(*  Title:      FOL/fologic.ML

     Author:     Lawrence C Paulson

 Abstract syntax operations for FOL.

 *)

 signature FOLOGIC =

 sig

   val oT: typ

   val mk_Trueprop: term -> term

   val dest_Trueprop: term -> term

   val not: term

   val conj: term

   val disj: term

   val imp: term

   val iff: term

   val mk_conj: term * term -> term

   val mk_disj: term * term -> term

   val mk_imp: term * term -> term

   val dest_imp: term -> term * term

   val dest_conj: term -> term list

   val mk_iff: term * term -> term

   val dest_iff: term -> term * term

   val all_const: typ -> term

   val mk_all: term * term -> term

   val exists_const: typ -> term

   val mk_exists: term * term -> term

   val eq_const: typ -> term

   val mk_eq: term * term -> term

   val dest_eq: term -> term * term

   val mk_binop: string -> term * term -> term

   val mk_binrel: string -> term * term -> term

   val dest_bin: string -> typ -> term -> term * term

 end;

 structure FOLogic: FOLOGIC =

 struct

 val oT = Type(@{type_name o},[]);

 val Trueprop = Const(@{const_name Trueprop}, oT-->propT);

 fun mk_Trueprop P = Trueprop $ P;

 fun dest_Trueprop (Const (@{const_name Trueprop}, _) $ P) = P

   | dest_Trueprop t = raise TERM ("dest_Trueprop", [t]);

 (* Logical constants *)

 val not = Const (@{const_name Not}, oT --> oT);

 val conj = Const(@{const_name conj}, [oT,oT]--->oT);

 val disj = Const(@{const_name disj}, [oT,oT]--->oT);

 val imp = Const(@{const_name imp}, [oT,oT]--->oT)

 val iff = Const(@{const_name iff}, [oT,oT]--->oT);

 fun mk_conj (t1, t2) = conj $ t1 $ t2

 and mk_disj (t1, t2) = disj $ t1 $ t2

 and mk_imp (t1, t2) = imp $ t1 $ t2

 and mk_iff (t1, t2) = iff $ t1 $ t2;

 fun dest_imp (Const(@{const_name imp},_) $ A $ B) = (A, B)

   | dest_imp  t = raise TERM ("dest_imp", [t]);

 fun dest_conj (Const (@{const_name conj}, _) $ t $ t') = t :: dest_conj t'

   | dest_conj t = [t];

 fun dest_iff (Const(@{const_name iff},_) $ A $ B) = (A, B)

   | dest_iff  t = raise TERM ("dest_iff", [t]);

 fun eq_const T = Const (@{const_name eq}, [T, T] ---> oT);

 fun mk_eq (t, u) = eq_const (fastype_of t) $ t $ u;

 fun dest_eq (Const (@{const_name eq}, _) $ lhs $ rhs) = (lhs, rhs)

   | dest_eq t = raise TERM ("dest_eq", [t])

 fun all_const T = Const (@{const_name All}, [T --> oT] ---> oT);

 fun mk_all (Free(x,T),P) = all_const T $ (absfree (x,T,P));

 fun exists_const T = Const (@{const_name Ex}, [T --> oT] ---> oT);

 fun mk_exists (Free(x,T),P) = exists_const T $ (absfree (x,T,P));

 (* binary oprations and relations *)

 fun mk_binop c (t, u) =

   let val T = fastype_of t in

     Const (c, [T, T] ---> T) $ t $ u

   end;

 fun mk_binrel c (t, u) =

   let val T = fastype_of t in

     Const (c, [T, T] ---> oT) $ t $ u

   end;

 fun dest_bin c T (tm as Const (c', Type ("fun", [T', _])) $ t $ u) =

       if c = c' andalso T = T' then (t, u)

       else raise TERM ("dest_bin " ^ c, [tm])

   | dest_bin c _ tm = raise TERM ("dest_bin " ^ c, [tm]);

 end;