Now some functions try to avoid name clashes when introducing new free
variables.
(* Title: TFL/usyntax.sml
ID: $Id$
Author: Konrad Slind, Cambridge University Computer Laboratory
Copyright 1997 University of Cambridge
Emulation of HOL's abstract syntax functions.
*)
signature USyntax_sig =
sig
datatype lambda = VAR of {Name : string, Ty : typ}
| CONST of {Name : string, Ty : typ}
| COMB of {Rator: term, Rand : term}
| LAMB of {Bvar : term, Body : term}
val alpha : typ
(* Types *)
val type_vars : typ -> typ list
val type_varsl : typ list -> typ list
val mk_vartype : string -> typ
val is_vartype : typ -> bool
val strip_prod_type : typ -> typ list
(* Terms *)
val free_vars_lr : term -> term list
val type_vars_in_term : term -> typ list
val dest_term : term -> lambda
(* Prelogic *)
val inst : (typ*typ) list -> term -> term
(* Construction routines *)
val mk_abs :{Bvar : term, Body : term} -> term
val mk_imp :{ant : term, conseq : term} -> term
val mk_select :{Bvar : term, Body : term} -> term
val mk_forall :{Bvar : term, Body : term} -> term
val mk_exists :{Bvar : term, Body : term} -> term
val mk_conj :{conj1 : term, conj2 : term} -> term
val mk_disj :{disj1 : term, disj2 : term} -> term
val mk_pabs :{varstruct : term, body : term} -> term
(* Destruction routines *)
val dest_const: term -> {Name : string, Ty : typ}
val dest_comb : term -> {Rator : term, Rand : term}
val dest_abs : string list -> term -> {Bvar : term, Body : term} * string list
val dest_eq : term -> {lhs : term, rhs : term}
val dest_imp : term -> {ant : term, conseq : term}
val dest_forall : term -> {Bvar : term, Body : term}
val dest_exists : term -> {Bvar : term, Body : term}
val dest_neg : term -> term
val dest_conj : term -> {conj1 : term, conj2 : term}
val dest_disj : term -> {disj1 : term, disj2 : term}
val dest_pair : term -> {fst : term, snd : term}
val dest_pabs : string list -> term -> {varstruct : term, body : term, used : string list}
val lhs : term -> term
val rhs : term -> term
val rand : term -> term
(* Query routines *)
val is_imp : term -> bool
val is_forall : term -> bool
val is_exists : term -> bool
val is_neg : term -> bool
val is_conj : term -> bool
val is_disj : term -> bool
val is_pair : term -> bool
val is_pabs : term -> bool
(* Construction of a term from a list of Preterms *)
val list_mk_abs : (term list * term) -> term
val list_mk_imp : (term list * term) -> term
val list_mk_forall : (term list * term) -> term
val list_mk_conj : term list -> term
(* Destructing a term to a list of Preterms *)
val strip_comb : term -> (term * term list)
val strip_abs : term -> (term list * term)
val strip_imp : term -> (term list * term)
val strip_forall : term -> (term list * term)
val strip_exists : term -> (term list * term)
val strip_disj : term -> term list
(* Miscellaneous *)
val mk_vstruct : typ -> term list -> term
val gen_all : term -> term
val find_term : (term -> bool) -> term -> term option
val dest_relation : term -> term * term * term
val is_WFR : term -> bool
val ARB : typ -> term
end;
structure USyntax : USyntax_sig =
struct
open Utils;
infix 4 ##;
fun USYN_ERR{func,mesg} = Utils.ERR{module = "USyntax", func = func, mesg = mesg};
(*---------------------------------------------------------------------------
*
* Types
*
*---------------------------------------------------------------------------*)
val mk_prim_vartype = TVar;
fun mk_vartype s = mk_prim_vartype((s,0),["term"]);
(* But internally, it's useful *)
fun dest_vtype (TVar x) = x
| dest_vtype _ = raise USYN_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 = distinct (Utils.rev_itlist (curry op @ o type_vars) L []);
val alpha = mk_vartype "'a"
val beta = mk_vartype "'b"
val strip_prod_type = HOLogic.prodT_factors;
(*---------------------------------------------------------------------------
*
* Terms
*
*---------------------------------------------------------------------------*)
(* 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;
val type_vars_in_term = map mk_prim_vartype o term_tvars;
(* Prelogic *)
fun dest_tybinding (v,ty) = (#1(dest_vtype v),ty)
fun inst theta = subst_vars (map dest_tybinding theta,[])
(* Construction routines *)
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 USYN_ERR{func = "mk_abs", mesg = "Bvar is not a variable"};
fun mk_imp{ant,conseq} =
let val c = Const("op -->",HOLogic.boolT --> HOLogic.boolT --> HOLogic.boolT)
in list_comb(c,[ant,conseq])
end;
fun mk_select (r as {Bvar,Body}) =
let val ty = type_of Bvar
val c = Const("Eps",(ty --> HOLogic.boolT) --> ty)
in list_comb(c,[mk_abs r])
end;
fun mk_forall (r as {Bvar,Body}) =
let val ty = type_of Bvar
val c = Const("All",(ty --> HOLogic.boolT) --> HOLogic.boolT)
in list_comb(c,[mk_abs r])
end;
fun mk_exists (r as {Bvar,Body}) =
let val ty = type_of Bvar
val c = Const("Ex",(ty --> HOLogic.boolT) --> HOLogic.boolT)
in list_comb(c,[mk_abs r])
end;
fun mk_conj{conj1,conj2} =
let val c = Const("op &",HOLogic.boolT --> HOLogic.boolT --> HOLogic.boolT)
in list_comb(c,[conj1,conj2])
end;
fun mk_disj{disj1,disj2} =
let val c = Const("op |",HOLogic.boolT --> HOLogic.boolT --> HOLogic.boolT)
in list_comb(c,[disj1,disj2])
end;
fun prod_ty ty1 ty2 = HOLogic.mk_prodT (ty1,ty2);
local
fun mk_uncurry(xt,yt,zt) =
Const("split",(xt --> yt --> zt) --> prod_ty xt yt --> zt)
fun dest_pair(Const("Pair",_) $ M $ N) = {fst=M, snd=N}
| dest_pair _ = raise USYN_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_uncurry(type_of fst,type_of snd,type_of body) $
mpa(fst,mpa(snd,body))
end
in mpa(varstruct,body)
end
handle _ => raise USYN_ERR{func = "mk_pabs", mesg = ""}; (* FIXME do not handle _ !!! *)
end;
(* Destruction routines *)
datatype lambda = VAR of {Name : string, Ty : typ}
| CONST of {Name : string, Ty : typ}
| COMB of {Rator: term, Rand : term}
| LAMB of {Bvar : term, Body : term};
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 = Free(s,ty)
in LAMB{Bvar = v, Body = betapply (M,v)}
end
| dest_term(Bound _) = raise USYN_ERR{func = "dest_term",mesg = "Bound"};
fun dest_const(Const(s,ty)) = {Name = s, Ty = ty}
| dest_const _ = raise USYN_ERR{func = "dest_const", mesg = "not a constant"};
fun dest_comb(t1 $ t2) = {Rator = t1, Rand = t2}
| dest_comb _ = raise USYN_ERR{func = "dest_comb", mesg = "not a comb"};
fun dest_abs used (a as Abs(s, ty, M)) =
let
val s' = variant used s;
val v = Free(s', ty);
in ({Bvar = v, Body = betapply (a,v)}, s'::used)
end
| dest_abs _ _ = raise USYN_ERR{func = "dest_abs", mesg = "not an abstraction"};
fun dest_eq(Const("op =",_) $ M $ N) = {lhs=M, rhs=N}
| dest_eq _ = raise USYN_ERR{func = "dest_eq", mesg = "not an equality"};
fun dest_imp(Const("op -->",_) $ M $ N) = {ant=M, conseq=N}
| dest_imp _ = raise USYN_ERR{func = "dest_imp", mesg = "not an implication"};
fun dest_forall(Const("All",_) $ (a as Abs _)) = fst (dest_abs [] a)
| dest_forall _ = raise USYN_ERR{func = "dest_forall", mesg = "not a forall"};
fun dest_exists(Const("Ex",_) $ (a as Abs _)) = fst (dest_abs [] a)
| dest_exists _ = raise USYN_ERR{func = "dest_exists", mesg="not an existential"};
fun dest_neg(Const("not",_) $ M) = M
| dest_neg _ = raise USYN_ERR{func = "dest_neg", mesg = "not a negation"};
fun dest_conj(Const("op &",_) $ M $ N) = {conj1=M, conj2=N}
| dest_conj _ = raise USYN_ERR{func = "dest_conj", mesg = "not a conjunction"};
fun dest_disj(Const("op |",_) $ M $ N) = {disj1=M, disj2=N}
| dest_disj _ = raise USYN_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 = Const("Pair",ty1 --> ty2 --> prod_ty ty1 ty2)
in list_comb(c,[fst,snd])
end;
fun dest_pair(Const("Pair",_) $ M $ N) = {fst=M, snd=N}
| dest_pair _ = raise USYN_ERR{func = "dest_pair", mesg = "not a pair"};
local fun ucheck t = (if #Name(dest_const t) = "split" then t
else raise Match)
in
fun dest_pabs used tm =
let val ({Bvar,Body}, used') = dest_abs used tm
in {varstruct = Bvar, body = Body, used = used'}
end
handle (* FIXME do not handle _ !!! *)
_ => let val {Rator,Rand} = dest_comb tm
val _ = ucheck Rator
val {varstruct = lv, body, used = used'} = dest_pabs used Rand
val {varstruct = rv, body, used = used''} = dest_pabs used' body
in {varstruct = mk_pair {fst = lv, snd = rv}, body = body, used = used''}
end
end;
val lhs = #lhs o dest_eq
val rhs = #rhs o dest_eq
val rand = #Rand o dest_comb
(* Query routines *)
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 cterm 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_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})
(* Need to reverse? *)
fun gen_all tm = list_mk_forall(term_frees tm, tm);
(* Destructing a cterm to a list of Terms *)
fun strip_comb tm =
let fun dest(M$N, A) = dest(M, N::A)
| dest x = x
in dest(tm,[])
end;
fun strip_abs(tm as Abs _) =
let val ({Bvar,Body}, _) = dest_abs [] tm
val (bvs, core) = strip_abs Body
in (Bvar::bvs, core)
end
| strip_abs M = ([],M);
fun strip_imp fm =
if (is_imp fm)
then let val {ant,conseq} = dest_imp fm
val (was,wb) = strip_imp conseq
in ((ant::was), wb)
end
else ([],fm);
fun strip_forall fm =
if (is_forall fm)
then let val {Bvar,Body} = dest_forall fm
val (bvs,core) = strip_forall Body
in ((Bvar::bvs), core)
end
else ([],fm);
fun strip_exists fm =
if (is_exists fm)
then let val {Bvar, Body} = dest_exists fm
val (bvs,core) = strip_exists Body
in (Bvar::bvs, core)
end
else ([],fm);
fun strip_disj w =
if (is_disj w)
then let val {disj1,disj2} = dest_disj w
in (strip_disj disj1@strip_disj disj2)
end
else [w];
(* Miscellaneous *)
fun mk_vstruct ty V =
let fun follow_prod_type (Type("*",[ty1,ty2])) vs =
let val (ltm,vs1) = follow_prod_type ty1 vs
val (rtm,vs2) = follow_prod_type ty2 vs1
in (mk_pair{fst=ltm, snd=rtm}, vs2) end
| follow_prod_type _ (v::vs) = (v,vs)
in #1 (follow_prod_type ty V) end;
(* Search a term for a sub-term satisfying the predicate p. *)
fun find_term p =
let fun find tm =
if (p tm) then Some tm
else case tm of
Abs(_,_,body) => find body
| (t$u) => (Some (the (find t)) handle _ => find u) (* FIXME do not handle _ !!! *)
| _ => None
in find
end;
fun dest_relation tm =
if (type_of tm = HOLogic.boolT)
then let val (Const("op :",_) $ (Const("Pair",_)$y$x) $ R) = tm
in (R,y,x)
end handle _ => raise USYN_ERR{func="dest_relation",
mesg="unexpected term structure"} (* FIXME do not handle _ !!! *)
else raise USYN_ERR{func="dest_relation",mesg="not a boolean term"};
fun is_WFR (Const("WF.wf",_)$_) = true
| is_WFR _ = false;
fun ARB ty = mk_select{Bvar=Free("v",ty),
Body=Const("True",HOLogic.boolT)};
end; (* Syntax *)