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(* Title: TFL/usyntax.ML


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ID: $Id$


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Author: Konrad Slind, Cambridge University Computer Laboratory


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Copyright 1997 University of Cambridge


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Emulation of HOL's abstract syntax functions.


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*)


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signature USYNTAX =


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sig


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datatype lambda = VAR of {Name : string, Ty : typ}


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 CONST of {Name : string, Ty : typ}


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 COMB of {Rator: term, Rand : term}


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 LAMB of {Bvar : term, Body : term}


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val alpha : typ


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(* Types *)


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val type_vars : typ > typ list


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val type_varsl : typ list > typ list


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val mk_vartype : string > typ


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val is_vartype : typ > bool


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val strip_prod_type : typ > typ list


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(* Terms *)


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val free_vars_lr : term > term list


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val type_vars_in_term : term > typ list


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val dest_term : term > lambda


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(* Prelogic *)


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val inst : (typ*typ) list > term > term


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(* Construction routines *)


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val mk_abs :{Bvar : term, Body : term} > term


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val mk_imp :{ant : term, conseq : term} > term


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val mk_select :{Bvar : term, Body : term} > term


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val mk_forall :{Bvar : term, Body : term} > term


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val mk_exists :{Bvar : term, Body : term} > term


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val mk_conj :{conj1 : term, conj2 : term} > term


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val mk_disj :{disj1 : term, disj2 : term} > term


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val mk_pabs :{varstruct : term, body : term} > term


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(* Destruction routines *)


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val dest_const: term > {Name : string, Ty : typ}


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val dest_comb : term > {Rator : term, Rand : term}


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val dest_abs : string list > term > {Bvar : term, Body : term} * string list


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val dest_eq : term > {lhs : term, rhs : term}


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val dest_imp : term > {ant : term, conseq : term}


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val dest_forall : term > {Bvar : term, Body : term}


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val dest_exists : term > {Bvar : term, Body : term}


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val dest_neg : term > term


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val dest_conj : term > {conj1 : term, conj2 : term}


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val dest_disj : term > {disj1 : term, disj2 : term}


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val dest_pair : term > {fst : term, snd : term}


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val dest_pabs : string list > term > {varstruct : term, body : term, used : string list}


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val lhs : term > term


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val rhs : term > term


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val rand : term > term


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(* Query routines *)


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val is_imp : term > bool


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val is_forall : term > bool


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val is_exists : term > bool


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val is_neg : term > bool


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val is_conj : term > bool


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val is_disj : term > bool


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val is_pair : term > bool


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val is_pabs : term > bool


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(* Construction of a term from a list of Preterms *)


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val list_mk_abs : (term list * term) > term


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val list_mk_imp : (term list * term) > term


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val list_mk_forall : (term list * term) > term


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val list_mk_conj : term list > term


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(* Destructing a term to a list of Preterms *)


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val strip_comb : term > (term * term list)


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val strip_abs : term > (term list * term)


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val strip_imp : term > (term list * term)


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val strip_forall : term > (term list * term)


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val strip_exists : term > (term list * term)


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val strip_disj : term > term list


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(* Miscellaneous *)


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val mk_vstruct : typ > term list > term


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val gen_all : term > term


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val find_term : (term > bool) > term > term option


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val dest_relation : term > term * term * term


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val is_WFR : term > bool


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val ARB : typ > term


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end;


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structure USyntax: USYNTAX =


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struct


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infix 4 ##;


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fun USYN_ERR func mesg = Utils.ERR {module = "USyntax", func = func, mesg = mesg};


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(*


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*


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* Types


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*


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**)


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val mk_prim_vartype = TVar;

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fun mk_vartype s = mk_prim_vartype ((s, 0), HOLogic.typeS);

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(* But internally, it's useful *)


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fun dest_vtype (TVar x) = x


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 dest_vtype _ = raise USYN_ERR "dest_vtype" "not a flexible type variable";


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val is_vartype = can dest_vtype;


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val type_vars = map mk_prim_vartype o typ_tvars

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fun type_varsl L = distinct (fold (curry op @ o type_vars) L []);

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val alpha = mk_vartype "'a"


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val beta = mk_vartype "'b"


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val strip_prod_type = HOLogic.prodT_factors;


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(*


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*


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* Terms


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*


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**)


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(* Free variables, in order of occurrence, from left to right in the


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* syntax tree. *)


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fun free_vars_lr tm =


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let fun memb x = let fun m[] = false  m(y::rst) = (x=y)orelse m rst in m end


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fun add (t, frees) = case t of


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Free _ => if (memb t frees) then frees else t::frees


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 Abs (_,_,body) => add(body,frees)


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 f$t => add(t, add(f, frees))


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 _ => frees


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in rev(add(tm,[]))


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end;


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val type_vars_in_term = map mk_prim_vartype o term_tvars;


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(* Prelogic *)


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fun dest_tybinding (v,ty) = (#1(dest_vtype v),ty)


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fun inst theta = subst_vars (map dest_tybinding theta,[])


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(* Construction routines *)


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fun mk_abs{Bvar as Var((s,_),ty),Body} = Abs(s,ty,abstract_over(Bvar,Body))


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 mk_abs{Bvar as Free(s,ty),Body} = Abs(s,ty,abstract_over(Bvar,Body))


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 mk_abs _ = raise USYN_ERR "mk_abs" "Bvar is not a variable";


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fun mk_imp{ant,conseq} =


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let val c = Const("op >",HOLogic.boolT > HOLogic.boolT > HOLogic.boolT)


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in list_comb(c,[ant,conseq])


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end;


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fun mk_select (r as {Bvar,Body}) =


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let val ty = type_of Bvar

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val c = Const("Hilbert_Choice.Eps",(ty > HOLogic.boolT) > ty)

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in list_comb(c,[mk_abs r])


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end;


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fun mk_forall (r as {Bvar,Body}) =


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let val ty = type_of Bvar


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val c = Const("All",(ty > HOLogic.boolT) > HOLogic.boolT)


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in list_comb(c,[mk_abs r])


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end;


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fun mk_exists (r as {Bvar,Body}) =


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let val ty = type_of Bvar


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val c = Const("Ex",(ty > HOLogic.boolT) > HOLogic.boolT)


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in list_comb(c,[mk_abs r])


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end;


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fun mk_conj{conj1,conj2} =


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let val c = Const("op &",HOLogic.boolT > HOLogic.boolT > HOLogic.boolT)


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in list_comb(c,[conj1,conj2])


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end;


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fun mk_disj{disj1,disj2} =


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let val c = Const("op ",HOLogic.boolT > HOLogic.boolT > HOLogic.boolT)


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in list_comb(c,[disj1,disj2])


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end;


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fun prod_ty ty1 ty2 = HOLogic.mk_prodT (ty1,ty2);


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local


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fun mk_uncurry(xt,yt,zt) =


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Const("split",(xt > yt > zt) > prod_ty xt yt > zt)


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fun dest_pair(Const("Pair",_) $ M $ N) = {fst=M, snd=N}


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 dest_pair _ = raise USYN_ERR "dest_pair" "not a pair"


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fun is_var (Var _) = true  is_var (Free _) = true  is_var _ = false


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in


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fun mk_pabs{varstruct,body} =


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let fun mpa (varstruct, body) =


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if is_var varstruct


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then mk_abs {Bvar = varstruct, Body = body}


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else let val {fst, snd} = dest_pair varstruct


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in mk_uncurry (type_of fst, type_of snd, type_of body) $


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mpa (fst, mpa (snd, body))


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end


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in mpa (varstruct, body) end


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handle TYPE _ => raise USYN_ERR "mk_pabs" "";


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end;


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(* Destruction routines *)


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datatype lambda = VAR of {Name : string, Ty : typ}


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 CONST of {Name : string, Ty : typ}


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 COMB of {Rator: term, Rand : term}


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 LAMB of {Bvar : term, Body : term};


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fun dest_term(Var((s,i),ty)) = VAR{Name = s, Ty = ty}


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 dest_term(Free(s,ty)) = VAR{Name = s, Ty = ty}


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 dest_term(Const(s,ty)) = CONST{Name = s, Ty = ty}


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 dest_term(M$N) = COMB{Rator=M,Rand=N}


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 dest_term(Abs(s,ty,M)) = let val v = Free(s,ty)


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in LAMB{Bvar = v, Body = betapply (M,v)}


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end


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 dest_term(Bound _) = raise USYN_ERR "dest_term" "Bound";


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fun dest_const(Const(s,ty)) = {Name = s, Ty = ty}


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 dest_const _ = raise USYN_ERR "dest_const" "not a constant";


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fun dest_comb(t1 $ t2) = {Rator = t1, Rand = t2}


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 dest_comb _ = raise USYN_ERR "dest_comb" "not a comb";


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fun dest_abs used (a as Abs(s, ty, M)) =


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let


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val s' = variant used s;


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val v = Free(s', ty);


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in ({Bvar = v, Body = betapply (a,v)}, s'::used)


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end


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 dest_abs _ _ = raise USYN_ERR "dest_abs" "not an abstraction";


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fun dest_eq(Const("op =",_) $ M $ N) = {lhs=M, rhs=N}


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 dest_eq _ = raise USYN_ERR "dest_eq" "not an equality";


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fun dest_imp(Const("op >",_) $ M $ N) = {ant=M, conseq=N}


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 dest_imp _ = raise USYN_ERR "dest_imp" "not an implication";


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fun dest_forall(Const("All",_) $ (a as Abs _)) = fst (dest_abs [] a)


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 dest_forall _ = raise USYN_ERR "dest_forall" "not a forall";


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fun dest_exists(Const("Ex",_) $ (a as Abs _)) = fst (dest_abs [] a)


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 dest_exists _ = raise USYN_ERR "dest_exists" "not an existential";


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fun dest_neg(Const("not",_) $ M) = M


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 dest_neg _ = raise USYN_ERR "dest_neg" "not a negation";


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fun dest_conj(Const("op &",_) $ M $ N) = {conj1=M, conj2=N}


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 dest_conj _ = raise USYN_ERR "dest_conj" "not a conjunction";


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fun dest_disj(Const("op ",_) $ M $ N) = {disj1=M, disj2=N}


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 dest_disj _ = raise USYN_ERR "dest_disj" "not a disjunction";


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fun mk_pair{fst,snd} =


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let val ty1 = type_of fst


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val ty2 = type_of snd


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val c = Const("Pair",ty1 > ty2 > prod_ty ty1 ty2)


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in list_comb(c,[fst,snd])


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end;


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fun dest_pair(Const("Pair",_) $ M $ N) = {fst=M, snd=N}


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 dest_pair _ = raise USYN_ERR "dest_pair" "not a pair";


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local fun ucheck t = (if #Name(dest_const t) = "split" then t


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else raise Match)


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in


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fun dest_pabs used tm =


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let val ({Bvar,Body}, used') = dest_abs used tm


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in {varstruct = Bvar, body = Body, used = used'}


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end handle Utils.ERR _ =>


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let val {Rator,Rand} = dest_comb tm


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val _ = ucheck Rator


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val {varstruct = lv, body, used = used'} = dest_pabs used Rand


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val {varstruct = rv, body, used = used''} = dest_pabs used' body


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in {varstruct = mk_pair {fst = lv, snd = rv}, body = body, used = used''}


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end


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end;


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val lhs = #lhs o dest_eq


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val rhs = #rhs o dest_eq


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val rand = #Rand o dest_comb


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(* Query routines *)


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val is_imp = can dest_imp


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val is_forall = can dest_forall


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val is_exists = can dest_exists


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val is_neg = can dest_neg


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val is_conj = can dest_conj


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val is_disj = can dest_disj


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val is_pair = can dest_pair


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val is_pabs = can (dest_pabs [])


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(* Construction of a cterm from a list of Terms *)


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fun list_mk_abs(L,tm) = fold_rev (fn v => fn M => mk_abs{Bvar=v, Body=M}) L tm;

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(* These others are almost never used *)

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fun list_mk_imp(A,c) = fold_rev (fn a => fn tm => mk_imp{ant=a,conseq=tm}) A c;


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fun list_mk_forall(V,t) = fold_rev (fn v => fn b => mk_forall{Bvar=v, Body=b})V t;

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val list_mk_conj = Utils.end_itlist(fn c1 => fn tm => mk_conj{conj1=c1, conj2=tm})


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(* Need to reverse? *)


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fun gen_all tm = list_mk_forall(term_frees tm, tm);


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(* Destructing a cterm to a list of Terms *)


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fun strip_comb tm =


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let fun dest(M$N, A) = dest(M, N::A)


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 dest x = x


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in dest(tm,[])


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end;


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fun strip_abs(tm as Abs _) =


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let val ({Bvar,Body}, _) = dest_abs [] tm


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val (bvs, core) = strip_abs Body


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in (Bvar::bvs, core)


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end


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 strip_abs M = ([],M);


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fun strip_imp fm =


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if (is_imp fm)


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then let val {ant,conseq} = dest_imp fm


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val (was,wb) = strip_imp conseq


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in ((ant::was), wb)


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end


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else ([],fm);


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fun strip_forall fm =


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if (is_forall fm)


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then let val {Bvar,Body} = dest_forall fm


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val (bvs,core) = strip_forall Body


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in ((Bvar::bvs), core)


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end


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else ([],fm);


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fun strip_exists fm =


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if (is_exists fm)


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then let val {Bvar, Body} = dest_exists fm


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val (bvs,core) = strip_exists Body


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in (Bvar::bvs, core)


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end


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else ([],fm);


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fun strip_disj w =


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if (is_disj w)


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then let val {disj1,disj2} = dest_disj w


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in (strip_disj disj1@strip_disj disj2)


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end


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else [w];


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(* Miscellaneous *)


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fun mk_vstruct ty V =


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let fun follow_prod_type (Type("*",[ty1,ty2])) vs =


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let val (ltm,vs1) = follow_prod_type ty1 vs


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val (rtm,vs2) = follow_prod_type ty2 vs1


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in (mk_pair{fst=ltm, snd=rtm}, vs2) end


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 follow_prod_type _ (v::vs) = (v,vs)


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in #1 (follow_prod_type ty V) end;


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(* Search a term for a subterm satisfying the predicate p. *)


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fun find_term p =


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let fun find tm =

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if (p tm) then SOME tm

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else case tm of


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Abs(_,_,body) => find body

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 (t$u) => (case find t of NONE => find u  some => some)


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 _ => NONE

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in find


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end;


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fun dest_relation tm =


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if (type_of tm = HOLogic.boolT)


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then let val (Const("op :",_) $ (Const("Pair",_)$y$x) $ R) = tm


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in (R,y,x)


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end handle Bind => raise USYN_ERR "dest_relation" "unexpected term structure"


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else raise USYN_ERR "dest_relation" "not a boolean term";


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fun is_WFR (Const("Wellfounded_Recursion.wf",_)$_) = true


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 is_WFR _ = false;


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fun ARB ty = mk_select{Bvar=Free("v",ty),


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Body=Const("True",HOLogic.boolT)};


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end;
