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-rw-r--r--language/l2.lem163
-rw-r--r--language/l2.ml201
-rw-r--r--language/l2.ott153
-rw-r--r--language/l2_parse.ml174
-rw-r--r--language/l2_parse.ott124
-rw-r--r--language/l2_rules.ott20
6 files changed, 403 insertions, 432 deletions
diff --git a/language/l2.lem b/language/l2.lem
index 177f73cc..8e56f69e 100644
--- a/language/l2.lem
+++ b/language/l2.lem
@@ -22,73 +22,70 @@ val subst : forall 'a. list 'a -> list 'a -> bool
type x = string (* identifier *)
type ix = string (* infix identifier *)
+type kid = (* variables with kind, ticked to differntiate from program variables *)
+ | Var of x
+
+
type base_kind = (* base kind *)
| BK_type (* kind of types *)
| BK_nat (* kind of natural number size expressions *)
| BK_order (* kind of vector order specifications *)
- | BK_effects (* kind of effect sets *)
-
-
-type id = (* Identifier *)
- | Id of x
- | DeIid of x (* remove infix status *)
-
-
-type var = (* variables with kind, ticked to differntiate from program variables *)
- | Var of x
-
-
-type kind = (* kinds *)
- | K_kind of list base_kind
+ | BK_effect (* kind of effect sets *)
type nexp = (* expression of kind $Nat$, for vector sizes and origins *)
- | Nexp_id of id (* identifier *)
- | Nexp_var of var (* variable *)
+ | Nexp_var of kid (* variable *)
| Nexp_constant of nat (* constant *)
| Nexp_times of nexp * nexp (* product *)
| Nexp_sum of nexp * nexp (* sum *)
| Nexp_exp of nexp (* exponential *)
-type efct = (* effect *)
- | Effect_rreg (* read register *)
- | Effect_wreg (* write register *)
- | Effect_rmem (* read memory *)
- | Effect_wmem (* write memory *)
- | Effect_undef (* undefined-instruction exception *)
- | Effect_unspec (* unspecified values *)
- | Effect_nondet (* nondeterminism from intra-instruction parallelism *)
+type kind = (* kinds *)
+ | K_kind of list base_kind
-type kinded_id = (* optionally kind-annotated identifier *)
- | KOpt_none of var (* identifier *)
- | KOpt_kind of kind * var (* kind-annotated variable *)
+type base_effect = (* effect *)
+ | BE_rreg (* read register *)
+ | BE_wreg (* write register *)
+ | BE_rmem (* read memory *)
+ | BE_wmem (* write memory *)
+ | BE_undef (* undefined-instruction exception *)
+ | BE_unspec (* unspecified values *)
+ | BE_nondet (* nondeterminism from intra-instruction parallelism *)
-type nexp_constraint = (* constraint over kind $Nat$ *)
+type n_constraint = (* constraint over kind $Nat$ *)
| NC_fixed of nexp * nexp
| NC_bounded_ge of nexp * nexp
| NC_bounded_le of nexp * nexp
- | NC_nat_set_bounded of id * list nat
+ | NC_nat_set_bounded of kid * list nat
+
+
+type kinded_id = (* optionally kind-annotated identifier *)
+ | KOpt_none of kid (* identifier *)
+ | KOpt_kind of kind * kid (* kind-annotated variable *)
type order = (* vector order specifications, of kind $Order$ *)
- | Ord_id of id (* identifier *)
- | Ord_var of var (* variable *)
+ | Ord_var of kid (* variable *)
| Ord_inc (* increasing (little-endian) *)
| Ord_dec (* decreasing (big-endian) *)
-type effects = (* effect set, of kind $Effects$ *)
- | Effects_id of id
- | Effects_var of var
- | Effects_set of list efct (* effect set *)
+type effect = (* effect set, of kind $Effects$ *)
+ | Effect_var of kid
+ | Effect_set of list base_effect (* effect set *)
+
+
+type id = (* Identifier *)
+ | Id of x
+ | DeIid of x (* remove infix status *)
type quant_item = (* Either a kinded identifier or a nexp constraint for a typquant *)
| QI_id of kinded_id (* An optionally kinded identifier *)
- | QI_const of nexp_constraint (* A constraint for this type *)
+ | QI_const of n_constraint (* A constraint for this type *)
type lit = (* Literal constant *)
@@ -107,8 +104,8 @@ type lit = (* Literal constant *)
type typ = (* Type expressions, of kind $Type$ *)
| Typ_wild (* Unspecified type *)
| Typ_id of id (* Defined type *)
- | Typ_var of var (* Type variable *)
- | Typ_fn of typ * typ * effects (* Function type (first-order only in user code) *)
+ | Typ_var of kid (* Type variable *)
+ | Typ_fn of typ * typ * effect (* Function type (first-order only in user code) *)
| Typ_tup of list typ (* Tuple type *)
| Typ_app of id * list typ_arg (* type constructor application *)
@@ -116,7 +113,7 @@ and typ_arg = (* Type constructor arguments of all kinds *)
| Typ_arg_nexp of nexp
| Typ_arg_typ of typ
| Typ_arg_order of order
- | Typ_arg_effects of effects
+ | Typ_arg_effect of effect
type typquant = (* type quantifiers and constraints *)
@@ -173,7 +170,7 @@ type exp = (* Expression *)
and lexp = (* lvalue expression *)
| LEXP_id of id (* identifier *)
- | LEXP_memory of id * exp (* memory write via function call *)
+ | LEXP_memory of id * list exp (* memory write via function call *)
| LEXP_vector of lexp * exp (* vector element *)
| LEXP_vector_range of lexp * exp * exp (* subvector *)
| LEXP_field of lexp * id (* struct field *)
@@ -192,15 +189,25 @@ and letbind = (* Let binding *)
| LB_val_implicit of pat * exp (* value binding, implicit type (pat must be total) *)
-type effects_opt = (* Optional effect annotation for functions *)
- | Effects_opt_pure (* sugar for empty effect set *)
- | Effects_opt_effects of effects
+type type_union = (* Type union constructors *)
+ | Tu_id of id
+ | Tu_ty_id of typ * id
type funcl = (* Function clause *)
| FCL_Funcl of id * pat * exp
+type effect_opt = (* Optional effect annotation for functions *)
+ | Effect_opt_pure (* sugar for empty effect set *)
+ | Effect_opt_effect of effect
+
+
+type name_scm_opt = (* Optional variable-naming-scheme specification for variables of defined type *)
+ | Name_sect_none
+ | Name_sect_some of string
+
+
type rec_opt = (* Optional recursive annotation for functions *)
| Rec_nonrec (* non-recursive *)
| Rec_rec (* recursive *)
@@ -210,42 +217,41 @@ type tannot_opt = (* Optional type annotation for functions *)
| Typ_annot_opt_some of typquant * typ
-type type_union = (* Type union constructors *)
- | Tu_id of id
- | Tu_ty_id of typ * id
-
-
-type naming_scheme_opt = (* Optional variable-naming-scheme specification for variables of defined type *)
- | Name_sect_none
- | Name_sect_some of string
-
-
type index_range = (* index specification, for bitfields in register types *)
| BF_single of nat (* single index *)
| BF_range of nat * nat (* index range *)
| BF_concat of index_range * index_range (* concatenation of index ranges *)
-type fundef = (* Function definition *)
- | FD_function of rec_opt * tannot_opt * effects_opt * list funcl
-
-
-type default_typing_spec = (* Default kinding or typing assumption *)
- | DT_kind of base_kind * var
- | DT_typ of typschm * id
-
-
type val_spec = (* Value type specification *)
| VS_val_spec of typschm * id
| VS_extern_no_rename of typschm * id
| VS_extern_spec of typschm * id * string (* Specify the type and id of a function from Lem, where the string must provide an explicit path to the required function but will not be checked *)
+type scattered_def = (* Function and type union definitions that can be spread across
+ a file. Each one must end in $id$ *)
+ | SD_scattered_function of rec_opt * tannot_opt * effect_opt * id (* scattered function definition header *)
+ | SD_scattered_funcl of funcl (* scattered function definition clause *)
+ | SD_scattered_variant of id * name_scm_opt * typquant (* scattered union definition header *)
+ | SD_scattered_unioncl of id * type_union (* scattered union definition member *)
+ | SD_scattered_end of id (* scattered definition end *)
+
+
+type fundef = (* Function definition *)
+ | FD_function of rec_opt * tannot_opt * effect_opt * list funcl
+
+
+type default_spec = (* Default kinding or typing assumption *)
+ | DT_kind of base_kind * kid
+ | DT_typ of typschm * id
+
+
type type_def = (* Type definition body *)
- | TD_abbrev of id * naming_scheme_opt * typschm (* type abbreviation *)
- | TD_record of id * naming_scheme_opt * typquant * list (typ * id) * bool (* struct type definition *)
- | TD_variant of id * naming_scheme_opt * typquant * list type_union * bool (* union type definition *)
- | TD_enum of id * naming_scheme_opt * list id * bool (* enumeration type definition *)
+ | TD_abbrev of id * name_scm_opt * typschm (* type abbreviation *)
+ | TD_record of id * name_scm_opt * typquant * list (typ * id) * bool (* struct type definition *)
+ | TD_variant of id * name_scm_opt * typquant * list type_union * bool (* union type definition *)
+ | TD_enum of id * name_scm_opt * list id * bool (* enumeration type definition *)
| TD_register of id * nexp * nexp * list (index_range * id) (* register mutable bitfield type definition *)
@@ -254,34 +260,13 @@ type def = (* Top-level definition *)
| DEF_fundef of fundef (* function definition *)
| DEF_val of letbind (* value definition *)
| DEF_spec of val_spec (* top-level type constraint *)
- | DEF_default of default_typing_spec (* default kind and type assumptions *)
+ | DEF_default of default_spec (* default kind and type assumptions *)
+ | DEF_scattered of scattered_def (* scattered function and type definition *)
| DEF_reg_dec of typ * id (* register declaration *)
- | DEF_scattered_function of rec_opt * tannot_opt * effects_opt * id (* scattered function definition header *)
- | DEF_scattered_funcl of funcl (* scattered function definition clause *)
- | DEF_scattered_variant of id * naming_scheme_opt * typquant (* scattered union definition header *)
- | DEF_scattered_unioncl of id * typ * id (* scattered union definition member *)
- | DEF_scattered_end of id (* scattered definition end *)
type defs = (* Definition sequence *)
| Defs of list def
-type typ_lib = (* library types and syntactic sugar for them *)
- | Typ_lib_unit (* unit type with value $()$ *)
- | Typ_lib_bool (* booleans $true$ and $false$ *)
- | Typ_lib_bit (* pure bit values (not mutable bits) *)
- | Typ_lib_nat (* natural numbers 0,1,2,... *)
- | Typ_lib_string of string (* UTF8 strings *)
- | Typ_lib_enum of nexp * nexp * order (* natural numbers nexp .. nexp+nexp-1, ordered by order *)
- | Typ_lib_enum1 of nexp (* sugar for \texttt{enum nexp 0 inc} *)
- | Typ_lib_enum2 of nexp * nexp (* sugar for \texttt{enum (nexp'-nexp+1) nexp inc} or \texttt{enum (nexp-nexp'+1) nexp' dec} *)
- | Typ_lib_vector of nexp * nexp * order * typ (* vector of typ, indexed by natural range *)
- | Typ_lib_vector2 of typ * nexp (* sugar for vector indexed by [ nexp ] *)
- | Typ_lib_vector3 of typ * nexp * nexp (* sugar for vector indexed by [ nexp..nexp ] *)
- | Typ_lib_list of typ (* list of typ *)
- | Typ_lib_set of typ (* finite set of typ *)
- | Typ_lib_reg of typ (* mutable register components holding typ *)
-
-
diff --git a/language/l2.ml b/language/l2.ml
index 10b4fd7e..1ee2b64e 100644
--- a/language/l2.ml
+++ b/language/l2.ml
@@ -16,33 +16,22 @@ base_kind_aux = (* base kind *)
BK_type (* kind of types *)
| BK_nat (* kind of natural number size expressions *)
| BK_order (* kind of vector order specifications *)
- | BK_effects (* kind of effect sets *)
+ | BK_effect (* kind of effect sets *)
type
-var_aux = (* variables with kind, ticked to differntiate from program variables *)
+kid_aux = (* variables with kind, ticked to differntiate from program variables *)
Var of x
type
-id_aux = (* Identifier *)
- Id of x
- | DeIid of x (* remove infix status *)
-
-
-type
base_kind =
BK_aux of base_kind_aux * l
type
-var =
- Var_aux of var_aux * l
-
-
-type
-id =
- Id_aux of id_aux * l
+kid =
+ Kid_aux of kid_aux * l
type
@@ -52,8 +41,7 @@ kind_aux = (* kinds *)
type
nexp_aux = (* expression of kind $_$, for vector sizes and origins *)
- Nexp_id of id (* identifier *)
- | Nexp_var of var (* variable *)
+ Nexp_var of kid (* variable *)
| Nexp_constant of int (* constant *)
| Nexp_times of nexp * nexp (* product *)
| Nexp_sum of nexp * nexp (* sum *)
@@ -69,22 +57,22 @@ kind =
type
-nexp_constraint_aux = (* constraint over kind $_$ *)
+n_constraint_aux = (* constraint over kind $_$ *)
NC_fixed of nexp * nexp
| NC_bounded_ge of nexp * nexp
| NC_bounded_le of nexp * nexp
- | NC_nat_set_bounded of id * (int) list
+ | NC_nat_set_bounded of kid * (int) list
type
kinded_id_aux = (* optionally kind-annotated identifier *)
- KOpt_none of var (* identifier *)
- | KOpt_kind of kind * var (* kind-annotated variable *)
+ KOpt_none of kid (* identifier *)
+ | KOpt_kind of kind * kid (* kind-annotated variable *)
type
-nexp_constraint =
- NC_aux of nexp_constraint_aux * l
+n_constraint =
+ NC_aux of n_constraint_aux * l
type
@@ -93,25 +81,25 @@ kinded_id =
type
-efct_aux = (* effect *)
- Effect_rreg (* read register *)
- | Effect_wreg (* write register *)
- | Effect_rmem (* read memory *)
- | Effect_wmem (* write memory *)
- | Effect_undef (* undefined-instruction exception *)
- | Effect_unspec (* unspecified values *)
- | Effect_nondet (* nondeterminism from intra-instruction parallelism *)
+base_effect_aux = (* effect *)
+ BE_rreg (* read register *)
+ | BE_wreg (* write register *)
+ | BE_rmem (* read memory *)
+ | BE_wmem (* write memory *)
+ | BE_undef (* undefined-instruction exception *)
+ | BE_unspec (* unspecified values *)
+ | BE_nondet (* nondeterminism from intra-instruction parallelism *)
type
quant_item_aux = (* Either a kinded identifier or a nexp constraint for a typquant *)
QI_id of kinded_id (* An optionally kinded identifier *)
- | QI_const of nexp_constraint (* A constraint for this type *)
+ | QI_const of n_constraint (* A constraint for this type *)
type
-efct =
- Effect_aux of efct_aux * l
+base_effect =
+ BE_aux of base_effect_aux * l
type
@@ -120,29 +108,33 @@ quant_item =
type
-effects_aux = (* effect set, of kind $_$ *)
- Effects_id of id
- | Effects_var of var
- | Effects_set of (efct) list (* effect set *)
+effect_aux = (* effect set, of kind $_$ *)
+ Effect_var of kid
+ | Effect_set of (base_effect) list (* effect set *)
type
order_aux = (* vector order specifications, of kind $_$ *)
- Ord_id of id (* identifier *)
- | Ord_var of var (* variable *)
+ Ord_var of kid (* variable *)
| Ord_inc (* increasing (little-endian) *)
| Ord_dec (* decreasing (big-endian) *)
type
+id_aux = (* Identifier *)
+ Id of x
+ | DeIid of x (* remove infix status *)
+
+
+type
typquant_aux = (* type quantifiers and constraints *)
TypQ_tq of (quant_item) list
| TypQ_no_forall (* sugar, omitting quantifier and constraints *)
type
-effects =
- Effects_aux of effects_aux * l
+effect =
+ Effect_aux of effect_aux * l
type
@@ -151,6 +143,11 @@ order =
type
+id =
+ Id_aux of id_aux * l
+
+
+type
lit_aux = (* Literal constant *)
L_unit (* $() : _$ *)
| L_zero (* $_ : _$ *)
@@ -173,8 +170,8 @@ type
typ_aux = (* Type expressions, of kind $_$ *)
Typ_wild (* Unspecified type *)
| Typ_id of id (* Defined type *)
- | Typ_var of var (* Type variable *)
- | Typ_fn of typ * typ * effects (* Function type (first-order only in user code) *)
+ | Typ_var of kid (* Type variable *)
+ | Typ_fn of typ * typ * effect (* Function type (first-order only in user code) *)
| Typ_tup of (typ) list (* Tuple type *)
| Typ_app of id * (typ_arg) list (* type constructor application *)
@@ -185,7 +182,7 @@ and typ_arg_aux = (* Type constructor arguments of all kinds *)
Typ_arg_nexp of nexp
| Typ_arg_typ of typ
| Typ_arg_order of order
- | Typ_arg_effects of effects
+ | Typ_arg_effect of effect
and typ_arg =
Typ_arg_aux of typ_arg_aux * l
@@ -232,17 +229,7 @@ typschm =
type
-'a exp =
- E_aux of 'a exp_aux * 'a annot
-
-and 'a lexp_aux = (* lvalue expression *)
- LEXP_id of id (* identifier *)
- | LEXP_memory of id * 'a exp (* memory write via function call *)
- | LEXP_vector of 'a lexp * 'a exp (* vector element *)
- | LEXP_vector_range of 'a lexp * 'a exp * 'a exp (* subvector *)
- | LEXP_field of 'a lexp * id (* struct field *)
-
-and 'a lexp =
+'a lexp =
LEXP_aux of 'a lexp_aux * 'a annot
and 'a fexp_aux = (* Field-expression *)
@@ -295,11 +282,21 @@ and 'a exp_aux = (* Expression *)
| E_let of 'a letbind * 'a exp (* let expression *)
| E_assign of 'a lexp * 'a exp (* imperative assignment *)
+and 'a exp =
+ E_aux of 'a exp_aux * 'a annot
+
+and 'a lexp_aux = (* lvalue expression *)
+ LEXP_id of id (* identifier *)
+ | LEXP_memory of id * ('a exp) list (* memory write via function call *)
+ | LEXP_vector of 'a lexp * 'a exp (* vector element *)
+ | LEXP_vector_range of 'a lexp * 'a exp * 'a exp (* subvector *)
+ | LEXP_field of 'a lexp * id (* struct field *)
+
type
-'a effects_opt_aux = (* Optional effect annotation for functions *)
- Effects_opt_pure (* sugar for empty effect set *)
- | Effects_opt_effects of effects
+'a effect_opt_aux = (* Optional effect annotation for functions *)
+ Effect_opt_pure (* sugar for empty effect set *)
+ | Effect_opt_effect of effect
type
@@ -319,7 +316,7 @@ type
type
-naming_scheme_opt_aux = (* Optional variable-naming-scheme specification for variables of defined type *)
+name_scm_opt_aux = (* Optional variable-naming-scheme specification for variables of defined type *)
Name_sect_none
| Name_sect_some of string
@@ -331,8 +328,8 @@ type_union_aux = (* Type union constructors *)
type
-'a effects_opt =
- Effects_opt_aux of 'a effects_opt_aux * 'a annot
+'a effect_opt =
+ Effect_opt_aux of 'a effect_opt_aux * 'a annot
type
@@ -351,6 +348,16 @@ type
type
+name_scm_opt =
+ Name_sect_aux of name_scm_opt_aux * l
+
+
+type
+type_union =
+ Tu_aux of type_union_aux * l
+
+
+type
index_range_aux = (* index specification, for bitfields in register types *)
BF_single of int (* single index *)
| BF_range of int * int (* index range *)
@@ -361,32 +368,32 @@ and index_range =
type
-naming_scheme_opt =
- Name_sect_aux of naming_scheme_opt_aux * l
-
-
-type
-type_union =
- Tu_aux of type_union_aux * l
+'a fundef_aux = (* Function definition *)
+ FD_function of rec_opt * 'a tannot_opt * 'a effect_opt * ('a funcl) list
type
-'a fundef_aux = (* Function definition *)
- FD_function of rec_opt * 'a tannot_opt * 'a effects_opt * ('a funcl) list
+'a scattered_def_aux = (* Function and type union definitions that can be spread across
+ a file. Each one must end in $_$ *)
+ SD_scattered_function of rec_opt * 'a tannot_opt * 'a effect_opt * id (* scattered function definition header *)
+ | SD_scattered_funcl of 'a funcl (* scattered function definition clause *)
+ | SD_scattered_variant of id * name_scm_opt * typquant (* scattered union definition header *)
+ | SD_scattered_unioncl of id * type_union (* scattered union definition member *)
+ | SD_scattered_end of id (* scattered definition end *)
type
'a type_def_aux = (* Type definition body *)
- TD_abbrev of id * naming_scheme_opt * typschm (* type abbreviation *)
- | TD_record of id * naming_scheme_opt * typquant * ((typ * id)) list * bool (* struct type definition *)
- | TD_variant of id * naming_scheme_opt * typquant * (type_union) list * bool (* union type definition *)
- | TD_enum of id * naming_scheme_opt * (id) list * bool (* enumeration type definition *)
+ TD_abbrev of id * name_scm_opt * typschm (* type abbreviation *)
+ | TD_record of id * name_scm_opt * typquant * ((typ * id)) list * bool (* struct type definition *)
+ | TD_variant of id * name_scm_opt * typquant * (type_union) list * bool (* union type definition *)
+ | TD_enum of id * name_scm_opt * (id) list * bool (* enumeration type definition *)
| TD_register of id * nexp * nexp * ((index_range * id)) list (* register mutable bitfield type definition *)
type
-'a default_typing_spec_aux = (* Default kinding or typing assumption *)
- DT_kind of base_kind * var
+'a default_spec_aux = (* Default kinding or typing assumption *)
+ DT_kind of base_kind * kid
| DT_typ of typschm * id
@@ -403,13 +410,18 @@ type
type
+'a scattered_def =
+ SD_aux of 'a scattered_def_aux * 'a annot
+
+
+type
'a type_def =
TD_aux of 'a type_def_aux * 'a annot
type
-'a default_typing_spec =
- DT_aux of 'a default_typing_spec_aux * 'a annot
+'a default_spec =
+ DT_aux of 'a default_spec_aux * 'a annot
type
@@ -423,31 +435,9 @@ type
| DEF_fundef of 'a fundef (* function definition *)
| DEF_val of 'a letbind (* value definition *)
| DEF_spec of 'a val_spec (* top-level type constraint *)
- | DEF_default of 'a default_typing_spec (* default kind and type assumptions *)
+ | DEF_default of 'a default_spec (* default kind and type assumptions *)
+ | DEF_scattered of 'a scattered_def (* scattered function and type definition *)
| DEF_reg_dec of typ * id (* register declaration *)
- | DEF_scattered_function of rec_opt * 'a tannot_opt * 'a effects_opt * id (* scattered function definition header *)
- | DEF_scattered_funcl of 'a funcl (* scattered function definition clause *)
- | DEF_scattered_variant of id * naming_scheme_opt * typquant (* scattered union definition header *)
- | DEF_scattered_unioncl of id * typ * id (* scattered union definition member *)
- | DEF_scattered_end of id (* scattered definition end *)
-
-
-type
-'a typ_lib_aux = (* library types and syntactic sugar for them *)
- Typ_lib_unit (* unit type with value $()$ *)
- | Typ_lib_bool (* booleans $_$ and $_$ *)
- | Typ_lib_bit (* pure bit values (not mutable bits) *)
- | Typ_lib_nat (* natural numbers 0,1,2,... *)
- | Typ_lib_string of string (* UTF8 strings *)
- | Typ_lib_enum of nexp * nexp * order (* natural numbers nexp .. nexp+nexp-1, ordered by order *)
- | Typ_lib_enum1 of nexp (* sugar for \texttt{enum nexp 0 inc} *)
- | Typ_lib_enum2 of nexp * nexp (* sugar for \texttt{enum (nexp'-nexp+1) nexp inc} or \texttt{enum (nexp-nexp'+1) nexp' dec} *)
- | Typ_lib_vector of nexp * nexp * order * typ (* vector of typ, indexed by natural range *)
- | Typ_lib_vector2 of typ * nexp (* sugar for vector indexed by [ nexp ] *)
- | Typ_lib_vector3 of typ * nexp * nexp (* sugar for vector indexed by [ nexp..nexp ] *)
- | Typ_lib_list of typ (* list of typ *)
- | Typ_lib_set of typ (* finite set of typ *)
- | Typ_lib_reg of typ (* mutable register components holding typ *)
type
@@ -456,11 +446,6 @@ type
type
-'a typ_lib =
- Typ_lib_aux of 'a typ_lib_aux * l
-
-
-type
'a defs = (* Definition sequence *)
Defs of ('a def) list
diff --git a/language/l2.ott b/language/l2.ott
index 6b81b6e8..b3a3f8b8 100644
--- a/language/l2.ott
+++ b/language/l2.ott
@@ -116,7 +116,7 @@ id :: '' ::=
| bit :: M :: bit {{ ichlo bit_id }}
| unit :: M :: unit {{ ichlo unit_id }}
| nat :: M :: nat {{ ichlo nat_id }}
- | string :: M :: string {{ ichlo string_id }}
+ | string :: M :: string {{ tex \ottkw{string} }} {{ ichlo string_id }}
| enum :: M :: enum {{ ichlo enum_id }}
| vector :: M :: vector {{ ichlo vector_id }}
| list :: M :: list {{ ichlo list_id }}
@@ -129,7 +129,7 @@ id :: '' ::=
% We don't enforce a lexical convention on infix operators, as some of the
% targets use alphabetical infix operators.
-var :: '' ::=
+kid :: '' ::=
{{ com variables with kind, ticked to differntiate from program variables }}
{{ aux _ l }}
| ' x :: :: var
@@ -148,20 +148,18 @@ base_kind :: 'BK_' ::=
| Type :: :: type {{ com kind of types }}
| Nat :: :: nat {{ com kind of natural number size expressions }}
| Order :: :: order {{ com kind of vector order specifications }}
- | Effects :: :: effects {{ com kind of effect sets }}
+ | Effect :: :: effect {{ com kind of effect sets }}
kind :: 'K_' ::=
{{ com kinds}}
{{ aux _ l }}
| base_kind1 -> ... -> base_kindn :: :: kind
% we'll never use ...-> Nat , .. Order , .. or Effects
-
nexp :: 'Nexp_' ::=
{{ com expression of kind $[[Nat]]$, for vector sizes and origins }}
{{ aux _ l }}
- | id :: :: id {{ com identifier }}
- | var :: :: var {{ com variable }}
+ | kid :: :: var {{ com variable }}
| num :: :: constant {{ com constant }}
| nexp1 * nexp2 :: :: times {{ com product }}
%{{ com must be linear after normalisation... except for the type of *, ahem }}
@@ -172,13 +170,12 @@ nexp :: 'Nexp_' ::=
order :: 'Ord_' ::=
{{ com vector order specifications, of kind $[[Order]]$}}
{{ aux _ l }}
- | id :: :: id {{ com identifier }}
- | var :: :: var {{ com variable }}
+ | kid :: :: var {{ com variable }}
| inc :: :: inc {{ com increasing (little-endian) }}
| dec :: :: dec {{ com decreasing (big-endian) }}
| ( order ) :: S :: paren {{ ichlo [[order]] }}
-efct :: 'Effect_' ::=
+base_effect :: 'BE_' ::=
{{ com effect }}
{{ aux _ l }}
| rreg :: :: rreg {{ com read register }}
@@ -190,14 +187,13 @@ efct :: 'Effect_' ::=
| nondet :: :: nondet {{ com nondeterminism from intra-instruction parallelism }}
-effects :: 'Effects_' ::=
+effect :: 'Effect_' ::=
{{ com effect set, of kind $[[Effects]]$ }}
{{ aux _ l }}
- | effect id :: :: id
- | effect var :: :: var
- | effect { efct1 , .. , efctn } :: :: set {{ com effect set }}
+ | kid :: :: var
+ | { base_effect1 , .. , base_effectn } :: :: set {{ com effect set }}
| pure :: M :: pure {{ com sugar for empty effect set }} {{ ichlo [] }}
- | effects1 u+ .. u+ effectsn :: M :: union {{ com meta operation for combining sets of effects }} {{ ichlo [] }}
+ | effect1 u+ .. u+ effectn :: M :: union {{ com meta operation for combining sets of effects }} {{ ichlo [] }}
% TODO: are we going to need any effect polymorphism? Conceivably for built-in maps and folds. Yes. But we think we don't need any interesting effect-set expressions, eg effectset-variable union {rreg}.
@@ -208,18 +204,36 @@ typ :: 'Typ_' ::=
{{ com Unspecified type }}
| id :: :: id
{{ com Defined type }}
- | var :: :: var
+ | kid :: :: var
{{ com Type variable }}
- | typ1 -> typ2 effects :: :: fn
+ | typ1 -> typ2 effectkw effect :: :: fn
{{ com Function type (first-order only in user code) }}
% TODO: build first-order restriction into AST or just into type rules? neither - see note
% TODO: concrete syntax for effects in a function type? needed only for pp, not in user syntax.
| typ1 * .... * typn :: :: tup
{{ com Tuple type }}
% TODO union in the other kind grammars? or make a syntax of argument? or glom together the grammars and leave o the typechecker
- | id < typ_arg1 .. typ_argn > :: :: app
+ | id < typ_arg1 , .. , typ_argn > :: :: app
{{ com type constructor application }}
| ( typ ) :: S :: paren {{ ichlo [[typ]] }}
+% | enum < nexp1, nexp2, order> :: :: enum {{ com natural numbers [[nexp2]] .. [[nexp2]]+[[nexp1]]-1, ordered by [[order]] }}
+ | [| nexp |] :: S :: enum1 {{ichlo enum <[[nexp]], 0, inc> }} {{ com sugar for \texttt{enum nexp 0 inc} }}
+ | [| nexp : nexp' |] :: S :: enum2 {{ichlo enum <[[nexp]],[[nexp']],inc> }} {{ com sugar for \texttt{enum (nexp'-nexp+1) nexp inc} or \texttt{enum (nexp-nexp'+1) nexp' dec} }}
+% use .. not - to avoid ambiguity with nexp -
+% total maps and vectors indexed by finite subranges of nat
+% | vector nexp1 nexp2 order typ :: :: vector {{ com vector of [[typ]], indexed by natural range }}
+% probably some sugar for vector types, using [ ] similarly to enums:
+% (but with .. not : in the former, to avoid confusion...)
+ | typ [ nexp ] :: S :: vector2 {{ichlo vector < [[nexp]],0,inc,[[typ]] > }} {{ com sugar for vector indexed by [ [[nexp]] ] }}
+ | typ [ nexp : nexp' ] :: S :: vector3 {{ ichlo vector < [[nexp]],[[nexp']],inc,[[typ]] }} {{ com sugar for vector indexed by [ [[nexp]]..[[nexp']] ] }}
+% ...so bit [ nexp ] etc is just an instance of that
+% | List < typ > :: :: list {{ com list of [[typ]] }}
+% | Set < typ > :: :: set {{ com finite set of [[typ]] }}
+% | Reg < typ > :: :: reg {{ com mutable register components holding [[typ]] }}
+% "reg t" is basically the ML "t ref"
+% not sure how first-class it should be, though
+% use "reg word32" etc for the types of vanilla registers
+
typ_arg :: 'Typ_arg_' ::=
{{ com Type constructor arguments of all kinds }}
@@ -227,38 +241,21 @@ typ_arg :: 'Typ_arg_' ::=
| nexp :: :: nexp
| typ :: :: typ
| order :: :: order
- | effects :: :: effects
+ | effect :: :: effect
% plus more for l-value/r-value pairs, as introduced by the L3 'compound' declarations ... ref typ
-typ_lib :: 'Typ_lib_' ::=
- {{ com library types and syntactic sugar for them }}
- {{ aux _ l }} {{ auxparam 'a }}
+%typ_lib :: 'Typ_lib_' ::=
+% {{ com library types and syntactic sugar for them }}
+% {{ aux _ l }} {{ auxparam 'a }}
% boring base types:
- | unit :: :: unit {{ com unit type with value $()$ }}
- | bool :: :: bool {{ com booleans $[[true]]$ and $[[false]]$ }}
- | bit :: :: bit {{ com pure bit values (not mutable bits) }}
+%% | unit :: :: unit {{ com unit type with value $()$ }}
+% | bool :: :: bool {{ com booleans $[[true]]$ and $[[false]]$ }}
+% | bit :: :: bit {{ com pure bit values (not mutable bits) }}
% experimentally trying with two distinct types of bool and bit ...
- | nat :: :: nat {{ com natural numbers 0,1,2,... }}
- | string :: :: string {{ com UTF8 strings }}
+% | nat :: :: nat {{ com natural numbers 0,1,2,... }}
+% | string :: :: string {{ com UTF8 strings }}
% finite subranges of nat
- | Enum nexp1 nexp2 order :: :: enum {{ com natural numbers [[nexp2]] .. [[nexp2]]+[[nexp1]]-1, ordered by [[order]] }}
- | [ 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} }}
-% use .. not - to avoid ambiguity with nexp -
-% total maps and vectors indexed by finite subranges of nat
- | Vector nexp1 nexp2 order typ :: :: vector {{ com vector of [[typ]], indexed by natural range }}
-% probably some sugar for vector types, using [ ] similarly to enums:
-% (but with .. not : in the former, to avoid confusion...)
- | typ [ nexp ] :: :: vector2 {{ com sugar for vector indexed by [ [[nexp]] ] }}
- | typ [ nexp : nexp' ] :: :: vector3 {{ com sugar for vector indexed by [ [[nexp]]..[[nexp']] ] }}
-% ...so bit [ nexp ] etc is just an instance of that
- | List < typ > :: :: list {{ com list of [[typ]] }}
- | Set < typ > :: :: set {{ com finite set of [[typ]] }}
- | Reg < typ > :: :: reg {{ com mutable register components holding [[typ]] }}
-% "reg t" is basically the ML "t ref"
-% not sure how first-class it should be, though
-% use "reg word32" etc for the types of vanilla registers
parsing
@@ -270,13 +267,13 @@ Typ_fn <= Typ_tup
grammar
-nexp_constraint :: 'NC_' ::=
+n_constraint :: 'NC_' ::=
{{ com constraint over kind $[[Nat]]$ }}
{{ aux _ l }}
| nexp = nexp' :: :: fixed
| nexp >= nexp' :: :: bounded_ge
| nexp '<=' nexp' :: :: bounded_le
- | id 'IN' { num1 , ... , numn } :: :: nat_set_bounded
+ | kid 'IN' { num1 , ... , numn } :: :: nat_set_bounded
% Note only id on the left and constants on the right in a
% finite-set-bound, as we don't think we need anything more
@@ -284,14 +281,14 @@ nexp_constraint :: 'NC_' ::=
kinded_id :: 'KOpt_' ::=
{{ com optionally kind-annotated identifier }}
{{ aux _ l }}
- | var :: :: none {{ com identifier }}
- | kind var :: :: kind {{ com kind-annotated variable }}
+ | kid :: :: none {{ com identifier }}
+ | kind kid :: :: kind {{ com kind-annotated variable }}
quant_item :: 'QI_' ::=
{{ com Either a kinded identifier or a nexp constraint for a typquant }}
{{ aux _ l }}
| kinded_id :: :: id {{ com An optionally kinded identifier }}
- | nexp_constraint :: :: const {{ com A constraint for this type }}
+ | n_constraint :: :: const {{ com A constraint for this type }}
typquant :: 'TypQ_' ::=
{{ com type quantifiers and constraints}}
@@ -332,7 +329,7 @@ grammar
%% | enumeration_flag_opt '|' ctor_def1 '|' ... '|' ctor_defn :: :: variant
%% {{ com Variant types }}
%%
- naming_scheme_opt :: 'Name_sect_' ::=
+ name_scm_opt :: 'Name_sect_' ::=
{{ com Optional variable-naming-scheme specification for variables of defined type }}
{{ aux _ l }}
| :: :: none
@@ -353,18 +350,18 @@ grammar
type_def :: 'TD_' ::=
{{ com Type definition body }}
{{ aux _ annot }} {{ auxparam 'a }}
- | typedef id naming_scheme_opt = typschm :: :: abbrev
+ | typedef id name_scm_opt = typschm :: :: abbrev
{{ com type abbreviation }} {{ texlong }}
- | typedef id naming_scheme_opt = const struct typquant { typ1 id1 ; ... ; typn idn semi_opt } :: :: record
+ | typedef id name_scm_opt = const struct typquant { typ1 id1 ; ... ; typn idn semi_opt } :: :: record
{{ com struct type definition }} {{ texlong }}
% for specifying constructor result types of nat-indexed GADTs, we can
% let the typi be function types (as constructors are not allowed to
% take parameters of function types)
% concrete syntax: to be even closer to C, could have a postfix id rather than prefix id =
- | typedef id naming_scheme_opt = const union typquant { type_union1 ; ... ; type_unionn semi_opt } :: :: variant
+ | typedef id name_scm_opt = const union typquant { type_union1 ; ... ; type_unionn semi_opt } :: :: variant
{{ com union type definition}} {{ texlong }}
- | typedef id naming_scheme_opt = enumerate { id1 ; ... ; idn semi_opt } :: :: enum
+ | typedef id name_scm_opt = enumerate { id1 ; ... ; idn semi_opt } :: :: enum
{{ com enumeration type definition}} {{ texlong }}
| typedef id = register bits [ nexp : nexp' ] { index_range1 : id1 ; ... ; index_rangen : idn }
@@ -521,9 +518,9 @@ exp :: 'E_' ::=
| id ( exp1 , .. , expn ) :: :: app
{{ com function application }}
+ | id exp :: S :: tup_app {{ ichlo [[id ( exp ) ]] }} {{ com No extra parens needed when exp is a tuple }}
+
% Note: fully applied function application only
-% We might restrict exp to be an identifier
-% We might require expn to have outermost parentheses (but not two sets if it's a tuple)
| exp1 id exp2 :: :: app_infix
{{ com infix function application }}
@@ -620,7 +617,8 @@ lexp :: 'LEXP_' ::= {{ com lvalue expression }}
{{ aux _ annot }} {{ auxparam 'a }}
| id :: :: id
{{ com identifier }}
- | id exp :: :: memory {{ com memory write via function call }}
+ | id ( exp1 , .. , expn ) :: :: memory {{ com memory write via function call }}
+ | id exp :: S :: mem_tup {{ ichlo [[id (exp)]] }}
| lexp [ exp ] :: :: vector {{ com vector element }}
| lexp [ exp1 : exp2 ] :: :: vector_range {{ com subvector }}
% maybe comma-sep such lists too
@@ -727,11 +725,11 @@ rec_opt :: 'Rec_' ::=
| :: :: nonrec {{ com non-recursive }}
| rec :: :: rec {{ com recursive }}
-effects_opt :: 'Effects_opt_' ::=
+effect_opt :: 'Effect_opt_' ::=
{{ com Optional effect annotation for functions }}
{{ aux _ annot }} {{ auxparam 'a }}
| :: :: pure {{ com sugar for empty effect set }}
- | effects :: :: effects
+ | effectkw effect :: :: effect
funcl :: 'FCL_' ::=
{{ com Function clause }}
@@ -742,7 +740,7 @@ funcl :: 'FCL_' ::=
fundef :: 'FD_' ::=
{{ com Function definition}}
{{ aux _ annot }} {{ auxparam 'a }}
- | function rec_opt tannot_opt effects_opt funcl1 and ... and funcln :: :: function {{ texlong }}
+ | function rec_opt tannot_opt effect_opt funcl1 and ... and funcln :: :: function {{ texlong }}
% {{ com function definition }}
% TODO note that the typ in the tannot_opt is the *result* type, not
% the type of the whole function. The argument type comes from the
@@ -769,10 +767,10 @@ val_spec :: 'VS_' ::=
| val extern typschm id = string :: :: extern_spec
{{ com Specify the type and id of a function from Lem, where the string must provide an explicit path to the required function but will not be checked }}
-default_typing_spec :: 'DT_' ::=
+default_spec :: 'DT_' ::=
{{ com Default kinding or typing assumption }}
{{ aux _ annot }} {{ auxparam 'a }}
- | default base_kind var :: :: kind
+ | default base_kind kid :: :: kind
| default typschm id :: :: typ
% The intended semantics of these is that if an id in binding position
% doesn't have a kind or type annotation, then we look through the
@@ -781,6 +779,22 @@ default_typing_spec :: 'DT_' ::=
% Otherwise we try to infer. Perhaps warn if there are multiple matches.
% For example, we might often have default Type ['alphanum]
+scattered_def :: 'SD_' ::=
+ {{ com Function and type union definitions that can be spread across
+ a file. Each one must end in $[[end id]]$ }}
+ {{ aux _ annot }} {{ auxparam 'a }}
+ | scattered function rec_opt tannot_opt effect_opt id :: :: scattered_function {{ texlong }} {{ com scattered function definition header }}
+
+ | function clause funcl :: :: scattered_funcl
+{{ com scattered function definition clause }}
+
+ | scattered typedef id name_scm_opt = const union typquant :: :: scattered_variant {{ texlong }} {{ com scattered union definition header }}
+
+ | union id member type_union :: :: scattered_unioncl {{ com scattered union definition member }}
+ | end id :: :: scattered_end
+{{ com scattered definition end }}
+
+
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Top-level definitions %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@@ -796,21 +810,13 @@ def :: 'DEF_' ::=
{{ com value definition }}
| val_spec :: :: spec
{{ com top-level type constraint }}
- | default_typing_spec :: :: default
+ | default_spec :: :: default
{{ com default kind and type assumptions }}
+ | scattered_def :: :: scattered
+ {{ com scattered function and type definition }}
| register typ id :: :: reg_dec
{{ com register declaration }}
- | scattered function rec_opt tannot_opt effects_opt id :: :: scattered_function {{ texlong }} {{ com scattered function definition header }}
-
- | function clause funcl :: :: scattered_funcl
-{{ com scattered function definition clause }}
-
- | scattered typedef id naming_scheme_opt = const union typquant :: :: scattered_variant {{ texlong }} {{ com scattered union definition header }}
-
- | union id member typ id' :: :: scattered_unioncl {{ com scattered union definition member }}
- | end id :: :: scattered_end
-{{ com scattered definition end }}
defs :: '' ::=
{{ com Definition sequence }}
@@ -886,6 +892,8 @@ terminals :: '' ::=
{{ tex \ensuremath{\Rightarrow} }}
| -- :: :: dashdash
{{ tex \mbox{--} }}
+ | effectkw :: :: effectkw
+ {{ tex \ottkw{effect} }}
| empty :: :: empty
{{ tex \ensuremath{\epsilon} }}
| consistent_increase :: :: ci
@@ -894,3 +902,4 @@ terminals :: '' ::=
{{ tex \ottkw{consistent\_decrease}~ }}
+
diff --git a/language/l2_parse.ml b/language/l2_parse.ml
index b196f007..a6ada0ec 100644
--- a/language/l2_parse.ml
+++ b/language/l2_parse.ml
@@ -1,4 +1,4 @@
-(* generated by Ott 0.22 from: l2_parse.ott *)
+(* generated by Ott 0.23 from: l2_parse.ott *)
type text = string
@@ -21,7 +21,7 @@ base_kind_aux = (* base kind *)
BK_type (* kind of types *)
| BK_nat (* kind of natural number size expressions *)
| BK_order (* kind of vector order specifications *)
- | BK_effects (* kind of effect sets *)
+ | BK_effect (* kind of effect sets *)
type
@@ -31,19 +31,19 @@ id_aux = (* Identifier *)
type
-var_aux = (* variables with kind, ticked to differntiate from program variables *)
+kid_aux = (* identifiers with kind, ticked to differntiate from program variables *)
Var of x
type
-efct_aux = (* effect *)
- Effect_rreg (* read register *)
- | Effect_wreg (* write register *)
- | Effect_rmem (* read memory *)
- | Effect_wmem (* write memory *)
- | Effect_undef (* undefined-instruction exception *)
- | Effect_unspec (* unspecified values *)
- | Effect_nondet (* nondeterminism from intra-instruction parallelism *)
+base_effect_aux = (* effect *)
+ BE_rreg (* read register *)
+ | BE_wreg (* write register *)
+ | BE_rmem (* read memory *)
+ | BE_wmem (* write memory *)
+ | BE_undef (* undefined-instruction exception *)
+ | BE_unspec (* unspecified values *)
+ | BE_nondet (* nondeterminism from intra-instruction parallelism *)
type
@@ -57,13 +57,13 @@ id =
type
-var =
- Var_aux of var_aux * l
+kid =
+ Kid_aux of kid_aux * l
type
-efct =
- Effect_aux of efct_aux * l
+base_effect =
+ BE_aux of base_effect_aux * l
type
@@ -74,17 +74,14 @@ kind_aux = (* kinds *)
type
atyp_aux = (* expressions of all kinds, to be translated to types, nats, orders, and effects after parsing *)
ATyp_id of id (* identifier *)
- | ATyp_var of var (* ticked variable *)
+ | ATyp_var of kid (* ticked variable *)
| ATyp_constant of int (* constant *)
| ATyp_times of atyp * atyp (* product *)
| ATyp_sum of atyp * atyp (* sum *)
| ATyp_exp of atyp (* exponential *)
| ATyp_inc (* increasing (little-endian) *)
| ATyp_dec (* decreasing (big-endian) *)
- | ATyp_efid of id
- | ATyp_efvar of var
- | ATyp_set of (efct) list (* effect set *)
- | ATyp_wild (* Unspecified type *)
+ | ATyp_set of (base_effect) list (* effect set *)
| ATyp_fn of atyp * atyp * atyp (* Function type (first-order only in user code), last atyp is an effect *)
| ATyp_tup of (atyp) list (* Tuple type *)
| ATyp_app of id * (atyp) list (* type constructor application *)
@@ -99,22 +96,22 @@ kind =
type
-nexp_constraint_aux = (* constraint over kind $_$ *)
+n_constraint_aux = (* constraint over kind $_$ *)
NC_fixed of atyp * atyp
| NC_bounded_ge of atyp * atyp
| NC_bounded_le of atyp * atyp
- | NC_nat_set_bounded of id * (int) list
+ | NC_nat_set_bounded of kid * (int) list
type
kinded_id_aux = (* optionally kind-annotated identifier *)
- KOpt_none of var (* identifier *)
- | KOpt_kind of kind * var (* kind-annotated variable *)
+ KOpt_none of kid (* identifier *)
+ | KOpt_kind of kind * kid (* kind-annotated variable *)
type
-nexp_constraint =
- NC_aux of nexp_constraint_aux * l
+n_constraint =
+ NC_aux of n_constraint_aux * l
type
@@ -125,7 +122,7 @@ kinded_id =
type
quant_item_aux = (* Either a kinded identifier or a nexp constraint for a typquant *)
QI_id of kinded_id (* An optionally kinded identifier *)
- | QI_const of nexp_constraint (* A constraint for this type *)
+ | QI_const of n_constraint (* A constraint for this type *)
type
@@ -254,15 +251,21 @@ and letbind =
type
+name_scm_opt_aux = (* Optional variable-naming-scheme specification for variables of defined type *)
+ Name_sect_none
+ | Name_sect_some of string
+
+
+type
type_union_aux = (* Type union constructors *)
Tu_id of id
| Tu_ty_id of atyp * id
type
-naming_scheme_opt_aux = (* Optional variable-naming-scheme specification for variables of defined type *)
- Name_sect_none
- | Name_sect_some of string
+rec_opt_aux = (* Optional recursive annotation for functions *)
+ Rec_nonrec (* non-recursive *)
+ | Rec_rec (* recursive *)
type
@@ -272,9 +275,9 @@ tannot_opt_aux = (* Optional type annotation for functions *)
type
-rec_opt_aux = (* Optional recursive annotation for functions *)
- Rec_nonrec (* non-recursive *)
- | Rec_rec (* recursive *)
+effect_opt_aux = (* Optional effect annotation for functions *)
+ Effect_opt_pure (* sugar for empty effect set *)
+ | Effect_opt_effect of atyp
type
@@ -283,14 +286,8 @@ funcl_aux = (* Function clause *)
type
-effects_opt_aux = (* Optional effect annotation for functions *)
- Effects_opt_pure (* sugar for empty effect set *)
- | Effects_opt_effects of atyp
-
-
-type
-type_union =
- Tu_aux of type_union_aux * l
+name_scm_opt =
+ Name_sect_aux of name_scm_opt_aux * l
type
@@ -304,8 +301,13 @@ and index_range =
type
-naming_scheme_opt =
- Name_sect_aux of naming_scheme_opt_aux * l
+type_union =
+ Tu_aux of type_union_aux * l
+
+
+type
+rec_opt =
+ Rec_aux of rec_opt_aux * l
type
@@ -314,8 +316,8 @@ tannot_opt =
type
-rec_opt =
- Rec_aux of rec_opt_aux * l
+effect_opt =
+ Effect_opt_aux of effect_opt_aux * l
type
@@ -324,40 +326,55 @@ funcl =
type
-effects_opt =
- Effects_opt_aux of effects_opt_aux * l
+type_def_aux = (* Type definition body *)
+ TD_abbrev of id * name_scm_opt * typschm (* type abbreviation *)
+ | TD_record of id * name_scm_opt * typquant * ((atyp * id)) list * bool (* struct type definition *)
+ | TD_variant of id * name_scm_opt * typquant * (type_union) list * bool (* union type definition *)
+ | TD_enum of id * name_scm_opt * (id) list * bool (* enumeration type definition *)
+ | TD_register of id * atyp * atyp * ((index_range * id)) list (* register mutable bitfield type definition *)
type
-type_def_aux = (* Type definition body *)
- TD_abbrev of id * naming_scheme_opt * typschm (* type abbreviation *)
- | TD_record of id * naming_scheme_opt * typquant * ((atyp * id)) list * bool (* struct type definition *)
- | TD_variant of id * naming_scheme_opt * typquant * (type_union) list * bool (* union type definition *)
- | TD_enum of id * naming_scheme_opt * (id) list * bool (* enumeration type definition *)
- | TD_register of id * atyp * atyp * ((index_range * id)) list (* register mutable bitfield type definition *)
+scattered_def_aux = (* Function and type union definitions that can be spread across
+ a file. Each one must end in $_$ *)
+ SD_scattered_function of rec_opt * tannot_opt * effect_opt * id (* scattered function definition header *)
+ | SD_scattered_funcl of funcl (* scattered function definition clause *)
+ | SD_scattered_variant of id * name_scm_opt * typquant (* scattered union definition header *)
+ | SD_scattered_unioncl of id * type_union (* scattered union definition member *)
+ | SD_scattered_end of id (* scattered definition end *)
+
+
+type
+val_spec_aux = (* Value type specification *)
+ VS_val_spec of typschm * id
+ | VS_extern_no_rename of typschm * id
+ | VS_extern_spec of typschm * id * string
type
default_typing_spec_aux = (* Default kinding or typing assumption *)
- DT_kind of base_kind * var
+ DT_kind of base_kind * kid
| DT_typ of typschm * id
type
fundef_aux = (* Function definition *)
- FD_function of rec_opt * tannot_opt * effects_opt * (funcl) list
+ FD_function of rec_opt * tannot_opt * effect_opt * (funcl) list
type
-val_spec_aux = (* Value type specification *)
- VS_val_spec of typschm * id
- | VS_extern_no_rename of typschm * id
- | VS_extern_spec of typschm * id * string
+type_def =
+ TD_aux of type_def_aux * l
type
-type_def =
- TD_aux of type_def_aux * l
+scattered_def =
+ SD_aux of scattered_def_aux * l
+
+
+type
+val_spec =
+ VS_aux of val_spec_aux * l
type
@@ -371,23 +388,14 @@ fundef =
type
-val_spec =
- VS_aux of val_spec_aux * l
-
-
-type
def_aux = (* Top-level definition *)
DEF_type of type_def (* type definition *)
| DEF_fundef of fundef (* function definition *)
| DEF_val of letbind (* value definition *)
| DEF_spec of val_spec (* top-level type constraint *)
| DEF_default of default_typing_spec (* default kind and type assumptions *)
+ | DEF_scattered of scattered_def (* scattered definition *)
| DEF_reg_dec of atyp * id (* register declaration *)
- | DEF_scattered_function of rec_opt * tannot_opt * effects_opt * id (* scattered function definition header *)
- | DEF_scattered_funcl of funcl (* scattered function definition clause *)
- | DEF_scattered_variant of id * naming_scheme_opt * typquant (* scattered union definition header *)
- | DEF_scattered_unioncl of id * atyp * id (* scattered union definition member *)
- | DEF_scattered_end of id (* scattered definition end *)
type
@@ -396,26 +404,9 @@ def =
type
-typ_lib_aux = (* library types and syntactic sugar for them *)
- Typ_lib_unit (* unit type with value $()$ *)
- | Typ_lib_bool (* booleans $_$ and $_$ *)
- | Typ_lib_bit (* pure bit values (not mutable bits) *)
- | Typ_lib_nat (* natural numbers 0,1,2,... *)
- | Typ_lib_string of string (* UTF8 strings *)
- | Typ_lib_enum (* natural numbers _ .. _+_-1, ordered by order *)
- | Typ_lib_enum1 (* sugar for \texttt{enum nexp 0 inc} *)
- | Typ_lib_enum2 (* sugar for \texttt{enum (nexp'-nexp+1) nexp inc} or \texttt{enum (nexp-nexp'+1) nexp' dec} *)
- | Typ_lib_vector of atyp (* vector of atyp, indexed by natural range *)
- | Typ_lib_vector2 of atyp (* sugar for vector indexed by [ atyp ] *)
- | Typ_lib_vector3 of atyp (* sugar for vector indexed by [ atyp.._ ] *)
- | Typ_lib_list of atyp (* list of atyp *)
- | Typ_lib_set of atyp (* finite set of atyp *)
- | Typ_lib_reg of atyp (* mutable register components holding atyp *)
-
-
-type
lexp_aux = (* lvalue expression *)
LEXP_id of id (* identifier *)
+ | LEXP_mem of id * (exp) list
| LEXP_vector of lexp * exp (* vector element *)
| LEXP_vector_range of lexp * exp * exp (* subvector *)
| LEXP_field of lexp * id (* struct field *)
@@ -429,9 +420,4 @@ defs = (* Definition sequence *)
Defs of (def) list
-type
-typ_lib =
- Typ_lib_aux of typ_lib_aux * l
-
-
diff --git a/language/l2_parse.ott b/language/l2_parse.ott
index f96c3f99..af90abaa 100644
--- a/language/l2_parse.ott
+++ b/language/l2_parse.ott
@@ -119,8 +119,8 @@ id :: '' ::=
| ( deinfix x ) :: :: deIid {{ com remove infix status }}
-var :: '' ::=
- {{ com variables with kind, ticked to differntiate from program variables }}
+kid :: '' ::=
+ {{ com identifiers with kind, ticked to differntiate from program variables }}
{{ aux _ l }}
| ' x :: :: var
@@ -145,7 +145,7 @@ base_kind :: 'BK_' ::=
| Type :: :: type {{ com kind of types }}
| Nat :: :: nat {{ com kind of natural number size expressions }}
| Order :: :: order {{ com kind of vector order specifications }}
- | Effects :: :: effects {{ com kind of effect sets }}
+ | Effect :: :: effect {{ com kind of effect sets }}
kind :: 'K_' ::=
{{ com kinds}}
@@ -153,7 +153,7 @@ kind :: 'K_' ::=
| base_kind1 -> ... -> base_kindn :: :: kind
% we'll never use ...-> Nat
-efct :: 'Effect_' ::=
+base_effect :: 'BE_' ::=
{{ com effect }}
{{ aux _ l }}
| rreg :: :: rreg {{ com read register }}
@@ -168,7 +168,7 @@ atyp :: 'ATyp_' ::=
{{ com expressions of all kinds, to be translated to types, nats, orders, and effects after parsing }}
{{ aux _ l }}
| id :: :: id {{ com identifier }}
- | var :: :: var {{ com ticked variable }}
+ | kid :: :: var {{ com ticked variable }}
| num :: :: constant {{ com constant }}
| atyp1 * atyp2 :: :: times {{ com product }}
| atyp1 + atyp2 :: :: sum {{ com sum }}
@@ -177,48 +177,43 @@ atyp :: 'ATyp_' ::=
| inc :: :: inc {{ com increasing (little-endian) }}
| dec :: :: dec {{ com decreasing (big-endian) }}
- | effect id :: :: efid
- | effect var :: :: efvar
- | effect { efct1 , .. , efctn } :: :: set {{ com effect set }}
+ | { base_effect1 , .. , base_effectn } :: :: set {{ com effect set }}
| pure :: M :: pure {{ com sugar for empty effect set }} {{ icho [] }}
-
- | _ :: :: wild
- {{ com Unspecified type }}
- | atyp1 -> atyp2 atyp3 :: :: fn
+ | atyp1 -> atyp2 effect atyp3 :: :: fn
{{ com Function type (first-order only in user code), last atyp is an effect }}
| atyp1 * .... * atypn :: :: tup
{{ com Tuple type }}
- | id < atyp1 .. atypn > :: :: app
+ | id < atyp1 , .. , atypn > :: :: app
{{ com type constructor application }}
% plus more for l-value/r-value pairs, as introduced by the L3 'compound' declarations ... ref typ
-typ_lib :: 'Typ_lib_' ::=
- {{ com library types and syntactic sugar for them }}
- {{ aux _ l }} %{{ auxparam 'a }}
+%typ_lib :: 'Typ_lib_' ::=
+% {{ com library types and syntactic sugar for them }}
+% {{ aux _ l }} %{{ auxparam 'a }}
% boring base types:
- | unit :: :: unit {{ com unit type with value $()$ }}
- | bool :: :: bool {{ com booleans $[[true]]$ and $[[false]]$ }}
- | bit :: :: bit {{ com pure bit values (not mutable bits) }}
+% | unit :: :: unit {{ com unit type with value $()$ }}
+% | bool :: :: bool {{ com booleans $[[true]]$ and $[[false]]$ }}
+% | bit :: :: bit {{ com pure bit values (not mutable bits) }}
% experimentally trying with two distinct types of bool and bit ...
- | nat :: :: nat {{ com natural numbers 0,1,2,... }}
- | string :: :: string {{ com UTF8 strings }}
+% | nat :: :: nat {{ com natural numbers 0,1,2,... }}
+% | string :: :: string {{ com UTF8 strings }}
% finite subranges of nat
- | enum nexp1 nexp2 order :: :: enum {{ com natural numbers [[atyp2]] .. [[atyp2]]+[[atyp1]]-1, ordered by order }}
- | [ 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} }}
+% | enum nexp1 nexp2 order :: :: enum {{ com natural numbers [[atyp2]] .. [[atyp2]]+[[atyp1]]-1, ordered by order }}
+% | [ 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} }}
% use .. not - to avoid ambiguity with nexp -
% total maps and vectors indexed by finite subranges of nat
- | vector nexp1 nexp2 order atyp :: :: vector {{ com vector of [[atyp]], indexed by natural range }}
+% | vector nexp1 nexp2 order atyp :: :: vector {{ com vector of [[atyp]], indexed by natural range }}
% probably some sugar for vector types, using [ ] similarly to enums:
% (but with .. not : in the former, to avoid confusion...)
- | atyp [ nexp ] :: :: vector2 {{ com sugar for vector indexed by [ [[atyp]] ] }}
- | atyp [ nexp : nexp' ] :: :: vector3 {{ com sugar for vector indexed by [ [[atyp]]..[[atyp']] ] }}
+% | atyp [ nexp ] :: :: vector2 {{ com sugar for vector indexed by [ [[atyp]] ] }}
+% | atyp [ nexp : nexp' ] :: :: vector3 {{ com sugar for vector indexed by [ [[atyp]]..[[atyp']] ] }}
% ...so bit [ nexp ] etc is just an instance of that
- | list atyp :: :: list {{ com list of [[atyp]] }}
- | set atyp :: :: set {{ com finite set of [[atyp]] }}
- | reg atyp :: :: reg {{ com mutable register components holding [[atyp]] }}
+% | list atyp :: :: list {{ com list of [[atyp]] }}
+% | set atyp :: :: set {{ com finite set of [[atyp]] }}
+% | reg atyp :: :: reg {{ com mutable register components holding [[atyp]] }}
% "reg t" is basically the ML "t ref"
% not sure how first-class it should be, though
% use "reg word32" etc for the types of vanilla registers
@@ -231,13 +226,13 @@ ATyp_fn <= ATyp_tup
grammar
-nexp_constraint :: 'NC_' ::=
+n_constraint :: 'NC_' ::=
{{ com constraint over kind $[[Nat]]$ }}
{{ aux _ l }}
| atyp = atyp' :: :: fixed
| atyp >= atyp' :: :: bounded_ge
| atyp '<=' atyp' :: :: bounded_le
- | id 'IN' { num1 , ... , numn } :: :: nat_set_bounded
+ | kid 'IN' { num1 , ... , numn } :: :: nat_set_bounded
% Note only id on the left and constants on the right in a
% finite-set-bound, as we don't think we need anything more
@@ -245,14 +240,14 @@ nexp_constraint :: 'NC_' ::=
kinded_id :: 'KOpt_' ::=
{{ com optionally kind-annotated identifier }}
{{ aux _ l }}
- | var :: :: none {{ com identifier }}
- | kind var :: :: kind {{ com kind-annotated variable }}
+ | kid :: :: none {{ com identifier }}
+ | kind kid :: :: kind {{ com kind-annotated variable }}
quant_item :: 'QI_' ::=
{{ com Either a kinded identifier or a nexp constraint for a typquant }}
{{ aux _ l }}
| kinded_id :: :: id {{ com An optionally kinded identifier }}
- | nexp_constraint :: :: const {{ com A constraint for this type }}
+ | n_constraint :: :: const {{ com A constraint for this type }}
typquant :: 'TypQ_' ::=
{{ com type quantifiers and constraints}}
@@ -279,7 +274,7 @@ grammar
% but we could get away with disallowing constraints in typschm, we
% think - if it's useful to do that
- naming_scheme_opt :: 'Name_sect_' ::=
+ name_scm_opt :: 'Name_sect_' ::=
{{ com Optional variable-naming-scheme specification for variables of defined type }}
{{ aux _ l }}
| :: :: none
@@ -294,16 +289,16 @@ type_union :: 'Tu_' ::=
type_def :: 'TD_' ::=
{{ com Type definition body }}
{{ aux _ l }}
- | typedef id naming_scheme_opt = typschm :: :: abbrev
+ | typedef id name_scm_opt = typschm :: :: abbrev
{{ com type abbreviation }} {{ texlong }}
- | typedef id naming_scheme_opt = const struct typquant { atyp1 id1 ; ... ; atypn idn semi_opt } :: :: record
+ | typedef id name_scm_opt = const struct typquant { atyp1 id1 ; ... ; atypn idn semi_opt } :: :: record
{{ com struct type definition }} {{ texlong }}
- | typedef id naming_scheme_opt = const union typquant { type_union1 ; ... ; type_unionn semi_opt } :: :: variant
+ | typedef id name_scm_opt = const union typquant { type_union1 ; ... ; type_unionn semi_opt } :: :: variant
{{ com union type definition}} {{ texlong }}
- | typedef id naming_scheme_opt = enumerate { id1 ; ... ; idn semi_opt } :: :: enum
+ | typedef id name_scm_opt = enumerate { id1 ; ... ; idn semi_opt } :: :: enum
{{ com enumeration type definition}} {{ texlong }}
- | typedef id = register bits [ atyp : atyp' ] { index_range1 : id1 ; ... ; index_rangen : idn }
+ | typedef id = register bits [ atyp : atyp' ] { index_range1 : id1 ; ... ; index_rangen : idn }
:: :: register {{ com register mutable bitfield type definition }} {{ texlong }}
% also sugar [ nexp ]
@@ -371,7 +366,7 @@ pat :: 'P_' ::=
{{ com wildcard }}
| ( pat as id ) :: :: as
{{ com named pattern }}
- | ( ( atyp ) pat ) :: :: typ
+ | ( atyp ) pat :: :: typ
{{ com typed pattern }}
| id :: :: id
@@ -432,11 +427,11 @@ exp :: 'E_' ::=
| ( atyp ) exp :: :: cast
{{ com cast }}
+
+ | id exp :: S :: tup_app {{ ichlo [[id ( exp ) ]] }} {{ com No extra parens needed when exp is a tuple }}
| id ( exp1 , .. , expn ) :: :: app
{{ com function application }}
% Note: fully applied function application only
-% We might restrict exp to be an identifier
-% We might require expn to have outermost parentheses (but not two sets if it's a tuple)
| exp1 id exp2 :: :: app_infix
{{ com infix function application }}
@@ -532,6 +527,8 @@ lexp :: 'LEXP_' ::= {{ com lvalue expression }}
% {{ aux _ annot }} {{ auxparam 'a }}
| id :: :: id
{{ com identifier }}
+ | id ( exp1 , .. , expn ) :: :: mem
+ | id exp :: S :: mem_tup {{ ichlo [[id (exp)]] }}
| lexp [ exp ] :: :: vector {{ com vector element }}
| lexp [ exp1 : exp2 ] :: :: vector_range {{ com subvector }}
% maybe comma-sep such lists too
@@ -641,12 +638,12 @@ rec_opt :: 'Rec_' ::=
| :: :: nonrec {{ com non-recursive }}
| rec :: :: rec {{ com recursive }}
-effects_opt :: 'Effects_opt_' ::=
+effect_opt :: 'Effect_opt_' ::=
{{ com Optional effect annotation for functions }}
{{ aux _ l }}
% {{ aux _ annot }} {{ auxparam 'a }}
| :: :: pure {{ com sugar for empty effect set }}
- | atyp :: :: effects
+ | effectkw atyp :: :: effect
funcl :: 'FCL_' ::=
{{ com Function clause }}
@@ -659,7 +656,7 @@ fundef :: 'FD_' ::=
{{ com Function definition}}
{{ aux _ l }}
% {{ aux _ annot }} {{ auxparam 'a }}
- | function rec_opt tannot_opt effects_opt funcl1 and ... and funcln :: :: function {{ texlong }}
+ | function rec_opt tannot_opt effect_opt funcl1 and ... and funcln :: :: function {{ texlong }}
% {{ com function definition }}
% TODO note that the typ in the tannot_opt is the *result* type, not
% the type of the whole function. The argument type comes from the
@@ -690,7 +687,7 @@ default_typing_spec :: 'DT_' ::=
{{ com Default kinding or typing assumption }}
{{ aux _ l }}
% {{ aux _ annot }} {{ auxparam 'a }}
- | default base_kind var :: :: kind
+ | default base_kind kid :: :: kind
| default typschm id :: :: typ
% The intended semantics of these is that if an id in binding position
% doesn't have a kind or type annotation, then we look through the
@@ -699,6 +696,22 @@ default_typing_spec :: 'DT_' ::=
% Otherwise we try to infer. Perhaps warn if there are multiple matches.
% For example, we might often have default Type ['alphanum]
+scattered_def :: 'SD_' ::=
+ {{ com Function and type union definitions that can be spread across
+ a file. Each one must end in $[[end id]]$ }}
+ {{ aux _ l }}
+ | scattered function rec_opt tannot_opt effect_opt id :: :: scattered_function {{ texlong }} {{ com scattered function definition header }}
+
+ | function clause funcl :: :: scattered_funcl
+{{ com scattered function definition clause }}
+
+ | scattered typedef id name_scm_opt = const union typquant :: :: scattered_variant {{ texlong }} {{ com scattered union definition header }}
+
+ | union id member type_union :: :: scattered_unioncl {{ com scattered union definition member }}
+ | end id :: :: scattered_end
+{{ com scattered definition end }}
+
+
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Top-level definitions %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@@ -717,20 +730,11 @@ def :: 'DEF_' ::=
{{ com top-level type constraint }}
| default_typing_spec :: :: default
{{ com default kind and type assumptions }}
+ | scattered_def :: :: scattered
+ {{ com scattered definition }}
| register atyp id :: :: reg_dec
{{ com register declaration }}
- | scattered function rec_opt tannot_opt effects_opt id :: :: scattered_function {{ texlong }} {{ com scattered function definition header }}
-
- | function clause funcl :: :: scattered_funcl
-{{ com scattered function definition clause }}
-
- | scattered typedef id naming_scheme_opt = const union typquant :: :: scattered_variant {{ texlong }} {{ com scattered union definition header }}
-
- | union id member atyp id' :: :: scattered_unioncl {{ com scattered union definition member }}
- | end id :: :: scattered_end
-{{ com scattered definition end }}
-
defs :: '' ::=
{{ com Definition sequence }}
% {{ auxparam 'a }}
@@ -1193,6 +1197,8 @@ terminals :: '' ::=
{{ tex \mbox{--} }}
| empty :: :: empty
{{ tex \ensuremath{\epsilon} }}
+ | effectkw :: :: effectkw
+ {{ tex \ottkw{effect} }}
formula :: formula_ ::=
diff --git a/language/l2_rules.ott b/language/l2_rules.ott
index fd546b0c..8287f77a 100644
--- a/language/l2_rules.ott
+++ b/language/l2_rules.ott
@@ -19,7 +19,7 @@ k :: 'Ki_' ::=
t , u :: 'T_' ::= {{ phantom }}
{{ com Internal types }}
| id :: :: id
- | var :: :: var
+ | 'id :: :: var
| t1 -> t2 effects tag S_N :: :: fn {{ com [[S_N]] are constraints for the function, [[tag]] holds generation data }}
| ( t1 * .... * tn ) :: :: tup
| id t_args :: :: app
@@ -36,7 +36,7 @@ tag :: 'Tag_' ::= {{ phantom }}
ne :: 'Ne_' ::=
{{ com internal numeric expressions }}
- | id :: :: var
+ | 'id :: :: var
| num :: :: const
| ne1 * ne2 :: :: mult
| ne1 + ... + nen :: :: add
@@ -189,7 +189,7 @@ S_N {{ tex {\Sigma^{\textsc{N} } } }} :: '' ::= {{ phantom }}
tid :: 'tid_' ::=
{{ com A type identifier or type variable }}
| id :: :: id
- | var :: :: var
+ | 'id :: :: var
E_k {{ tex \ottnt{E}^{\textsc{k} } }} :: 'E_k_' ::= {{ phantom }}
{{ hol (tid-> k) }}
@@ -541,11 +541,11 @@ by
E_k |- kind ~> k
----------------------------------------------------------- :: kind
-<E_k,E_r,E_e> |- kind var ~> {var |-> k}, {}
+<E_k,E_r,E_e> |- kind 'id ~> {'id |-> k}, {}
-E_k(var) gives k
+E_k('id) gives k
----------------------------------------------------------- :: nokind
-<E_k,E_r,E_e> |- var ~> {var |-> k},{}
+<E_k,E_r,E_e> |- 'id ~> {'id |-> k},{}
|- nexp1 ~> ne1
|- nexp2 ~> ne2
@@ -585,9 +585,9 @@ E_d |- typ ~> t :: :: convert_typ :: convert_typ_
{{ com Convert source types to internal types }}
by
-E_k(var) gives K_Typ
+E_k('id) gives K_Typ
------------------------------------------------------------ :: var
-<E_k,E_r,E_e> |- :Typ_var: var ~> var
+<E_k,E_r,E_e> |- :Typ_var: 'id ~> 'id
E_k(id) gives K_Typ
------------------------------------------------------------ :: id
@@ -623,7 +623,7 @@ defn
by
------------------------------------------------------------ :: var
-|- id ~> id
+|- 'id ~> 'id
------------------------------------------------------------ :: num
|- num ~> num
@@ -1001,7 +1001,7 @@ E |- exp1 : enum ne1 ne2 order gives I1,E_t
E |- exp2 : enum ne3 ne4 order gives I2,E_t
E |- lexp : vector ne5 ne6 order t gives I3,E_t
---------------------------------------------------------- :: wslice
-E |- lexp [exp1 : exp2] : vector :Ne_var: id1 :Ne_var: id2 order t gives I1 u+ I2 u+ I3 u+ <{ne5<=ne1, ne1+ne2 <= ne3, ne3+ne4<= ne5+ne6, id1 <= ne1, id2 <= ne2+ne3+ne4},pure> ,E_t
+E |- lexp [exp1 : exp2] : vector :Ne_var: 'id1 :Ne_var: 'id2 order t gives I1 u+ I2 u+ I3 u+ <{ne5<=ne1, ne1+ne2 <= ne3, ne3+ne4<= ne5+ne6, 'id1 <= ne1, 'id2 <= ne2+ne3+ne4},pure> ,E_t
E |- exp1 : enum ne1 ne2 order gives I1,E_t
E |- exp2 : enum ne3 ne4 order gives I2,E_t