(* Title: envir
ID: $Id$
Author: Lawrence C Paulson, Cambridge University Computer Laboratory
Copyright 1988 University of Cambridge
*)
(*Environments
Should take account that typ is part of variable name,
otherwise two variables with same name and different types
will cause errors!
*)
signature ENVIR =
sig
type 'a xolist
exception ENVIR of string * indexname;
datatype env = Envir of {asol: term xolist,
iTs: (indexname * typ) list,
maxidx: int}
val alist_of : env -> (indexname * term) list
val alist_of_olist : 'a xolist -> (indexname * 'a) list
val empty : int->env
val genvar : string -> env * typ -> env * term
val genvars : string -> env * typ list -> env * term list
val lookup : env * indexname -> term option
val norm_term : env -> term -> term
val null_olist : 'a xolist
val olist_of_alist: (indexname * 'a) list -> 'a xolist
val update : (indexname * term) * env -> env
val vupdate : (indexname * term) * env -> env
end;
functor EnvirFun () : ENVIR =
struct
(*association lists with keys in ascending order, no repeated keys*)
datatype 'a xolist = Olist of (indexname * 'a) list;
exception ENVIR of string * indexname;
(*look up key in ordered list*)
fun xsearch (Olist[], key) = None
| xsearch (Olist ((keyi,xi)::pairs), key) =
if xless(keyi,key) then xsearch (Olist pairs, key)
else if key=keyi then Some xi
else None;
(*insert pair in ordered list, reject if key already present*)
fun xinsert_new (newpr as (key, x), Olist al) =
let fun insert [] = [newpr]
| insert ((pair as (keyi,xi)) :: pairs) =
if xless(keyi,key) then pair :: insert pairs
else if key=keyi then
raise ENVIR("xinsert_new: already present",key)
else newpr::pair::pairs
in Olist (insert al) end;
(*insert pair in ordered list, overwrite if key already present*)
fun xinsert (newpr as (key, x), Olist al) =
let fun insert [] = [newpr]
| insert ((pair as (keyi,xi)) :: pairs) =
if xless(keyi,key) then pair :: insert pairs
else if key=keyi then newpr::pairs
else newpr::pair::pairs
in Olist (insert al) end;
(*apply function to the contents part of each pair*)
fun xmap f (Olist pairs) =
let fun xmp [] = []
| xmp ((key,x)::pairs) = (key, f x) :: xmp pairs
in Olist (xmp pairs) end;
(*allows redefinition of a key by "join"ing the contents parts*)
fun xmerge_olists join (Olist pairsa, Olist pairsb) =
let fun xmrg ([],pairsb) = pairsb
| xmrg (pairsa,[]) = pairsa
| xmrg ((keya,x)::pairsa, (keyb,y)::pairsb) =
if xless(keya,keyb) then
(keya,x) :: xmrg (pairsa, (keyb,y)::pairsb)
else if xless(keyb,keya) then
(keyb,y) :: xmrg ((keya,x)::pairsa, pairsb)
else (*equal*) (keya, join(x,y)) :: xmrg (pairsa, pairsb)
in Olist (xmrg (pairsa,pairsb)) end;
val null_olist = Olist[];
fun alist_of_olist (Olist pairs) = pairs;
fun olist_of_alist pairs = foldr xinsert (pairs, Olist[]);
(*updating can destroy environment in 2 ways!!
(1) variables out of range (2) circular assignments
*)
datatype env = Envir of
{maxidx: int, (*maximum index of vars*)
asol: term xolist, (*table of assignments to Vars*)
iTs: (indexname*typ)list} (*table of assignments to TVars*)
(*Generate a list of distinct variables.
Increments index to make them distinct from ALL present variables. *)
fun genvars name (Envir{maxidx, asol, iTs}, Ts) : env * term list =
let fun genvs (_, [] : typ list) : term list = []
| genvs (n, [T]) = [ Var((name, maxidx+1), T) ]
| genvs (n, T::Ts) =
Var((name ^ radixstring(26,"a",n), maxidx+1), T)
:: genvs(n+1,Ts)
in (Envir{maxidx=maxidx+1, asol=asol, iTs=iTs}, genvs (0,Ts)) end;
(*Generate a variable.*)
fun genvar name (env,T) : env * term =
let val (env',[v]) = genvars name (env,[T])
in (env',v) end;
fun lookup (Envir{asol,...}, xname) : term option = xsearch (asol,xname);
fun update ((xname, t), Envir{maxidx, asol, iTs}) =
Envir{maxidx=maxidx, asol=xinsert_new ((xname,t), asol), iTs=iTs};
(*The empty environment. New variables will start with the given index.*)
fun empty m = Envir{maxidx=m, asol=null_olist, iTs=[]};
(*Update, checking Var-Var assignments: try to suppress higher indexes*)
fun vupdate((a,t), env) = case t of
Var(name',T) =>
if a=name' then env (*cycle!*)
else if xless(a, name') then
(case lookup(env,name') of (*if already assigned, chase*)
None => update((name', Var(a,T)), env)
| Some u => vupdate((a,u), env))
else update((a,t), env)
| _ => update((a,t), env);
(*Convert environment to alist*)
fun alist_of (Envir{maxidx,asol,...}) = alist_of_olist asol;
(*Beta normal form for terms (not eta normal form).
Chases variables in env; Does not exploit sharing of variable bindings
Does not check types, so could loop. *)
local
(*raised when norm has no effect on a term,
to encourage sharing instead of copying*)
exception SAME;
fun norm_term1 (asol,t) : term =
let fun norm (Var (w,T)) =
(case xsearch(asol,w) of
Some u => normh u
| None => raise SAME)
| norm (Abs(a,T,body)) = Abs(a, T, norm body)
| norm (Abs(_,_,body) $ t) = normh(subst_bounds([t], body))
| norm (f $ t) =
((case norm f of
Abs(_,_,body) => normh(subst_bounds([t], body))
| nf => nf $ normh t)
handle SAME => f $ norm t)
| norm _ = raise SAME
and normh t = (norm t) handle SAME => t
in normh t end
and norm_term2(asol,iTs,t) : term =
let fun normT(Type(a,Ts)) = Type(a, normTs Ts)
| normT(TFree _) = raise SAME
| normT(TVar(v,_)) = (case assoc(iTs,v) of
Some(U) => normTh U
| None => raise SAME)
and normTh T = ((normT T) handle SAME => T)
and normTs([]) = raise SAME
| normTs(T::Ts) = ((normT T :: normTsh Ts)
handle SAME => T :: normTs Ts)
and normTsh Ts = ((normTs Ts) handle SAME => Ts)
and norm(Const(a,T)) = Const(a, normT T)
| norm(Free(a,T)) = Free(a, normT T)
| norm(Var (w,T)) =
(case xsearch(asol,w) of
Some u => normh u
| None => Var(w,normT T))
| norm(Abs(a,T,body)) =
(Abs(a,normT T,normh body) handle SAME => Abs(a, T, norm body))
| norm(Abs(_,_,body) $ t) = normh(subst_bounds([t], body))
| norm(f $ t) =
((case norm f of
Abs(_,_,body) => normh(subst_bounds([t], body))
| nf => nf $ normh t)
handle SAME => f $ norm t)
| norm _ = raise SAME
and normh t = (norm t) handle SAME => t
in normh t end;
in
(*curried version might be slower in recursive calls*)
fun norm_term (env as Envir{asol,iTs,...}) t : term =
if iTs=[] then norm_term1(asol, t) else norm_term2(asol,iTs, t)
end;
end;