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(* Title: Pure/old_goals.ML
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Author: Lawrence C Paulson, Cambridge University Computer Laboratory
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Copyright 1993 University of Cambridge
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Old-style goal stack package. The goal stack initially holds a dummy
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proof, and can never become empty. Each goal stack consists of a list
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of levels. The undo list is a list of goal stacks. Finally, there
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may be a stack of pending proofs.
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*)
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signature OLD_GOALS =
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sig
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val strip_context: term -> (string * typ) list * term list * term
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val metahyps_thms: int -> thm -> thm list option
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val METAHYPS: (thm list -> tactic) -> int -> tactic
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val simple_read_term: theory -> typ -> string -> term
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val read_term: theory -> string -> term
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val read_prop: theory -> string -> term
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val get_def: theory -> xstring -> thm
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type proof
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val premises: unit -> thm list
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val reset_goals: unit -> unit
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val result_error_fn: (thm -> string -> thm) Unsynchronized.ref
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val print_sign_exn: theory -> exn -> 'a
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val prove_goalw_cterm: thm list->cterm->(thm list->tactic list)->thm
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val prove_goalw_cterm_nocheck: thm list->cterm->(thm list->tactic list)->thm
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val prove_goalw: theory -> thm list -> string -> (thm list -> tactic list) -> thm
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val prove_goal: theory -> string -> (thm list -> tactic list) -> thm
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val topthm: unit -> thm
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val result: unit -> thm
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val uresult: unit -> thm
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val getgoal: int -> term
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val gethyps: int -> thm list
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val print_exn: exn -> 'a
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val filter_goal: (term*term->bool) -> thm list -> int -> thm list
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val prlev: int -> unit
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val pr: unit -> unit
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val prlim: int -> unit
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val goalw_cterm: thm list -> cterm -> thm list
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val goalw: theory -> thm list -> string -> thm list
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val goal: theory -> string -> thm list
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val Goalw: thm list -> string -> thm list
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val Goal: string -> thm list
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val simple_prove_goal_cterm: cterm->(thm list->tactic list)->thm
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val by: tactic -> unit
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val byev: tactic list -> unit
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val back: unit -> unit
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val choplev: int -> unit
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val chop: unit -> unit
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val undo: unit -> unit
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val save_proof: unit -> proof
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val restore_proof: proof -> thm list
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val push_proof: unit -> unit
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val pop_proof: unit -> thm list
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val rotate_proof: unit -> thm list
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val qed: string -> unit
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val qed_goal: string -> theory -> string -> (thm list -> tactic list) -> unit
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val qed_goalw: string -> theory -> thm list -> string
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-> (thm list -> tactic list) -> unit
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val qed_spec_mp: string -> unit
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val qed_goal_spec_mp: string -> theory -> string -> (thm list -> tactic list) -> unit
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val qed_goalw_spec_mp: string -> theory -> thm list -> string
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-> (thm list -> tactic list) -> unit
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end;
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structure OldGoals: OLD_GOALS =
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struct
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(**** METAHYPS -- tactical for using hypotheses as meta-level assumptions
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METAHYPS (fn prems => tac prems) i
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converts subgoal i, of the form !!x1...xm. [| A1;...;An] ==> A into a new
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proof state A==>A, supplying A1,...,An as meta-level assumptions (in
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"prems"). The parameters x1,...,xm become free variables. If the
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resulting proof state is [| B1;...;Bk] ==> C (possibly assuming A1,...,An)
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then it is lifted back into the original context, yielding k subgoals.
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Replaces unknowns in the context by Frees having the prefix METAHYP_
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New unknowns in [| B1;...;Bk] ==> C are lifted over x1,...,xm.
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DOES NOT HANDLE TYPE UNKNOWNS.
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NOTE: This version does not observe the proof context, and thus cannot
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work reliably. See also Subgoal.SUBPROOF and Subgoal.FOCUS for
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properly localized variants of the same idea.
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****)
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(*Strips assumptions in goal yielding ( [x1,...,xm], [H1,...,Hn], B )
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H1,...,Hn are the hypotheses; x1...xm are variants of the parameters.
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Main difference from strip_assums concerns parameters:
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it replaces the bound variables by free variables. *)
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fun strip_context_aux (params, Hs, Const ("==>", _) $ H $ B) =
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strip_context_aux (params, H :: Hs, B)
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| strip_context_aux (params, Hs, Const ("all",_) $ Abs (a, T, t)) =
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let val (b, u) = Syntax.variant_abs (a, T, t)
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in strip_context_aux ((b, T) :: params, Hs, u) end
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| strip_context_aux (params, Hs, B) = (rev params, rev Hs, B);
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fun strip_context A = strip_context_aux ([], [], A);
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local
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(*Left-to-right replacements: ctpairs = [...,(vi,ti),...].
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Instantiates distinct free variables by terms of same type.*)
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fun free_instantiate ctpairs =
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forall_elim_list (map snd ctpairs) o forall_intr_list (map fst ctpairs);
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fun free_of s ((a, i), T) =
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Free (s ^ (case i of 0 => a | _ => a ^ "_" ^ string_of_int i), T)
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fun mk_inst v = (Var v, free_of "METAHYP1_" v)
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in
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(*Common code for METAHYPS and metahyps_thms*)
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fun metahyps_split_prem prem =
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let (*find all vars in the hyps -- should find tvars also!*)
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val hyps_vars = fold Term.add_vars (Logic.strip_assums_hyp prem) []
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val insts = map mk_inst hyps_vars
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(*replace the hyps_vars by Frees*)
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val prem' = subst_atomic insts prem
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val (params,hyps,concl) = strip_context prem'
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in (insts,params,hyps,concl) end;
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fun metahyps_aux_tac tacf (prem,gno) state =
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let val (insts,params,hyps,concl) = metahyps_split_prem prem
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val maxidx = Thm.maxidx_of state
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val cterm = Thm.cterm_of (Thm.theory_of_thm state)
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val chyps = map cterm hyps
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val hypths = map assume chyps
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val subprems = map (Thm.forall_elim_vars 0) hypths
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val fparams = map Free params
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val cparams = map cterm fparams
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fun swap_ctpair (t,u) = (cterm u, cterm t)
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(*Subgoal variables: make Free; lift type over params*)
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fun mk_subgoal_inst concl_vars (v, T) =
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if member (op =) concl_vars (v, T)
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then ((v, T), true, free_of "METAHYP2_" (v, T))
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else ((v, T), false, free_of "METAHYP2_" (v, map #2 params ---> T))
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(*Instantiate subgoal vars by Free applied to params*)
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fun mk_ctpair (v, in_concl, u) =
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if in_concl then (cterm (Var v), cterm u)
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else (cterm (Var v), cterm (list_comb (u, fparams)))
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(*Restore Vars with higher type and index*)
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fun mk_subgoal_swap_ctpair (((a, i), T), in_concl, u as Free (_, U)) =
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if in_concl then (cterm u, cterm (Var ((a, i), T)))
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else (cterm u, cterm (Var ((a, i + maxidx), U)))
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(*Embed B in the original context of params and hyps*)
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fun embed B = list_all_free (params, Logic.list_implies (hyps, B))
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(*Strip the context using elimination rules*)
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fun elim Bhyp = implies_elim_list (forall_elim_list cparams Bhyp) hypths
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(*A form of lifting that discharges assumptions.*)
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fun relift st =
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let val prop = Thm.prop_of st
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val subgoal_vars = (*Vars introduced in the subgoals*)
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fold Term.add_vars (Logic.strip_imp_prems prop) []
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and concl_vars = Term.add_vars (Logic.strip_imp_concl prop) []
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val subgoal_insts = map (mk_subgoal_inst concl_vars) subgoal_vars
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val st' = Thm.instantiate ([], map mk_ctpair subgoal_insts) st
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val emBs = map (cterm o embed) (prems_of st')
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val Cth = implies_elim_list st' (map (elim o assume) emBs)
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in (*restore the unknowns to the hypotheses*)
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free_instantiate (map swap_ctpair insts @
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map mk_subgoal_swap_ctpair subgoal_insts)
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(*discharge assumptions from state in same order*)
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(implies_intr_list emBs
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(forall_intr_list cparams (implies_intr_list chyps Cth)))
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end
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(*function to replace the current subgoal*)
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fun next st = Thm.bicompose false (false, relift st, nprems_of st) gno state
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in Seq.maps next (tacf subprems (trivial (cterm concl))) end;
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end;
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(*Returns the theorem list that METAHYPS would supply to its tactic*)
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fun metahyps_thms i state =
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let val prem = Logic.nth_prem (i, Thm.prop_of state)
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and cterm = cterm_of (Thm.theory_of_thm state)
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val (_,_,hyps,_) = metahyps_split_prem prem
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in SOME (map (Thm.forall_elim_vars 0 o Thm.assume o cterm) hyps) end
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handle TERM ("nth_prem", [A]) => NONE;
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local
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fun print_vars_terms thy (n,thm) =
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let
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fun typed ty = " has type: " ^ Syntax.string_of_typ_global thy ty;
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fun find_vars thy (Const (c, ty)) =
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if null (Term.add_tvarsT ty []) then I
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else insert (op =) (c ^ typed ty)
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| find_vars thy (Var (xi, ty)) = insert (op =) (Term.string_of_vname xi ^ typed ty)
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| find_vars _ (Free _) = I
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| find_vars _ (Bound _) = I
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| find_vars thy (Abs (_, _, t)) = find_vars thy t
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| find_vars thy (t1 $ t2) =
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find_vars thy t1 #> find_vars thy t1;
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val prem = Logic.nth_prem (n, Thm.prop_of thm)
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val tms = find_vars thy prem []
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in
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(warning "Found schematic vars in assumptions:"; warning (cat_lines tms))
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end;
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in
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fun METAHYPS tacf n thm = SUBGOAL (metahyps_aux_tac tacf) n thm
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handle THM("assume: variables",_,_) => (print_vars_terms (theory_of_thm thm) (n,thm); Seq.empty)
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end;
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(* old ways of reading terms *)
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fun simple_read_term thy T s =
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let
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val ctxt = ProofContext.init thy
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|> ProofContext.allow_dummies
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|> ProofContext.set_mode ProofContext.mode_schematic;
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val parse = if T = propT then Syntax.parse_prop else Syntax.parse_term;
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in parse ctxt s |> TypeInfer.constrain T |> Syntax.check_term ctxt end;
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fun read_term thy = simple_read_term thy dummyT;
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fun read_prop thy = simple_read_term thy propT;
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fun get_def thy = Thm.axiom thy o Name_Space.intern (Theory.axiom_space thy) o Thm.def_name;
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(*** Goal package ***)
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(*Each level of goal stack includes a proof state and alternative states,
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the output of the tactic applied to the preceeding level. *)
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type gstack = (thm * thm Seq.seq) list;
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datatype proof = Proof of gstack list * thm list * (bool*thm->thm);
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(*** References ***)
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(*Current assumption list -- set by "goal".*)
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val curr_prems = Unsynchronized.ref([] : thm list);
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(*Return assumption list -- useful if you didn't save "goal"'s result. *)
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fun premises() = !curr_prems;
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(*Current result maker -- set by "goal", used by "result". *)
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fun init_mkresult _ = error "No goal has been supplied in subgoal module";
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val curr_mkresult = Unsynchronized.ref (init_mkresult: bool*thm->thm);
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(*List of previous goal stacks, for the undo operation. Set by setstate.
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A list of lists!*)
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val undo_list = Unsynchronized.ref([[(asm_rl, Seq.empty)]] : gstack list);
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(* Stack of proof attempts *)
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val proofstack = Unsynchronized.ref([]: proof list);
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(*reset all refs*)
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fun reset_goals () =
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(curr_prems := []; curr_mkresult := init_mkresult;
|
wenzelm@26429
|
258 |
undo_list := [[(asm_rl, Seq.empty)]]);
|
wenzelm@18120
|
259 |
|
wenzelm@18120
|
260 |
|
wenzelm@18120
|
261 |
(*** Setting up goal-directed proof ***)
|
wenzelm@18120
|
262 |
|
wenzelm@18120
|
263 |
(*Generates the list of new theories when the proof state's theory changes*)
|
wenzelm@18120
|
264 |
fun thy_error (thy,thy') =
|
haftmann@33040
|
265 |
let val names = subtract (op =) (Context.display_names thy) (Context.display_names thy')
|
wenzelm@18120
|
266 |
in case names of
|
wenzelm@18120
|
267 |
[name] => "\nNew theory: " ^ name
|
wenzelm@18120
|
268 |
| _ => "\nNew theories: " ^ space_implode ", " names
|
wenzelm@18120
|
269 |
end;
|
wenzelm@18120
|
270 |
|
wenzelm@18120
|
271 |
(*Default action is to print an error message; could be suppressed for
|
wenzelm@18120
|
272 |
special applications.*)
|
wenzelm@18120
|
273 |
fun result_error_default state msg : thm =
|
wenzelm@32145
|
274 |
Pretty.str "Bad final proof state:" ::
|
wenzelm@32187
|
275 |
Goal_Display.pretty_goals_without_context (!goals_limit) state @
|
wenzelm@18120
|
276 |
[Pretty.str msg, Pretty.str "Proof failed!"] |> Pretty.chunks |> Pretty.string_of |> error;
|
wenzelm@18120
|
277 |
|
wenzelm@32738
|
278 |
val result_error_fn = Unsynchronized.ref result_error_default;
|
wenzelm@18120
|
279 |
|
wenzelm@18120
|
280 |
|
wenzelm@18120
|
281 |
(*Common treatment of "goal" and "prove_goal":
|
wenzelm@18120
|
282 |
Return assumptions, initial proof state, and function to make result.
|
wenzelm@18120
|
283 |
"atomic" indicates if the goal should be wrapped up in the function
|
wenzelm@18120
|
284 |
"Goal::prop=>prop" to avoid assumptions being returned separately.
|
wenzelm@18120
|
285 |
*)
|
wenzelm@18120
|
286 |
fun prepare_proof atomic rths chorn =
|
wenzelm@18120
|
287 |
let
|
wenzelm@26291
|
288 |
val _ = legacy_feature "Old goal command";
|
wenzelm@26626
|
289 |
val thy = Thm.theory_of_cterm chorn;
|
wenzelm@26626
|
290 |
val horn = Thm.term_of chorn;
|
wenzelm@18120
|
291 |
val _ = Term.no_dummy_patterns horn handle TERM (msg, _) => error msg;
|
wenzelm@18120
|
292 |
val (As, B) = Logic.strip_horn horn;
|
wenzelm@18120
|
293 |
val atoms = atomic andalso
|
wenzelm@27332
|
294 |
forall (fn t => not (can Logic.dest_implies t orelse Logic.is_all t)) As;
|
wenzelm@18120
|
295 |
val (As,B) = if atoms then ([],horn) else (As,B);
|
wenzelm@18120
|
296 |
val cAs = map (cterm_of thy) As;
|
wenzelm@26653
|
297 |
val prems = map (rewrite_rule rths o Thm.forall_elim_vars 0 o Thm.assume) cAs;
|
wenzelm@18120
|
298 |
val cB = cterm_of thy B;
|
wenzelm@18120
|
299 |
val st0 = let val st = Goal.init cB |> fold Thm.weaken cAs
|
wenzelm@18120
|
300 |
in rewrite_goals_rule rths st end
|
wenzelm@18120
|
301 |
(*discharges assumptions from state in the order they appear in goal;
|
wenzelm@18120
|
302 |
checks (if requested) that resulting theorem is equivalent to goal. *)
|
wenzelm@18120
|
303 |
fun mkresult (check,state) =
|
wenzelm@18120
|
304 |
let val state = Seq.hd (flexflex_rule state)
|
wenzelm@18120
|
305 |
handle THM _ => state (*smash flexflex pairs*)
|
wenzelm@18120
|
306 |
val ngoals = nprems_of state
|
wenzelm@18120
|
307 |
val ath = implies_intr_list cAs state
|
wenzelm@18120
|
308 |
val th = Goal.conclude ath
|
wenzelm@26626
|
309 |
val thy' = Thm.theory_of_thm th
|
wenzelm@26626
|
310 |
val {hyps, prop, ...} = Thm.rep_thm th
|
wenzelm@35021
|
311 |
val final_th = Drule.export_without_context th
|
wenzelm@18120
|
312 |
in if not check then final_th
|
wenzelm@26665
|
313 |
else if not (Theory.eq_thy(thy,thy')) then !result_error_fn state
|
wenzelm@18120
|
314 |
("Theory of proof state has changed!" ^
|
wenzelm@18120
|
315 |
thy_error (thy,thy'))
|
wenzelm@18120
|
316 |
else if ngoals>0 then !result_error_fn state
|
wenzelm@18120
|
317 |
(string_of_int ngoals ^ " unsolved goals!")
|
wenzelm@18120
|
318 |
else if not (null hyps) then !result_error_fn state
|
wenzelm@18120
|
319 |
("Additional hypotheses:\n" ^
|
wenzelm@26939
|
320 |
cat_lines (map (Syntax.string_of_term_global thy) hyps))
|
wenzelm@18120
|
321 |
else if Pattern.matches thy
|
wenzelm@18120
|
322 |
(Envir.beta_norm (term_of chorn), Envir.beta_norm prop)
|
wenzelm@18120
|
323 |
then final_th
|
wenzelm@18120
|
324 |
else !result_error_fn state "proved a different theorem"
|
wenzelm@18120
|
325 |
end
|
wenzelm@18120
|
326 |
in
|
wenzelm@26665
|
327 |
if Theory.eq_thy(thy, Thm.theory_of_thm st0)
|
wenzelm@18120
|
328 |
then (prems, st0, mkresult)
|
wenzelm@18120
|
329 |
else error ("Definitions would change the proof state's theory" ^
|
wenzelm@18120
|
330 |
thy_error (thy, Thm.theory_of_thm st0))
|
wenzelm@18120
|
331 |
end
|
wenzelm@18120
|
332 |
handle THM(s,_,_) => error("prepare_proof: exception THM was raised!\n" ^ s);
|
wenzelm@18120
|
333 |
|
wenzelm@18120
|
334 |
(*Prints exceptions readably to users*)
|
wenzelm@18120
|
335 |
fun print_sign_exn_unit thy e =
|
wenzelm@18120
|
336 |
case e of
|
wenzelm@18120
|
337 |
THM (msg,i,thms) =>
|
wenzelm@18120
|
338 |
(writeln ("Exception THM " ^ string_of_int i ^ " raised:\n" ^ msg);
|
wenzelm@32111
|
339 |
List.app (writeln o Display.string_of_thm_global thy) thms)
|
wenzelm@18120
|
340 |
| THEORY (msg,thys) =>
|
wenzelm@18120
|
341 |
(writeln ("Exception THEORY raised:\n" ^ msg);
|
wenzelm@18120
|
342 |
List.app (writeln o Context.str_of_thy) thys)
|
wenzelm@18120
|
343 |
| TERM (msg,ts) =>
|
wenzelm@18120
|
344 |
(writeln ("Exception TERM raised:\n" ^ msg);
|
wenzelm@26939
|
345 |
List.app (writeln o Syntax.string_of_term_global thy) ts)
|
wenzelm@18120
|
346 |
| TYPE (msg,Ts,ts) =>
|
wenzelm@18120
|
347 |
(writeln ("Exception TYPE raised:\n" ^ msg);
|
wenzelm@26939
|
348 |
List.app (writeln o Syntax.string_of_typ_global thy) Ts;
|
wenzelm@26939
|
349 |
List.app (writeln o Syntax.string_of_term_global thy) ts)
|
wenzelm@18120
|
350 |
| e => raise e;
|
wenzelm@18120
|
351 |
|
wenzelm@18120
|
352 |
(*Prints an exception, then fails*)
|
wenzelm@18678
|
353 |
fun print_sign_exn thy e = (print_sign_exn_unit thy e; raise ERROR "");
|
wenzelm@18120
|
354 |
|
wenzelm@18120
|
355 |
(** the prove_goal.... commands
|
wenzelm@18120
|
356 |
Prove theorem using the listed tactics; check it has the specified form.
|
wenzelm@18120
|
357 |
Augment theory with all type assignments of goal.
|
wenzelm@18120
|
358 |
Syntax is similar to "goal" command for easy keyboard use. **)
|
wenzelm@18120
|
359 |
|
wenzelm@18120
|
360 |
(*Version taking the goal as a cterm*)
|
wenzelm@18120
|
361 |
fun prove_goalw_cterm_general check rths chorn tacsf =
|
wenzelm@18120
|
362 |
let val (prems, st0, mkresult) = prepare_proof false rths chorn
|
wenzelm@18120
|
363 |
val tac = EVERY (tacsf prems)
|
wenzelm@18120
|
364 |
fun statef() =
|
wenzelm@18120
|
365 |
(case Seq.pull (tac st0) of
|
wenzelm@18120
|
366 |
SOME(st,_) => st
|
wenzelm@18120
|
367 |
| _ => error ("prove_goal: tactic failed"))
|
wenzelm@32445
|
368 |
in mkresult (check, cond_timeit (!Output.timing) "" statef) end;
|
wenzelm@18120
|
369 |
|
wenzelm@18120
|
370 |
(*Two variants: one checking the result, one not.
|
wenzelm@18120
|
371 |
Neither prints runtime messages: they are for internal packages.*)
|
wenzelm@18120
|
372 |
fun prove_goalw_cterm rths chorn =
|
wenzelm@32966
|
373 |
setmp_CRITICAL Output.timing false (prove_goalw_cterm_general true rths chorn)
|
wenzelm@18120
|
374 |
and prove_goalw_cterm_nocheck rths chorn =
|
wenzelm@32966
|
375 |
setmp_CRITICAL Output.timing false (prove_goalw_cterm_general false rths chorn);
|
wenzelm@18120
|
376 |
|
wenzelm@18120
|
377 |
|
wenzelm@18120
|
378 |
(*Version taking the goal as a string*)
|
wenzelm@18120
|
379 |
fun prove_goalw thy rths agoal tacsf =
|
wenzelm@27256
|
380 |
let val chorn = cterm_of thy (read_prop thy agoal)
|
wenzelm@18120
|
381 |
in prove_goalw_cterm_general true rths chorn tacsf end
|
wenzelm@27256
|
382 |
handle ERROR msg => cat_error msg (*from read_prop?*)
|
wenzelm@18120
|
383 |
("The error(s) above occurred for " ^ quote agoal);
|
wenzelm@18120
|
384 |
|
wenzelm@18120
|
385 |
(*String version with no meta-rewrite-rules*)
|
wenzelm@18120
|
386 |
fun prove_goal thy = prove_goalw thy [];
|
wenzelm@18120
|
387 |
|
wenzelm@18120
|
388 |
|
wenzelm@18120
|
389 |
|
wenzelm@18120
|
390 |
(*** Commands etc ***)
|
wenzelm@18120
|
391 |
|
wenzelm@18120
|
392 |
(*Return the current goal stack, if any, from undo_list*)
|
wenzelm@18120
|
393 |
fun getstate() : gstack = case !undo_list of
|
wenzelm@18120
|
394 |
[] => error"No current state in subgoal module"
|
wenzelm@18120
|
395 |
| x::_ => x;
|
wenzelm@18120
|
396 |
|
wenzelm@18120
|
397 |
(*Pops the given goal stack*)
|
wenzelm@18120
|
398 |
fun pop [] = error"Cannot go back past the beginning of the proof!"
|
wenzelm@18120
|
399 |
| pop (pair::pairs) = (pair,pairs);
|
wenzelm@18120
|
400 |
|
wenzelm@18120
|
401 |
|
wenzelm@23635
|
402 |
(* Print a level of the goal stack *)
|
wenzelm@18120
|
403 |
|
wenzelm@18120
|
404 |
fun print_top ((th, _), pairs) =
|
wenzelm@23635
|
405 |
let
|
wenzelm@23635
|
406 |
val n = length pairs;
|
wenzelm@23635
|
407 |
val m = (! goals_limit);
|
wenzelm@23635
|
408 |
val ngoals = nprems_of th;
|
wenzelm@23635
|
409 |
in
|
wenzelm@23635
|
410 |
[Pretty.str ("Level " ^ string_of_int n ^
|
wenzelm@23635
|
411 |
(if ngoals > 0 then " (" ^ string_of_int ngoals ^ " subgoal" ^
|
wenzelm@23635
|
412 |
(if ngoals <> 1 then "s" else "") ^ ")"
|
wenzelm@23635
|
413 |
else ""))] @
|
wenzelm@32187
|
414 |
Goal_Display.pretty_goals_without_context m th
|
wenzelm@23635
|
415 |
end |> Pretty.chunks |> Pretty.writeln;
|
wenzelm@18120
|
416 |
|
wenzelm@18120
|
417 |
(*Printing can raise exceptions, so the assignment occurs last.
|
wenzelm@18120
|
418 |
Can do setstate[(st,Seq.empty)] to set st as the state. *)
|
wenzelm@18120
|
419 |
fun setstate newgoals =
|
wenzelm@18120
|
420 |
(print_top (pop newgoals); undo_list := newgoals :: !undo_list);
|
wenzelm@18120
|
421 |
|
wenzelm@18120
|
422 |
(*Given a proof state transformation, return a command that updates
|
wenzelm@18120
|
423 |
the goal stack*)
|
wenzelm@18120
|
424 |
fun make_command com = setstate (com (pop (getstate())));
|
wenzelm@18120
|
425 |
|
wenzelm@18120
|
426 |
(*Apply a function on proof states to the current goal stack*)
|
wenzelm@18120
|
427 |
fun apply_fun f = f (pop(getstate()));
|
wenzelm@18120
|
428 |
|
wenzelm@18120
|
429 |
(*Return the top theorem, representing the proof state*)
|
wenzelm@18120
|
430 |
fun topthm () = apply_fun (fn ((th,_), _) => th);
|
wenzelm@18120
|
431 |
|
wenzelm@18120
|
432 |
(*Return the final result. *)
|
wenzelm@18120
|
433 |
fun result () = !curr_mkresult (true, topthm());
|
wenzelm@18120
|
434 |
|
wenzelm@18120
|
435 |
(*Return the result UNCHECKED that it equals the goal -- for synthesis,
|
wenzelm@18120
|
436 |
answer extraction, or other instantiation of Vars *)
|
wenzelm@18120
|
437 |
fun uresult () = !curr_mkresult (false, topthm());
|
wenzelm@18120
|
438 |
|
wenzelm@18120
|
439 |
(*Get subgoal i from goal stack*)
|
wenzelm@18120
|
440 |
fun getgoal i = Logic.get_goal (prop_of (topthm())) i;
|
wenzelm@18120
|
441 |
|
wenzelm@18120
|
442 |
(*Return subgoal i's hypotheses as meta-level assumptions.
|
wenzelm@18120
|
443 |
For debugging uses of METAHYPS*)
|
wenzelm@18120
|
444 |
local exception GETHYPS of thm list
|
wenzelm@18120
|
445 |
in
|
wenzelm@18120
|
446 |
fun gethyps i =
|
wenzelm@18120
|
447 |
(METAHYPS (fn hyps => raise (GETHYPS hyps)) i (topthm()); [])
|
wenzelm@18120
|
448 |
handle GETHYPS hyps => hyps
|
wenzelm@18120
|
449 |
end;
|
wenzelm@18120
|
450 |
|
wenzelm@18120
|
451 |
(*Prints exceptions nicely at top level;
|
wenzelm@18120
|
452 |
raises the exception in order to have a polymorphic type!*)
|
wenzelm@18120
|
453 |
fun print_exn e = (print_sign_exn_unit (Thm.theory_of_thm (topthm())) e; raise e);
|
wenzelm@18120
|
454 |
|
wenzelm@18120
|
455 |
(*Which thms could apply to goal i? (debugs tactics involving filter_thms) *)
|
wenzelm@18120
|
456 |
fun filter_goal could ths i = filter_thms could (999, getgoal i, ths);
|
wenzelm@18120
|
457 |
|
wenzelm@18120
|
458 |
(*For inspecting earlier levels of the backward proof*)
|
wenzelm@18120
|
459 |
fun chop_level n (pair,pairs) =
|
wenzelm@18120
|
460 |
let val level = length pairs
|
wenzelm@18120
|
461 |
in if n<0 andalso ~n <= level
|
wenzelm@18120
|
462 |
then List.drop (pair::pairs, ~n)
|
wenzelm@18120
|
463 |
else if 0<=n andalso n<= level
|
wenzelm@18120
|
464 |
then List.drop (pair::pairs, level - n)
|
wenzelm@18120
|
465 |
else error ("Level number must lie between 0 and " ^
|
wenzelm@18120
|
466 |
string_of_int level)
|
wenzelm@18120
|
467 |
end;
|
wenzelm@18120
|
468 |
|
wenzelm@18120
|
469 |
(*Print the given level of the proof; prlev ~1 prints previous level*)
|
wenzelm@23635
|
470 |
fun prlev n = apply_fun (print_top o pop o (chop_level n));
|
wenzelm@23635
|
471 |
fun pr () = apply_fun print_top;
|
wenzelm@18120
|
472 |
|
wenzelm@18120
|
473 |
(*Set goals_limit and print again*)
|
wenzelm@18120
|
474 |
fun prlim n = (goals_limit:=n; pr());
|
wenzelm@18120
|
475 |
|
wenzelm@18120
|
476 |
(** the goal.... commands
|
wenzelm@18120
|
477 |
Read main goal. Set global variables curr_prems, curr_mkresult.
|
wenzelm@18120
|
478 |
Initial subgoal and premises are rewritten using rths. **)
|
wenzelm@18120
|
479 |
|
wenzelm@18120
|
480 |
(*Version taking the goal as a cterm; if you have a term t and theory thy, use
|
wenzelm@18120
|
481 |
goalw_cterm rths (cterm_of thy t); *)
|
wenzelm@18120
|
482 |
fun agoalw_cterm atomic rths chorn =
|
wenzelm@18120
|
483 |
let val (prems, st0, mkresult) = prepare_proof atomic rths chorn
|
wenzelm@18120
|
484 |
in undo_list := [];
|
wenzelm@18120
|
485 |
setstate [ (st0, Seq.empty) ];
|
wenzelm@18120
|
486 |
curr_prems := prems;
|
wenzelm@18120
|
487 |
curr_mkresult := mkresult;
|
wenzelm@18120
|
488 |
prems
|
wenzelm@18120
|
489 |
end;
|
wenzelm@18120
|
490 |
|
wenzelm@18120
|
491 |
val goalw_cterm = agoalw_cterm false;
|
wenzelm@18120
|
492 |
|
wenzelm@18120
|
493 |
(*Version taking the goal as a string*)
|
wenzelm@18120
|
494 |
fun agoalw atomic thy rths agoal =
|
wenzelm@27256
|
495 |
agoalw_cterm atomic rths (cterm_of thy (read_prop thy agoal))
|
wenzelm@18678
|
496 |
handle ERROR msg => cat_error msg (*from type_assign, etc via prepare_proof*)
|
wenzelm@18120
|
497 |
("The error(s) above occurred for " ^ quote agoal);
|
wenzelm@18120
|
498 |
|
wenzelm@18120
|
499 |
val goalw = agoalw false;
|
wenzelm@18120
|
500 |
fun goal thy = goalw thy [];
|
wenzelm@18120
|
501 |
|
wenzelm@18120
|
502 |
(*now the versions that wrap the goal up in `Goal' to make it atomic*)
|
wenzelm@26429
|
503 |
fun Goalw thms s = agoalw true (ML_Context.the_global_context ()) thms s;
|
wenzelm@18120
|
504 |
val Goal = Goalw [];
|
wenzelm@18120
|
505 |
|
wenzelm@18120
|
506 |
(*simple version with minimal amount of checking and postprocessing*)
|
wenzelm@18120
|
507 |
fun simple_prove_goal_cterm G f =
|
wenzelm@18120
|
508 |
let
|
wenzelm@26291
|
509 |
val _ = legacy_feature "Old goal command";
|
wenzelm@18120
|
510 |
val As = Drule.strip_imp_prems G;
|
wenzelm@18120
|
511 |
val B = Drule.strip_imp_concl G;
|
wenzelm@20229
|
512 |
val asms = map Assumption.assume As;
|
wenzelm@18120
|
513 |
fun check NONE = error "prove_goal: tactic failed"
|
wenzelm@18120
|
514 |
| check (SOME (thm, _)) = (case nprems_of thm of
|
wenzelm@18120
|
515 |
0 => thm
|
wenzelm@18120
|
516 |
| i => !result_error_fn thm (string_of_int i ^ " unsolved goals!"))
|
wenzelm@18120
|
517 |
in
|
wenzelm@35021
|
518 |
Drule.export_without_context (implies_intr_list As
|
wenzelm@18120
|
519 |
(check (Seq.pull (EVERY (f asms) (trivial B)))))
|
wenzelm@18120
|
520 |
end;
|
wenzelm@18120
|
521 |
|
wenzelm@18120
|
522 |
|
wenzelm@18120
|
523 |
(*Proof step "by" the given tactic -- apply tactic to the proof state*)
|
wenzelm@18120
|
524 |
fun by_com tac ((th,ths), pairs) : gstack =
|
wenzelm@18120
|
525 |
(case Seq.pull(tac th) of
|
wenzelm@18120
|
526 |
NONE => error"by: tactic failed"
|
wenzelm@18120
|
527 |
| SOME(th2,ths2) =>
|
wenzelm@22360
|
528 |
(if Thm.eq_thm(th,th2)
|
wenzelm@18120
|
529 |
then warning "Warning: same as previous level"
|
wenzelm@22360
|
530 |
else if Thm.eq_thm_thy(th,th2) then ()
|
wenzelm@18120
|
531 |
else warning ("Warning: theory of proof state has changed" ^
|
wenzelm@18120
|
532 |
thy_error (Thm.theory_of_thm th, Thm.theory_of_thm th2));
|
wenzelm@18120
|
533 |
((th2,ths2)::(th,ths)::pairs)));
|
wenzelm@18120
|
534 |
|
wenzelm@25685
|
535 |
fun by tac = cond_timeit (!Output.timing) ""
|
wenzelm@18120
|
536 |
(fn() => make_command (by_com tac));
|
wenzelm@18120
|
537 |
|
wenzelm@18120
|
538 |
(* byev[tac1,...,tacn] applies tac1 THEN ... THEN tacn.
|
wenzelm@18120
|
539 |
Good for debugging proofs involving prove_goal.*)
|
wenzelm@18120
|
540 |
val byev = by o EVERY;
|
wenzelm@18120
|
541 |
|
wenzelm@18120
|
542 |
|
wenzelm@18120
|
543 |
(*Backtracking means find an alternative result from a tactic.
|
wenzelm@18120
|
544 |
If none at this level, try earlier levels*)
|
wenzelm@18120
|
545 |
fun backtrack [] = error"back: no alternatives"
|
wenzelm@18120
|
546 |
| backtrack ((th,thstr) :: pairs) =
|
wenzelm@18120
|
547 |
(case Seq.pull thstr of
|
wenzelm@18120
|
548 |
NONE => (writeln"Going back a level..."; backtrack pairs)
|
wenzelm@18120
|
549 |
| SOME(th2,thstr2) =>
|
wenzelm@22360
|
550 |
(if Thm.eq_thm(th,th2)
|
wenzelm@18120
|
551 |
then warning "Warning: same as previous choice at this level"
|
wenzelm@22360
|
552 |
else if Thm.eq_thm_thy(th,th2) then ()
|
wenzelm@18120
|
553 |
else warning "Warning: theory of proof state has changed";
|
wenzelm@18120
|
554 |
(th2,thstr2)::pairs));
|
wenzelm@18120
|
555 |
|
wenzelm@18120
|
556 |
fun back() = setstate (backtrack (getstate()));
|
wenzelm@18120
|
557 |
|
wenzelm@18120
|
558 |
(*Chop back to previous level of the proof*)
|
wenzelm@18120
|
559 |
fun choplev n = make_command (chop_level n);
|
wenzelm@18120
|
560 |
|
wenzelm@18120
|
561 |
(*Chopping back the goal stack*)
|
wenzelm@18120
|
562 |
fun chop () = make_command (fn (_,pairs) => pairs);
|
wenzelm@18120
|
563 |
|
wenzelm@18120
|
564 |
(*Restore the previous proof state; discard current state. *)
|
wenzelm@18120
|
565 |
fun undo() = case !undo_list of
|
wenzelm@18120
|
566 |
[] => error"No proof state"
|
wenzelm@18120
|
567 |
| [_] => error"Already at initial state"
|
wenzelm@18120
|
568 |
| _::newundo => (undo_list := newundo; pr()) ;
|
wenzelm@18120
|
569 |
|
wenzelm@18120
|
570 |
|
wenzelm@18120
|
571 |
(*** Managing the proof stack ***)
|
wenzelm@18120
|
572 |
|
wenzelm@18120
|
573 |
fun save_proof() = Proof(!undo_list, !curr_prems, !curr_mkresult);
|
wenzelm@18120
|
574 |
|
wenzelm@18120
|
575 |
fun restore_proof(Proof(ul,prems,mk)) =
|
wenzelm@18120
|
576 |
(undo_list:= ul; curr_prems:= prems; curr_mkresult := mk; prems);
|
wenzelm@18120
|
577 |
|
wenzelm@18120
|
578 |
|
wenzelm@18120
|
579 |
fun top_proof() = case !proofstack of
|
wenzelm@18120
|
580 |
[] => error("Stack of proof attempts is empty!")
|
wenzelm@18120
|
581 |
| p::ps => (p,ps);
|
wenzelm@18120
|
582 |
|
wenzelm@18120
|
583 |
(* push a copy of the current proof state on to the stack *)
|
wenzelm@18120
|
584 |
fun push_proof() = (proofstack := (save_proof() :: !proofstack));
|
wenzelm@18120
|
585 |
|
wenzelm@18120
|
586 |
(* discard the top proof state of the stack *)
|
wenzelm@18120
|
587 |
fun pop_proof() =
|
wenzelm@18120
|
588 |
let val (p,ps) = top_proof()
|
wenzelm@18120
|
589 |
val prems = restore_proof p
|
wenzelm@18120
|
590 |
in proofstack := ps; pr(); prems end;
|
wenzelm@18120
|
591 |
|
wenzelm@18120
|
592 |
(* rotate the stack so that the top element goes to the bottom *)
|
wenzelm@32173
|
593 |
fun rotate_proof() =
|
wenzelm@32173
|
594 |
let val (p,ps) = top_proof()
|
wenzelm@32173
|
595 |
in proofstack := ps@[save_proof()];
|
wenzelm@32173
|
596 |
restore_proof p;
|
wenzelm@32173
|
597 |
pr();
|
wenzelm@32173
|
598 |
!curr_prems
|
wenzelm@32173
|
599 |
end;
|
wenzelm@18120
|
600 |
|
wenzelm@18120
|
601 |
|
wenzelm@26414
|
602 |
(** theorem bindings **)
|
wenzelm@18120
|
603 |
|
wenzelm@26414
|
604 |
fun qed name = ML_Context.ml_store_thm (name, result ());
|
wenzelm@26414
|
605 |
fun qed_goal name thy goal tacsf = ML_Context.ml_store_thm (name, prove_goal thy goal tacsf);
|
wenzelm@18120
|
606 |
fun qed_goalw name thy rews goal tacsf =
|
wenzelm@26414
|
607 |
ML_Context.ml_store_thm (name, prove_goalw thy rews goal tacsf);
|
wenzelm@18120
|
608 |
fun qed_spec_mp name =
|
wenzelm@35625
|
609 |
ML_Context.ml_store_thm (name, Object_Logic.rulify_no_asm (result ()));
|
wenzelm@18120
|
610 |
fun qed_goal_spec_mp name thy s p =
|
wenzelm@35625
|
611 |
bind_thm (name, Object_Logic.rulify_no_asm (prove_goal thy s p));
|
wenzelm@18120
|
612 |
fun qed_goalw_spec_mp name thy defs s p =
|
wenzelm@35625
|
613 |
bind_thm (name, Object_Logic.rulify_no_asm (prove_goalw thy defs s p));
|
wenzelm@18120
|
614 |
|
wenzelm@18120
|
615 |
end;
|
wenzelm@18120
|
616 |
|