structure USyntax : USyntax_sig =
struct
structure Utils = Utils;
open Utils;
open Mask;
infix 7 |->;
infix 4 ##;
fun ERR{func,mesg} = Utils.ERR{module = "USyntax", func = func, mesg = mesg};
type Type = typ
type Term = cterm
type Preterm = term
(*---------------------------------------------------------------------------
*
* Types
*
*---------------------------------------------------------------------------*)
fun mk_type{Tyop, Args} = Type(Tyop,Args);
val mk_prim_vartype = TVar;
fun mk_vartype s = mk_prim_vartype((s,0),["term"]);
fun dest_type(Type(ty,args)) = {Tyop = ty, Args = args}
| dest_type _ = raise ERR{func = "dest_type", mesg = "Not a compound type"};
(* But internally, it's useful *)
fun dest_vtype (TVar x) = x
| dest_vtype _ = raise ERR{func = "dest_vtype",
mesg = "not a flexible type variable"};
val is_vartype = Utils.can dest_vtype;
val type_vars = map mk_prim_vartype o typ_tvars
fun type_varsl L = Utils.mk_set (Utils.curry op=)
(Utils.rev_itlist (Utils.curry op @ o type_vars) L []);
val alpha = mk_vartype "'a"
val beta = mk_vartype "'b"
val bool = Type("bool",[]);
fun match_type ty1 ty2 = raise ERR{func="match_type",mesg="not implemented"};
(* What nonsense *)
nonfix -->;
val --> = -->;
infixr 3 -->;
(* hol_type -> hol_type list * hol_type *)
fun strip_type ty =
let val {Tyop = "fun", Args = [ty1,ty2]} = dest_type ty
val (D,r) = strip_type ty2
in (ty1::D, r)
end
handle _ => ([],ty);
(* hol_type -> hol_type list *)
fun strip_prod_type ty =
let val {Tyop = "*", Args = [ty1,ty2]} = dest_type ty
in strip_prod_type ty1 @ strip_prod_type ty2
end handle _ => [ty];
(*---------------------------------------------------------------------------
*
* Terms
*
*---------------------------------------------------------------------------*)
nonfix aconv;
val aconv = Utils.curry (op aconv);
fun free_vars tm = add_term_frees(tm,[]);
(* Free variables, in order of occurrence, from left to right in the
* syntax tree. *)
fun free_vars_lr tm =
let fun memb x = let fun m[] = false | m(y::rst) = (x=y)orelse m rst in m end
fun add (t, frees) = case t of
Free _ => if (memb t frees) then frees else t::frees
| Abs (_,_,body) => add(body,frees)
| f$t => add(t, add(f, frees))
| _ => frees
in rev(add(tm,[]))
end;
fun free_varsl L = Utils.mk_set aconv
(Utils.rev_itlist (Utils.curry op @ o free_vars) L []);
val type_of = type_of;
val type_vars_in_term = map mk_prim_vartype o term_tvars;
(* Can't really be very exact in Isabelle *)
fun all_vars tm =
let fun memb x = let fun m[] = false | m(y::rst) = (x=y)orelse m rst in m end
fun add (t, A) = case t of
Free _ => if (memb t A) then A else t::A
| Abs (s,ty,body) => add(body, add(Free(s,ty),A))
| f$t => add(t, add(f, A))
| _ => A
in rev(add(tm,[]))
end;
fun all_varsl L = Utils.mk_set aconv
(Utils.rev_itlist (Utils.curry op @ o all_vars) L []);
(* Prelogic *)
val subst = subst_free o map (fn (a |-> b) => (a,b));
fun dest_tybinding (v |-> ty) = (#1(dest_vtype v),ty)
fun inst theta = subst_vars (map dest_tybinding theta,[])
fun beta_conv((t1 as Abs _ ) $ t2) = betapply(t1,t2)
| beta_conv _ = raise ERR{func = "beta_conv", mesg = "Not a beta-redex"};
(* Construction routines *)
(* fun mk_var{Name,Ty} = Var((Name,0),Ty); *)
fun mk_var{Name,Ty} = Free(Name,Ty);
val mk_prim_var = Var;
val string_variant = variant;
local fun var_name(Var((Name,_),_)) = Name
| var_name(Free(s,_)) = s
| var_name _ = raise ERR{func = "variant",
mesg = "list elem. is not a variable"}
in
fun variant [] v = v
| variant vlist (Var((Name,i),ty)) =
Var((string_variant (map var_name vlist) Name,i),ty)
| variant vlist (Free(Name,ty)) =
Free(string_variant (map var_name vlist) Name,ty)
| variant _ _ = raise ERR{func = "variant",
mesg = "2nd arg. should be a variable"}
end;
fun mk_const{Name,Ty} = Const(Name,Ty)
fun mk_comb{Rator,Rand} = Rator $ Rand;
fun mk_abs{Bvar as Var((s,_),ty),Body} = Abs(s,ty,abstract_over(Bvar,Body))
| mk_abs{Bvar as Free(s,ty),Body} = Abs(s,ty,abstract_over(Bvar,Body))
| mk_abs _ = raise ERR{func = "mk_abs", mesg = "Bvar is not a variable"};
fun list_mk_comb (h,[]) = h
| list_mk_comb (h,L) =
rev_itlist (fn t1 => fn t2 => mk_comb{Rator = t2, Rand = t1}) L h;
fun mk_eq{lhs,rhs} =
let val ty = type_of lhs
val c = mk_const{Name = "op =", Ty = ty --> ty --> bool}
in list_mk_comb(c,[lhs,rhs])
end
fun mk_imp{ant,conseq} =
let val c = mk_const{Name = "op -->", Ty = bool --> bool --> bool}
in list_mk_comb(c,[ant,conseq])
end;
fun mk_select (r as {Bvar,Body}) =
let val ty = type_of Bvar
val c = mk_const{Name = "Eps", Ty = (ty --> bool) --> ty}
in list_mk_comb(c,[mk_abs r])
end;
fun mk_forall (r as {Bvar,Body}) =
let val ty = type_of Bvar
val c = mk_const{Name = "All", Ty = (ty --> bool) --> bool}
in list_mk_comb(c,[mk_abs r])
end;
fun mk_exists (r as {Bvar,Body}) =
let val ty = type_of Bvar
val c = mk_const{Name = "Ex", Ty = (ty --> bool) --> bool}
in list_mk_comb(c,[mk_abs r])
end;
fun mk_conj{conj1,conj2} =
let val c = mk_const{Name = "op &", Ty = bool --> bool --> bool}
in list_mk_comb(c,[conj1,conj2])
end;
fun mk_disj{disj1,disj2} =
let val c = mk_const{Name = "op |", Ty = bool --> bool --> bool}
in list_mk_comb(c,[disj1,disj2])
end;
fun prod_ty ty1 ty2 = mk_type{Tyop = "*", Args = [ty1,ty2]};
local
fun mk_uncurry(xt,yt,zt) =
mk_const{Name = "split", Ty = (xt --> yt --> zt) --> prod_ty xt yt --> zt}
fun dest_pair(Const("Pair",_) $ M $ N) = {fst=M, snd=N}
| dest_pair _ = raise ERR{func = "dest_pair", mesg = "not a pair"}
fun is_var(Var(_)) = true | is_var (Free _) = true | is_var _ = false
in
fun mk_pabs{varstruct,body} =
let fun mpa(varstruct,body) =
if (is_var varstruct)
then mk_abs{Bvar = varstruct, Body = body}
else let val {fst,snd} = dest_pair varstruct
in mk_comb{Rator= mk_uncurry(type_of fst,type_of snd,type_of body),
Rand = mpa(fst,mpa(snd,body))}
end
in mpa(varstruct,body)
end
handle _ => raise ERR{func = "mk_pabs", mesg = ""};
end;
(* Destruction routines *)
datatype lambda = VAR of {Name : string, Ty : Type}
| CONST of {Name : string, Ty : Type}
| COMB of {Rator: Preterm, Rand : Preterm}
| LAMB of {Bvar : Preterm, Body : Preterm};
fun dest_term(Var((s,i),ty)) = VAR{Name = s, Ty = ty}
| dest_term(Free(s,ty)) = VAR{Name = s, Ty = ty}
| dest_term(Const(s,ty)) = CONST{Name = s, Ty = ty}
| dest_term(M$N) = COMB{Rator=M,Rand=N}
| dest_term(Abs(s,ty,M)) = let val v = mk_var{Name = s, Ty = ty}
in LAMB{Bvar = v, Body = betapply (M,v)}
end
| dest_term(Bound _) = raise ERR{func = "dest_term",mesg = "Bound"};
fun dest_var(Var((s,i),ty)) = {Name = s, Ty = ty}
| dest_var(Free(s,ty)) = {Name = s, Ty = ty}
| dest_var _ = raise ERR{func = "dest_var", mesg = "not a variable"};
fun dest_const(Const(s,ty)) = {Name = s, Ty = ty}
| dest_const _ = raise ERR{func = "dest_const", mesg = "not a constant"};
fun dest_comb(t1 $ t2) = {Rator = t1, Rand = t2}
| dest_comb _ = raise ERR{func = "dest_comb", mesg = "not a comb"};
fun dest_abs(a as Abs(s,ty,M)) =
let val v = mk_var{Name = s, Ty = ty}
in {Bvar = v, Body = betapply (a,v)}
end
| dest_abs _ = raise ERR{func = "dest_abs", mesg = "not an abstraction"};
fun dest_eq(Const("op =",_) $ M $ N) = {lhs=M, rhs=N}
| dest_eq _ = raise ERR{func = "dest_eq", mesg = "not an equality"};
fun dest_imp(Const("op -->",_) $ M $ N) = {ant=M, conseq=N}
| dest_imp _ = raise ERR{func = "dest_imp", mesg = "not an implication"};
fun dest_select(Const("Eps",_) $ (a as Abs _)) = dest_abs a
| dest_select _ = raise ERR{func = "dest_select", mesg = "not a select"};
fun dest_forall(Const("All",_) $ (a as Abs _)) = dest_abs a
| dest_forall _ = raise ERR{func = "dest_forall", mesg = "not a forall"};
fun dest_exists(Const("Ex",_) $ (a as Abs _)) = dest_abs a
| dest_exists _ = raise ERR{func = "dest_exists", mesg="not an existential"};
fun dest_neg(Const("not",_) $ M) = M
| dest_neg _ = raise ERR{func = "dest_neg", mesg = "not a negation"};
fun dest_conj(Const("op &",_) $ M $ N) = {conj1=M, conj2=N}
| dest_conj _ = raise ERR{func = "dest_conj", mesg = "not a conjunction"};
fun dest_disj(Const("op |",_) $ M $ N) = {disj1=M, disj2=N}
| dest_disj _ = raise ERR{func = "dest_disj", mesg = "not a disjunction"};
fun mk_pair{fst,snd} =
let val ty1 = type_of fst
val ty2 = type_of snd
val c = mk_const{Name = "Pair", Ty = ty1 --> ty2 --> prod_ty ty1 ty2}
in list_mk_comb(c,[fst,snd])
end;
fun dest_pair(Const("Pair",_) $ M $ N) = {fst=M, snd=N}
| dest_pair _ = raise ERR{func = "dest_pair", mesg = "not a pair"};
local val ucheck = Utils.assert (curry (op =) "split" o #Name o dest_const)
in
fun dest_pabs tm =
let val {Bvar,Body} = dest_abs tm
in {varstruct = Bvar, body = Body}
end handle _
=> let val {Rator,Rand} = dest_comb tm
val _ = ucheck Rator
val {varstruct = lv,body} = dest_pabs Rand
val {varstruct = rv,body} = dest_pabs body
in {varstruct = mk_pair{fst = lv, snd = rv}, body = body}
end
end;
(* Garbage - ought to be dropped *)
val lhs = #lhs o dest_eq
val rhs = #rhs o dest_eq
val rator = #Rator o dest_comb
val rand = #Rand o dest_comb
val bvar = #Bvar o dest_abs
val body = #Body o dest_abs
(* Query routines *)
val is_var = can dest_var
val is_const = can dest_const
val is_comb = can dest_comb
val is_abs = can dest_abs
val is_eq = can dest_eq
val is_imp = can dest_imp
val is_forall = can dest_forall
val is_exists = can dest_exists
val is_neg = can dest_neg
val is_conj = can dest_conj
val is_disj = can dest_disj
val is_pair = can dest_pair
val is_pabs = can dest_pabs
(* Construction of a Term from a list of Terms *)
fun list_mk_abs(L,tm) = itlist (fn v => fn M => mk_abs{Bvar=v, Body=M}) L tm;
(* These others are almost never used *)
fun list_mk_imp(A,c) = itlist(fn a => fn tm => mk_imp{ant=a,conseq=tm}) A c;
fun list_mk_exists(V,t) = itlist(fn v => fn b => mk_exists{Bvar=v, Body=b})V t;
fun list_mk_forall(V,t) = itlist(fn v => fn b => mk_forall{Bvar=v, Body=b})V t;
val list_mk_conj = end_itlist(fn c1 => fn tm => mk_conj{conj1=c1, conj2=tm})
val list_mk_disj = end_itlist(fn d1 => fn tm => mk_disj{disj1=d1, disj2=tm})
(* Need to reverse? *)
fun gen_all tm = list_mk_forall(free_vars tm, tm);
(* Destructing a Term to a list of Terms *)
fun strip_comb tm =
let fun dest(M$N, A) = dest(M, N::A)
| dest x = x
in dest(tm,[])
end;
fun strip_abs(tm as Abs _) =
let val {Bvar,Body} = dest_abs tm
val (bvs, core) = strip_abs Body
in (Bvar::bvs, core)
end
| strip_abs M = ([],M);
fun strip_imp fm =
if (is_imp fm)
then let val {ant,conseq} = dest_imp fm
val (was,wb) = strip_imp conseq
in ((ant::was), wb)
end
else ([],fm);
fun strip_forall fm =
if (is_forall fm)
then let val {Bvar,Body} = dest_forall fm
val (bvs,core) = strip_forall Body
in ((Bvar::bvs), core)
end
else ([],fm);
fun strip_exists fm =
if (is_exists fm)
then let val {Bvar, Body} = dest_exists fm
val (bvs,core) = strip_exists Body
in (Bvar::bvs, core)
end
else ([],fm);
fun strip_conj w =
if (is_conj w)
then let val {conj1,conj2} = dest_conj w
in (strip_conj conj1@strip_conj conj2)
end
else [w];
fun strip_disj w =
if (is_disj w)
then let val {disj1,disj2} = dest_disj w
in (strip_disj disj1@strip_disj disj2)
end
else [w];
fun strip_pair tm =
if (is_pair tm)
then let val {fst,snd} = dest_pair tm
fun dtuple t =
if (is_pair t)
then let val{fst,snd} = dest_pair t
in (fst :: dtuple snd)
end
else [t]
in fst::dtuple snd
end
else [tm];
fun mk_preterm tm = #t(rep_cterm tm);
fun mk_prop (tm as Const("Trueprop",_) $ _) = tm
| mk_prop tm = mk_comb{Rator=mk_const{Name = "Trueprop",
Ty = bool --> mk_type{Tyop = "prop",Args=[]}},
Rand = tm};
fun drop_Trueprop (Const("Trueprop",_) $ X) = X
| drop_Trueprop X = X;
(* Miscellaneous *)
fun mk_vstruct ty V =
let fun follow_prod_type ty vs =
let val {Tyop = "*", Args = [ty1,ty2]} = dest_type ty
val (ltm,vs1) = follow_prod_type ty1 vs
val (rtm,vs2) = follow_prod_type ty2 vs1
in (mk_pair{fst=ltm, snd=rtm}, vs2)
end handle _ => (hd vs, tl vs)
in fst(follow_prod_type ty V)
end;
(* Search a term for a sub-term satisfying the predicate p. *)
fun find_term p =
let fun find tm =
if (p tm)
then tm
else if (is_abs tm)
then find (#Body(dest_abs tm))
else let val {Rator,Rand} = dest_comb tm
in find Rator handle _ => find Rand
end handle _ => raise ERR{func = "find_term",mesg = ""}
in find
end;
(*******************************************************************
* find_terms: (term -> bool) -> term -> term list
*
* Find all subterms in a term that satisfy a given predicate p.
*
*******************************************************************)
fun find_terms p =
let fun accum tl tm =
let val tl' = if (p tm) then (tm::tl) else tl
in if (is_abs tm)
then accum tl' (#Body(dest_abs tm))
else let val {Rator,Rand} = dest_comb tm
in accum (accum tl' Rator) Rand
end handle _ => tl'
end
in accum []
end;
val Term_to_string = string_of_cterm;
fun dest_relation tm =
if (type_of tm = bool)
then let val (Const("op :",_) $ (Const("Pair",_)$y$x) $ R) = tm
in (R,y,x)
end handle _ => raise ERR{func="dest_relation",
mesg="unexpected term structure"}
else raise ERR{func="dest_relation",mesg="not a boolean term"};
fun is_WFR tm = (#Name(dest_const(rator tm)) = "wf") handle _ => false;
fun ARB ty = mk_select{Bvar=mk_var{Name="v",Ty=ty},
Body=mk_const{Name="True",Ty=bool}};
end; (* Syntax *)