%% % by +%% % +%% % ------------------------------------------------------------ :: empty +%% % TD,E,E_l |- list gives {},{} +%% % +%% % TD,E,E_l1 |- pat : t gives E_l3 +%% % TD,E,E_l1 |- exp : __list t gives S_c1,S_N1 +%% % TD,E,E_l1 u+ E_l3 |- </qbindi//i/> gives E_l2,S_c2 +%% % disjoint doms(E_l3, E_l2) +%% % ------------------------------------------------------------ :: restr +%% % TD,E,E_l1 |- list (pat MEM exp) </qbindi//i/> gives E_l2 u+ E_l3,S_c1 union S_c2 +%% % +%% % +%% % defn +%% % TD , E , E_l |- funcl gives { x |-> t } , S_c , S_N :: :: check_funcl :: check_funcl_ +%% % {{ com Build the environment for a function definition clause, collecting typeclass and index constraints }} +%% % by +%% % +%% % TD,E,E_l |- pat1 : t1 gives E_l1 ... TD,E,E_l |- patn : tn gives E_ln +%% % TD,E,E_l u+ E_l1 u+ ... u+ E_ln |- exp : u gives S_c,S_N +%% % disjoint doms(E_l1,...,E_ln) +%% % TD,E |- typ ~> u +%% % ------------------------------------------------------------ :: annot +%% % TD,E,E_l |- x l1 pat1 ... patn : typ = exp l2 gives {x |-> curry((t1 * ... * tn), u)}, S_c,S_N +%% % +%% % TD,E,E_l |- pat1 : t1 gives E_l1 ... TD,E,E_l |- patn : tn gives E_ln +%% % TD,E,E_l u+ E_l1 u+ ... u+ E_ln |- exp : u gives S_c,S_N +%% % disjoint doms(E_l1,...,E_ln) +%% % ------------------------------------------------------------ :: noannot +%% % TD,E,E_l |- x l1 pat1 ... patn = exp l2 gives {x |-> curry((t1 * ... * tn), u)}, S_c,S_N +%% % +%% % +%% % defn +%% % TD , E , E_l1 |- letbind gives E_l2 , S_c , S_N :: :: check_letbind :: check_letbind_ +%% % {{ com Build the environment for a let binding, collecting typeclass and index constraints }} +%% % by +%% % +%% % %TODO similar type equality issues to above ones +%% % TD,E,E_l1 |- pat : t gives E_l2 +%% % TD,E,E_l1 |- exp : t gives S_c,S_N +%% % TD,E |- typ ~> t +%% % ------------------------------------------------------------ :: val_annot +%% % TD,E,E_l1 |- pat : typ = exp l gives E_l2,S_c,S_N +%% % +%% % TD,E,E_l1 |- pat : t gives E_l2 +%% % TD,E,E_l1 |- exp : t gives S_c,S_N +%% % ------------------------------------------------------------ :: val_noannot +%% % TD,E,E_l1 |- pat = exp l gives E_l2,S_c,S_N +%% % +%% % :check_funcl:TD,E,E_l1 |- funcl_aux l gives {x|->t},S_c,S_N +%% % ------------------------------------------------------------ :: fn +%% % TD,E,E_l1 |- funcl_aux l gives {x|->t},S_c,S_N +%% % +%% % defns +%% % check_rule :: '' ::= +%% % +%% % defn +%% % TD , E , E_l |- rule gives { x |-> t } , S_c , S_N :: :: check_rule :: check_rule_ +%% % {{ com Build the environment for an inductive relation clause, collecting typeclass and index constraints }} +%% % by +%% % +%% % </TD |- ti ok//i/> +%% % E_l2 = {</yi|->ti//i/>} +%% % TD,E,E_l1 u+ E_l2 |- exp' : __bool gives S_c',S_N' +%% % TD,E,E_l1 u+ E_l2 |- exp1 : u1 gives S_c1,S_N1 .. TD,E,E_l1 u+ E_l2 |- expn : un gives S_cn,S_Nn +%% % ------------------------------------------------------------ :: rule +%% % TD,E,E_l1 |- x_l_opt forall </yi li//i/> . exp' ==> x l exp1 .. expn l' gives {x|->curry((u1 * .. * un) , __bool)}, S_c' union S_c1 union .. union S_cn,S_N' union S_N1 union .. union S_Nn +%% % +%% % defns +%% % check_texp_tc :: '' ::= +%% % +%% % defn +%% % xs , TD1 , E |- tc td gives TD2 , E_p :: :: check_texp_tc :: check_texp_tc_ +%% % {{ com Extract the type constructor information }} +%% % by +%% % +%% % tnvars ~> tnvs +%% % TD,E |- typ ~> t +%% % duplicates(tnvs) = emptyset +%% % FV(t) SUBSET tnvs +%% % </yi.//i/>x NOTIN dom(TD) +%% % ------------------------------------------------------------ :: abbrev +%% % </yi//i/>,TD,E |- tc x l tnvars = typ gives {</yi.//i/>x|->tnvs.t},{x|-></yi.//i/>x} +%% % +%% % tnvars ~> tnvs +%% % duplicates(tnvs) = emptyset +%% % </yi.//i/>x NOTIN dom(TD) +%% % ------------------------------------------------------------ :: abstract +%% % </yi//i/>,TD,E1 |- tc x l tnvars gives {</yi.//i/>x|->tnvs},{x|-></yi.//i/>x} +%% % +%% % tnvars ~> tnvs +%% % duplicates(tnvs) = emptyset +%% % </yi.//i/>x NOTIN dom(TD) +%% % ------------------------------------------------------------ :: rec +%% % </yi//i/>,TD1,E |- tc x l tnvars = <| x_l1 : typ1 ; ... ; x_lj : typj semi_opt |> gives {</yi.//i/>x|->tnvs},{x|-></yi.//i/>x} +%% % +%% % tnvars ~> tnvs +%% % duplicates(tnvs) = emptyset +%% % </yi.//i/>x NOTIN dom(TD) +%% % ------------------------------------------------------------ :: var +%% % </yi//i/>,TD1,E |- tc x l tnvars = bar_opt ctor_def1 | ... | ctor_defj gives {</yi.//i/>x|->tnvs},{x|-></yi.//i/>x} +%% % +%% % defns +%% % check_texps_tc :: '' ::= +%% % +%% % defn +%% % xs , TD1 , E |- tc td1 .. tdi gives TD2 , E_p :: :: check_texps_tc :: check_texps_tc_ +%% % {{ com Extract the type constructor information }} +%% % by +%% % +%% % ------------------------------------------------------------ :: empty +%% % xs,TD,E |- tc gives {},{} +%% % +%% % :check_texp_tc: xs,TD1,E |- tc td gives TD2,E_p2 +%% % xs,TD1 u+ TD2,E u+ <{},E_p2,{},{}> |- tc </tdi//i/> gives TD3,E_p3 +%% % dom(E_p2) inter dom(E_p3) = emptyset +%% % ------------------------------------------------------------ :: abbrev +%% % xs,TD1,E |- tc td </tdi//i/> gives TD2 u+ TD3,E_p2 u+ E_p3 +%% % +%% % defns +%% % check_texp :: '' ::= +%% % +%% % defn +%% % TD , E |- tnvs p = texp gives < E_f , E_x > :: :: check_texp :: check_texp_ +%% % {{ com Check a type definition, with its path already resolved }} +%% % by +%% % +%% % ------------------------------------------------------------ :: abbrev +%% % TD,E |- tnvs p = typ gives <{},{}> +%% % +%% % </TD,E |- typi ~> ti//i/> +%% % names = {</xi//i/>} +%% % duplicates(</xi//i/>) = emptyset +%% % </FV(ti) SUBSET tnvs//i/> +%% % E_f = {</xi|-> <forall tnvs. p -> ti, (xi of names)>//i/>} +%% % ------------------------------------------------------------ :: rec +%% % TD,E |- tnvs p = <| </x_li:typi//i/> semi_opt |> gives <E_f,{}> +%% % +%% % </TD,E |- typsi ~> t_multii//i/> +%% % names = {</xi//i/>} +%% % duplicates(</xi//i/>) = emptyset +%% % </FV(t_multii) SUBSET tnvs//i/> +%% % E_x = {</xi|-><forall tnvs. t_multii -> p, (xi of names)>//i/>} +%% % ------------------------------------------------------------ :: var +%% % TD,E |- tnvs p = bar_opt </x_li of typsi//i/> gives <{},E_x> +%% % +%% % defns +%% % check_texps :: '' ::= +%% % +%% % defn +%% % xs , TD , E |- td1 .. tdn gives < E_f , E_x > :: :: check_texps :: check_texps_ by +%% % +%% % ------------------------------------------------------------ :: empty +%% % </yi//i/>,TD,E |- gives <{},{}> +%% % +%% % tnvars ~> tnvs +%% % TD,E1 |- tnvs </yi.//i/>x = texp gives <E_f1,E_x1> +%% % </yi//i/>,TD,E |- </tdj//j/> gives <E_f2,E_x2> +%% % dom(E_x1) inter dom(E_x2) = emptyset +%% % dom(E_f1) inter dom(E_f2) = emptyset +%% % ------------------------------------------------------------ :: cons_concrete +%% % </yi//i/>,TD,E |- x l tnvars = texp </tdj//j/> gives <E_f1 u+ E_f2, E_x1 u+ E_x2> +%% % +%% % </yi//i/>,TD,E |- </tdj//j/> gives <E_f,E_x> +%% % ------------------------------------------------------------ :: cons_abstract +%% % </yi//i/>,TD,E |- x l tnvars </tdj//j/> gives <E_f,E_x> +%% % +%% % defns +%% % convert_class :: '' ::= +%% % +%% % defn +%% % TC , E |- id ~> p :: :: convert_class :: convert_class_ +%% % {{ com Lookup a type class }} +%% % by +%% % +%% % E(id) gives p +%% % TC(p) gives xs +%% % ------------------------------------------------------------ :: all +%% % TC,E |- id ~> p +%% % +%% % defns +%% % solve_class_constraint :: '' ::= +%% % +%% % defn +%% % I |- ( p t ) 'IN' semC :: :: solve_class_constraint :: solve_class_constraint_ +%% % {{ com Solve class constraint }} +%% % by +%% % +%% % ------------------------------------------------------------ :: immediate +%% % I |- (p a) IN (p1 tnv1) .. (pi tnvi) (p a) (p'1 tnv'1) .. (p'j tnv'j) +%% % +%% % (p1 tnv1)..(pn tnvn)=>(p t) IN I +%% % I |- (p1 t_subst(tnv1)) IN semC .. I |- (pn t_subst(tnvn)) IN semC +%% % ------------------------------------------------------------ :: chain +%% % I |- (p t_subst(t)) IN semC +%% % +%% % defns +%% % solve_class_constraints :: '' ::= +%% % +%% % defn +%% % I |- S_c gives semC :: :: solve_class_constraints :: solve_class_constraints_ +%% % {{ com Solve class constraints }} +%% % by +%% % +%% % I |- (p1 t1) IN semC .. I |- (pn tn) IN semC +%% % ------------------------------------------------------------ :: all +%% % I |- {(p1 t1), .., (pn tn)} gives semC +%% % +%% % defns +%% % check_val_def :: '' ::= +%% % +%% % defn +%% % TD , I , E |- val_def gives E_x :: :: check_val_def :: check_val_def_ +%% % {{ com Check a value definition }} +%% % by +%% % +%% % TD,E,{} |- letbind gives {</xi|->ti//i/>},S_c,S_N +%% % %TODO, check S_N constraints +%% % I |- S_c gives semC +%% % </FV(ti) SUBSET tnvs//i/> +%% % FV(semC) SUBSET tnvs +%% % ------------------------------------------------------------ :: val +%% % TD,I,E1 |- let targets_opt letbind gives {</xi |-> <forall tnvs. semC => ti, let>//i/>} +%% % +%% % </TD,E,E_l |- funcli gives {xi|->ti},S_ci,S_Ni//i/> +%% % I |- S_c gives semC +%% % </FV(ti) SUBSET tnvs//i/> +%% % FV(semC) SUBSET tnvs +%% % compatible overlap(</xi|->ti//i/>) +%% % E_l = {</xi|->ti//i/>} +%% % ------------------------------------------------------------ :: recfun +%% % TD,I,E |- let rec targets_opt </funcli//i/> gives {</xi|-><forall tnvs. semC => ti,let>//i/>} +%% % +%% % defns +%% % check_t_instance :: '' ::= +%% % +%% % defn +%% % +%% % TD , ( a1 , .. , an ) |- t instance :: :: check_t_instance :: check_t_instance_ +%% % {{ com Check that $\ottnt{t}$ be a typeclass instance }} +%% % by +%% % +%% % ------------------------------------------------------------ :: var +%% % TD , (a) |- a instance +%% % +%% % ------------------------------------------------------------ :: tup +%% % TD , (a1, ...., an) |- a1 * .... * an instance +%% % +%% % ------------------------------------------------------------ :: fn +%% % TD , (a1, a2) |- a1 -> an instance +%% % +%% % TD(p) gives a'1..a'n +%% % ------------------------------------------------------------ :: tc +%% % TD , (a1, .., an) |- p a1 .. an instance +%% % +%% % defns +%% % check_defs :: '' ::= +%% % +%% % defn +%% % +%% % </ zj // j /> , D1 , E1 |- def gives D2 , E2 :: :: check_def :: check_def_ +%% % {{ com Check a definition }} +%% % by +%% % +%% % +%% % </zj//j/>,TD1,E |- tc </tdi//i/> gives TD2,E_p +%% % </zj//j/>,TD1 u+ TD2,E u+ <{},E_p,{},{}> |- </tdi//i/> gives <E_f,E_x> +%% % ------------------------------------------------------------ :: type +%% % </zj//j/>,<TD1,TC,I>,E |- type </tdi//i/> l gives <TD2,{},{}>,<{},E_p,E_f,E_x> +%% % +%% % TD,I,E |- val_def gives E_x +%% % ------------------------------------------------------------ :: val_def +%% % </zj//j/>,<TD,TC,I>,E |- val_def l gives empty,<{},{},{},E_x> +%% % +%% % </TD,E1,E_l |- rulei gives {xi|->ti},S_ci,S_Ni//i/> +%% % %TODO Check S_N constraints +%% % I |- </S_ci//i/> gives semC +%% % </FV(ti) SUBSET tnvs//i/> +%% % FV(semC) SUBSET tnvs +%% % compatible overlap(</xi|->ti//i/>) +%% % E_l = {</xi|->ti//i/>} +%% % E2 = <{},{},{},{</xi |-><forall tnvs. semC => ti,let>//i/>}> +%% % ------------------------------------------------------------ :: indreln +%% % </zj//j/>,<TD,TC,I>,E1 |- indreln targets_opt </rulei//i/> l gives empty,E2 +%% % +%% % </zj//j/> x,D1,E1 |- defs gives D2,E2 +%% % ------------------------------------------------------------ :: module +%% % </zj//j/>,D1,E1 |- module x l1 = struct defs end l2 gives D2,<{x|->E2},{},{},{}> +%% % +%% % E1(id) gives E2 +%% % ------------------------------------------------------------ :: module_rename +%% % </zj//j/>,D,E1 |- module x l1 = id l2 gives empty,<{x|->E2},{},{},{}> +%% % +%% % TD,E |- typ ~> t +%% % FV(t) SUBSET </ai//i/> +%% % FV(</a'k//k/>) SUBSET </ai//i/> +%% % </TC,E |- idk ~> pk//k/> +%% % E' = <{},{},{},{x|-><forall </ai//i/>. </(pk a'k)//k/> => t,val>}> +%% % ------------------------------------------------------------ :: spec +%% % </zj//j/>,<TD,TC,I>,E |- val x l1 : forall </ai l''i//i/>. </idk a'k l'k//k/> => typ l2 gives empty,E' +%% % +%% % </TD,E1 |- typi ~> ti//i/> +%% % </FV(ti) SUBSET a//i/> +%% % :formula_p_eq: p = </zj.//j/>x +%% % E2 = <{},{x|->p},{},{</yi |-><forall a. (p a) => ti,method>//i/>}> +%% % TC2 = {p|-></yi//i/>} +%% % p NOTIN dom(TC1) +%% % ------------------------------------------------------------ :: class +%% % </zj//j/>,<TD,TC1,I>,E1 |- class (x l a l'') </val yi li : typi li//i/> end l' gives <{},TC2,{}>,E2 +%% % +%% % E = <E_m,E_p,E_f,E_x> +%% % TD,E |- typ' ~> t' +%% % TD,(</ai//i/>) |- t' instance +%% % tnvs = </ai//i/> +%% % duplicates(tnvs) = emptyset +%% % </TC,E |- idk ~> pk//k/> +%% % FV(</a'k//k/>) SUBSET tnvs +%% % E(id) gives p +%% % TC(p) gives </zj//j/> +%% % I2 = { </=> (pk a'k)//k/> } +%% % </TD,I union I2,E |- val_defn gives E_xn//n/> +%% % disjoint doms(</E_xn//n/>) +%% % </E_x(xk) gives <forall a''. (p a'') => tk,method>//k/> +%% % {</xk |-> <forall tnvs. => {a''|->t'}(tk),let>//k/>} = </E_xn//n/> +%% % :formula_xs_eq:</xk//k/> = </zj//j/> +%% % I3 = {</(pk a'k) => (p t')//k/>} +%% % (p {</ai |-> a'''i//i/>}(t')) NOTIN I +%% % ------------------------------------------------------------ :: instance_tc +%% % </zj//j/>,<TD,TC,I>,E |- instance forall </ai l'i//i/>. </idk a'k l''k//k/> => (id typ') </val_defn ln//n/> end l' gives <{},{},I3>,empty +%% % +%% % defn +%% % </ zj // j /> , D1 , E1 |- defs gives D2 , E2 :: :: check_defs :: check_defs_ +%% % {{ com Check definitions, given module path, definitions and environment }} +%% % by +%% % +%% % % TODO: Check compatibility for duplicate definitions +%% % +%% % ------------------------------------------------------------ :: empty +%% % </zj//j/>,D,E |- gives empty,empty +%% % +%% % :check_def: </zj//j/>,D1,E1 |- def gives D2,E2 +%% % </zj//j/>,D1 u+ D2,E1 u+ E2 |- </defi semisemi_opti // i/> gives D3,E3 +%% % ------------------------------------------------------------ :: relevant_def +%% % </zj//j/>,D1,E1 |- def semisemi_opt </defi semisemi_opti // i/> gives D2 u+ D3, E2 u+ E3 +%% % +%% % E1(id) gives E2 +%% % </zj//j/>,D1,E1 u+ E2 |- </defi semisemi_opti // i/> gives D3,E3 +%% % ------------------------------------------------------------ :: open +%% % </zj//j/>,D1,E1 |- open id l semisemi_opt </defi semisemi_opti // i/> gives D3,E3 +%% % + |