src/HOL/Tools/TFL/usyntax.ML

+(*  Title:      HOL/Tools/TFL/usyntax.ML
+    ID:         $Id$
+    Author:     Konrad Slind, Cambridge University Computer Laboratory
+    Copyright   1997  University of Cambridge
+
+Emulation of HOL's abstract syntax functions.
+*)
+
+signature USYNTAX =
+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 =
+struct
+
+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), HOLogic.typeS);
+
+(* But internally, it's useful *)
+fun dest_vtype (TVar x) = x
+  | dest_vtype _ = raise USYN_ERR "dest_vtype" "not a flexible type variable";
+
+val is_vartype = can dest_vtype;
+
+val type_vars  = map mk_prim_vartype o typ_tvars
+fun type_varsl L = distinct (op =) (fold (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 "mk_abs" "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("Hilbert_Choice.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 "dest_pair" "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 TYPE _ => raise USYN_ERR "mk_pabs" "";
+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 = Term.betapply (M,v)}
+                               end
+  | dest_term(Bound _)       = raise USYN_ERR "dest_term" "Bound";
+
+fun dest_const(Const(s,ty)) = {Name = s, Ty = ty}
+  | dest_const _ = raise USYN_ERR "dest_const" "not a constant";
+
+fun dest_comb(t1 $ t2) = {Rator = t1, Rand = t2}
+  | dest_comb _ =  raise USYN_ERR "dest_comb" "not a comb";
+
+fun dest_abs used (a as Abs(s, ty, M)) =
+     let
+       val s' = Name.variant used s;
+       val v = Free(s', ty);
+     in ({Bvar = v, Body = Term.betapply (a,v)}, s'::used)
+     end
+  | dest_abs _ _ =  raise USYN_ERR "dest_abs" "not an abstraction";
+
+fun dest_eq(Const("op =",_) $ M $ N) = {lhs=M, rhs=N}
+  | dest_eq _ = raise USYN_ERR "dest_eq" "not an equality";
+
+fun dest_imp(Const("op -->",_) $ M $ N) = {ant=M, conseq=N}
+  | dest_imp _ = raise USYN_ERR "dest_imp" "not an implication";
+
+fun dest_forall(Const("All",_) $ (a as Abs _)) = fst (dest_abs [] a)
+  | dest_forall _ = raise USYN_ERR "dest_forall" "not a forall";
+
+fun dest_exists(Const("Ex",_) $ (a as Abs _)) = fst (dest_abs [] a)
+  | dest_exists _ = raise USYN_ERR "dest_exists" "not an existential";
+
+fun dest_neg(Const("not",_) $ M) = M
+  | dest_neg _ = raise USYN_ERR "dest_neg" "not a negation";
+
+fun dest_conj(Const("op &",_) $ M $ N) = {conj1=M, conj2=N}
+  | dest_conj _ = raise USYN_ERR "dest_conj" "not a conjunction";
+
+fun dest_disj(Const("op |",_) $ M $ N) = {disj1=M, disj2=N}
+  | dest_disj _ = raise USYN_ERR "dest_disj" "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 "dest_pair" "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 Utils.ERR _ =>
+          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) = fold_rev (fn v => fn M => mk_abs{Bvar=v, Body=M}) L tm;
+
+(* These others are almost never used *)
+fun list_mk_imp(A,c) = fold_rev (fn a => fn tm => mk_imp{ant=a,conseq=tm}) A c;
+fun list_mk_forall(V,t) = fold_rev (fn v => fn b => mk_forall{Bvar=v, Body=b})V t;
+val list_mk_conj = Utils.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)         => (case find t of NONE => find u | some => some)
+        | _             => 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 Bind => raise USYN_ERR "dest_relation" "unexpected term structure"
+   else raise USYN_ERR "dest_relation" "not a boolean term";
+
+fun is_WFR (Const("Wellfounded_Recursion.wf",_)$_) = true
+  | is_WFR _                 = false;
+
+fun ARB ty = mk_select{Bvar=Free("v",ty),
+                       Body=Const("True",HOLogic.boolT)};
+
+end;