Mark McGranaghan 8d31ec147c move to vendor
2012-11-17 08:21:42 -08:00

676 lines
22 KiB
Standard ML

(* Internal Syntax *)
(* Author: Frank Pfenning, Carsten Schuermann *)
(* Modified: Roberto Virga *)
functor IntSyn (structure Global : GLOBAL) :> INTSYN =
struct
type cid = int (* Constant identifier *)
type name = string (* Variable name *)
type mid = int (* Structure identifier *)
type csid = int (* CS module identifier *)
(* Contexts *)
datatype 'a Ctx = (* Contexts *)
Null (* G ::= . *)
| Decl of 'a Ctx * 'a (* | G, D *)
(* ctxPop (G) => G'
Invariant: G = G',D
*)
fun ctxPop (Decl (G, D)) = G
exception Error of string (* raised if out of space *)
(* ctxLookup (G, k) = D, kth declaration in G from right to left
Invariant: 1 <= k <= |G|, where |G| is length of G
*)
fun ctxLookup (Decl (G', D), 1) = D
| ctxLookup (Decl (G', _), k') = ctxLookup (G', k'-1)
(* | ctxLookup (Null, k') = (print ("Looking up k' = " ^ Int.toString k' ^ "\n"); raise Error "Out of Bounce\n")*)
(* ctxLookup (Null, k') should not occur by invariant *)
(* ctxLength G = |G|, the number of declarations in G *)
fun ctxLength G =
let
fun ctxLength' (Null, n) = n
| ctxLength' (Decl(G, _), n)= ctxLength' (G, n+1)
in
ctxLength' (G, 0)
end
type FgnExp = exn (* foreign expression representation *)
exception UnexpectedFgnExp of FgnExp
(* raised by a constraint solver
if passed an incorrect arg *)
type FgnCnstr = exn (* foreign unification constraint
representation *)
exception UnexpectedFgnCnstr of FgnCnstr
(* raised by a constraint solver
if passed an incorrect arg *)
datatype Depend = (* Dependency information *)
No (* P ::= No *)
| Maybe (* | Maybe *)
| Meta (* | Meta *)
(* Expressions *)
datatype Uni = (* Universes: *)
Kind (* L ::= Kind *)
| Type (* | Type *)
datatype Exp = (* Expressions: *)
Uni of Uni (* U ::= L *)
| Pi of (Dec * Depend) * Exp (* | bPi (D, P). V *)
| Root of Head * Spine (* | C @ S *)
| Redex of Exp * Spine (* | U @ S *)
| Lam of Dec * Exp (* | lam D. U *)
| EVar of Exp option ref * Dec Ctx * Exp * (Cnstr ref) list ref
(* | X<I> : G|-V, Cnstr *)
| EClo of Exp * Sub (* | U[s] *)
| AVar of Exp option ref (* | A<I> *)
| NVar of int (* | n (linear, fully applied) *)
(* grafting variable *)
| FgnExp of csid * FgnExp
(* | (foreign expression) *)
and Head = (* Heads: *)
BVar of int (* H ::= k *)
| Const of cid (* | c *)
| Proj of Block * int (* | #k(b) *)
| Skonst of cid (* | c# *)
| Def of cid (* | d *)
| NSDef of cid (* | d (non strict) *)
| FVar of name * Exp * Sub (* | F[s] *)
| FgnConst of csid * ConDec (* | (foreign constant) *)
and Spine = (* Spines: *)
Nil (* S ::= Nil *)
| App of Exp * Spine (* | U ; S *)
| SClo of Spine * Sub (* | S[s] *)
and Sub = (* Explicit substitutions: *)
Shift of int (* s ::= ^n *)
| Dot of Front * Sub (* | Ft.s *)
and Front = (* Fronts: *)
Idx of int (* Ft ::= k *)
| Exp of Exp (* | U *)
| Axp of Exp (* | U (assignable) *)
| Block of Block (* | _x *)
| Undef (* | _ *)
and Dec = (* Declarations: *)
Dec of name option * Exp (* D ::= x:V *)
| BDec of name option * (cid * Sub) (* | v:l[s] *)
| ADec of name option * int (* | v[^-d] *)
| NDec of name option
and Block = (* Blocks: *)
Bidx of int (* b ::= v *)
| LVar of Block option ref * Sub * (cid * Sub)
(* | L(l[^k],t) *)
| Inst of Exp list (* | u1, ..., Un *)
(* Constraints *)
and Cnstr = (* Constraint: *)
Solved (* Cnstr ::= solved *)
| Eqn of Dec Ctx * Exp * Exp (* | G|-(U1 == U2) *)
| FgnCnstr of csid * FgnCnstr (* | (foreign) *)
and Status = (* Status of a constant: *)
Normal (* inert *)
| Constraint of csid * (Dec Ctx * Spine * int -> Exp option)
(* acts as constraint *)
| Foreign of csid * (Spine -> Exp) (* is converted to foreign *)
and FgnUnify = (* Result of foreign unify *)
Succeed of FgnUnifyResidual list
(* succeed with a list of residual operations *)
| Fail
and FgnUnifyResidual = (* Residual of foreign unify *)
Assign of Dec Ctx * Exp * Exp * Sub
(* perform the assignment G |- X = U [ss] *)
| Delay of Exp * Cnstr ref
(* delay cnstr, associating it with all the rigid EVars in U *)
(* Global signature *)
and ConDec = (* Constant declaration *)
ConDec of string * mid option * int * Status
(* a : K : kind or *)
* Exp * Uni (* c : A : type *)
| ConDef of string * mid option * int (* a = A : K : kind or *)
* Exp * Exp * Uni (* d = M : A : type *)
* Ancestor (* Ancestor info for d or a *)
| AbbrevDef of string * mid option * int
(* a = A : K : kind or *)
* Exp * Exp * Uni (* d = M : A : type *)
| BlockDec of string * mid option (* %block l : SOME G1 PI G2 *)
* Dec Ctx * Dec list
| BlockDef of string * mid option * cid list
(* %block l = (l1 | ... | ln) *)
| SkoDec of string * mid option * int (* sa: K : kind or *)
* Exp * Uni (* sc: A : type *)
and Ancestor = (* Ancestor of d or a *)
Anc of cid option * int * cid option (* head(expand(d)), height, head(expand[height](d)) *)
(* NONE means expands to {x:A}B *)
datatype StrDec = (* Structure declaration *)
StrDec of string * mid option
(* Form of constant declaration *)
datatype ConDecForm =
FromCS (* from constraint domain *)
| Ordinary (* ordinary declaration *)
| Clause (* %clause declaration *)
(* Type abbreviations *)
type dctx = Dec Ctx (* G = . | G,D *)
type eclo = Exp * Sub (* Us = U[s] *)
type bclo = Block * Sub (* Bs = B[s] *)
type cnstr = Cnstr ref
(* exception Error of string (* raised if out of space *) *)
structure FgnExpStd = struct
structure ToInternal = FgnOpnTable (type arg = unit
type result = Exp)
structure Map = FgnOpnTable (type arg = Exp -> Exp
type result = Exp)
structure App = FgnOpnTable (type arg = Exp -> unit
type result = unit)
structure EqualTo = FgnOpnTable (type arg = Exp
type result = bool)
structure UnifyWith = FgnOpnTable (type arg = Dec Ctx * Exp
type result = FgnUnify)
fun fold csfe f b = let
val r = ref b
fun g U = r := f (U,!r)
in
App.apply csfe g ; !r
end
end
structure FgnCnstrStd = struct
structure ToInternal = FgnOpnTable (type arg = unit
type result = (Dec Ctx * Exp) list)
structure Awake = FgnOpnTable (type arg = unit
type result = bool)
structure Simplify = FgnOpnTable (type arg = unit
type result = bool)
end
fun conDecName (ConDec (name, _, _, _, _, _)) = name
| conDecName (ConDef (name, _, _, _, _, _, _)) = name
| conDecName (AbbrevDef (name, _, _, _, _, _)) = name
| conDecName (SkoDec (name, _, _, _, _)) = name
| conDecName (BlockDec (name, _, _, _)) = name
| conDecName (BlockDef (name, _, _)) = name
fun conDecParent (ConDec (_, parent, _, _, _, _)) = parent
| conDecParent (ConDef (_, parent, _, _, _, _, _)) = parent
| conDecParent (AbbrevDef (_, parent, _, _, _, _)) = parent
| conDecParent (SkoDec (_, parent, _, _, _)) = parent
| conDecParent (BlockDec (_, parent, _, _)) = parent
| conDecParent (BlockDef (_, parent, _)) = parent
(* conDecImp (CD) = k
Invariant:
If CD is either a declaration, definition, abbreviation, or
a Skolem constant
then k stands for the number of implicit elements.
*)
fun conDecImp (ConDec (_, _, i, _, _, _)) = i
| conDecImp (ConDef (_, _, i, _, _, _, _)) = i
| conDecImp (AbbrevDef (_, _, i, _, _, _)) = i
| conDecImp (SkoDec (_, _, i, _, _)) = i
| conDecImp (BlockDec (_, _, _, _)) = 0 (* watch out -- carsten *)
fun conDecStatus (ConDec (_, _, _, status, _, _)) = status
| conDecStatus _ = Normal
(* conDecType (CD) = V
Invariant:
If CD is either a declaration, definition, abbreviation, or
a Skolem constant
then V is the respective type
*)
fun conDecType (ConDec (_, _, _, _, V, _)) = V
| conDecType (ConDef (_, _, _, _, V, _, _)) = V
| conDecType (AbbrevDef (_, _, _, _, V, _)) = V
| conDecType (SkoDec (_, _, _, V, _)) = V
(* conDecBlock (CD) = (Gsome, Lpi)
Invariant:
If CD is block definition
then Gsome is the context of some variables
and Lpi is the list of pi variables
*)
fun conDecBlock (BlockDec (_, _, Gsome, Lpi)) = (Gsome, Lpi)
(* conDecUni (CD) = L
Invariant:
If CD is either a declaration, definition, abbreviation, or
a Skolem constant
then L is the respective universe
*)
fun conDecUni (ConDec (_, _, _, _, _, L)) = L
| conDecUni (ConDef (_, _, _, _, _, L, _)) = L
| conDecUni (AbbrevDef (_, _, _, _, _, L)) = L
| conDecUni (SkoDec (_, _, _, _, L)) = L
fun strDecName (StrDec (name, _)) = name
fun strDecParent (StrDec (_, parent)) = parent
local
val maxCid = Global.maxCid
val dummyEntry = ConDec("", NONE, 0, Normal, Uni (Kind), Kind)
val sgnArray = Array.array (maxCid+1, dummyEntry)
: ConDec Array.array
val nextCid = ref(0)
val maxMid = Global.maxMid
val sgnStructArray = Array.array (maxMid+1, StrDec("", NONE))
: StrDec Array.array
val nextMid = ref (0)
in
(* Invariants *)
(* Constant declarations are all well-typed *)
(* Constant declarations are stored in beta-normal form *)
(* All definitions are strict in all their arguments *)
(* If Const(cid) is valid, then sgnArray(cid) = ConDec _ *)
(* If Def(cid) is valid, then sgnArray(cid) = ConDef _ *)
fun sgnClean (i) = if i >= !nextCid then ()
else (Array.update (sgnArray, i, dummyEntry);
sgnClean (i+1))
fun sgnReset () = ((* Fri Dec 20 12:04:24 2002 -fp *)
(* this circumvents a space leak *)
sgnClean (0);
nextCid := 0; nextMid := 0)
fun sgnSize () = (!nextCid, !nextMid)
fun sgnAdd (conDec) =
let
val cid = !nextCid
in
if cid > maxCid
then raise Error ("Global signature size " ^ Int.toString (maxCid+1) ^ " exceeded")
else (Array.update (sgnArray, cid, conDec) ;
nextCid := cid + 1;
cid)
end
(* 0 <= cid < !nextCid *)
fun sgnLookup (cid) = Array.sub (sgnArray, cid)
fun sgnApp (f) =
let
fun sgnApp' (cid) =
if cid = !nextCid then () else (f cid; sgnApp' (cid+1))
in
sgnApp' (0)
end
fun sgnStructAdd (strDec) =
let
val mid = !nextMid
in
if mid > maxMid
then raise Error ("Global signature size " ^ Int.toString (maxMid+1) ^ " exceeded")
else (Array.update (sgnStructArray, mid, strDec) ;
nextMid := mid + 1;
mid)
end
(* 0 <= mid < !nextMid *)
fun sgnStructLookup (mid) = Array.sub (sgnStructArray, mid)
(* A hack used in Flit - jcreed 6/05 *)
fun rename (cid, new) =
let
val newConDec = case sgnLookup cid of
ConDec (n,m,i,s,e,u) => ConDec(new,m,i,s,e,u)
| ConDef (n,m,i,e,e',u,a) => ConDef(new,m,i,e,e',u,a)
| AbbrevDef (n,m,i,e,e',u) => AbbrevDef (new,m,i,e,e',u)
| BlockDec (n,m,d,d') => BlockDec (new,m,d,d')
| SkoDec (n,m,i,e,u) => SkoDec (new,m,i,e,u)
in
Array.update (sgnArray, cid, newConDec)
end
end
fun constDef (d) =
(case sgnLookup (d)
of ConDef(_, _, _, U,_, _, _) => U
| AbbrevDef (_, _, _, U,_, _) => U)
fun constType (c) = conDecType (sgnLookup c)
fun constImp (c) = conDecImp (sgnLookup c)
fun constUni (c) = conDecUni (sgnLookup c)
fun constBlock (c) = conDecBlock (sgnLookup c)
fun constStatus (c) =
(case sgnLookup (c)
of ConDec (_, _, _, status, _, _) => status
| _ => Normal)
(* Explicit Substitutions *)
(* id = ^0
Invariant:
G |- id : G id is patsub
*)
val id = Shift(0)
(* shift = ^1
Invariant:
G, V |- ^ : G ^ is patsub
*)
val shift = Shift(1)
(* invShift = ^-1 = _.^0
Invariant:
G |- ^-1 : G, V ^-1 is patsub
*)
val invShift = Dot(Undef, id)
(* comp (s1, s2) = s'
Invariant:
If G' |- s1 : G
and G'' |- s2 : G'
then s' = s1 o s2
and G'' |- s1 o s2 : G
If s1, s2 patsub
then s' patsub
*)
fun comp (Shift (0), s) = s
(* next line is an optimization *)
(* roughly 15% on standard suite for Twelf 1.1 *)
(* Sat Feb 14 10:15:16 1998 -fp *)
| comp (s, Shift (0)) = s
| comp (Shift (n), Dot (Ft, s)) = comp (Shift (n-1), s)
| comp (Shift (n), Shift (m)) = Shift (n+m)
| comp (Dot (Ft, s), s') = Dot (frontSub (Ft, s'), comp (s, s'))
(* bvarSub (n, s) = Ft'
Invariant:
If G |- s : G' G' |- n : V
then Ft' = Ftn if s = Ft1 .. Ftn .. ^k
or Ft' = ^(n+k) if s = Ft1 .. Ftm ^k and m<n
and G |- Ft' : V [s]
*)
and bvarSub (1, Dot(Ft, s)) = Ft
| bvarSub (n, Dot(Ft, s)) = bvarSub (n-1, s)
| bvarSub (n, Shift(k)) = Idx (n+k)
(* blockSub (B, s) = B'
Invariant:
If G |- s : G'
and G' |- B block
then G |- B' block
and B [s] == B'
*)
(* in front of substitutions, first case is irrelevant *)
(* Sun Dec 2 11:56:41 2001 -fp *)
and blockSub (Bidx k, s) =
(case bvarSub (k, s)
of Idx k' => Bidx k'
| Block B => B)
| blockSub (LVar (ref (SOME B), sk, _), s) =
blockSub (B, comp (sk, s))
(* -fp Sun Dec 1 21:18:30 2002 *)
(* --cs Sun Dec 1 11:25:41 2002 *)
(* Since always . |- t : Gsome, discard s *)
(* where is this needed? *)
(* Thu Dec 6 20:30:26 2001 -fp !!! *)
| blockSub (LVar (r as ref NONE, sk, (l, t)), s) =
LVar(r, comp(sk, s), (l, t))
(* was:
LVar (r, comp(sk, s), (l, comp (t, s)))
July 22, 2010 -fp -cs
*)
(* comp(^k, s) = ^k' for some k' by invariant *)
| blockSub (L as Inst ULs, s') = Inst (map (fn U => EClo (U, s')) ULs)
(* this should be right but somebody should verify *)
(* frontSub (Ft, s) = Ft'
Invariant:
If G |- s : G' G' |- Ft : V
then Ft' = Ft [s]
and G |- Ft' : V [s]
NOTE: EClo (U, s) might be undefined, so if this is ever
computed eagerly, we must introduce an "Undefined" exception,
raise it in whnf and handle it here so Exp (EClo (U, s)) => Undef
*)
and frontSub (Idx (n), s) = bvarSub (n, s)
| frontSub (Exp (U), s) = Exp (EClo (U, s))
| frontSub (Undef, s) = Undef
| frontSub (Block (B), s) = Block (blockSub (B, s))
(* decSub (x:V, s) = D'
Invariant:
If G |- s : G' G' |- V : L
then D' = x:V[s]
and G |- V[s] : L
*)
(* First line is an optimization suggested by cs *)
(* D[id] = D *)
(* Sat Feb 14 18:37:44 1998 -fp *)
(* seems to have no statistically significant effect *)
(* undo for now Sat Feb 14 20:22:29 1998 -fp *)
(*
fun decSub (D, Shift(0)) = D
| decSub (Dec (x, V), s) = Dec (x, EClo (V, s))
*)
fun decSub (Dec (x, V), s) = Dec (x, EClo (V, s))
| decSub (NDec x, s) = NDec x
| decSub (BDec (n, (l, t)), s) = BDec (n, (l, comp (t, s)))
(* dot1 (s) = s'
Invariant:
If G |- s : G'
then s' = 1. (s o ^)
and for all V s.t. G' |- V : L
G, V[s] |- s' : G', V
If s patsub then s' patsub
*)
(* first line is an optimization *)
(* roughly 15% on standard suite for Twelf 1.1 *)
(* Sat Feb 14 10:16:16 1998 -fp *)
fun dot1 (s as Shift (0)) = s
| dot1 s = Dot (Idx(1), comp(s, shift))
(* invDot1 (s) = s'
invDot1 (1. s' o ^) = s'
Invariant:
s = 1 . s' o ^
If G' |- s' : G
(so G',V[s] |- s : G,V)
*)
fun invDot1 (s) = comp (comp(shift, s), invShift)
(* Declaration Contexts *)
(* ctxDec (G, k) = x:V
Invariant:
If |G| >= k, where |G| is size of G,
then G |- k : V and G |- V : L
*)
fun ctxDec (G, k) =
let (* ctxDec' (G'', k') = x:V
where G |- ^(k-k') : G'', 1 <= k' <= k
*)
fun ctxDec' (Decl (G', Dec (x, V')), 1) = Dec (x, EClo (V', Shift (k)))
| ctxDec' (Decl (G', BDec (n, (l, s))), 1) = BDec (n, (l, comp (s, Shift (k))))
| ctxDec' (Decl (G', _), k') = ctxDec' (G', k'-1)
(* ctxDec' (Null, k') should not occur by invariant *)
in
ctxDec' (G, k)
end
(* blockDec (G, v, i) = V
Invariant:
If G (v) = l[s]
and Sigma (l) = SOME Gsome BLOCK Lblock
and G |- s : Gsome
then G |- pi (v, i) : V
*)
fun blockDec (G, v as (Bidx k), i) =
let
val BDec (_, (l, s)) = ctxDec (G, k)
(* G |- s : Gsome *)
val (Gsome, Lblock) = conDecBlock (sgnLookup l)
fun blockDec' (t, D :: L, 1, j) = decSub (D, t)
| blockDec' (t, _ :: L, n, j) =
blockDec' (Dot (Exp (Root (Proj (v, j), Nil)), t),
L, n-1, j+1)
in
blockDec' (s, Lblock, i, 1)
end
(* EVar related functions *)
(* newEVar (G, V) = newEVarCnstr (G, V, nil) *)
fun newEVar (G, V) = EVar(ref NONE, G, V, ref nil)
(* newAVar G = new AVar (assignable variable) *)
(* AVars carry no type, ctx, or cnstr *)
fun newAVar () = AVar(ref NONE)
(* newTypeVar (G) = X, X new
where G |- X : type
*)
fun newTypeVar (G) = EVar(ref NONE, G, Uni(Type), ref nil)
(* newLVar (l, s) = (l[s]) *)
fun newLVar (sk, (cid, t)) = LVar (ref NONE, sk, (cid, t))
(* Definition related functions *)
(* headOpt (U) = SOME(H) or NONE, U should be strict, normal *)
fun headOpt (Root (H, _)) = SOME(H)
| headOpt (Lam (_, U)) = headOpt U
| headOpt _ = NONE
fun ancestor' (NONE) = Anc(NONE, 0, NONE)
| ancestor' (SOME(Const(c))) = Anc(SOME(c), 1, SOME(c))
| ancestor' (SOME(Def(d))) =
(case sgnLookup(d)
of ConDef(_, _, _, _, _, _, Anc(_, height, cOpt))
=> Anc(SOME(d), height+1, cOpt))
| ancestor' (SOME _) = (* FgnConst possible, BVar impossible by strictness *)
Anc(NONE, 0, NONE)
(* ancestor(U) = ancestor info for d = U *)
fun ancestor (U) = ancestor' (headOpt U)
(* defAncestor(d) = ancestor of d, d must be defined *)
fun defAncestor (d) =
(case sgnLookup(d)
of ConDef(_, _, _, _, _, _, anc) => anc)
(* Type related functions *)
(* targetHeadOpt (V) = SOME(H) or NONE
where H is the head of the atomic target type of V,
NONE if V is a kind or object or have variable type.
Does not expand type definitions.
*)
(* should there possibly be a FgnConst case? also targetFamOpt -kw *)
fun targetHeadOpt (Root (H, _)) = SOME(H)
| targetHeadOpt (Pi(_, V)) = targetHeadOpt V
| targetHeadOpt (Redex (V, S)) = targetHeadOpt V
| targetHeadOpt (Lam (_, V)) = targetHeadOpt V
| targetHeadOpt (EVar (ref (SOME(V)),_,_,_)) = targetHeadOpt V
| targetHeadOpt (EClo (V, s)) = targetHeadOpt V
| targetHeadOpt _ = NONE
(* Root(Bvar _, _), Root(FVar _, _), Root(FgnConst _, _),
EVar(ref NONE,..), Uni, FgnExp _
*)
(* Root(Skonst _, _) can't occur *)
(* targetHead (A) = a
as in targetHeadOpt, except V must be a valid type
*)
fun targetHead (A) = valOf (targetHeadOpt A)
(* targetFamOpt (V) = SOME(cid) or NONE
where cid is the type family of the atomic target type of V,
NONE if V is a kind or object or have variable type.
Does expand type definitions.
*)
fun targetFamOpt (Root (Const(cid), _)) = SOME(cid)
| targetFamOpt (Pi(_, V)) = targetFamOpt V
| targetFamOpt (Root (Def(cid), _)) = targetFamOpt (constDef cid)
| targetFamOpt (Redex (V, S)) = targetFamOpt V
| targetFamOpt (Lam (_, V)) = targetFamOpt V
| targetFamOpt (EVar (ref (SOME(V)),_,_,_)) = targetFamOpt V
| targetFamOpt (EClo (V, s)) = targetFamOpt V
| targetFamOpt _ = NONE
(* Root(Bvar _, _), Root(FVar _, _), Root(FgnConst _, _),
EVar(ref NONE,..), Uni, FgnExp _
*)
(* Root(Skonst _, _) can't occur *)
(* targetFam (A) = a
as in targetFamOpt, except V must be a valid type
*)
fun targetFam (A) = valOf (targetFamOpt A)
end; (* functor IntSyn *)
structure IntSyn :> INTSYN =
IntSyn (structure Global = Global);