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(* Title: HOL/Tools/Nitpick/nitpick_mono.ML
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Author: Jasmin Blanchette, TU Muenchen
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Copyright 2009, 2010
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Monotonicity inference for higher-order logic.
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*)
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signature NITPICK_MONO =
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sig
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type hol_context = Nitpick_HOL.hol_context
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val formulas_monotonic :
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hol_context -> bool -> typ -> term list * term list -> bool
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val finitize_funs :
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hol_context -> bool -> (typ option * bool option) list -> typ
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-> term list * term list -> term list * term list
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end;
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structure Nitpick_Mono : NITPICK_MONO =
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struct
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open Nitpick_Util
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open Nitpick_HOL
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type var = int
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datatype sign = Plus | Minus
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datatype sign_atom = S of sign | V of var
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type literal = var * sign
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datatype mtyp =
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MAlpha |
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MFun of mtyp * sign_atom * mtyp |
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MPair of mtyp * mtyp |
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MType of string * mtyp list |
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MRec of string * typ list
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datatype mterm =
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MRaw of term * mtyp |
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MAbs of string * typ * mtyp * sign_atom * mterm |
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MApp of mterm * mterm
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type mdata =
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{hol_ctxt: hol_context,
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binarize: bool,
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alpha_T: typ,
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no_harmless: bool,
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max_fresh: int Unsynchronized.ref,
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datatype_mcache: ((string * typ list) * mtyp) list Unsynchronized.ref,
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constr_mcache: (styp * mtyp) list Unsynchronized.ref}
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exception MTYPE of string * mtyp list * typ list
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exception MTERM of string * mterm list
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(* string -> unit *)
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fun print_g (_ : string) = ()
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(* val print_g = tracing *)
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(* var -> string *)
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val string_for_var = signed_string_of_int
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(* string -> var list -> string *)
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fun string_for_vars sep [] = "0\<^bsub>" ^ sep ^ "\<^esub>"
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| string_for_vars sep xs = space_implode sep (map string_for_var xs)
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fun subscript_string_for_vars sep xs =
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if null xs then "" else "\<^bsub>" ^ string_for_vars sep xs ^ "\<^esub>"
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(* sign -> string *)
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fun string_for_sign Plus = "+"
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| string_for_sign Minus = "-"
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(* sign -> sign -> sign *)
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fun xor sn1 sn2 = if sn1 = sn2 then Plus else Minus
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(* sign -> sign *)
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val negate = xor Minus
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(* sign_atom -> string *)
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fun string_for_sign_atom (S sn) = string_for_sign sn
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| string_for_sign_atom (V x) = string_for_var x
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(* literal -> string *)
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fun string_for_literal (x, sn) = string_for_var x ^ " = " ^ string_for_sign sn
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val bool_M = MType (@{type_name bool}, [])
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val dummy_M = MType (nitpick_prefix ^ "dummy", [])
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(* mtyp -> bool *)
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fun is_MRec (MRec _) = true
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| is_MRec _ = false
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(* mtyp -> mtyp * sign_atom * mtyp *)
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fun dest_MFun (MFun z) = z
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| dest_MFun M = raise MTYPE ("Nitpick_Mono.dest_MFun", [M], [])
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val no_prec = 100
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(* mtyp -> int *)
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fun precedence_of_mtype (MFun _) = 1
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| precedence_of_mtype (MPair _) = 2
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| precedence_of_mtype _ = no_prec
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(* mtyp -> string *)
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val string_for_mtype =
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let
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(* int -> mtyp -> string *)
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fun aux outer_prec M =
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let
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val prec = precedence_of_mtype M
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val need_parens = (prec < outer_prec)
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in
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(if need_parens then "(" else "") ^
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(if M = dummy_M then
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"_"
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else case M of
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MAlpha => "\<alpha>"
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| MFun (M1, a, M2) =>
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aux (prec + 1) M1 ^ " \<Rightarrow>\<^bsup>" ^
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string_for_sign_atom a ^ "\<^esup> " ^ aux prec M2
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| MPair (M1, M2) => aux (prec + 1) M1 ^ " \<times> " ^ aux prec M2
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| MType (s, []) =>
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if s = @{type_name prop} orelse s = @{type_name bool} then "o"
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else s
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| MType (s, Ms) => "(" ^ commas (map (aux 0) Ms) ^ ") " ^ s
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| MRec (s, _) => "[" ^ s ^ "]") ^
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(if need_parens then ")" else "")
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end
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in aux 0 end
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(* mtyp -> mtyp list *)
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fun flatten_mtype (MPair (M1, M2)) = maps flatten_mtype [M1, M2]
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| flatten_mtype (MType (_, Ms)) = maps flatten_mtype Ms
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| flatten_mtype M = [M]
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(* mterm -> bool *)
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fun precedence_of_mterm (MRaw _) = no_prec
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| precedence_of_mterm (MAbs _) = 1
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| precedence_of_mterm (MApp _) = 2
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(* Proof.context -> mterm -> string *)
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fun string_for_mterm ctxt =
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let
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(* mtype -> string *)
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fun mtype_annotation M = "\<^bsup>" ^ string_for_mtype M ^ "\<^esup>"
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(* int -> mterm -> string *)
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fun aux outer_prec m =
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let
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val prec = precedence_of_mterm m
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val need_parens = (prec < outer_prec)
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in
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(if need_parens then "(" else "") ^
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(case m of
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MRaw (t, M) => Syntax.string_of_term ctxt t ^ mtype_annotation M
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| MAbs (s, _, M, a, m) =>
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"\<lambda>" ^ s ^ mtype_annotation M ^ ".\<^bsup>" ^
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string_for_sign_atom a ^ "\<^esup> " ^ aux prec m
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| MApp (m1, m2) => aux prec m1 ^ " " ^ aux (prec + 1) m2) ^
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(if need_parens then ")" else "")
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end
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in aux 0 end
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(* mterm -> mtyp *)
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fun mtype_of_mterm (MRaw (_, M)) = M
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| mtype_of_mterm (MAbs (_, _, M, a, m)) = MFun (M, a, mtype_of_mterm m)
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| mtype_of_mterm (MApp (m1, _)) =
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case mtype_of_mterm m1 of
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MFun (_, _, M12) => M12
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| M1 => raise MTYPE ("Nitpick_Mono.mtype_of_mterm", [M1], [])
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(* mterm -> mterm * mterm list *)
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fun strip_mcomb (MApp (m1, m2)) = strip_mcomb m1 ||> (fn ms => append ms [m2])
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| strip_mcomb m = (m, [])
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(* hol_context -> bool -> bool -> typ -> mdata *)
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fun initial_mdata hol_ctxt binarize no_harmless alpha_T =
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({hol_ctxt = hol_ctxt, binarize = binarize, alpha_T = alpha_T,
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no_harmless = no_harmless, max_fresh = Unsynchronized.ref 0,
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datatype_mcache = Unsynchronized.ref [],
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constr_mcache = Unsynchronized.ref []} : mdata)
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(* typ -> typ -> bool *)
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fun could_exist_alpha_subtype alpha_T (T as Type (_, Ts)) =
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T = alpha_T orelse (not (is_fp_iterator_type T) andalso
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exists (could_exist_alpha_subtype alpha_T) Ts)
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| could_exist_alpha_subtype alpha_T T = (T = alpha_T)
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(* theory -> typ -> typ -> bool *)
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fun could_exist_alpha_sub_mtype _ (alpha_T as TFree _) T =
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could_exist_alpha_subtype alpha_T T
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| could_exist_alpha_sub_mtype thy alpha_T T =
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(T = alpha_T orelse is_datatype thy [(NONE, true)] T)
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(* mtyp -> bool *)
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fun exists_alpha_sub_mtype MAlpha = true
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| exists_alpha_sub_mtype (MFun (M1, _, M2)) =
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exists exists_alpha_sub_mtype [M1, M2]
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| exists_alpha_sub_mtype (MPair (M1, M2)) =
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exists exists_alpha_sub_mtype [M1, M2]
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| exists_alpha_sub_mtype (MType (_, Ms)) = exists exists_alpha_sub_mtype Ms
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| exists_alpha_sub_mtype (MRec _) = true
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(* mtyp -> bool *)
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fun exists_alpha_sub_mtype_fresh MAlpha = true
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| exists_alpha_sub_mtype_fresh (MFun (_, V _, _)) = true
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| exists_alpha_sub_mtype_fresh (MFun (_, _, M2)) =
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exists_alpha_sub_mtype_fresh M2
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| exists_alpha_sub_mtype_fresh (MPair (M1, M2)) =
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exists exists_alpha_sub_mtype_fresh [M1, M2]
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| exists_alpha_sub_mtype_fresh (MType (_, Ms)) =
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exists exists_alpha_sub_mtype_fresh Ms
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| exists_alpha_sub_mtype_fresh (MRec _) = true
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(* string * typ list -> mtyp list -> mtyp *)
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fun constr_mtype_for_binders z Ms =
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fold_rev (fn M => curry3 MFun M (S Minus)) Ms (MRec z)
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(* ((string * typ list) * mtyp) list -> mtyp list -> mtyp -> mtyp *)
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fun repair_mtype _ _ MAlpha = MAlpha
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| repair_mtype cache seen (MFun (M1, a, M2)) =
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MFun (repair_mtype cache seen M1, a, repair_mtype cache seen M2)
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| repair_mtype cache seen (MPair Mp) =
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MPair (pairself (repair_mtype cache seen) Mp)
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| repair_mtype cache seen (MType (s, Ms)) =
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MType (s, maps (flatten_mtype o repair_mtype cache seen) Ms)
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| repair_mtype cache seen (MRec (z as (s, _))) =
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case AList.lookup (op =) cache z |> the of
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MRec _ => MType (s, [])
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| M => if member (op =) seen M then MType (s, [])
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else repair_mtype cache (M :: seen) M
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(* ((string * typ list) * mtyp) list Unsynchronized.ref -> unit *)
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fun repair_datatype_mcache cache =
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let
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(* (string * typ list) * mtyp -> unit *)
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fun repair_one (z, M) =
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Unsynchronized.change cache
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(AList.update (op =) (z, repair_mtype (!cache) [] M))
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in List.app repair_one (rev (!cache)) end
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(* (typ * mtyp) list -> (styp * mtyp) list Unsynchronized.ref -> unit *)
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fun repair_constr_mcache dtype_cache constr_mcache =
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let
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(* styp * mtyp -> unit *)
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fun repair_one (x, M) =
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Unsynchronized.change constr_mcache
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(AList.update (op =) (x, repair_mtype dtype_cache [] M))
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in List.app repair_one (!constr_mcache) end
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(* typ -> bool *)
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fun is_fin_fun_supported_type @{typ prop} = true
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| is_fin_fun_supported_type @{typ bool} = true
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| is_fin_fun_supported_type (Type (@{type_name option}, _)) = true
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| is_fin_fun_supported_type _ = false
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(* typ -> typ -> term -> term option *)
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fun fin_fun_body _ _ (t as @{term False}) = SOME t
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| fin_fun_body _ _ (t as Const (@{const_name None}, _)) = SOME t
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| fin_fun_body dom_T ran_T
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((t0 as Const (@{const_name If}, _))
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$ (t1 as Const (@{const_name "op ="}, _) $ Bound 0 $ t1')
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$ t2 $ t3) =
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(if loose_bvar1 (t1', 0) then
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NONE
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else case fin_fun_body dom_T ran_T t3 of
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NONE => NONE
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| SOME t3 =>
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SOME (t0 $ (Const (@{const_name is_unknown}, dom_T --> bool_T) $ t1')
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264 |
$ (Const (@{const_name unknown}, ran_T)) $ (t0 $ t1 $ t2 $ t3)))
|
blanchet@35665
|
265 |
| fin_fun_body _ _ _ = NONE
|
blanchet@33192
|
266 |
|
blanchet@35385
|
267 |
(* mdata -> typ -> typ -> mtyp * sign_atom * mtyp *)
|
blanchet@35385
|
268 |
fun fresh_mfun_for_fun_type (mdata as {max_fresh, ...} : mdata) T1 T2 =
|
blanchet@33192
|
269 |
let
|
blanchet@35385
|
270 |
val M1 = fresh_mtype_for_type mdata T1
|
blanchet@35385
|
271 |
val M2 = fresh_mtype_for_type mdata T2
|
blanchet@35665
|
272 |
val a = if is_fin_fun_supported_type (body_type T2) andalso
|
blanchet@35385
|
273 |
exists_alpha_sub_mtype_fresh M1 then
|
blanchet@35385
|
274 |
V (Unsynchronized.inc max_fresh)
|
blanchet@35385
|
275 |
else
|
blanchet@35385
|
276 |
S Minus
|
blanchet@35385
|
277 |
in (M1, a, M2) end
|
blanchet@35385
|
278 |
(* mdata -> typ -> mtyp *)
|
blanchet@35385
|
279 |
and fresh_mtype_for_type (mdata as {hol_ctxt as {thy, ...}, binarize, alpha_T,
|
blanchet@35665
|
280 |
datatype_mcache, constr_mcache, ...}) =
|
blanchet@35385
|
281 |
let
|
blanchet@35385
|
282 |
(* typ -> mtyp *)
|
blanchet@35385
|
283 |
fun do_type T =
|
blanchet@33192
|
284 |
if T = alpha_T then
|
blanchet@35385
|
285 |
MAlpha
|
blanchet@33192
|
286 |
else case T of
|
blanchet@35665
|
287 |
Type (@{type_name fun}, [T1, T2]) =>
|
blanchet@35665
|
288 |
MFun (fresh_mfun_for_fun_type mdata T1 T2)
|
blanchet@35665
|
289 |
| Type (@{type_name "*"}, [T1, T2]) => MPair (pairself do_type (T1, T2))
|
blanchet@33192
|
290 |
| Type (z as (s, _)) =>
|
blanchet@35385
|
291 |
if could_exist_alpha_sub_mtype thy alpha_T T then
|
blanchet@35665
|
292 |
case AList.lookup (op =) (!datatype_mcache) z of
|
blanchet@35385
|
293 |
SOME M => M
|
blanchet@33192
|
294 |
| NONE =>
|
blanchet@33192
|
295 |
let
|
blanchet@35665
|
296 |
val _ = Unsynchronized.change datatype_mcache (cons (z, MRec z))
|
blanchet@35219
|
297 |
val xs = binarized_and_boxed_datatype_constrs hol_ctxt binarize T
|
blanchet@35385
|
298 |
val (all_Ms, constr_Ms) =
|
blanchet@35385
|
299 |
fold_rev (fn (_, T') => fn (all_Ms, constr_Ms) =>
|
blanchet@33192
|
300 |
let
|
blanchet@35385
|
301 |
val binder_Ms = map do_type (binder_types T')
|
blanchet@35385
|
302 |
val new_Ms = filter exists_alpha_sub_mtype_fresh
|
blanchet@35385
|
303 |
binder_Ms
|
blanchet@35385
|
304 |
val constr_M = constr_mtype_for_binders z
|
blanchet@35385
|
305 |
binder_Ms
|
blanchet@33192
|
306 |
in
|
blanchet@35385
|
307 |
(union (op =) new_Ms all_Ms,
|
blanchet@35385
|
308 |
constr_M :: constr_Ms)
|
blanchet@33192
|
309 |
end)
|
blanchet@33192
|
310 |
xs ([], [])
|
blanchet@35385
|
311 |
val M = MType (s, all_Ms)
|
blanchet@35665
|
312 |
val _ = Unsynchronized.change datatype_mcache
|
blanchet@35385
|
313 |
(AList.update (op =) (z, M))
|
blanchet@35665
|
314 |
val _ = Unsynchronized.change constr_mcache
|
blanchet@35385
|
315 |
(append (xs ~~ constr_Ms))
|
blanchet@33192
|
316 |
in
|
blanchet@35665
|
317 |
if forall (not o is_MRec o snd) (!datatype_mcache) then
|
blanchet@35665
|
318 |
(repair_datatype_mcache datatype_mcache;
|
blanchet@35665
|
319 |
repair_constr_mcache (!datatype_mcache) constr_mcache;
|
blanchet@35665
|
320 |
AList.lookup (op =) (!datatype_mcache) z |> the)
|
blanchet@33192
|
321 |
else
|
blanchet@35385
|
322 |
M
|
blanchet@33192
|
323 |
end
|
blanchet@33192
|
324 |
else
|
blanchet@35385
|
325 |
MType (s, [])
|
blanchet@35385
|
326 |
| _ => MType (Refute.string_of_typ T, [])
|
blanchet@33192
|
327 |
in do_type end
|
blanchet@33192
|
328 |
|
blanchet@35385
|
329 |
(* mtyp -> mtyp list *)
|
blanchet@35385
|
330 |
fun prodM_factors (MPair (M1, M2)) = maps prodM_factors [M1, M2]
|
blanchet@35385
|
331 |
| prodM_factors M = [M]
|
blanchet@35385
|
332 |
(* mtyp -> mtyp list * mtyp *)
|
blanchet@35665
|
333 |
fun curried_strip_mtype (MFun (M1, _, M2)) =
|
blanchet@35385
|
334 |
curried_strip_mtype M2 |>> append (prodM_factors M1)
|
blanchet@35385
|
335 |
| curried_strip_mtype M = ([], M)
|
blanchet@35385
|
336 |
(* string -> mtyp -> mtyp *)
|
blanchet@35385
|
337 |
fun sel_mtype_from_constr_mtype s M =
|
blanchet@35385
|
338 |
let val (arg_Ms, dataM) = curried_strip_mtype M in
|
blanchet@35385
|
339 |
MFun (dataM, S Minus,
|
blanchet@35385
|
340 |
case sel_no_from_name s of ~1 => bool_M | n => nth arg_Ms n)
|
blanchet@33192
|
341 |
end
|
blanchet@33192
|
342 |
|
blanchet@35385
|
343 |
(* mdata -> styp -> mtyp *)
|
blanchet@35665
|
344 |
fun mtype_for_constr (mdata as {hol_ctxt = {thy, ...}, alpha_T, constr_mcache,
|
blanchet@33192
|
345 |
...}) (x as (_, T)) =
|
blanchet@35385
|
346 |
if could_exist_alpha_sub_mtype thy alpha_T T then
|
blanchet@35665
|
347 |
case AList.lookup (op =) (!constr_mcache) x of
|
blanchet@35385
|
348 |
SOME M => M
|
blanchet@35384
|
349 |
| NONE => if T = alpha_T then
|
blanchet@35385
|
350 |
let val M = fresh_mtype_for_type mdata T in
|
blanchet@35665
|
351 |
(Unsynchronized.change constr_mcache (cons (x, M)); M)
|
blanchet@35384
|
352 |
end
|
blanchet@35384
|
353 |
else
|
blanchet@35385
|
354 |
(fresh_mtype_for_type mdata (body_type T);
|
blanchet@35665
|
355 |
AList.lookup (op =) (!constr_mcache) x |> the)
|
blanchet@33192
|
356 |
else
|
blanchet@35385
|
357 |
fresh_mtype_for_type mdata T
|
blanchet@35385
|
358 |
fun mtype_for_sel (mdata as {hol_ctxt, binarize, ...}) (x as (s, _)) =
|
blanchet@35190
|
359 |
x |> binarized_and_boxed_constr_for_sel hol_ctxt binarize
|
blanchet@35385
|
360 |
|> mtype_for_constr mdata |> sel_mtype_from_constr_mtype s
|
blanchet@33192
|
361 |
|
blanchet@35665
|
362 |
(* literal list -> sign_atom -> sign_atom *)
|
blanchet@35665
|
363 |
fun resolve_sign_atom lits (V x) =
|
blanchet@35665
|
364 |
x |> AList.lookup (op =) lits |> Option.map S |> the_default (V x)
|
blanchet@35665
|
365 |
| resolve_sign_atom _ a = a
|
blanchet@35385
|
366 |
(* literal list -> mtyp -> mtyp *)
|
blanchet@35665
|
367 |
fun resolve_mtype lits =
|
blanchet@33192
|
368 |
let
|
blanchet@35385
|
369 |
(* mtyp -> mtyp *)
|
blanchet@35385
|
370 |
fun aux MAlpha = MAlpha
|
blanchet@35665
|
371 |
| aux (MFun (M1, a, M2)) = MFun (aux M1, resolve_sign_atom lits a, aux M2)
|
blanchet@35385
|
372 |
| aux (MPair Mp) = MPair (pairself aux Mp)
|
blanchet@35385
|
373 |
| aux (MType (s, Ms)) = MType (s, map aux Ms)
|
blanchet@35385
|
374 |
| aux (MRec z) = MRec z
|
blanchet@33192
|
375 |
in aux end
|
blanchet@33192
|
376 |
|
blanchet@33192
|
377 |
datatype comp_op = Eq | Leq
|
blanchet@33192
|
378 |
|
blanchet@33192
|
379 |
type comp = sign_atom * sign_atom * comp_op * var list
|
blanchet@33192
|
380 |
type sign_expr = literal list
|
blanchet@33192
|
381 |
|
blanchet@33192
|
382 |
datatype constraint_set =
|
blanchet@33192
|
383 |
UnsolvableCSet |
|
blanchet@33192
|
384 |
CSet of literal list * comp list * sign_expr list
|
blanchet@33192
|
385 |
|
blanchet@33192
|
386 |
(* comp_op -> string *)
|
blanchet@33192
|
387 |
fun string_for_comp_op Eq = "="
|
blanchet@33192
|
388 |
| string_for_comp_op Leq = "\<le>"
|
blanchet@33192
|
389 |
|
blanchet@33192
|
390 |
(* sign_expr -> string *)
|
blanchet@33192
|
391 |
fun string_for_sign_expr [] = "\<bot>"
|
blanchet@33192
|
392 |
| string_for_sign_expr lits =
|
blanchet@33192
|
393 |
space_implode " \<or> " (map string_for_literal lits)
|
blanchet@33192
|
394 |
|
blanchet@33192
|
395 |
(* constraint_set *)
|
blanchet@33192
|
396 |
val slack = CSet ([], [], [])
|
blanchet@33192
|
397 |
|
blanchet@33192
|
398 |
(* literal -> literal list option -> literal list option *)
|
blanchet@33192
|
399 |
fun do_literal _ NONE = NONE
|
blanchet@33192
|
400 |
| do_literal (x, sn) (SOME lits) =
|
blanchet@33192
|
401 |
case AList.lookup (op =) lits x of
|
blanchet@33192
|
402 |
SOME sn' => if sn = sn' then SOME lits else NONE
|
blanchet@33192
|
403 |
| NONE => SOME ((x, sn) :: lits)
|
blanchet@33192
|
404 |
|
blanchet@33192
|
405 |
(* comp_op -> var list -> sign_atom -> sign_atom -> literal list * comp list
|
blanchet@33192
|
406 |
-> (literal list * comp list) option *)
|
blanchet@33192
|
407 |
fun do_sign_atom_comp Eq [] a1 a2 (accum as (lits, comps)) =
|
blanchet@33192
|
408 |
(case (a1, a2) of
|
blanchet@33192
|
409 |
(S sn1, S sn2) => if sn1 = sn2 then SOME accum else NONE
|
blanchet@33192
|
410 |
| (V x1, S sn2) =>
|
blanchet@33192
|
411 |
Option.map (rpair comps) (do_literal (x1, sn2) (SOME lits))
|
blanchet@33192
|
412 |
| (V _, V _) => SOME (lits, insert (op =) (a1, a2, Eq, []) comps)
|
blanchet@33192
|
413 |
| _ => do_sign_atom_comp Eq [] a2 a1 accum)
|
blanchet@33192
|
414 |
| do_sign_atom_comp Leq [] a1 a2 (accum as (lits, comps)) =
|
blanchet@33192
|
415 |
(case (a1, a2) of
|
blanchet@34969
|
416 |
(_, S Minus) => SOME accum
|
blanchet@34969
|
417 |
| (S Plus, _) => SOME accum
|
blanchet@34969
|
418 |
| (S Minus, S Plus) => NONE
|
blanchet@33192
|
419 |
| (V _, V _) => SOME (lits, insert (op =) (a1, a2, Leq, []) comps)
|
blanchet@33192
|
420 |
| _ => do_sign_atom_comp Eq [] a1 a2 accum)
|
blanchet@35280
|
421 |
| do_sign_atom_comp cmp xs a1 a2 (lits, comps) =
|
blanchet@33192
|
422 |
SOME (lits, insert (op =) (a1, a2, cmp, xs) comps)
|
blanchet@33192
|
423 |
|
blanchet@35385
|
424 |
(* comp -> var list -> mtyp -> mtyp -> (literal list * comp list) option
|
blanchet@33192
|
425 |
-> (literal list * comp list) option *)
|
blanchet@35385
|
426 |
fun do_mtype_comp _ _ _ _ NONE = NONE
|
blanchet@35385
|
427 |
| do_mtype_comp _ _ MAlpha MAlpha accum = accum
|
blanchet@35385
|
428 |
| do_mtype_comp Eq xs (MFun (M11, a1, M12)) (MFun (M21, a2, M22))
|
blanchet@33192
|
429 |
(SOME accum) =
|
blanchet@35385
|
430 |
accum |> do_sign_atom_comp Eq xs a1 a2 |> do_mtype_comp Eq xs M11 M21
|
blanchet@35385
|
431 |
|> do_mtype_comp Eq xs M12 M22
|
blanchet@35385
|
432 |
| do_mtype_comp Leq xs (MFun (M11, a1, M12)) (MFun (M21, a2, M22))
|
blanchet@33192
|
433 |
(SOME accum) =
|
blanchet@35385
|
434 |
(if exists_alpha_sub_mtype M11 then
|
blanchet@33192
|
435 |
accum |> do_sign_atom_comp Leq xs a1 a2
|
blanchet@35385
|
436 |
|> do_mtype_comp Leq xs M21 M11
|
blanchet@33192
|
437 |
|> (case a2 of
|
blanchet@34969
|
438 |
S Minus => I
|
blanchet@35385
|
439 |
| S Plus => do_mtype_comp Leq xs M11 M21
|
blanchet@35385
|
440 |
| V x => do_mtype_comp Leq (x :: xs) M11 M21)
|
blanchet@33192
|
441 |
else
|
blanchet@33192
|
442 |
SOME accum)
|
blanchet@35385
|
443 |
|> do_mtype_comp Leq xs M12 M22
|
blanchet@35385
|
444 |
| do_mtype_comp cmp xs (M1 as MPair (M11, M12)) (M2 as MPair (M21, M22))
|
blanchet@33192
|
445 |
accum =
|
blanchet@35385
|
446 |
(accum |> fold (uncurry (do_mtype_comp cmp xs)) [(M11, M21), (M12, M22)]
|
blanchet@33192
|
447 |
handle Library.UnequalLengths =>
|
blanchet@35665
|
448 |
raise MTYPE ("Nitpick_Mono.do_mtype_comp", [M1, M2], []))
|
blanchet@35385
|
449 |
| do_mtype_comp _ _ (MType _) (MType _) accum =
|
blanchet@33192
|
450 |
accum (* no need to compare them thanks to the cache *)
|
blanchet@35665
|
451 |
| do_mtype_comp cmp _ M1 M2 _ =
|
blanchet@35665
|
452 |
raise MTYPE ("Nitpick_Mono.do_mtype_comp (" ^ string_for_comp_op cmp ^ ")",
|
blanchet@35665
|
453 |
[M1, M2], [])
|
blanchet@33192
|
454 |
|
blanchet@35385
|
455 |
(* comp_op -> mtyp -> mtyp -> constraint_set -> constraint_set *)
|
blanchet@35385
|
456 |
fun add_mtype_comp _ _ _ UnsolvableCSet = UnsolvableCSet
|
blanchet@35385
|
457 |
| add_mtype_comp cmp M1 M2 (CSet (lits, comps, sexps)) =
|
blanchet@35385
|
458 |
(print_g ("*** Add " ^ string_for_mtype M1 ^ " " ^ string_for_comp_op cmp ^
|
blanchet@35385
|
459 |
" " ^ string_for_mtype M2);
|
blanchet@35385
|
460 |
case do_mtype_comp cmp [] M1 M2 (SOME (lits, comps)) of
|
blanchet@33192
|
461 |
NONE => (print_g "**** Unsolvable"; UnsolvableCSet)
|
blanchet@33192
|
462 |
| SOME (lits, comps) => CSet (lits, comps, sexps))
|
blanchet@33192
|
463 |
|
blanchet@35385
|
464 |
(* mtyp -> mtyp -> constraint_set -> constraint_set *)
|
blanchet@35385
|
465 |
val add_mtypes_equal = add_mtype_comp Eq
|
blanchet@35385
|
466 |
val add_is_sub_mtype = add_mtype_comp Leq
|
blanchet@33192
|
467 |
|
blanchet@35385
|
468 |
(* sign -> sign_expr -> mtyp -> (literal list * sign_expr list) option
|
blanchet@33192
|
469 |
-> (literal list * sign_expr list) option *)
|
blanchet@35385
|
470 |
fun do_notin_mtype_fv _ _ _ NONE = NONE
|
blanchet@35385
|
471 |
| do_notin_mtype_fv Minus _ MAlpha accum = accum
|
blanchet@35385
|
472 |
| do_notin_mtype_fv Plus [] MAlpha _ = NONE
|
blanchet@35385
|
473 |
| do_notin_mtype_fv Plus [(x, sn)] MAlpha (SOME (lits, sexps)) =
|
blanchet@33192
|
474 |
SOME lits |> do_literal (x, sn) |> Option.map (rpair sexps)
|
blanchet@35385
|
475 |
| do_notin_mtype_fv Plus sexp MAlpha (SOME (lits, sexps)) =
|
blanchet@33192
|
476 |
SOME (lits, insert (op =) sexp sexps)
|
blanchet@35385
|
477 |
| do_notin_mtype_fv sn sexp (MFun (M1, S sn', M2)) accum =
|
blanchet@34969
|
478 |
accum |> (if sn' = Plus andalso sn = Plus then
|
blanchet@35385
|
479 |
do_notin_mtype_fv Plus sexp M1
|
blanchet@34969
|
480 |
else
|
blanchet@34969
|
481 |
I)
|
blanchet@34969
|
482 |
|> (if sn' = Minus orelse sn = Plus then
|
blanchet@35385
|
483 |
do_notin_mtype_fv Minus sexp M1
|
blanchet@34969
|
484 |
else
|
blanchet@34969
|
485 |
I)
|
blanchet@35385
|
486 |
|> do_notin_mtype_fv sn sexp M2
|
blanchet@35385
|
487 |
| do_notin_mtype_fv Plus sexp (MFun (M1, V x, M2)) accum =
|
blanchet@34969
|
488 |
accum |> (case do_literal (x, Minus) (SOME sexp) of
|
blanchet@33192
|
489 |
NONE => I
|
blanchet@35385
|
490 |
| SOME sexp' => do_notin_mtype_fv Plus sexp' M1)
|
blanchet@35385
|
491 |
|> do_notin_mtype_fv Minus sexp M1
|
blanchet@35385
|
492 |
|> do_notin_mtype_fv Plus sexp M2
|
blanchet@35385
|
493 |
| do_notin_mtype_fv Minus sexp (MFun (M1, V x, M2)) accum =
|
blanchet@34969
|
494 |
accum |> (case do_literal (x, Plus) (SOME sexp) of
|
blanchet@33192
|
495 |
NONE => I
|
blanchet@35385
|
496 |
| SOME sexp' => do_notin_mtype_fv Plus sexp' M1)
|
blanchet@35385
|
497 |
|> do_notin_mtype_fv Minus sexp M2
|
blanchet@35385
|
498 |
| do_notin_mtype_fv sn sexp (MPair (M1, M2)) accum =
|
blanchet@35385
|
499 |
accum |> fold (do_notin_mtype_fv sn sexp) [M1, M2]
|
blanchet@35385
|
500 |
| do_notin_mtype_fv sn sexp (MType (_, Ms)) accum =
|
blanchet@35385
|
501 |
accum |> fold (do_notin_mtype_fv sn sexp) Ms
|
blanchet@35385
|
502 |
| do_notin_mtype_fv _ _ M _ =
|
blanchet@35665
|
503 |
raise MTYPE ("Nitpick_Mono.do_notin_mtype_fv", [M], [])
|
blanchet@33192
|
504 |
|
blanchet@35385
|
505 |
(* sign -> mtyp -> constraint_set -> constraint_set *)
|
blanchet@35385
|
506 |
fun add_notin_mtype_fv _ _ UnsolvableCSet = UnsolvableCSet
|
blanchet@35385
|
507 |
| add_notin_mtype_fv sn M (CSet (lits, comps, sexps)) =
|
blanchet@35665
|
508 |
(print_g ("*** Add " ^ string_for_mtype M ^ " is " ^
|
blanchet@35665
|
509 |
(case sn of Minus => "concrete" | Plus => "complete") ^ ".");
|
blanchet@35385
|
510 |
case do_notin_mtype_fv sn [] M (SOME (lits, sexps)) of
|
blanchet@33192
|
511 |
NONE => (print_g "**** Unsolvable"; UnsolvableCSet)
|
blanchet@33192
|
512 |
| SOME (lits, sexps) => CSet (lits, comps, sexps))
|
blanchet@33192
|
513 |
|
blanchet@35385
|
514 |
(* mtyp -> constraint_set -> constraint_set *)
|
blanchet@35665
|
515 |
val add_mtype_is_concrete = add_notin_mtype_fv Minus
|
blanchet@35665
|
516 |
val add_mtype_is_complete = add_notin_mtype_fv Plus
|
blanchet@33192
|
517 |
|
blanchet@35384
|
518 |
val bool_from_minus = true
|
blanchet@35384
|
519 |
|
blanchet@33192
|
520 |
(* sign -> bool *)
|
blanchet@35384
|
521 |
fun bool_from_sign Plus = not bool_from_minus
|
blanchet@35384
|
522 |
| bool_from_sign Minus = bool_from_minus
|
blanchet@33192
|
523 |
(* bool -> sign *)
|
blanchet@35384
|
524 |
fun sign_from_bool b = if b = bool_from_minus then Minus else Plus
|
blanchet@33192
|
525 |
|
blanchet@33192
|
526 |
(* literal -> PropLogic.prop_formula *)
|
blanchet@33192
|
527 |
fun prop_for_literal (x, sn) =
|
blanchet@33192
|
528 |
(not (bool_from_sign sn) ? PropLogic.Not) (PropLogic.BoolVar x)
|
blanchet@33192
|
529 |
(* sign_atom -> PropLogic.prop_formula *)
|
blanchet@33192
|
530 |
fun prop_for_sign_atom_eq (S sn', sn) =
|
blanchet@33192
|
531 |
if sn = sn' then PropLogic.True else PropLogic.False
|
blanchet@33192
|
532 |
| prop_for_sign_atom_eq (V x, sn) = prop_for_literal (x, sn)
|
blanchet@33192
|
533 |
(* sign_expr -> PropLogic.prop_formula *)
|
blanchet@33192
|
534 |
fun prop_for_sign_expr xs = PropLogic.exists (map prop_for_literal xs)
|
blanchet@33192
|
535 |
(* var list -> sign -> PropLogic.prop_formula *)
|
blanchet@33192
|
536 |
fun prop_for_exists_eq xs sn =
|
blanchet@33192
|
537 |
PropLogic.exists (map (fn x => prop_for_literal (x, sn)) xs)
|
blanchet@33192
|
538 |
(* comp -> PropLogic.prop_formula *)
|
blanchet@33192
|
539 |
fun prop_for_comp (a1, a2, Eq, []) =
|
blanchet@33192
|
540 |
PropLogic.SAnd (prop_for_comp (a1, a2, Leq, []),
|
blanchet@33192
|
541 |
prop_for_comp (a2, a1, Leq, []))
|
blanchet@33192
|
542 |
| prop_for_comp (a1, a2, Leq, []) =
|
blanchet@34969
|
543 |
PropLogic.SOr (prop_for_sign_atom_eq (a1, Plus),
|
blanchet@34969
|
544 |
prop_for_sign_atom_eq (a2, Minus))
|
blanchet@33192
|
545 |
| prop_for_comp (a1, a2, cmp, xs) =
|
blanchet@34969
|
546 |
PropLogic.SOr (prop_for_exists_eq xs Minus, prop_for_comp (a1, a2, cmp, []))
|
blanchet@33192
|
547 |
|
blanchet@33192
|
548 |
(* var -> (int -> bool option) -> literal list -> literal list *)
|
blanchet@34120
|
549 |
fun literals_from_assignments max_var assigns lits =
|
blanchet@33192
|
550 |
fold (fn x => fn accum =>
|
blanchet@33192
|
551 |
if AList.defined (op =) lits x then
|
blanchet@33192
|
552 |
accum
|
blanchet@34120
|
553 |
else case assigns x of
|
blanchet@33192
|
554 |
SOME b => (x, sign_from_bool b) :: accum
|
blanchet@33192
|
555 |
| NONE => accum) (max_var downto 1) lits
|
blanchet@33192
|
556 |
|
blanchet@33192
|
557 |
(* comp -> string *)
|
blanchet@33192
|
558 |
fun string_for_comp (a1, a2, cmp, xs) =
|
blanchet@33192
|
559 |
string_for_sign_atom a1 ^ " " ^ string_for_comp_op cmp ^
|
blanchet@33192
|
560 |
subscript_string_for_vars " \<and> " xs ^ " " ^ string_for_sign_atom a2
|
blanchet@33192
|
561 |
|
blanchet@33192
|
562 |
(* literal list -> comp list -> sign_expr list -> unit *)
|
blanchet@33192
|
563 |
fun print_problem lits comps sexps =
|
blanchet@33192
|
564 |
print_g ("*** Problem:\n" ^ cat_lines (map string_for_literal lits @
|
blanchet@33192
|
565 |
map string_for_comp comps @
|
blanchet@33192
|
566 |
map string_for_sign_expr sexps))
|
blanchet@33192
|
567 |
|
blanchet@33192
|
568 |
(* literal list -> unit *)
|
blanchet@33192
|
569 |
fun print_solution lits =
|
blanchet@34969
|
570 |
let val (pos, neg) = List.partition (curry (op =) Plus o snd) lits in
|
blanchet@33192
|
571 |
print_g ("*** Solution:\n" ^
|
blanchet@33192
|
572 |
"+: " ^ commas (map (string_for_var o fst) pos) ^ "\n" ^
|
blanchet@33192
|
573 |
"-: " ^ commas (map (string_for_var o fst) neg))
|
blanchet@33192
|
574 |
end
|
blanchet@33192
|
575 |
|
blanchet@35384
|
576 |
(* var -> constraint_set -> literal list option *)
|
blanchet@33192
|
577 |
fun solve _ UnsolvableCSet = (print_g "*** Problem: Unsolvable"; NONE)
|
blanchet@33192
|
578 |
| solve max_var (CSet (lits, comps, sexps)) =
|
blanchet@33192
|
579 |
let
|
blanchet@35386
|
580 |
(* (int -> bool option) -> literal list option *)
|
blanchet@35386
|
581 |
fun do_assigns assigns =
|
blanchet@35386
|
582 |
SOME (literals_from_assignments max_var assigns lits
|
blanchet@35386
|
583 |
|> tap print_solution)
|
blanchet@33192
|
584 |
val _ = print_problem lits comps sexps
|
blanchet@33192
|
585 |
val prop = PropLogic.all (map prop_for_literal lits @
|
blanchet@33192
|
586 |
map prop_for_comp comps @
|
blanchet@33192
|
587 |
map prop_for_sign_expr sexps)
|
blanchet@35386
|
588 |
val default_val = bool_from_sign Minus
|
blanchet@33192
|
589 |
in
|
blanchet@35386
|
590 |
if PropLogic.eval (K default_val) prop then
|
blanchet@35386
|
591 |
do_assigns (K (SOME default_val))
|
blanchet@35386
|
592 |
else
|
blanchet@35386
|
593 |
let
|
blanchet@35386
|
594 |
(* use the first ML solver (to avoid startup overhead) *)
|
blanchet@35386
|
595 |
val solvers = !SatSolver.solvers
|
blanchet@35386
|
596 |
|> filter (member (op =) ["dptsat", "dpll"] o fst)
|
blanchet@35386
|
597 |
in
|
blanchet@35386
|
598 |
case snd (hd solvers) prop of
|
blanchet@35386
|
599 |
SatSolver.SATISFIABLE assigns => do_assigns assigns
|
blanchet@35386
|
600 |
| _ => NONE
|
blanchet@35386
|
601 |
end
|
blanchet@33192
|
602 |
end
|
blanchet@33192
|
603 |
|
blanchet@35385
|
604 |
type mtype_schema = mtyp * constraint_set
|
blanchet@35385
|
605 |
type mtype_context =
|
blanchet@35665
|
606 |
{bound_Ts: typ list,
|
blanchet@35665
|
607 |
bound_Ms: mtyp list,
|
blanchet@35385
|
608 |
frees: (styp * mtyp) list,
|
blanchet@35385
|
609 |
consts: (styp * mtyp) list}
|
blanchet@33192
|
610 |
|
blanchet@35385
|
611 |
type accumulator = mtype_context * constraint_set
|
blanchet@33192
|
612 |
|
blanchet@35665
|
613 |
val initial_gamma = {bound_Ts = [], bound_Ms = [], frees = [], consts = []}
|
blanchet@33192
|
614 |
val unsolvable_accum = (initial_gamma, UnsolvableCSet)
|
blanchet@33192
|
615 |
|
blanchet@35665
|
616 |
(* typ -> mtyp -> mtype_context -> mtype_context *)
|
blanchet@35665
|
617 |
fun push_bound T M {bound_Ts, bound_Ms, frees, consts} =
|
blanchet@35665
|
618 |
{bound_Ts = T :: bound_Ts, bound_Ms = M :: bound_Ms, frees = frees,
|
blanchet@35665
|
619 |
consts = consts}
|
blanchet@35385
|
620 |
(* mtype_context -> mtype_context *)
|
blanchet@35665
|
621 |
fun pop_bound {bound_Ts, bound_Ms, frees, consts} =
|
blanchet@35665
|
622 |
{bound_Ts = tl bound_Ts, bound_Ms = tl bound_Ms, frees = frees,
|
blanchet@35665
|
623 |
consts = consts}
|
blanchet@35665
|
624 |
handle List.Empty => initial_gamma (* FIXME: needed? *)
|
blanchet@33192
|
625 |
|
blanchet@35385
|
626 |
(* mdata -> term -> accumulator -> mterm * accumulator *)
|
blanchet@35386
|
627 |
fun consider_term (mdata as {hol_ctxt as {thy, ctxt, stds, fast_descrs,
|
blanchet@35665
|
628 |
def_table, ...},
|
blanchet@35220
|
629 |
alpha_T, max_fresh, ...}) =
|
blanchet@33192
|
630 |
let
|
blanchet@35385
|
631 |
(* typ -> mtyp *)
|
blanchet@35385
|
632 |
val mtype_for = fresh_mtype_for_type mdata
|
blanchet@35385
|
633 |
(* mtyp -> mtyp *)
|
blanchet@35665
|
634 |
fun plus_set_mtype_for_dom M =
|
blanchet@35385
|
635 |
MFun (M, S (if exists_alpha_sub_mtype M then Plus else Minus), bool_M)
|
blanchet@35385
|
636 |
(* typ -> accumulator -> mterm * accumulator *)
|
blanchet@35385
|
637 |
fun do_all T (gamma, cset) =
|
blanchet@33192
|
638 |
let
|
blanchet@35385
|
639 |
val abs_M = mtype_for (domain_type (domain_type T))
|
blanchet@35386
|
640 |
val body_M = mtype_for (body_type T)
|
blanchet@33192
|
641 |
in
|
blanchet@35385
|
642 |
(MFun (MFun (abs_M, S Minus, body_M), S Minus, body_M),
|
blanchet@35665
|
643 |
(gamma, cset |> add_mtype_is_complete abs_M))
|
blanchet@33192
|
644 |
end
|
blanchet@33192
|
645 |
fun do_equals T (gamma, cset) =
|
blanchet@35385
|
646 |
let val M = mtype_for (domain_type T) in
|
blanchet@35385
|
647 |
(MFun (M, S Minus, MFun (M, V (Unsynchronized.inc max_fresh),
|
blanchet@35385
|
648 |
mtype_for (nth_range_type 2 T))),
|
blanchet@35665
|
649 |
(gamma, cset |> add_mtype_is_concrete M))
|
blanchet@33192
|
650 |
end
|
blanchet@33192
|
651 |
fun do_robust_set_operation T (gamma, cset) =
|
blanchet@33192
|
652 |
let
|
blanchet@33192
|
653 |
val set_T = domain_type T
|
blanchet@35385
|
654 |
val M1 = mtype_for set_T
|
blanchet@35385
|
655 |
val M2 = mtype_for set_T
|
blanchet@35385
|
656 |
val M3 = mtype_for set_T
|
blanchet@33192
|
657 |
in
|
blanchet@35385
|
658 |
(MFun (M1, S Minus, MFun (M2, S Minus, M3)),
|
blanchet@35385
|
659 |
(gamma, cset |> add_is_sub_mtype M1 M3 |> add_is_sub_mtype M2 M3))
|
blanchet@33192
|
660 |
end
|
blanchet@33192
|
661 |
fun do_fragile_set_operation T (gamma, cset) =
|
blanchet@33192
|
662 |
let
|
blanchet@33192
|
663 |
val set_T = domain_type T
|
blanchet@35385
|
664 |
val set_M = mtype_for set_T
|
blanchet@35385
|
665 |
(* typ -> mtyp *)
|
blanchet@35665
|
666 |
fun custom_mtype_for (T as Type (@{type_name fun}, [T1, T2])) =
|
blanchet@35385
|
667 |
if T = set_T then set_M
|
blanchet@35385
|
668 |
else MFun (custom_mtype_for T1, S Minus, custom_mtype_for T2)
|
blanchet@35385
|
669 |
| custom_mtype_for T = mtype_for T
|
blanchet@33192
|
670 |
in
|
blanchet@35665
|
671 |
(custom_mtype_for T, (gamma, cset |> add_mtype_is_concrete set_M))
|
blanchet@33192
|
672 |
end
|
blanchet@35385
|
673 |
(* typ -> accumulator -> mtyp * accumulator *)
|
blanchet@33192
|
674 |
fun do_pair_constr T accum =
|
blanchet@35385
|
675 |
case mtype_for (nth_range_type 2 T) of
|
blanchet@35385
|
676 |
M as MPair (a_M, b_M) =>
|
blanchet@35385
|
677 |
(MFun (a_M, S Minus, MFun (b_M, S Minus, M)), accum)
|
blanchet@35665
|
678 |
| M => raise MTYPE ("Nitpick_Mono.consider_term.do_pair_constr", [M], [])
|
blanchet@35385
|
679 |
(* int -> typ -> accumulator -> mtyp * accumulator *)
|
blanchet@33192
|
680 |
fun do_nth_pair_sel n T =
|
blanchet@35385
|
681 |
case mtype_for (domain_type T) of
|
blanchet@35385
|
682 |
M as MPair (a_M, b_M) =>
|
blanchet@35385
|
683 |
pair (MFun (M, S Minus, if n = 0 then a_M else b_M))
|
blanchet@35665
|
684 |
| M => raise MTYPE ("Nitpick_Mono.consider_term.do_nth_pair_sel", [M], [])
|
blanchet@35385
|
685 |
(* mtyp * accumulator *)
|
blanchet@35386
|
686 |
val mtype_unsolvable = (dummy_M, unsolvable_accum)
|
blanchet@35385
|
687 |
(* term -> mterm * accumulator *)
|
blanchet@35386
|
688 |
fun mterm_unsolvable t = (MRaw (t, dummy_M), unsolvable_accum)
|
blanchet@35385
|
689 |
(* term -> string -> typ -> term -> term -> term -> accumulator
|
blanchet@35385
|
690 |
-> mterm * accumulator *)
|
blanchet@35385
|
691 |
fun do_bounded_quantifier t0 abs_s abs_T connective_t bound_t body_t accum =
|
blanchet@33192
|
692 |
let
|
blanchet@35385
|
693 |
val abs_M = mtype_for abs_T
|
blanchet@35665
|
694 |
val (bound_m, accum) =
|
blanchet@35665
|
695 |
accum |>> push_bound abs_T abs_M |> do_term bound_t
|
blanchet@35665
|
696 |
val expected_bound_M = plus_set_mtype_for_dom abs_M
|
blanchet@35385
|
697 |
val (body_m, accum) =
|
blanchet@35385
|
698 |
accum ||> add_mtypes_equal expected_bound_M (mtype_of_mterm bound_m)
|
blanchet@35385
|
699 |
|> do_term body_t ||> apfst pop_bound
|
blanchet@35385
|
700 |
val bound_M = mtype_of_mterm bound_m
|
blanchet@35385
|
701 |
val (M1, a, M2) = dest_MFun bound_M
|
blanchet@33192
|
702 |
in
|
blanchet@35386
|
703 |
(MApp (MRaw (t0, MFun (bound_M, S Minus, bool_M)),
|
blanchet@35385
|
704 |
MAbs (abs_s, abs_T, M1, a,
|
blanchet@35386
|
705 |
MApp (MApp (MRaw (connective_t,
|
blanchet@35386
|
706 |
mtype_for (fastype_of connective_t)),
|
blanchet@35386
|
707 |
MApp (bound_m, MRaw (Bound 0, M1))),
|
blanchet@35385
|
708 |
body_m))), accum)
|
blanchet@33192
|
709 |
end
|
blanchet@35385
|
710 |
(* term -> accumulator -> mterm * accumulator *)
|
blanchet@35385
|
711 |
and do_term t (_, UnsolvableCSet) = mterm_unsolvable t
|
blanchet@35665
|
712 |
| do_term t (accum as (gamma as {bound_Ts, bound_Ms, frees, consts},
|
blanchet@35665
|
713 |
cset)) =
|
blanchet@33192
|
714 |
(case t of
|
blanchet@33192
|
715 |
Const (x as (s, T)) =>
|
blanchet@33192
|
716 |
(case AList.lookup (op =) consts x of
|
blanchet@35385
|
717 |
SOME M => (M, accum)
|
blanchet@33192
|
718 |
| NONE =>
|
blanchet@33192
|
719 |
if not (could_exist_alpha_subtype alpha_T T) then
|
blanchet@35385
|
720 |
(mtype_for T, accum)
|
blanchet@33192
|
721 |
else case s of
|
blanchet@35385
|
722 |
@{const_name all} => do_all T accum
|
blanchet@33192
|
723 |
| @{const_name "=="} => do_equals T accum
|
blanchet@35385
|
724 |
| @{const_name All} => do_all T accum
|
blanchet@35385
|
725 |
| @{const_name Ex} =>
|
blanchet@35386
|
726 |
let val set_T = domain_type T in
|
blanchet@35386
|
727 |
do_term (Abs (Name.uu, set_T,
|
blanchet@35386
|
728 |
@{const Not} $ (HOLogic.mk_eq
|
blanchet@35386
|
729 |
(Abs (Name.uu, domain_type set_T,
|
blanchet@35386
|
730 |
@{const False}),
|
blanchet@35386
|
731 |
Bound 0)))) accum
|
blanchet@35386
|
732 |
|>> mtype_of_mterm
|
blanchet@35386
|
733 |
end
|
blanchet@33192
|
734 |
| @{const_name "op ="} => do_equals T accum
|
blanchet@35385
|
735 |
| @{const_name The} => (print_g "*** The"; mtype_unsolvable)
|
blanchet@35385
|
736 |
| @{const_name Eps} => (print_g "*** Eps"; mtype_unsolvable)
|
blanchet@33192
|
737 |
| @{const_name If} =>
|
blanchet@33192
|
738 |
do_robust_set_operation (range_type T) accum
|
blanchet@35385
|
739 |
|>> curry3 MFun bool_M (S Minus)
|
blanchet@33192
|
740 |
| @{const_name Pair} => do_pair_constr T accum
|
blanchet@33192
|
741 |
| @{const_name fst} => do_nth_pair_sel 0 T accum
|
blanchet@33192
|
742 |
| @{const_name snd} => do_nth_pair_sel 1 T accum
|
blanchet@33192
|
743 |
| @{const_name Id} =>
|
blanchet@35385
|
744 |
(MFun (mtype_for (domain_type T), S Minus, bool_M), accum)
|
blanchet@33192
|
745 |
| @{const_name insert} =>
|
blanchet@33192
|
746 |
let
|
blanchet@33192
|
747 |
val set_T = domain_type (range_type T)
|
blanchet@35385
|
748 |
val M1 = mtype_for (domain_type set_T)
|
blanchet@35665
|
749 |
val M1' = plus_set_mtype_for_dom M1
|
blanchet@35385
|
750 |
val M2 = mtype_for set_T
|
blanchet@35385
|
751 |
val M3 = mtype_for set_T
|
blanchet@33192
|
752 |
in
|
blanchet@35385
|
753 |
(MFun (M1, S Minus, MFun (M2, S Minus, M3)),
|
blanchet@35665
|
754 |
(gamma, cset |> add_mtype_is_concrete M1
|
blanchet@35385
|
755 |
|> add_is_sub_mtype M1' M3
|
blanchet@35385
|
756 |
|> add_is_sub_mtype M2 M3))
|
blanchet@33192
|
757 |
end
|
blanchet@33192
|
758 |
| @{const_name converse} =>
|
blanchet@33192
|
759 |
let
|
blanchet@33192
|
760 |
val x = Unsynchronized.inc max_fresh
|
blanchet@35385
|
761 |
(* typ -> mtyp *)
|
blanchet@35385
|
762 |
fun mtype_for_set T =
|
blanchet@35385
|
763 |
MFun (mtype_for (domain_type T), V x, bool_M)
|
blanchet@35385
|
764 |
val ab_set_M = domain_type T |> mtype_for_set
|
blanchet@35385
|
765 |
val ba_set_M = range_type T |> mtype_for_set
|
blanchet@35385
|
766 |
in (MFun (ab_set_M, S Minus, ba_set_M), accum) end
|
blanchet@33192
|
767 |
| @{const_name trancl} => do_fragile_set_operation T accum
|
blanchet@35385
|
768 |
| @{const_name rtrancl} =>
|
blanchet@35385
|
769 |
(print_g "*** rtrancl"; mtype_unsolvable)
|
blanchet@33192
|
770 |
| @{const_name finite} =>
|
blanchet@35386
|
771 |
if is_finite_type hol_ctxt T then
|
blanchet@35386
|
772 |
let val M1 = mtype_for (domain_type (domain_type T)) in
|
blanchet@35665
|
773 |
(MFun (plus_set_mtype_for_dom M1, S Minus, bool_M), accum)
|
blanchet@35386
|
774 |
end
|
blanchet@35386
|
775 |
else
|
blanchet@35386
|
776 |
(print_g "*** finite"; mtype_unsolvable)
|
blanchet@33192
|
777 |
| @{const_name rel_comp} =>
|
blanchet@33192
|
778 |
let
|
blanchet@33192
|
779 |
val x = Unsynchronized.inc max_fresh
|
blanchet@35385
|
780 |
(* typ -> mtyp *)
|
blanchet@35385
|
781 |
fun mtype_for_set T =
|
blanchet@35385
|
782 |
MFun (mtype_for (domain_type T), V x, bool_M)
|
blanchet@35385
|
783 |
val bc_set_M = domain_type T |> mtype_for_set
|
blanchet@35385
|
784 |
val ab_set_M = domain_type (range_type T) |> mtype_for_set
|
blanchet@35385
|
785 |
val ac_set_M = nth_range_type 2 T |> mtype_for_set
|
blanchet@33192
|
786 |
in
|
blanchet@35385
|
787 |
(MFun (bc_set_M, S Minus, MFun (ab_set_M, S Minus, ac_set_M)),
|
blanchet@33192
|
788 |
accum)
|
blanchet@33192
|
789 |
end
|
blanchet@33192
|
790 |
| @{const_name image} =>
|
blanchet@33192
|
791 |
let
|
blanchet@35385
|
792 |
val a_M = mtype_for (domain_type (domain_type T))
|
blanchet@35385
|
793 |
val b_M = mtype_for (range_type (domain_type T))
|
blanchet@33192
|
794 |
in
|
blanchet@35385
|
795 |
(MFun (MFun (a_M, S Minus, b_M), S Minus,
|
blanchet@35665
|
796 |
MFun (plus_set_mtype_for_dom a_M, S Minus,
|
blanchet@35665
|
797 |
plus_set_mtype_for_dom b_M)), accum)
|
blanchet@33192
|
798 |
end
|
blanchet@33192
|
799 |
| @{const_name Sigma} =>
|
blanchet@33192
|
800 |
let
|
blanchet@33192
|
801 |
val x = Unsynchronized.inc max_fresh
|
blanchet@35385
|
802 |
(* typ -> mtyp *)
|
blanchet@35385
|
803 |
fun mtype_for_set T =
|
blanchet@35385
|
804 |
MFun (mtype_for (domain_type T), V x, bool_M)
|
blanchet@33192
|
805 |
val a_set_T = domain_type T
|
blanchet@35385
|
806 |
val a_M = mtype_for (domain_type a_set_T)
|
blanchet@35385
|
807 |
val b_set_M = mtype_for_set (range_type (domain_type
|
blanchet@33192
|
808 |
(range_type T)))
|
blanchet@35385
|
809 |
val a_set_M = mtype_for_set a_set_T
|
blanchet@35385
|
810 |
val a_to_b_set_M = MFun (a_M, S Minus, b_set_M)
|
blanchet@35385
|
811 |
val ab_set_M = mtype_for_set (nth_range_type 2 T)
|
blanchet@33192
|
812 |
in
|
blanchet@35385
|
813 |
(MFun (a_set_M, S Minus,
|
blanchet@35385
|
814 |
MFun (a_to_b_set_M, S Minus, ab_set_M)), accum)
|
blanchet@33192
|
815 |
end
|
blanchet@33192
|
816 |
| @{const_name Tha} =>
|
blanchet@33192
|
817 |
let
|
blanchet@35385
|
818 |
val a_M = mtype_for (domain_type (domain_type T))
|
blanchet@35665
|
819 |
val a_set_M = plus_set_mtype_for_dom a_M
|
blanchet@35385
|
820 |
in (MFun (a_set_M, S Minus, a_M), accum) end
|
blanchet@35220
|
821 |
| _ =>
|
blanchet@35220
|
822 |
if s = @{const_name minus_class.minus} andalso
|
blanchet@35220
|
823 |
is_set_type (domain_type T) then
|
blanchet@35220
|
824 |
let
|
blanchet@35220
|
825 |
val set_T = domain_type T
|
blanchet@35385
|
826 |
val left_set_M = mtype_for set_T
|
blanchet@35385
|
827 |
val right_set_M = mtype_for set_T
|
blanchet@35220
|
828 |
in
|
blanchet@35385
|
829 |
(MFun (left_set_M, S Minus,
|
blanchet@35385
|
830 |
MFun (right_set_M, S Minus, left_set_M)),
|
blanchet@35665
|
831 |
(gamma, cset |> add_mtype_is_concrete right_set_M
|
blanchet@35385
|
832 |
|> add_is_sub_mtype right_set_M left_set_M))
|
blanchet@35220
|
833 |
end
|
blanchet@35220
|
834 |
else if s = @{const_name ord_class.less_eq} andalso
|
blanchet@35220
|
835 |
is_set_type (domain_type T) then
|
blanchet@35220
|
836 |
do_fragile_set_operation T accum
|
blanchet@35220
|
837 |
else if (s = @{const_name semilattice_inf_class.inf} orelse
|
blanchet@35220
|
838 |
s = @{const_name semilattice_sup_class.sup}) andalso
|
blanchet@35220
|
839 |
is_set_type (domain_type T) then
|
blanchet@35220
|
840 |
do_robust_set_operation T accum
|
blanchet@35220
|
841 |
else if is_sel s then
|
blanchet@35665
|
842 |
(mtype_for_sel mdata x, accum)
|
blanchet@35220
|
843 |
else if is_constr thy stds x then
|
blanchet@35385
|
844 |
(mtype_for_constr mdata x, accum)
|
blanchet@35665
|
845 |
else if is_built_in_const thy stds fast_descrs x andalso
|
blanchet@35665
|
846 |
s <> @{const_name is_unknown} andalso
|
blanchet@35665
|
847 |
s <> @{const_name unknown} then
|
blanchet@35665
|
848 |
(* the "unknown" part is a hack *)
|
blanchet@35220
|
849 |
case def_of_const thy def_table x of
|
blanchet@35385
|
850 |
SOME t' => do_term t' accum |>> mtype_of_mterm
|
blanchet@35385
|
851 |
| NONE => (print_g ("*** built-in " ^ s); mtype_unsolvable)
|
blanchet@35220
|
852 |
else
|
blanchet@35385
|
853 |
let val M = mtype_for T in
|
blanchet@35665
|
854 |
(M, ({bound_Ts = bound_Ts, bound_Ms = bound_Ms,
|
blanchet@35665
|
855 |
frees = frees, consts = (x, M) :: consts}, cset))
|
blanchet@35386
|
856 |
end) |>> curry MRaw t
|
blanchet@33192
|
857 |
| Free (x as (_, T)) =>
|
blanchet@33192
|
858 |
(case AList.lookup (op =) frees x of
|
blanchet@35385
|
859 |
SOME M => (M, accum)
|
blanchet@33192
|
860 |
| NONE =>
|
blanchet@35385
|
861 |
let val M = mtype_for T in
|
blanchet@35665
|
862 |
(M, ({bound_Ts = bound_Ts, bound_Ms = bound_Ms,
|
blanchet@35665
|
863 |
frees = (x, M) :: frees, consts = consts}, cset))
|
blanchet@35386
|
864 |
end) |>> curry MRaw t
|
blanchet@35385
|
865 |
| Var _ => (print_g "*** Var"; mterm_unsolvable t)
|
blanchet@35665
|
866 |
| Bound j => (MRaw (t, nth bound_Ms j), accum)
|
blanchet@35385
|
867 |
| Abs (s, T, t') =>
|
blanchet@35665
|
868 |
(case fin_fun_body T (fastype_of1 (T :: bound_Ts, t')) t' of
|
blanchet@35665
|
869 |
SOME t' =>
|
blanchet@35665
|
870 |
let
|
blanchet@35665
|
871 |
val M = mtype_for T
|
blanchet@35665
|
872 |
val a = V (Unsynchronized.inc max_fresh)
|
blanchet@35665
|
873 |
val (m', accum) = do_term t' (accum |>> push_bound T M)
|
blanchet@35665
|
874 |
in (MAbs (s, T, M, a, m'), accum |>> pop_bound) end
|
blanchet@35665
|
875 |
| NONE =>
|
blanchet@35665
|
876 |
((case t' of
|
blanchet@35665
|
877 |
t1' $ Bound 0 =>
|
blanchet@35665
|
878 |
if not (loose_bvar1 (t1', 0)) then
|
blanchet@35665
|
879 |
do_term (incr_boundvars ~1 t1') accum
|
blanchet@35665
|
880 |
else
|
blanchet@35665
|
881 |
raise SAME ()
|
blanchet@35665
|
882 |
| _ => raise SAME ())
|
blanchet@35665
|
883 |
handle SAME () =>
|
blanchet@35665
|
884 |
let
|
blanchet@35665
|
885 |
val M = mtype_for T
|
blanchet@35665
|
886 |
val (m', accum) = do_term t' (accum |>> push_bound T M)
|
blanchet@35665
|
887 |
in
|
blanchet@35665
|
888 |
(MAbs (s, T, M, S Minus, m'), accum |>> pop_bound)
|
blanchet@35665
|
889 |
end))
|
blanchet@35385
|
890 |
| (t0 as Const (@{const_name All}, _))
|
blanchet@35385
|
891 |
$ Abs (s', T', (t10 as @{const "op -->"}) $ (t11 $ Bound 0) $ t12) =>
|
blanchet@35385
|
892 |
do_bounded_quantifier t0 s' T' t10 t11 t12 accum
|
blanchet@35385
|
893 |
| (t0 as Const (@{const_name Ex}, _))
|
blanchet@35385
|
894 |
$ Abs (s', T', (t10 as @{const "op &"}) $ (t11 $ Bound 0) $ t12) =>
|
blanchet@35385
|
895 |
do_bounded_quantifier t0 s' T' t10 t11 t12 accum
|
blanchet@33192
|
896 |
| Const (@{const_name Let}, _) $ t1 $ t2 =>
|
blanchet@33192
|
897 |
do_term (betapply (t2, t1)) accum
|
blanchet@33192
|
898 |
| t1 $ t2 =>
|
blanchet@33192
|
899 |
let
|
blanchet@35385
|
900 |
val (m1, accum) = do_term t1 accum
|
blanchet@35385
|
901 |
val (m2, accum) = do_term t2 accum
|
blanchet@33192
|
902 |
in
|
blanchet@33192
|
903 |
case accum of
|
blanchet@35385
|
904 |
(_, UnsolvableCSet) => mterm_unsolvable t
|
blanchet@35386
|
905 |
| _ =>
|
blanchet@35386
|
906 |
let
|
blanchet@35665
|
907 |
val T11 = domain_type (fastype_of1 (bound_Ts, t1))
|
blanchet@35665
|
908 |
val T2 = fastype_of1 (bound_Ts, t2)
|
blanchet@35386
|
909 |
val M11 = mtype_of_mterm m1 |> dest_MFun |> #1
|
blanchet@35386
|
910 |
val M2 = mtype_of_mterm m2
|
blanchet@35386
|
911 |
in (MApp (m1, m2), accum ||> add_is_sub_mtype M2 M11) end
|
blanchet@33192
|
912 |
end)
|
blanchet@35385
|
913 |
|> tap (fn (m, _) => print_g (" \<Gamma> \<turnstile> " ^
|
blanchet@35385
|
914 |
string_for_mterm ctxt m))
|
blanchet@33192
|
915 |
in do_term end
|
blanchet@33192
|
916 |
|
blanchet@35665
|
917 |
(*
|
blanchet@35665
|
918 |
accum |> (case a of
|
blanchet@35665
|
919 |
S Minus => accum
|
blanchet@35665
|
920 |
| S Plus => unsolvable_accum
|
blanchet@35665
|
921 |
| V x => do_literal (x, Minus) lits)
|
blanchet@35665
|
922 |
*)
|
blanchet@35665
|
923 |
|
blanchet@35665
|
924 |
(* int -> mtyp -> accumulator -> accumulator *)
|
blanchet@35665
|
925 |
fun force_minus_funs 0 _ = I
|
blanchet@35665
|
926 |
| force_minus_funs n (M as MFun (M1, _, M2)) =
|
blanchet@35665
|
927 |
add_mtypes_equal M (MFun (M1, S Minus, M2))
|
blanchet@35665
|
928 |
#> force_minus_funs (n - 1) M2
|
blanchet@35665
|
929 |
| force_minus_funs _ M =
|
blanchet@35665
|
930 |
raise MTYPE ("Nitpick_Mono.force_minus_funs", [M], [])
|
blanchet@35665
|
931 |
(* mdata -> bool -> styp -> term -> term -> mterm * accumulator *)
|
blanchet@35665
|
932 |
fun consider_general_equals mdata def (x as (_, T)) t1 t2 accum =
|
blanchet@35386
|
933 |
let
|
blanchet@35386
|
934 |
val (m1, accum) = consider_term mdata t1 accum
|
blanchet@35386
|
935 |
val (m2, accum) = consider_term mdata t2 accum
|
blanchet@35386
|
936 |
val M1 = mtype_of_mterm m1
|
blanchet@35386
|
937 |
val M2 = mtype_of_mterm m2
|
blanchet@35665
|
938 |
val accum = accum ||> add_mtypes_equal M1 M2
|
blanchet@35386
|
939 |
val body_M = fresh_mtype_for_type mdata (nth_range_type 2 T)
|
blanchet@35665
|
940 |
val m = MApp (MApp (MRaw (Const x,
|
blanchet@35665
|
941 |
MFun (M1, S Minus, MFun (M2, S Minus, body_M))), m1), m2)
|
blanchet@35386
|
942 |
in
|
blanchet@35665
|
943 |
(m, if def then
|
blanchet@35665
|
944 |
let val (head_m, arg_ms) = strip_mcomb m1 in
|
blanchet@35665
|
945 |
accum ||> force_minus_funs (length arg_ms) (mtype_of_mterm head_m)
|
blanchet@35665
|
946 |
end
|
blanchet@35665
|
947 |
else
|
blanchet@35665
|
948 |
accum)
|
blanchet@35386
|
949 |
end
|
blanchet@35386
|
950 |
|
blanchet@35386
|
951 |
(* mdata -> sign -> term -> accumulator -> mterm * accumulator *)
|
blanchet@35385
|
952 |
fun consider_general_formula (mdata as {hol_ctxt = {ctxt, ...}, ...}) =
|
blanchet@33192
|
953 |
let
|
blanchet@35385
|
954 |
(* typ -> mtyp *)
|
blanchet@35385
|
955 |
val mtype_for = fresh_mtype_for_type mdata
|
blanchet@35386
|
956 |
(* term -> accumulator -> mterm * accumulator *)
|
blanchet@35386
|
957 |
val do_term = consider_term mdata
|
blanchet@35386
|
958 |
(* sign -> term -> accumulator -> mterm * accumulator *)
|
blanchet@35386
|
959 |
fun do_formula _ t (_, UnsolvableCSet) =
|
blanchet@35386
|
960 |
(MRaw (t, dummy_M), unsolvable_accum)
|
blanchet@35386
|
961 |
| do_formula sn t accum =
|
blanchet@33192
|
962 |
let
|
blanchet@35386
|
963 |
(* styp -> string -> typ -> term -> mterm * accumulator *)
|
blanchet@35386
|
964 |
fun do_quantifier (quant_x as (quant_s, _)) abs_s abs_T body_t =
|
blanchet@33192
|
965 |
let
|
blanchet@35385
|
966 |
val abs_M = mtype_for abs_T
|
blanchet@34969
|
967 |
val side_cond = ((sn = Minus) = (quant_s = @{const_name Ex}))
|
blanchet@35386
|
968 |
val (body_m, accum) =
|
blanchet@35665
|
969 |
accum ||> side_cond ? add_mtype_is_complete abs_M
|
blanchet@35665
|
970 |
|>> push_bound abs_T abs_M |> do_formula sn body_t
|
blanchet@35386
|
971 |
val body_M = mtype_of_mterm body_m
|
blanchet@33192
|
972 |
in
|
blanchet@35665
|
973 |
(MApp (MRaw (Const quant_x,
|
blanchet@35665
|
974 |
MFun (MFun (abs_M, S Minus, body_M), S Minus,
|
blanchet@35665
|
975 |
body_M)),
|
blanchet@35386
|
976 |
MAbs (abs_s, abs_T, abs_M, S Minus, body_m)),
|
blanchet@35386
|
977 |
accum |>> pop_bound)
|
blanchet@33192
|
978 |
end
|
blanchet@35386
|
979 |
(* styp -> term -> term -> mterm * accumulator *)
|
blanchet@35386
|
980 |
fun do_equals x t1 t2 =
|
blanchet@33192
|
981 |
case sn of
|
blanchet@35386
|
982 |
Plus => do_term t accum
|
blanchet@35665
|
983 |
| Minus => consider_general_equals mdata false x t1 t2 accum
|
blanchet@33192
|
984 |
in
|
blanchet@33192
|
985 |
case t of
|
blanchet@35386
|
986 |
Const (x as (@{const_name all}, _)) $ Abs (s1, T1, t1) =>
|
blanchet@35386
|
987 |
do_quantifier x s1 T1 t1
|
blanchet@35386
|
988 |
| Const (x as (@{const_name "=="}, _)) $ t1 $ t2 => do_equals x t1 t2
|
blanchet@35386
|
989 |
| @{const Trueprop} $ t1 =>
|
blanchet@35386
|
990 |
let val (m1, accum) = do_formula sn t1 accum in
|
blanchet@35386
|
991 |
(MApp (MRaw (@{const Trueprop}, mtype_for (bool_T --> prop_T)),
|
blanchet@35386
|
992 |
m1), accum)
|
blanchet@35386
|
993 |
end
|
blanchet@35386
|
994 |
| @{const Not} $ t1 =>
|
blanchet@35386
|
995 |
let val (m1, accum) = do_formula (negate sn) t1 accum in
|
blanchet@35386
|
996 |
(MApp (MRaw (@{const Not}, mtype_for (bool_T --> bool_T)), m1),
|
blanchet@35386
|
997 |
accum)
|
blanchet@35386
|
998 |
end
|
blanchet@35386
|
999 |
| Const (x as (@{const_name All}, _)) $ Abs (s1, T1, t1) =>
|
blanchet@35386
|
1000 |
do_quantifier x s1 T1 t1
|
blanchet@35386
|
1001 |
| Const (x0 as (s0 as @{const_name Ex}, T0))
|
blanchet@35386
|
1002 |
$ (t1 as Abs (s1, T1, t1')) =>
|
blanchet@35385
|
1003 |
(case sn of
|
blanchet@35386
|
1004 |
Plus => do_quantifier x0 s1 T1 t1'
|
blanchet@35385
|
1005 |
| Minus =>
|
blanchet@35665
|
1006 |
(* FIXME: Move elsewhere *)
|
blanchet@35385
|
1007 |
do_term (@{const Not}
|
blanchet@35385
|
1008 |
$ (HOLogic.eq_const (domain_type T0) $ t1
|
blanchet@35386
|
1009 |
$ Abs (Name.uu, T1, @{const False}))) accum)
|
blanchet@35386
|
1010 |
| Const (x as (@{const_name "op ="}, _)) $ t1 $ t2 =>
|
blanchet@35386
|
1011 |
do_equals x t1 t2
|
blanchet@35386
|
1012 |
| (t0 as Const (s0, _)) $ t1 $ t2 =>
|
blanchet@35386
|
1013 |
if s0 = @{const_name "==>"} orelse s0 = @{const_name "op &"} orelse
|
blanchet@35386
|
1014 |
s0 = @{const_name "op |"} orelse s0 = @{const_name "op -->"} then
|
blanchet@35386
|
1015 |
let
|
blanchet@35386
|
1016 |
val impl = (s0 = @{const_name "==>"} orelse
|
blanchet@35386
|
1017 |
s0 = @{const_name "op -->"})
|
blanchet@35386
|
1018 |
val (m1, accum) = do_formula (sn |> impl ? negate) t1 accum
|
blanchet@35386
|
1019 |
val (m2, accum) = do_formula sn t2 accum
|
blanchet@35386
|
1020 |
in
|
blanchet@35386
|
1021 |
(MApp (MApp (MRaw (t0, mtype_for (fastype_of t0)), m1), m2),
|
blanchet@35386
|
1022 |
accum)
|
blanchet@35386
|
1023 |
end
|
blanchet@35386
|
1024 |
else
|
blanchet@35386
|
1025 |
do_term t accum
|
blanchet@35386
|
1026 |
| _ => do_term t accum
|
blanchet@33192
|
1027 |
end
|
blanchet@35386
|
1028 |
|> tap (fn (m, _) =>
|
blanchet@35386
|
1029 |
print_g ("\<Gamma> \<turnstile> " ^
|
blanchet@35386
|
1030 |
string_for_mterm ctxt m ^ " : o\<^sup>" ^
|
blanchet@35386
|
1031 |
string_for_sign sn))
|
blanchet@33192
|
1032 |
in do_formula end
|
blanchet@33192
|
1033 |
|
blanchet@33192
|
1034 |
(* The harmless axiom optimization below is somewhat too aggressive in the face
|
blanchet@33192
|
1035 |
of (rather peculiar) user-defined axioms. *)
|
blanchet@33192
|
1036 |
val harmless_consts =
|
blanchet@33192
|
1037 |
[@{const_name ord_class.less}, @{const_name ord_class.less_eq}]
|
blanchet@33192
|
1038 |
val bounteous_consts = [@{const_name bisim}]
|
blanchet@33192
|
1039 |
|
blanchet@35665
|
1040 |
(* mdata -> term -> bool *)
|
blanchet@35665
|
1041 |
fun is_harmless_axiom ({no_harmless = true, ...} : mdata) _ = false
|
blanchet@35665
|
1042 |
| is_harmless_axiom {hol_ctxt = {thy, stds, fast_descrs, ...}, ...} t =
|
blanchet@35665
|
1043 |
Term.add_consts t []
|
blanchet@35665
|
1044 |
|> filter_out (is_built_in_const thy stds fast_descrs)
|
blanchet@35665
|
1045 |
|> (forall (member (op =) harmless_consts o original_name o fst) orf
|
blanchet@35665
|
1046 |
exists (member (op =) bounteous_consts o fst))
|
blanchet@33192
|
1047 |
|
blanchet@35386
|
1048 |
(* mdata -> term -> accumulator -> mterm * accumulator *)
|
blanchet@35665
|
1049 |
fun consider_nondefinitional_axiom mdata t =
|
blanchet@35665
|
1050 |
if is_harmless_axiom mdata t then pair (MRaw (t, dummy_M))
|
blanchet@35386
|
1051 |
else consider_general_formula mdata Plus t
|
blanchet@33192
|
1052 |
|
blanchet@35386
|
1053 |
(* mdata -> term -> accumulator -> mterm * accumulator *)
|
blanchet@35665
|
1054 |
fun consider_definitional_axiom (mdata as {hol_ctxt = {thy, ...}, ...}) t =
|
blanchet@33192
|
1055 |
if not (is_constr_pattern_formula thy t) then
|
blanchet@35386
|
1056 |
consider_nondefinitional_axiom mdata t
|
blanchet@35665
|
1057 |
else if is_harmless_axiom mdata t then
|
blanchet@35386
|
1058 |
pair (MRaw (t, dummy_M))
|
blanchet@33192
|
1059 |
else
|
blanchet@33192
|
1060 |
let
|
blanchet@35386
|
1061 |
(* typ -> mtyp *)
|
blanchet@35386
|
1062 |
val mtype_for = fresh_mtype_for_type mdata
|
blanchet@35386
|
1063 |
(* term -> accumulator -> mterm * accumulator *)
|
blanchet@35386
|
1064 |
val do_term = consider_term mdata
|
blanchet@35386
|
1065 |
(* term -> string -> typ -> term -> accumulator -> mterm * accumulator *)
|
blanchet@35386
|
1066 |
fun do_all quant_t abs_s abs_T body_t accum =
|
blanchet@35386
|
1067 |
let
|
blanchet@35386
|
1068 |
val abs_M = mtype_for abs_T
|
blanchet@35386
|
1069 |
val (body_m, accum) =
|
blanchet@35665
|
1070 |
accum |>> push_bound abs_T abs_M |> do_formula body_t
|
blanchet@35386
|
1071 |
val body_M = mtype_of_mterm body_m
|
blanchet@35386
|
1072 |
in
|
blanchet@35665
|
1073 |
(MApp (MRaw (quant_t,
|
blanchet@35665
|
1074 |
MFun (MFun (abs_M, S Minus, body_M), S Minus, body_M)),
|
blanchet@35386
|
1075 |
MAbs (abs_s, abs_T, abs_M, S Minus, body_m)),
|
blanchet@35386
|
1076 |
accum |>> pop_bound)
|
blanchet@33192
|
1077 |
end
|
blanchet@35386
|
1078 |
(* term -> term -> term -> accumulator -> mterm * accumulator *)
|
blanchet@35386
|
1079 |
and do_conjunction t0 t1 t2 accum =
|
blanchet@33192
|
1080 |
let
|
blanchet@35386
|
1081 |
val (m1, accum) = do_formula t1 accum
|
blanchet@35386
|
1082 |
val (m2, accum) = do_formula t2 accum
|
blanchet@35386
|
1083 |
in
|
blanchet@35386
|
1084 |
(MApp (MApp (MRaw (t0, mtype_for (fastype_of t0)), m1), m2), accum)
|
blanchet@35386
|
1085 |
end
|
blanchet@35386
|
1086 |
and do_implies t0 t1 t2 accum =
|
blanchet@35386
|
1087 |
let
|
blanchet@35386
|
1088 |
val (m1, accum) = do_term t1 accum
|
blanchet@35386
|
1089 |
val (m2, accum) = do_formula t2 accum
|
blanchet@35386
|
1090 |
in
|
blanchet@35386
|
1091 |
(MApp (MApp (MRaw (t0, mtype_for (fastype_of t0)), m1), m2), accum)
|
blanchet@35386
|
1092 |
end
|
blanchet@33192
|
1093 |
(* term -> accumulator -> accumulator *)
|
blanchet@35386
|
1094 |
and do_formula t (_, UnsolvableCSet) =
|
blanchet@35386
|
1095 |
(MRaw (t, dummy_M), unsolvable_accum)
|
blanchet@33192
|
1096 |
| do_formula t accum =
|
blanchet@33192
|
1097 |
case t of
|
blanchet@35386
|
1098 |
(t0 as Const (@{const_name all}, _)) $ Abs (s1, T1, t1) =>
|
blanchet@35386
|
1099 |
do_all t0 s1 T1 t1 accum
|
blanchet@35665
|
1100 |
| @{const Trueprop} $ t1 =>
|
blanchet@35665
|
1101 |
let val (m1, accum) = do_formula t1 accum in
|
blanchet@35665
|
1102 |
(MApp (MRaw (@{const Trueprop}, mtype_for (bool_T --> prop_T)),
|
blanchet@35665
|
1103 |
m1), accum)
|
blanchet@35665
|
1104 |
end
|
blanchet@35386
|
1105 |
| Const (x as (@{const_name "=="}, _)) $ t1 $ t2 =>
|
blanchet@35665
|
1106 |
consider_general_equals mdata true x t1 t2 accum
|
blanchet@35386
|
1107 |
| (t0 as @{const "==>"}) $ t1 $ t2 => do_implies t0 t1 t2 accum
|
blanchet@35386
|
1108 |
| (t0 as @{const Pure.conjunction}) $ t1 $ t2 =>
|
blanchet@35386
|
1109 |
do_conjunction t0 t1 t2 accum
|
blanchet@35386
|
1110 |
| (t0 as Const (@{const_name All}, _)) $ Abs (s0, T1, t1) =>
|
blanchet@35386
|
1111 |
do_all t0 s0 T1 t1 accum
|
blanchet@35386
|
1112 |
| Const (x as (@{const_name "op ="}, _)) $ t1 $ t2 =>
|
blanchet@35665
|
1113 |
consider_general_equals mdata true x t1 t2 accum
|
blanchet@35386
|
1114 |
| (t0 as @{const "op &"}) $ t1 $ t2 => do_conjunction t0 t1 t2 accum
|
blanchet@35386
|
1115 |
| (t0 as @{const "op -->"}) $ t1 $ t2 => do_implies t0 t1 t2 accum
|
blanchet@33224
|
1116 |
| _ => raise TERM ("Nitpick_Mono.consider_definitional_axiom.\
|
blanchet@33192
|
1117 |
\do_formula", [t])
|
blanchet@33192
|
1118 |
in do_formula t end
|
blanchet@33192
|
1119 |
|
blanchet@35385
|
1120 |
(* Proof.context -> literal list -> term -> mtyp -> string *)
|
blanchet@35385
|
1121 |
fun string_for_mtype_of_term ctxt lits t M =
|
blanchet@35665
|
1122 |
Syntax.string_of_term ctxt t ^ " : " ^ string_for_mtype (resolve_mtype lits M)
|
blanchet@33192
|
1123 |
|
blanchet@35385
|
1124 |
(* theory -> literal list -> mtype_context -> unit *)
|
blanchet@35385
|
1125 |
fun print_mtype_context ctxt lits ({frees, consts, ...} : mtype_context) =
|
blanchet@35385
|
1126 |
map (fn (x, M) => string_for_mtype_of_term ctxt lits (Free x) M) frees @
|
blanchet@35385
|
1127 |
map (fn (x, M) => string_for_mtype_of_term ctxt lits (Const x) M) consts
|
blanchet@33192
|
1128 |
|> cat_lines |> print_g
|
blanchet@33192
|
1129 |
|
blanchet@35386
|
1130 |
(* ('a -> 'b -> 'c * 'd) -> 'a -> 'c list * 'b -> 'c list * 'd *)
|
blanchet@35665
|
1131 |
fun amass f t (ms, accum) =
|
blanchet@35386
|
1132 |
let val (m, accum) = f t accum in (m :: ms, accum) end
|
blanchet@35386
|
1133 |
|
blanchet@35665
|
1134 |
(* string -> bool -> hol_context -> bool -> typ -> term list * term list
|
blanchet@35665
|
1135 |
-> (literal list * (mterm list * mterm list) * (styp * mtyp) list) option *)
|
blanchet@35665
|
1136 |
fun infer which no_harmless (hol_ctxt as {ctxt, ...}) binarize alpha_T
|
blanchet@35665
|
1137 |
(nondef_ts, def_ts) =
|
blanchet@33192
|
1138 |
let
|
blanchet@35665
|
1139 |
val _ = print_g ("****** " ^ which ^ " analysis: " ^
|
blanchet@35385
|
1140 |
string_for_mtype MAlpha ^ " is " ^
|
blanchet@33192
|
1141 |
Syntax.string_of_typ ctxt alpha_T)
|
blanchet@35665
|
1142 |
val mdata as {max_fresh, constr_mcache, ...} =
|
blanchet@35665
|
1143 |
initial_mdata hol_ctxt binarize no_harmless alpha_T
|
blanchet@35386
|
1144 |
val accum = (initial_gamma, slack)
|
blanchet@35386
|
1145 |
val (nondef_ms, accum) =
|
blanchet@35665
|
1146 |
([], accum) |> amass (consider_general_formula mdata Plus) (hd nondef_ts)
|
blanchet@35665
|
1147 |
|> fold (amass (consider_nondefinitional_axiom mdata))
|
blanchet@35386
|
1148 |
(tl nondef_ts)
|
blanchet@35386
|
1149 |
val (def_ms, (gamma, cset)) =
|
blanchet@35665
|
1150 |
([], accum) |> fold (amass (consider_definitional_axiom mdata)) def_ts
|
blanchet@33192
|
1151 |
in
|
blanchet@33192
|
1152 |
case solve (!max_fresh) cset of
|
blanchet@35665
|
1153 |
SOME lits => (print_mtype_context ctxt lits gamma;
|
blanchet@35665
|
1154 |
SOME (lits, (nondef_ms, def_ms), !constr_mcache))
|
blanchet@35665
|
1155 |
| _ => NONE
|
blanchet@33192
|
1156 |
end
|
blanchet@35665
|
1157 |
handle MTYPE (loc, Ms, Ts) =>
|
blanchet@35665
|
1158 |
raise BAD (loc, commas (map string_for_mtype Ms @
|
blanchet@35665
|
1159 |
map (Syntax.string_of_typ ctxt) Ts))
|
blanchet@35665
|
1160 |
| MTERM (loc, ms) =>
|
blanchet@35665
|
1161 |
raise BAD (loc, commas (map (string_for_mterm ctxt) ms))
|
blanchet@35665
|
1162 |
|
blanchet@35665
|
1163 |
(* hol_context -> bool -> typ -> term list * term list -> bool *)
|
blanchet@35665
|
1164 |
val formulas_monotonic = is_some oooo infer "Monotonicity" false
|
blanchet@35665
|
1165 |
|
blanchet@35665
|
1166 |
(* typ -> typ -> styp *)
|
blanchet@35665
|
1167 |
fun fin_fun_constr T1 T2 =
|
blanchet@35665
|
1168 |
(@{const_name FinFun}, (T1 --> T2) --> Type (@{type_name fin_fun}, [T1, T2]))
|
blanchet@35665
|
1169 |
|
blanchet@35665
|
1170 |
(* hol_context -> bool -> (typ option * bool option) list -> typ
|
blanchet@35665
|
1171 |
-> term list * term list -> term list * term list *)
|
blanchet@35665
|
1172 |
fun finitize_funs (hol_ctxt as {thy, stds, fast_descrs, constr_cache, ...})
|
blanchet@35665
|
1173 |
binarize finitizes alpha_T tsp =
|
blanchet@35665
|
1174 |
case infer "Finiteness" true hol_ctxt binarize alpha_T tsp of
|
blanchet@35665
|
1175 |
SOME (lits, msp, constr_mtypes) =>
|
blanchet@35665
|
1176 |
let
|
blanchet@35665
|
1177 |
(* typ -> sign_atom -> bool *)
|
blanchet@35665
|
1178 |
fun should_finitize T a =
|
blanchet@35665
|
1179 |
case triple_lookup (type_match thy) finitizes T of
|
blanchet@35665
|
1180 |
SOME (SOME false) => false
|
blanchet@35665
|
1181 |
| _ => resolve_sign_atom lits a = S Plus
|
blanchet@35665
|
1182 |
(* typ -> mtyp -> typ *)
|
blanchet@35665
|
1183 |
fun type_from_mtype T M =
|
blanchet@35665
|
1184 |
case (M, T) of
|
blanchet@35665
|
1185 |
(MAlpha, _) => T
|
blanchet@35665
|
1186 |
| (MFun (M1, a, M2), Type (@{type_name fun}, Ts)) =>
|
blanchet@35665
|
1187 |
Type (if should_finitize T a then @{type_name fin_fun}
|
blanchet@35665
|
1188 |
else @{type_name fun}, map2 type_from_mtype Ts [M1, M2])
|
blanchet@35665
|
1189 |
| (MPair (M1, M2), Type (@{type_name "*"}, Ts)) =>
|
blanchet@35665
|
1190 |
Type (@{type_name "*"}, map2 type_from_mtype Ts [M1, M2])
|
blanchet@35665
|
1191 |
| (MType _, _) => T
|
blanchet@35665
|
1192 |
| _ => raise MTYPE ("Nitpick_Mono.finitize_funs.type_from_mtype",
|
blanchet@35665
|
1193 |
[M], [T])
|
blanchet@35665
|
1194 |
(* styp -> styp *)
|
blanchet@35665
|
1195 |
fun finitize_constr (x as (s, T)) =
|
blanchet@35665
|
1196 |
(s, case AList.lookup (op =) constr_mtypes x of
|
blanchet@35665
|
1197 |
SOME M => type_from_mtype T M
|
blanchet@35665
|
1198 |
| NONE => T)
|
blanchet@35665
|
1199 |
(* typ list -> mterm -> term *)
|
blanchet@35665
|
1200 |
fun term_from_mterm Ts m =
|
blanchet@35665
|
1201 |
case m of
|
blanchet@35665
|
1202 |
MRaw (t, M) =>
|
blanchet@35665
|
1203 |
let
|
blanchet@35665
|
1204 |
val T = fastype_of1 (Ts, t)
|
blanchet@35665
|
1205 |
val T' = type_from_mtype T M
|
blanchet@35665
|
1206 |
in
|
blanchet@35665
|
1207 |
case t of
|
blanchet@35665
|
1208 |
Const (x as (s, T)) =>
|
blanchet@35665
|
1209 |
if member (op =) [@{const_name "=="}, @{const_name "op ="}] s then
|
blanchet@35665
|
1210 |
Const (s, T')
|
blanchet@35665
|
1211 |
else if is_built_in_const thy stds fast_descrs x then
|
blanchet@35665
|
1212 |
coerce_term hol_ctxt Ts T' T t
|
blanchet@35665
|
1213 |
else if is_constr thy stds x then
|
blanchet@35665
|
1214 |
Const (finitize_constr x)
|
blanchet@35665
|
1215 |
else if is_sel s then
|
blanchet@35665
|
1216 |
let
|
blanchet@35665
|
1217 |
val n = sel_no_from_name s
|
blanchet@35665
|
1218 |
val x' = x |> binarized_and_boxed_constr_for_sel hol_ctxt
|
blanchet@35665
|
1219 |
binarize
|
blanchet@35665
|
1220 |
|> finitize_constr
|
blanchet@35665
|
1221 |
val x'' = binarized_and_boxed_nth_sel_for_constr hol_ctxt
|
blanchet@35665
|
1222 |
binarize x' n
|
blanchet@35665
|
1223 |
in Const x'' end
|
blanchet@35665
|
1224 |
else
|
blanchet@35665
|
1225 |
Const (s, T')
|
blanchet@35665
|
1226 |
| Free (s, T) => Free (s, type_from_mtype T M)
|
blanchet@35665
|
1227 |
| Bound _ => t
|
blanchet@35665
|
1228 |
| _ => raise MTERM ("Nitpick_Mono.finitize_funs.term_from_mterm",
|
blanchet@35665
|
1229 |
[m])
|
blanchet@35665
|
1230 |
end
|
blanchet@35665
|
1231 |
| MAbs (s, T, M, a, m') =>
|
blanchet@35665
|
1232 |
let
|
blanchet@35665
|
1233 |
val T = type_from_mtype T M
|
blanchet@35665
|
1234 |
val t' = term_from_mterm (T :: Ts) m'
|
blanchet@35665
|
1235 |
val T' = fastype_of1 (T :: Ts, t')
|
blanchet@35665
|
1236 |
in
|
blanchet@35665
|
1237 |
Abs (s, T, t')
|
blanchet@35665
|
1238 |
|> should_finitize (T --> T') a
|
blanchet@35665
|
1239 |
? construct_value thy stds (fin_fun_constr T T') o single
|
blanchet@35665
|
1240 |
end
|
blanchet@35665
|
1241 |
| MApp (m1, m2) =>
|
blanchet@35665
|
1242 |
let
|
blanchet@35665
|
1243 |
val (t1, t2) = pairself (term_from_mterm Ts) (m1, m2)
|
blanchet@35665
|
1244 |
val (T1, T2) = pairself (curry fastype_of1 Ts) (t1, t2)
|
blanchet@35665
|
1245 |
val (t1', T2') =
|
blanchet@35665
|
1246 |
case T1 of
|
blanchet@35665
|
1247 |
Type (s, [T11, T12]) =>
|
blanchet@35665
|
1248 |
(if s = @{type_name fin_fun} then
|
blanchet@35665
|
1249 |
select_nth_constr_arg thy stds (fin_fun_constr T11 T12) t1 0
|
blanchet@35665
|
1250 |
(T11 --> T12)
|
blanchet@35665
|
1251 |
else
|
blanchet@35665
|
1252 |
t1, T11)
|
blanchet@35665
|
1253 |
| _ => raise TYPE ("Nitpick_Mono.finitize_funs.term_from_mterm",
|
blanchet@35665
|
1254 |
[T1], [])
|
blanchet@35665
|
1255 |
in betapply (t1', coerce_term hol_ctxt Ts T2' T2 t2) end
|
blanchet@35665
|
1256 |
in
|
blanchet@35665
|
1257 |
Unsynchronized.change constr_cache (map (apsnd (map finitize_constr)));
|
blanchet@35665
|
1258 |
pairself (map (term_from_mterm [])) msp
|
blanchet@35665
|
1259 |
end
|
blanchet@35665
|
1260 |
| NONE => tsp
|
blanchet@33192
|
1261 |
|
blanchet@33192
|
1262 |
end;
|