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(* Title: HOL/Tools/SMT/smt_utils.ML


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Author: Sascha Boehme, TU Muenchen


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General utility functions.


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*)


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signature SMT_UTILS =


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sig

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(*basic combinators*)

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val repeat: ('a > 'a option) > 'a > 'a


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val repeat_yield: ('a > 'b > ('a * 'b) option) > 'a > 'b > 'a * 'b


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(*types*)

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val dest_funT: int > typ > typ list * typ


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(*terms*)

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val dest_conj: term > term * term


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val dest_disj: term > term * term


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(*patterns and instantiations*)

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val mk_const_pat: theory > string > (ctyp > 'a) > 'a * cterm


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val destT1: ctyp > ctyp


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val destT2: ctyp > ctyp


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val instTs: ctyp list > ctyp list * cterm > cterm


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val instT: ctyp > ctyp * cterm > cterm


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val instT': cterm > ctyp * cterm > cterm


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(*certified terms*)

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val certify: Proof.context > term > cterm

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val typ_of: cterm > typ

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val dest_cabs: cterm > Proof.context > cterm * Proof.context


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val dest_all_cabs: cterm > Proof.context > cterm * Proof.context


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val dest_cbinder: cterm > Proof.context > cterm * Proof.context


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val dest_all_cbinders: cterm > Proof.context > cterm * Proof.context


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val mk_cprop: cterm > cterm


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val dest_cprop: cterm > cterm


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val mk_cequals: cterm > cterm > cterm


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(*conversions*)

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val if_conv: (term > bool) > conv > conv > conv


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val if_true_conv: (term > bool) > conv > conv


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val binders_conv: (Proof.context > conv) > Proof.context > conv


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val prop_conv: conv > conv


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end


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structure SMT_Utils: SMT_UTILS =


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struct


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(* basic combinators *)


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fun repeat f =


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let fun rep x = (case f x of SOME y => rep y  NONE => x)


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in rep end


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fun repeat_yield f =


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let fun rep x y = (case f x y of SOME (x', y') => rep x' y'  NONE => (x, y))


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in rep end


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(* types *)


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val dest_funT =


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let


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fun dest Ts 0 T = (rev Ts, T)


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 dest Ts i (Type ("fun", [T, U])) = dest (T::Ts) (i1) U


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 dest _ _ T = raise TYPE ("not a function type", [T], [])


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in dest [] end


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(* terms *)


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fun dest_conj (@{const HOL.conj} $ t $ u) = (t, u)


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 dest_conj t = raise TERM ("not a conjunction", [t])


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fun dest_disj (@{const HOL.disj} $ t $ u) = (t, u)


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 dest_disj t = raise TERM ("not a disjunction", [t])


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(* patterns and instantiations *)


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fun mk_const_pat thy name destT =


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let val cpat = Thm.cterm_of thy (Const (name, Sign.the_const_type thy name))


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in (destT (Thm.ctyp_of_term cpat), cpat) end


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val destT1 = hd o Thm.dest_ctyp


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val destT2 = hd o tl o Thm.dest_ctyp


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fun instTs cUs (cTs, ct) = Thm.instantiate_cterm (cTs ~~ cUs, []) ct


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fun instT cU (cT, ct) = instTs [cU] ([cT], ct)


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fun instT' ct = instT (Thm.ctyp_of_term ct)


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(* certified terms *)


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fun certify ctxt = Thm.cterm_of (ProofContext.theory_of ctxt)


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fun typ_of ct = #T (Thm.rep_cterm ct)


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fun dest_cabs ct ctxt =


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(case Thm.term_of ct of


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Abs _ =>


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let val (n, ctxt') = yield_singleton Variable.variant_fixes Name.uu ctxt


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in (snd (Thm.dest_abs (SOME n) ct), ctxt') end


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 _ => raise CTERM ("no abstraction", [ct]))


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val dest_all_cabs = repeat_yield (try o dest_cabs)


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fun dest_cbinder ct ctxt =


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(case Thm.term_of ct of


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Const _ $ Abs _ => dest_cabs (Thm.dest_arg ct) ctxt


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 _ => raise CTERM ("not a binder", [ct]))


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val dest_all_cbinders = repeat_yield (try o dest_cbinder)


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val mk_cprop = Thm.capply (Thm.cterm_of @{theory} @{const Trueprop})

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fun dest_cprop ct =


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(case Thm.term_of ct of


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@{const Trueprop} $ _ => Thm.dest_arg ct


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 _ => raise CTERM ("not a property", [ct]))


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val equals = mk_const_pat @{theory} @{const_name "=="} destT1


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fun mk_cequals ct cu = Thm.mk_binop (instT' ct equals) ct cu


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(* conversions *)


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fun if_conv pred cv1 cv2 ct = if pred (Thm.term_of ct) then cv1 ct else cv2 ct

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fun if_true_conv pred cv = if_conv pred cv Conv.all_conv

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fun binders_conv cv ctxt =


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Conv.binder_conv (binders_conv cv o snd) ctxt else_conv cv ctxt


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fun prop_conv cv ct =


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(case Thm.term_of ct of


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@{const Trueprop} $ _ => Conv.arg_conv cv ct


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 _ => raise CTERM ("not a property", [ct]))


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end
