(* Title: HOL/Tools/SMT/smt_utils.ML
Author: Sascha Boehme, TU Muenchen
General utility functions.
*)
signature SMT_UTILS =
sig
val repeat: ('a -> 'a option) -> 'a -> 'a
val repeat_yield: ('a -> 'b -> ('a * 'b) option) -> 'a -> 'b -> 'a * 'b
(* types *)
val dest_funT: int -> typ -> typ list * typ
(* terms *)
val dest_conj: term -> term * term
val dest_disj: term -> term * term
(* patterns and instantiations *)
val mk_const_pat: theory -> string -> (ctyp -> 'a) -> 'a * cterm
val destT1: ctyp -> ctyp
val destT2: ctyp -> ctyp
val instTs: ctyp list -> ctyp list * cterm -> cterm
val instT: ctyp -> ctyp * cterm -> cterm
val instT': cterm -> ctyp * cterm -> cterm
(* certified terms *)
val certify: Proof.context -> term -> cterm
val typ_of: cterm -> typ
val dest_cabs: cterm -> Proof.context -> cterm * Proof.context
val dest_all_cabs: cterm -> Proof.context -> cterm * Proof.context
val dest_cbinder: cterm -> Proof.context -> cterm * Proof.context
val dest_all_cbinders: cterm -> Proof.context -> cterm * Proof.context
val mk_cprop: cterm -> cterm
val dest_cprop: cterm -> cterm
val mk_cequals: cterm -> cterm -> cterm
(* conversions *)
val if_conv: (term -> bool) -> conv -> conv -> conv
val if_true_conv: (term -> bool) -> conv -> conv
val binders_conv: (Proof.context -> conv) -> Proof.context -> conv
val prop_conv: conv -> conv
end
structure SMT_Utils: SMT_UTILS =
struct
fun repeat f =
let fun rep x = (case f x of SOME y => rep y | NONE => x)
in rep end
fun repeat_yield f =
let fun rep x y = (case f x y of SOME (x', y') => rep x' y' | NONE => (x, y))
in rep end
(* types *)
val dest_funT =
let
fun dest Ts 0 T = (rev Ts, T)
| dest Ts i (Type ("fun", [T, U])) = dest (T::Ts) (i-1) U
| dest _ _ T = raise TYPE ("not a function type", [T], [])
in dest [] end
(* terms *)
fun dest_conj (@{const HOL.conj} $ t $ u) = (t, u)
| dest_conj t = raise TERM ("not a conjunction", [t])
fun dest_disj (@{const HOL.disj} $ t $ u) = (t, u)
| dest_disj t = raise TERM ("not a disjunction", [t])
(* patterns and instantiations *)
fun mk_const_pat thy name destT =
let val cpat = Thm.cterm_of thy (Const (name, Sign.the_const_type thy name))
in (destT (Thm.ctyp_of_term cpat), cpat) end
val destT1 = hd o Thm.dest_ctyp
val destT2 = hd o tl o Thm.dest_ctyp
fun instTs cUs (cTs, ct) = Thm.instantiate_cterm (cTs ~~ cUs, []) ct
fun instT cU (cT, ct) = instTs [cU] ([cT], ct)
fun instT' ct = instT (Thm.ctyp_of_term ct)
(* certified terms *)
fun certify ctxt = Thm.cterm_of (ProofContext.theory_of ctxt)
fun typ_of ct = #T (Thm.rep_cterm ct)
fun dest_cabs ct ctxt =
(case Thm.term_of ct of
Abs _ =>
let val (n, ctxt') = yield_singleton Variable.variant_fixes Name.uu ctxt
in (snd (Thm.dest_abs (SOME n) ct), ctxt') end
| _ => raise CTERM ("no abstraction", [ct]))
val dest_all_cabs = repeat_yield (try o dest_cabs)
fun dest_cbinder ct ctxt =
(case Thm.term_of ct of
Const _ $ Abs _ => dest_cabs (Thm.dest_arg ct) ctxt
| _ => raise CTERM ("not a binder", [ct]))
val dest_all_cbinders = repeat_yield (try o dest_cbinder)
val mk_cprop = Thm.capply (Thm.cterm_of @{theory} @{const Trueprop})
fun dest_cprop ct =
(case Thm.term_of ct of
@{const Trueprop} $ _ => Thm.dest_arg ct
| _ => raise CTERM ("not a property", [ct]))
val equals = mk_const_pat @{theory} @{const_name "=="} destT1
fun mk_cequals ct cu = Thm.mk_binop (instT' ct equals) ct cu
(* conversions *)
fun if_conv pred cv1 cv2 ct = if pred (Thm.term_of ct) then cv1 ct else cv2 ct
fun if_true_conv pred cv = if_conv pred cv Conv.all_conv
fun binders_conv cv ctxt =
Conv.binder_conv (binders_conv cv o snd) ctxt else_conv cv ctxt
fun prop_conv cv ct =
(case Thm.term_of ct of
@{const Trueprop} $ _ => Conv.arg_conv cv ct
| _ => raise CTERM ("not a property", [ct]))
end