src/Pure/term.ML
author wenzelm
Wed Jul 12 21:19:22 2006 +0200 (2006-07-12)
changeset 20116 f2aecd6e58ec
parent 20109 47fef41c68fb
child 20122 27255556b762
permissions -rw-r--r--
removed obsolete adhoc_freeze_vars (may use Variable.import_terms instead);
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(*  Title:      Pure/term.ML
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    ID:         $Id$
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    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
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    Copyright   Cambridge University 1992
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Simply typed lambda-calculus: types, terms, and basic operations.
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*)
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infix 9  $;
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infixr 5 -->;
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infixr --->;
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infix aconv;
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signature BASIC_TERM =
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sig
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  type indexname
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  type class
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  type sort
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  type arity
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  datatype typ =
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    Type  of string * typ list |
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    TFree of string * sort |
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    TVar  of indexname * sort
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  datatype term =
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    Const of string * typ |
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    Free of string * typ |
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    Var of indexname * typ |
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    Bound of int |
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    Abs of string * typ * term |
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    $ of term * term
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  exception TYPE of string * typ list * term list
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  exception TERM of string * term list
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  val dummyT: typ
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  val no_dummyT: typ -> typ
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  val --> : typ * typ -> typ
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  val ---> : typ list * typ -> typ
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  val dest_Type: typ -> string * typ list
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  val dest_TVar: typ -> indexname * sort
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  val dest_TFree: typ -> string * sort
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  val is_Bound: term -> bool
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  val is_Const: term -> bool
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  val is_Free: term -> bool
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  val is_Var: term -> bool
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  val is_TVar: typ -> bool
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  val is_funtype: typ -> bool
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  val dest_Const: term -> string * typ
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  val dest_Free: term -> string * typ
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  val dest_Var: term -> indexname * typ
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  val domain_type: typ -> typ
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  val range_type: typ -> typ
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  val binder_types: typ -> typ list
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  val body_type: typ -> typ
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  val strip_type: typ -> typ list * typ
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  val type_of1: typ list * term -> typ
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  val type_of: term -> typ
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  val fastype_of1: typ list * term -> typ
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  val fastype_of: term -> typ
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  val list_abs: (string * typ) list * term -> term
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  val strip_abs: term -> (string * typ) list * term
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  val strip_abs_body: term -> term
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  val strip_abs_vars: term -> (string * typ) list
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  val strip_qnt_body: string -> term -> term
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  val strip_qnt_vars: string -> term -> (string * typ) list
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  val list_comb: term * term list -> term
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  val strip_comb: term -> term * term list
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  val head_of: term -> term
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  val size_of_term: term -> int
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  val map_atyps: (typ -> typ) -> typ -> typ
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  val map_aterms: (term -> term) -> term -> term
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  val map_type_tvar: (indexname * sort -> typ) -> typ -> typ
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  val map_type_tfree: (string * sort -> typ) -> typ -> typ
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  val map_term_types: (typ -> typ) -> term -> term
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  val fold_atyps: (typ -> 'a -> 'a) -> typ -> 'a -> 'a
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  val fold_aterms: (term -> 'a -> 'a) -> term -> 'a -> 'a
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  val fold_term_types: (term -> typ -> 'a -> 'a) -> term -> 'a -> 'a
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  val fold_types: (typ -> 'a -> 'a) -> term -> 'a -> 'a
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  val it_term_types: (typ * 'a -> 'a) -> term * 'a -> 'a
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  val add_term_names: term * string list -> string list
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  val add_term_varnames: term -> indexname list -> indexname list
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  val term_varnames: term -> indexname list
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  val find_free: term -> string -> term option
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  val aconv: term * term -> bool
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  val aconvs: term list * term list -> bool
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  structure Vartab: TABLE
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  structure Typtab: TABLE
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  structure Termtab: TABLE
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  val propT: typ
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  val implies: term
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  val all: typ -> term
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  val equals: typ -> term
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  val strip_all_body: term -> term
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  val strip_all_vars: term -> (string * typ) list
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  val incr_bv: int * int * term -> term
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  val incr_boundvars: int -> term -> term
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  val add_loose_bnos: term * int * int list -> int list
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  val loose_bnos: term -> int list
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  val loose_bvar: term * int -> bool
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  val loose_bvar1: term * int -> bool
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  val subst_bounds: term list * term -> term
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  val subst_bound: term * term -> term
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  val betapply: term * term -> term
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  val betapplys: term * term list -> term
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  val eq_ix: indexname * indexname -> bool
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  val could_unify: term * term -> bool
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  val subst_free: (term * term) list -> term -> term
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  val abstract_over: term * term -> term
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  val lambda: term -> term -> term
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  val absfree: string * typ * term -> term
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  val absdummy: typ * term -> term
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  val list_abs_free: (string * typ) list * term -> term
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  val list_all_free: (string * typ) list * term -> term
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  val list_all: (string * typ) list * term -> term
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  val subst_atomic: (term * term) list -> term -> term
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  val typ_subst_atomic: (typ * typ) list -> typ -> typ
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  val subst_atomic_types: (typ * typ) list -> term -> term
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  val typ_subst_TVars: (indexname * typ) list -> typ -> typ
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  val subst_TVars: (indexname * typ) list -> term -> term
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  val subst_Vars: (indexname * term) list -> term -> term
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  val subst_vars: (indexname * typ) list * (indexname * term) list -> term -> term
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  val is_first_order: string list -> term -> bool
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  val maxidx_of_typ: typ -> int
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  val maxidx_of_typs: typ list -> int
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  val maxidx_of_term: term -> int
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  val add_term_consts: term * string list -> string list
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  val term_consts: term -> string list
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  val exists_subtype: (typ -> bool) -> typ -> bool
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  val exists_subterm: (term -> bool) -> term -> bool
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  val exists_Const: (string * typ -> bool) -> term -> bool
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  val add_term_free_names: term * string list -> string list
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  val add_typ_tvars: typ * (indexname * sort) list -> (indexname * sort) list
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  val add_typ_tfree_names: typ * string list -> string list
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  val add_typ_tfrees: typ * (string * sort) list -> (string * sort) list
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  val add_typ_varnames: typ * string list -> string list
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  val add_term_tvars: term * (indexname * sort) list -> (indexname * sort) list
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  val add_term_tfrees: term * (string * sort) list -> (string * sort) list
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  val add_term_tfree_names: term * string list -> string list
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  val add_term_tvarnames: term * string list -> string list
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  val typ_tfrees: typ -> (string * sort) list
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  val typ_tvars: typ -> (indexname * sort) list
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  val term_tfrees: term -> (string * sort) list
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  val term_tvars: term -> (indexname * sort) list
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  val add_typ_ixns: indexname list * typ -> indexname list
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  val add_term_tvar_ixns: term * indexname list -> indexname list
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  val add_term_vars: term * term list -> term list
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  val term_vars: term -> term list
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  val add_term_frees: term * term list -> term list
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  val term_frees: term -> term list
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  val variant_abs: string * typ * term -> string * term
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  val rename_wrt_term: term -> (string * typ) list -> (string * typ) list
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  val show_question_marks: bool ref
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end;
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signature TERM =
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sig
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  include BASIC_TERM
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  val aT: sort -> typ
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  val itselfT: typ -> typ
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  val a_itselfT: typ
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  val argument_type_of: term -> typ
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  val add_tvarsT: typ -> (indexname * sort) list -> (indexname * sort) list
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  val add_tvars: term -> (indexname * sort) list -> (indexname * sort) list
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  val add_vars: term -> (indexname * typ) list -> (indexname * typ) list
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  val add_tfreesT: typ -> (string * sort) list -> (string * sort) list
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  val add_tfrees: term -> (string * sort) list -> (string * sort) list
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  val add_frees: term -> (string * typ) list -> (string * typ) list
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  val strip_abs_eta: int -> term -> (string * typ) list * term
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  val fast_indexname_ord: indexname * indexname -> order
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  val indexname_ord: indexname * indexname -> order
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  val sort_ord: sort * sort -> order
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  val typ_ord: typ * typ -> order
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  val fast_term_ord: term * term -> order
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  val term_ord: term * term -> order
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  val hd_ord: term * term -> order
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  val termless: term * term -> bool
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  val term_lpo: (string -> int) -> term * term -> order
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  val match_bvars: (term * term) * (string * string) list -> (string * string) list
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  val rename_abs: term -> term -> term -> term option
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  val eq_tvar: (indexname * sort) * (indexname * sort) -> bool
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  val eq_var: (indexname * typ) * (indexname * typ) -> bool
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  val tvar_ord: (indexname * sort) * (indexname * sort) -> order
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  val var_ord: (indexname * typ) * (indexname * typ) -> order
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  val generalize: string list * string list -> int -> term -> term
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  val generalizeT: string list -> int -> typ -> typ
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  val generalize_option: string list * string list -> int -> term -> term option
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  val generalizeT_option: string list -> int -> typ -> typ option
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  val instantiate: ((indexname * sort) * typ) list * ((indexname * typ) * term) list
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    -> term -> term
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  val instantiateT: ((indexname * sort) * typ) list -> typ -> typ
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  val instantiate_option: ((indexname * sort) * typ) list * ((indexname * typ) * term) list
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    -> term -> term option
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  val instantiateT_option: ((indexname * sort) * typ) list -> typ -> typ option
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  val maxidx_typ: typ -> int -> int
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  val maxidx_typs: typ list -> int -> int
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  val maxidx_term: term -> int -> int
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  val dest_abs: string * typ * term -> string * term
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  val zero_var_indexesT: typ -> typ
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  val zero_var_indexes: term -> term
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  val zero_var_indexes_inst: term ->
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    ((indexname * sort) * typ) list * ((indexname * typ) * term) list
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  val dummy_patternN: string
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  val dummy_pattern: typ -> term
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  val no_dummy_patterns: term -> term
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  val replace_dummy_patterns: int * term -> int * term
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  val is_replaced_dummy_pattern: indexname -> bool
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  val show_dummy_patterns: term -> term
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  val string_of_vname: indexname -> string
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  val string_of_vname': indexname -> string
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end;
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structure Term: TERM =
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struct
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(*Indexnames can be quickly renamed by adding an offset to the integer part,
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  for resolution.*)
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type indexname = string * int;
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(* Types are classified by sorts. *)
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type class = string;
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type sort  = class list;
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type arity = string * sort list * sort;
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(* The sorts attached to TFrees and TVars specify the sort of that variable *)
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datatype typ = Type  of string * typ list
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             | TFree of string * sort
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             | TVar  of indexname * sort;
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(*Terms.  Bound variables are indicated by depth number.
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  Free variables, (scheme) variables and constants have names.
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  An term is "closed" if every bound variable of level "lev"
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  is enclosed by at least "lev" abstractions.
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  It is possible to create meaningless terms containing loose bound vars
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  or type mismatches.  But such terms are not allowed in rules. *)
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datatype term =
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    Const of string * typ
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  | Free  of string * typ
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  | Var   of indexname * typ
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  | Bound of int
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  | Abs   of string*typ*term
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  | op $  of term*term;
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(*Errors involving type mismatches*)
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exception TYPE of string * typ list * term list;
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(*Errors errors involving terms*)
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exception TERM of string * term list;
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(*Note variable naming conventions!
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    a,b,c: string
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    f,g,h: functions (including terms of function type)
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    i,j,m,n: int
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    t,u: term
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    v,w: indexnames
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    x,y: any
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    A,B,C: term (denoting formulae)
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    T,U: typ
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*)
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(** Types **)
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(*dummy type for parsing and printing etc.*)
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val dummyT = Type ("dummy", []);
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fun no_dummyT typ =
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  let
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    fun check (T as Type ("dummy", _)) =
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          raise TYPE ("Illegal occurrence of '_' dummy type", [T], [])
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      | check (Type (_, Ts)) = List.app check Ts
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      | check _ = ();
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  in check typ; typ end;
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fun S --> T = Type("fun",[S,T]);
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(*handy for multiple args: [T1,...,Tn]--->T  gives  T1-->(T2--> ... -->T)*)
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val op ---> = Library.foldr (op -->);
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fun dest_Type (Type x) = x
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  | dest_Type T = raise TYPE ("dest_Type", [T], []);
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fun dest_TVar (TVar x) = x
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  | dest_TVar T = raise TYPE ("dest_TVar", [T], []);
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fun dest_TFree (TFree x) = x
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  | dest_TFree T = raise TYPE ("dest_TFree", [T], []);
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(** Discriminators **)
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fun is_Bound (Bound _) = true
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  | is_Bound _         = false;
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fun is_Const (Const _) = true
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  | is_Const _ = false;
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fun is_Free (Free _) = true
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  | is_Free _ = false;
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fun is_Var (Var _) = true
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  | is_Var _ = false;
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fun is_TVar (TVar _) = true
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  | is_TVar _ = false;
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(*Differs from proofterm/is_fun in its treatment of TVar*)
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fun is_funtype (Type("fun",[_,_])) = true
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  | is_funtype _ = false;
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(** Destructors **)
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fun dest_Const (Const x) =  x
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  | dest_Const t = raise TERM("dest_Const", [t]);
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fun dest_Free (Free x) =  x
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  | dest_Free t = raise TERM("dest_Free", [t]);
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fun dest_Var (Var x) =  x
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  | dest_Var t = raise TERM("dest_Var", [t]);
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fun domain_type (Type("fun", [T,_])) = T
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and range_type  (Type("fun", [_,T])) = T;
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(* maps  [T1,...,Tn]--->T  to the list  [T1,T2,...,Tn]*)
clasohm@0
   325
fun binder_types (Type("fun",[S,T])) = S :: binder_types T
clasohm@0
   326
  | binder_types _   =  [];
clasohm@0
   327
clasohm@0
   328
(* maps  [T1,...,Tn]--->T  to T*)
clasohm@0
   329
fun body_type (Type("fun",[S,T])) = body_type T
clasohm@0
   330
  | body_type T   =  T;
clasohm@0
   331
clasohm@0
   332
(* maps  [T1,...,Tn]--->T  to   ([T1,T2,...,Tn], T)  *)
clasohm@0
   333
fun strip_type T : typ list * typ =
clasohm@0
   334
  (binder_types T, body_type T);
clasohm@0
   335
clasohm@0
   336
clasohm@0
   337
(*Compute the type of the term, checking that combinations are well-typed
clasohm@0
   338
  Ts = [T0,T1,...] holds types of bound variables 0, 1, ...*)
clasohm@0
   339
fun type_of1 (Ts, Const (_,T)) = T
clasohm@0
   340
  | type_of1 (Ts, Free  (_,T)) = T
skalberg@15570
   341
  | type_of1 (Ts, Bound i) = (List.nth (Ts,i)
skalberg@15570
   342
        handle Subscript => raise TYPE("type_of: bound variable", [], [Bound i]))
clasohm@0
   343
  | type_of1 (Ts, Var (_,T)) = T
clasohm@0
   344
  | type_of1 (Ts, Abs (_,T,body)) = T --> type_of1(T::Ts, body)
wenzelm@13000
   345
  | type_of1 (Ts, f$u) =
clasohm@0
   346
      let val U = type_of1(Ts,u)
clasohm@0
   347
          and T = type_of1(Ts,f)
clasohm@0
   348
      in case T of
wenzelm@9536
   349
            Type("fun",[T1,T2]) =>
wenzelm@9536
   350
              if T1=U then T2  else raise TYPE
wenzelm@9536
   351
                    ("type_of: type mismatch in application", [T1,U], [f$u])
wenzelm@13000
   352
          | _ => raise TYPE
wenzelm@9536
   353
                    ("type_of: function type is expected in application",
wenzelm@9536
   354
                     [T,U], [f$u])
clasohm@0
   355
      end;
clasohm@0
   356
clasohm@0
   357
fun type_of t : typ = type_of1 ([],t);
clasohm@0
   358
clasohm@0
   359
(*Determines the type of a term, with minimal checking*)
wenzelm@13000
   360
fun fastype_of1 (Ts, f$u) =
lcp@61
   361
    (case fastype_of1 (Ts,f) of
wenzelm@9536
   362
        Type("fun",[_,T]) => T
wenzelm@9536
   363
        | _ => raise TERM("fastype_of: expected function type", [f$u]))
lcp@61
   364
  | fastype_of1 (_, Const (_,T)) = T
lcp@61
   365
  | fastype_of1 (_, Free (_,T)) = T
skalberg@15570
   366
  | fastype_of1 (Ts, Bound i) = (List.nth(Ts,i)
skalberg@15570
   367
         handle Subscript => raise TERM("fastype_of: Bound", [Bound i]))
wenzelm@13000
   368
  | fastype_of1 (_, Var (_,T)) = T
lcp@61
   369
  | fastype_of1 (Ts, Abs (_,T,u)) = T --> fastype_of1 (T::Ts, u);
lcp@61
   370
lcp@61
   371
fun fastype_of t : typ = fastype_of1 ([],t);
clasohm@0
   372
wenzelm@16678
   373
(*Determine the argument type of a function*)
wenzelm@16678
   374
fun argument_type_of tm =
wenzelm@16678
   375
  let
wenzelm@16678
   376
    fun argT i (Type ("fun", [T, U])) = if i = 0 then T else argT (i - 1) U
wenzelm@16678
   377
      | argT _ T = raise TYPE ("argument_type_of", [T], []);
wenzelm@16678
   378
wenzelm@16678
   379
    fun arg 0 _ (Abs (_, T, _)) = T
wenzelm@16678
   380
      | arg i Ts (Abs (_, T, t)) = arg (i - 1) (T :: Ts) t
wenzelm@16678
   381
      | arg i Ts (t $ _) = arg (i + 1) Ts t
wenzelm@16678
   382
      | arg i Ts a = argT i (fastype_of1 (Ts, a));
wenzelm@16678
   383
  in arg 0 [] tm end;
wenzelm@16678
   384
clasohm@0
   385
wenzelm@19473
   386
val list_abs = uncurry (fold_rev (fn (x, T) => fn t => Abs (x, T, t)));
wenzelm@10806
   387
haftmann@18927
   388
fun strip_abs (Abs (a, T, t)) =
haftmann@18927
   389
      let val (a', t') = strip_abs t
haftmann@18927
   390
      in ((a, T) :: a', t') end
haftmann@18927
   391
  | strip_abs t = ([], t);
haftmann@18927
   392
clasohm@0
   393
(* maps  (x1,...,xn)t   to   t  *)
wenzelm@13000
   394
fun strip_abs_body (Abs(_,_,t))  =  strip_abs_body t
clasohm@0
   395
  | strip_abs_body u  =  u;
clasohm@0
   396
clasohm@0
   397
(* maps  (x1,...,xn)t   to   [x1, ..., xn]  *)
wenzelm@13000
   398
fun strip_abs_vars (Abs(a,T,t))  =  (a,T) :: strip_abs_vars t
clasohm@0
   399
  | strip_abs_vars u  =  [] : (string*typ) list;
clasohm@0
   400
clasohm@0
   401
clasohm@0
   402
fun strip_qnt_body qnt =
clasohm@0
   403
let fun strip(tm as Const(c,_)$Abs(_,_,t)) = if c=qnt then strip t else tm
clasohm@0
   404
      | strip t = t
clasohm@0
   405
in strip end;
clasohm@0
   406
clasohm@0
   407
fun strip_qnt_vars qnt =
clasohm@0
   408
let fun strip(Const(c,_)$Abs(a,T,t)) = if c=qnt then (a,T)::strip t else []
clasohm@0
   409
      | strip t  =  [] : (string*typ) list
clasohm@0
   410
in strip end;
clasohm@0
   411
clasohm@0
   412
clasohm@0
   413
(* maps   (f, [t1,...,tn])  to  f(t1,...,tn) *)
skalberg@15570
   414
val list_comb : term * term list -> term = Library.foldl (op $);
clasohm@0
   415
clasohm@0
   416
clasohm@0
   417
(* maps   f(t1,...,tn)  to  (f, [t1,...,tn]) ; naturally tail-recursive*)
wenzelm@13000
   418
fun strip_comb u : term * term list =
clasohm@0
   419
    let fun stripc (f$t, ts) = stripc (f, t::ts)
wenzelm@13000
   420
        |   stripc  x =  x
clasohm@0
   421
    in  stripc(u,[])  end;
clasohm@0
   422
clasohm@0
   423
clasohm@0
   424
(* maps   f(t1,...,tn)  to  f , which is never a combination *)
clasohm@0
   425
fun head_of (f$t) = head_of f
clasohm@0
   426
  | head_of u = u;
clasohm@0
   427
clasohm@0
   428
wenzelm@16599
   429
(*number of atoms and abstractions in a term*)
wenzelm@16599
   430
fun size_of_term tm =
wenzelm@16599
   431
  let
wenzelm@16678
   432
    fun add_size (t $ u, n) = add_size (t, add_size (u, n))
wenzelm@16678
   433
      | add_size (Abs (_ ,_, t), n) = add_size (t, n + 1)
wenzelm@16678
   434
      | add_size (_, n) = n + 1;
wenzelm@16678
   435
  in add_size (tm, 0) end;
clasohm@0
   436
haftmann@18847
   437
fun map_atyps f (Type (a, Ts)) = Type (a, map (map_atyps f) Ts)
haftmann@18976
   438
  | map_atyps f T = f T;
haftmann@18847
   439
haftmann@18847
   440
fun map_aterms f (t $ u) = map_aterms f t $ map_aterms f u
haftmann@18847
   441
  | map_aterms f (Abs (a, T, t)) = Abs (a, T, map_aterms f t)
haftmann@18847
   442
  | map_aterms f t = f t;
haftmann@18847
   443
wenzelm@18981
   444
fun map_type_tvar f = map_atyps (fn TVar x => f x | T => T);
wenzelm@18981
   445
fun map_type_tfree f = map_atyps (fn TFree x => f x | T => T);
nipkow@949
   446
clasohm@0
   447
fun map_term_types f =
wenzelm@16678
   448
  let
wenzelm@16678
   449
    fun map_aux (Const (a, T)) = Const (a, f T)
wenzelm@16678
   450
      | map_aux (Free (a, T)) = Free (a, f T)
wenzelm@16678
   451
      | map_aux (Var (v, T)) = Var (v, f T)
wenzelm@16678
   452
      | map_aux (t as Bound _)  = t
wenzelm@16678
   453
      | map_aux (Abs (a, T, t)) = Abs (a, f T, map_aux t)
wenzelm@16678
   454
      | map_aux (t $ u) = map_aux t $ map_aux u;
wenzelm@16678
   455
  in map_aux end;
clasohm@0
   456
clasohm@0
   457
(* iterate a function over all types in a term *)
clasohm@0
   458
fun it_term_types f =
clasohm@0
   459
let fun iter(Const(_,T), a) = f(T,a)
clasohm@0
   460
      | iter(Free(_,T), a) = f(T,a)
clasohm@0
   461
      | iter(Var(_,T), a) = f(T,a)
clasohm@0
   462
      | iter(Abs(_,T,t), a) = iter(t,f(T,a))
clasohm@0
   463
      | iter(f$u, a) = iter(f, iter(u, a))
clasohm@0
   464
      | iter(Bound _, a) = a
clasohm@0
   465
in iter end
clasohm@0
   466
clasohm@0
   467
wenzelm@16943
   468
(* fold types and terms *)
wenzelm@16943
   469
wenzelm@16943
   470
(*fold atoms of type*)
wenzelm@16943
   471
fun fold_atyps f (Type (_, Ts)) = fold (fold_atyps f) Ts
wenzelm@16943
   472
  | fold_atyps f T = f T;
wenzelm@16943
   473
wenzelm@16943
   474
(*fold atoms of term*)
wenzelm@16943
   475
fun fold_aterms f (t $ u) = fold_aterms f t #> fold_aterms f u
wenzelm@16943
   476
  | fold_aterms f (Abs (_, _, t)) = fold_aterms f t
wenzelm@16943
   477
  | fold_aterms f a = f a;
wenzelm@16943
   478
wenzelm@16943
   479
(*fold types of term*)
wenzelm@16943
   480
fun fold_term_types f (t as Const (_, T)) = f t T
wenzelm@16943
   481
  | fold_term_types f (t as Free (_, T)) = f t T
wenzelm@16943
   482
  | fold_term_types f (t as Var (_, T)) = f t T
wenzelm@16943
   483
  | fold_term_types f (Bound _) = I
wenzelm@16943
   484
  | fold_term_types f (t as Abs (_, T, b)) = f t T #> fold_term_types f b
wenzelm@16943
   485
  | fold_term_types f (t $ u) = fold_term_types f t #> fold_term_types f u;
wenzelm@16943
   486
wenzelm@16943
   487
fun fold_types f = fold_term_types (K f);
wenzelm@16943
   488
wenzelm@16943
   489
(*collect variables*)
wenzelm@16943
   490
val add_tvarsT = fold_atyps (fn TVar v => insert (op =) v | _ => I);
wenzelm@16943
   491
val add_tvars = fold_types add_tvarsT;
wenzelm@16943
   492
val add_vars = fold_aterms (fn Var v => insert (op =) v | _ => I);
wenzelm@16943
   493
val add_tfreesT = fold_atyps (fn TFree v => insert (op =) v | _ => I);
wenzelm@16943
   494
val add_tfrees = fold_types add_tfreesT;
wenzelm@16943
   495
val add_frees = fold_aterms (fn Free v => insert (op =) v | _ => I);
wenzelm@16943
   496
wenzelm@16943
   497
(*collect variable names*)
wenzelm@16943
   498
val add_term_varnames = fold_aterms (fn Var (xi, _) => insert (op =) xi | _ => I);
wenzelm@16943
   499
fun term_varnames t = add_term_varnames t [];
wenzelm@16943
   500
wenzelm@18149
   501
fun find_free t x =
wenzelm@18149
   502
  let
wenzelm@18149
   503
    exception Found of term;
wenzelm@18149
   504
    fun find (t as Free (x', _)) = if x = x' then raise Found t else I
wenzelm@18149
   505
      | find _ = I;
wenzelm@18149
   506
  in (fold_aterms find t (); NONE) handle Found v => SOME v end;
wenzelm@18149
   507
wenzelm@18149
   508
wenzelm@16943
   509
wenzelm@16678
   510
(** Comparing terms, types, sorts etc. **)
wenzelm@16537
   511
wenzelm@16678
   512
(* fast syntactic comparison *)
wenzelm@16678
   513
wenzelm@16678
   514
fun fast_indexname_ord ((x, i), (y, j)) =
wenzelm@16678
   515
  (case int_ord (i, j) of EQUAL => fast_string_ord (x, y) | ord => ord);
wenzelm@16537
   516
wenzelm@16599
   517
fun sort_ord SS =
wenzelm@16599
   518
  if pointer_eq SS then EQUAL
wenzelm@16990
   519
  else dict_ord fast_string_ord SS;
wenzelm@16678
   520
wenzelm@16678
   521
local
wenzelm@16537
   522
wenzelm@16678
   523
fun cons_nr (TVar _) = 0
wenzelm@16678
   524
  | cons_nr (TFree _) = 1
wenzelm@16678
   525
  | cons_nr (Type _) = 2;
wenzelm@16537
   526
wenzelm@16678
   527
in
wenzelm@16537
   528
wenzelm@16537
   529
fun typ_ord TU =
wenzelm@16537
   530
  if pointer_eq TU then EQUAL
wenzelm@16537
   531
  else
wenzelm@16537
   532
    (case TU of
wenzelm@16678
   533
      (Type (a, Ts), Type (b, Us)) =>
wenzelm@16990
   534
        (case fast_string_ord (a, b) of EQUAL => dict_ord typ_ord (Ts, Us) | ord => ord)
wenzelm@16678
   535
    | (TFree (a, S), TFree (b, S')) =>
wenzelm@16678
   536
        (case fast_string_ord (a, b) of EQUAL => sort_ord (S, S') | ord => ord)
wenzelm@16678
   537
    | (TVar (xi, S), TVar (yj, S')) =>
wenzelm@16678
   538
        (case fast_indexname_ord (xi, yj) of EQUAL => sort_ord (S, S') | ord => ord)
wenzelm@16678
   539
    | (T, U) => int_ord (cons_nr T, cons_nr U));
wenzelm@16678
   540
wenzelm@16678
   541
end;
wenzelm@16678
   542
wenzelm@16678
   543
local
wenzelm@16678
   544
wenzelm@16678
   545
fun cons_nr (Const _) = 0
wenzelm@16678
   546
  | cons_nr (Free _) = 1
wenzelm@16678
   547
  | cons_nr (Var _) = 2
wenzelm@16678
   548
  | cons_nr (Bound _) = 3
wenzelm@16678
   549
  | cons_nr (Abs _) = 4
wenzelm@16678
   550
  | cons_nr (_ $ _) = 5;
wenzelm@16678
   551
wenzelm@16678
   552
fun struct_ord (Abs (_, _, t), Abs (_, _, u)) = struct_ord (t, u)
wenzelm@16678
   553
  | struct_ord (t1 $ t2, u1 $ u2) =
wenzelm@16678
   554
      (case struct_ord (t1, u1) of EQUAL => struct_ord (t2, u2) | ord => ord)
wenzelm@16678
   555
  | struct_ord (t, u) = int_ord (cons_nr t, cons_nr u);
wenzelm@16678
   556
wenzelm@16678
   557
fun atoms_ord (Abs (_, _, t), Abs (_, _, u)) = atoms_ord (t, u)
wenzelm@16678
   558
  | atoms_ord (t1 $ t2, u1 $ u2) =
wenzelm@16678
   559
      (case atoms_ord (t1, u1) of EQUAL => atoms_ord (t2, u2) | ord => ord)
wenzelm@16678
   560
  | atoms_ord (Const (a, _), Const (b, _)) = fast_string_ord (a, b)
wenzelm@16678
   561
  | atoms_ord (Free (x, _), Free (y, _)) = fast_string_ord (x, y)
wenzelm@16678
   562
  | atoms_ord (Var (xi, _), Var (yj, _)) = fast_indexname_ord (xi, yj)
wenzelm@16678
   563
  | atoms_ord (Bound i, Bound j) = int_ord (i, j)
wenzelm@16678
   564
  | atoms_ord _ = sys_error "atoms_ord";
wenzelm@16678
   565
wenzelm@16678
   566
fun types_ord (Abs (_, T, t), Abs (_, U, u)) =
wenzelm@16678
   567
      (case typ_ord (T, U) of EQUAL => types_ord (t, u) | ord => ord)
wenzelm@16678
   568
  | types_ord (t1 $ t2, u1 $ u2) =
wenzelm@16678
   569
      (case types_ord (t1, u1) of EQUAL => types_ord (t2, u2) | ord => ord)
wenzelm@16678
   570
  | types_ord (Const (_, T), Const (_, U)) = typ_ord (T, U)
wenzelm@16678
   571
  | types_ord (Free (_, T), Free (_, U)) = typ_ord (T, U)
wenzelm@16678
   572
  | types_ord (Var (_, T), Var (_, U)) = typ_ord (T, U)
wenzelm@16678
   573
  | types_ord (Bound _, Bound _) = EQUAL
wenzelm@16678
   574
  | types_ord _ = sys_error "types_ord";
wenzelm@16678
   575
wenzelm@16678
   576
in
wenzelm@16678
   577
wenzelm@16678
   578
fun fast_term_ord tu =
wenzelm@16678
   579
  if pointer_eq tu then EQUAL
wenzelm@16678
   580
  else
wenzelm@16678
   581
    (case struct_ord tu of
wenzelm@16678
   582
      EQUAL => (case atoms_ord tu of EQUAL => types_ord tu | ord => ord)
wenzelm@16678
   583
    | ord => ord);
wenzelm@16678
   584
wenzelm@16678
   585
fun op aconv tu = (fast_term_ord tu = EQUAL);
wenzelm@16678
   586
fun aconvs ts_us = (list_ord fast_term_ord ts_us = EQUAL);
wenzelm@16678
   587
wenzelm@16678
   588
structure Vartab = TableFun(type key = indexname val ord = fast_indexname_ord);
wenzelm@16678
   589
structure Typtab = TableFun(type key = typ val ord = typ_ord);
wenzelm@16678
   590
structure Termtab = TableFun(type key = term val ord = fast_term_ord);
wenzelm@16678
   591
wenzelm@16678
   592
end;
wenzelm@16537
   593
wenzelm@16537
   594
wenzelm@16537
   595
(* term_ord *)
wenzelm@16537
   596
wenzelm@16537
   597
(*a linear well-founded AC-compatible ordering for terms:
wenzelm@16537
   598
  s < t <=> 1. size(s) < size(t) or
wenzelm@16537
   599
            2. size(s) = size(t) and s=f(...) and t=g(...) and f<g or
wenzelm@16537
   600
            3. size(s) = size(t) and s=f(s1..sn) and t=f(t1..tn) and
wenzelm@16537
   601
               (s1..sn) < (t1..tn) (lexicographically)*)
wenzelm@16678
   602
wenzelm@16678
   603
fun indexname_ord ((x, i), (y, j)) =
wenzelm@16678
   604
  (case int_ord (i, j) of EQUAL => string_ord (x, y) | ord => ord);
wenzelm@16678
   605
wenzelm@16667
   606
local
wenzelm@16667
   607
wenzelm@16667
   608
fun hd_depth (t $ _, n) = hd_depth (t, n + 1)
wenzelm@16667
   609
  | hd_depth p = p;
wenzelm@16537
   610
wenzelm@16537
   611
fun dest_hd (Const (a, T)) = (((a, 0), T), 0)
wenzelm@16537
   612
  | dest_hd (Free (a, T)) = (((a, 0), T), 1)
wenzelm@16537
   613
  | dest_hd (Var v) = (v, 2)
wenzelm@16537
   614
  | dest_hd (Bound i) = ((("", i), dummyT), 3)
wenzelm@16537
   615
  | dest_hd (Abs (_, T, _)) = ((("", 0), T), 4);
wenzelm@16537
   616
wenzelm@16667
   617
in
wenzelm@16667
   618
wenzelm@16537
   619
fun term_ord tu =
wenzelm@16537
   620
  if pointer_eq tu then EQUAL
wenzelm@16537
   621
  else
wenzelm@16537
   622
    (case tu of
wenzelm@16537
   623
      (Abs (_, T, t), Abs(_, U, u)) =>
wenzelm@16537
   624
        (case term_ord (t, u) of EQUAL => typ_ord (T, U) | ord => ord)
wenzelm@16667
   625
    | (t, u) =>
wenzelm@16537
   626
        (case int_ord (size_of_term t, size_of_term u) of
wenzelm@16537
   627
          EQUAL =>
wenzelm@16943
   628
            (case prod_ord hd_ord int_ord (hd_depth (t, 0), hd_depth (u, 0)) of
wenzelm@16943
   629
              EQUAL => args_ord (t, u) | ord => ord)
wenzelm@16537
   630
        | ord => ord))
wenzelm@16537
   631
and hd_ord (f, g) =
wenzelm@16537
   632
  prod_ord (prod_ord indexname_ord typ_ord) int_ord (dest_hd f, dest_hd g)
wenzelm@16667
   633
and args_ord (f $ t, g $ u) =
wenzelm@16667
   634
      (case args_ord (f, g) of EQUAL => term_ord (t, u) | ord => ord)
wenzelm@16667
   635
  | args_ord _ = EQUAL;
wenzelm@16537
   636
wenzelm@16537
   637
fun termless tu = (term_ord tu = LESS);
wenzelm@16537
   638
wenzelm@16667
   639
end;
wenzelm@16667
   640
wenzelm@16667
   641
wenzelm@16667
   642
(** Lexicographic path order on terms **)
wenzelm@16667
   643
wenzelm@16667
   644
(*
nipkow@16570
   645
  See Baader & Nipkow, Term rewriting, CUP 1998.
nipkow@16570
   646
  Without variables.  Const, Var, Bound, Free and Abs are treated all as
nipkow@16570
   647
  constants.
nipkow@16570
   648
nipkow@16570
   649
  f_ord maps strings to integers and serves two purposes:
nipkow@16570
   650
  - Predicate on constant symbols.  Those that are not recognised by f_ord
nipkow@16570
   651
    must be mapped to ~1.
nipkow@16570
   652
  - Order on the recognised symbols.  These must be mapped to distinct
nipkow@16570
   653
    integers >= 0.
nipkow@16570
   654
wenzelm@16667
   655
*)
nipkow@16570
   656
nipkow@16570
   657
local
wenzelm@16667
   658
fun dest_hd f_ord (Const (a, T)) =
nipkow@16570
   659
      let val ord = f_ord a in
nipkow@16570
   660
        if ord = ~1 then ((1, ((a, 0), T)), 0) else ((0, (("", ord), T)), 0)
nipkow@16570
   661
      end
nipkow@16570
   662
  | dest_hd _ (Free (a, T)) = ((1, ((a, 0), T)), 0)
nipkow@16570
   663
  | dest_hd _ (Var v) = ((1, v), 1)
nipkow@16570
   664
  | dest_hd _ (Bound i) = ((1, (("", i), dummyT)), 2)
nipkow@16570
   665
  | dest_hd _ (Abs (_, T, _)) = ((1, (("", 0), T)), 3);
nipkow@16570
   666
nipkow@16570
   667
fun term_lpo f_ord (s, t) =
nipkow@16570
   668
  let val (f, ss) = strip_comb s and (g, ts) = strip_comb t in
nipkow@16570
   669
    if forall (fn si => term_lpo f_ord (si, t) = LESS) ss
nipkow@16570
   670
    then case hd_ord f_ord (f, g) of
wenzelm@16667
   671
        GREATER =>
wenzelm@16667
   672
          if forall (fn ti => term_lpo f_ord (s, ti) = GREATER) ts
wenzelm@16667
   673
          then GREATER else LESS
nipkow@16570
   674
      | EQUAL =>
wenzelm@16667
   675
          if forall (fn ti => term_lpo f_ord (s, ti) = GREATER) ts
wenzelm@16667
   676
          then list_ord (term_lpo f_ord) (ss, ts)
wenzelm@16667
   677
          else LESS
nipkow@16570
   678
      | LESS => LESS
nipkow@16570
   679
    else GREATER
nipkow@16570
   680
  end
nipkow@16570
   681
and hd_ord f_ord (f, g) = case (f, g) of
nipkow@16570
   682
    (Abs (_, T, t), Abs (_, U, u)) =>
nipkow@16570
   683
      (case term_lpo f_ord (t, u) of EQUAL => typ_ord (T, U) | ord => ord)
nipkow@16570
   684
  | (_, _) => prod_ord (prod_ord int_ord
nipkow@16570
   685
                  (prod_ord indexname_ord typ_ord)) int_ord
nipkow@16570
   686
                (dest_hd f_ord f, dest_hd f_ord g)
nipkow@16570
   687
in
nipkow@16570
   688
val term_lpo = term_lpo
nipkow@16570
   689
end;
nipkow@16570
   690
wenzelm@16537
   691
clasohm@0
   692
(** Connectives of higher order logic **)
clasohm@0
   693
wenzelm@19394
   694
fun aT S = TFree ("'a", S);
wenzelm@19394
   695
wenzelm@375
   696
fun itselfT ty = Type ("itself", [ty]);
wenzelm@14854
   697
val a_itselfT = itselfT (TFree ("'a", []));
wenzelm@375
   698
clasohm@0
   699
val propT : typ = Type("prop",[]);
clasohm@0
   700
clasohm@0
   701
val implies = Const("==>", propT-->propT-->propT);
clasohm@0
   702
clasohm@0
   703
fun all T = Const("all", (T-->propT)-->propT);
clasohm@0
   704
clasohm@0
   705
fun equals T = Const("==", T-->T-->propT);
clasohm@0
   706
clasohm@0
   707
(* maps  !!x1...xn. t   to   t  *)
wenzelm@13000
   708
fun strip_all_body (Const("all",_)$Abs(_,_,t))  =  strip_all_body t
clasohm@0
   709
  | strip_all_body t  =  t;
clasohm@0
   710
clasohm@0
   711
(* maps  !!x1...xn. t   to   [x1, ..., xn]  *)
clasohm@0
   712
fun strip_all_vars (Const("all",_)$Abs(a,T,t))  =
wenzelm@13000
   713
                (a,T) :: strip_all_vars t
clasohm@0
   714
  | strip_all_vars t  =  [] : (string*typ) list;
clasohm@0
   715
clasohm@0
   716
(*increments a term's non-local bound variables
clasohm@0
   717
  required when moving a term within abstractions
clasohm@0
   718
     inc is  increment for bound variables
clasohm@0
   719
     lev is  level at which a bound variable is considered 'loose'*)
wenzelm@13000
   720
fun incr_bv (inc, lev, u as Bound i) = if i>=lev then Bound(i+inc) else u
clasohm@0
   721
  | incr_bv (inc, lev, Abs(a,T,body)) =
wenzelm@9536
   722
        Abs(a, T, incr_bv(inc,lev+1,body))
wenzelm@13000
   723
  | incr_bv (inc, lev, f$t) =
clasohm@0
   724
      incr_bv(inc,lev,f) $ incr_bv(inc,lev,t)
clasohm@0
   725
  | incr_bv (inc, lev, u) = u;
clasohm@0
   726
clasohm@0
   727
fun incr_boundvars  0  t = t
clasohm@0
   728
  | incr_boundvars inc t = incr_bv(inc,0,t);
clasohm@0
   729
wenzelm@12981
   730
(*Scan a pair of terms; while they are similar,
wenzelm@12981
   731
  accumulate corresponding bound vars in "al"*)
wenzelm@12981
   732
fun match_bvs(Abs(x,_,s),Abs(y,_,t), al) =
wenzelm@12981
   733
      match_bvs(s, t, if x="" orelse y="" then al
wenzelm@12981
   734
                                          else (x,y)::al)
wenzelm@12981
   735
  | match_bvs(f$s, g$t, al) = match_bvs(f,g,match_bvs(s,t,al))
wenzelm@12981
   736
  | match_bvs(_,_,al) = al;
wenzelm@12981
   737
wenzelm@12981
   738
(* strip abstractions created by parameters *)
wenzelm@12981
   739
fun match_bvars((s,t),al) = match_bvs(strip_abs_body s, strip_abs_body t, al);
wenzelm@12981
   740
wenzelm@12981
   741
fun rename_abs pat obj t =
wenzelm@12981
   742
  let
wenzelm@12981
   743
    val ren = match_bvs (pat, obj, []);
wenzelm@12981
   744
    fun ren_abs (Abs (x, T, b)) =
wenzelm@18942
   745
          Abs (the_default x (AList.lookup (op =) ren x), T, ren_abs b)
wenzelm@12981
   746
      | ren_abs (f $ t) = ren_abs f $ ren_abs t
wenzelm@12981
   747
      | ren_abs t = t
skalberg@15531
   748
  in if null ren then NONE else SOME (ren_abs t) end;
clasohm@0
   749
clasohm@0
   750
(*Accumulate all 'loose' bound vars referring to level 'lev' or beyond.
clasohm@0
   751
   (Bound 0) is loose at level 0 *)
wenzelm@13000
   752
fun add_loose_bnos (Bound i, lev, js) =
wenzelm@9536
   753
        if i<lev then js  else  (i-lev) ins_int js
clasohm@0
   754
  | add_loose_bnos (Abs (_,_,t), lev, js) = add_loose_bnos (t, lev+1, js)
clasohm@0
   755
  | add_loose_bnos (f$t, lev, js) =
wenzelm@13000
   756
        add_loose_bnos (f, lev, add_loose_bnos (t, lev, js))
clasohm@0
   757
  | add_loose_bnos (_, _, js) = js;
clasohm@0
   758
clasohm@0
   759
fun loose_bnos t = add_loose_bnos (t, 0, []);
clasohm@0
   760
clasohm@0
   761
(* loose_bvar(t,k) iff t contains a 'loose' bound variable referring to
clasohm@0
   762
   level k or beyond. *)
clasohm@0
   763
fun loose_bvar(Bound i,k) = i >= k
clasohm@0
   764
  | loose_bvar(f$t, k) = loose_bvar(f,k) orelse loose_bvar(t,k)
clasohm@0
   765
  | loose_bvar(Abs(_,_,t),k) = loose_bvar(t,k+1)
clasohm@0
   766
  | loose_bvar _ = false;
clasohm@0
   767
nipkow@2792
   768
fun loose_bvar1(Bound i,k) = i = k
nipkow@2792
   769
  | loose_bvar1(f$t, k) = loose_bvar1(f,k) orelse loose_bvar1(t,k)
nipkow@2792
   770
  | loose_bvar1(Abs(_,_,t),k) = loose_bvar1(t,k+1)
nipkow@2792
   771
  | loose_bvar1 _ = false;
clasohm@0
   772
clasohm@0
   773
(*Substitute arguments for loose bound variables.
clasohm@0
   774
  Beta-reduction of arg(n-1)...arg0 into t replacing (Bound i) with (argi).
wenzelm@4626
   775
  Note that for ((%x y. c) a b), the bound vars in c are x=1 and y=0
wenzelm@9536
   776
        and the appropriate call is  subst_bounds([b,a], c) .
clasohm@0
   777
  Loose bound variables >=n are reduced by "n" to
clasohm@0
   778
     compensate for the disappearance of lambdas.
clasohm@0
   779
*)
wenzelm@13000
   780
fun subst_bounds (args: term list, t) : term =
wenzelm@19065
   781
  let
wenzelm@19065
   782
    exception SAME;
wenzelm@19065
   783
    val n = length args;
wenzelm@19065
   784
    fun subst (t as Bound i, lev) =
wenzelm@19065
   785
         (if i < lev then raise SAME   (*var is locally bound*)
wenzelm@19065
   786
          else incr_boundvars lev (List.nth (args, i - lev))
wenzelm@19065
   787
            handle Subscript => Bound (i - n))  (*loose: change it*)
wenzelm@19065
   788
      | subst (Abs (a, T, body), lev) = Abs (a, T, subst (body, lev + 1))
wenzelm@19065
   789
      | subst (f $ t, lev) =
wenzelm@19065
   790
          (subst (f, lev) $ (subst (t, lev) handle SAME => t) handle SAME => f $ subst (t, lev))
wenzelm@19065
   791
      | subst _ = raise SAME;
wenzelm@19065
   792
  in case args of [] => t | _ => (subst (t, 0) handle SAME => t) end;
clasohm@0
   793
paulson@2192
   794
(*Special case: one argument*)
wenzelm@13000
   795
fun subst_bound (arg, t) : term =
wenzelm@19065
   796
  let
wenzelm@19065
   797
    exception SAME;
wenzelm@19065
   798
    fun subst (Bound i, lev) =
wenzelm@19065
   799
          if i < lev then raise SAME   (*var is locally bound*)
wenzelm@19065
   800
          else if i = lev then incr_boundvars lev arg
wenzelm@19065
   801
          else Bound (i - 1)   (*loose: change it*)
wenzelm@19065
   802
      | subst (Abs (a, T, body), lev) = Abs (a, T, subst (body, lev + 1))
wenzelm@19065
   803
      | subst (f $ t, lev) =
wenzelm@19065
   804
          (subst (f, lev) $ (subst (t, lev) handle SAME => t) handle SAME => f $ subst (t, lev))
wenzelm@19065
   805
      | subst _ = raise SAME;
wenzelm@19065
   806
  in subst (t, 0) handle SAME => t end;
paulson@2192
   807
clasohm@0
   808
(*beta-reduce if possible, else form application*)
paulson@2192
   809
fun betapply (Abs(_,_,t), u) = subst_bound (u,t)
clasohm@0
   810
  | betapply (f,u) = f$u;
clasohm@0
   811
wenzelm@18183
   812
val betapplys = Library.foldl betapply;
wenzelm@18183
   813
wenzelm@14786
   814
haftmann@20109
   815
(*unfolding abstractions with substitution
haftmann@20109
   816
  of bound variables and implicit eta-expansion*)
haftmann@20109
   817
fun strip_abs_eta k t =
haftmann@20109
   818
  let
haftmann@20109
   819
    val used = fold_aterms (fn Free (v, _) => cons v | _ => I) t [];
haftmann@20109
   820
    fun strip_abs t (0, used) = (([], t), (0, used))
haftmann@20109
   821
      | strip_abs (Abs (v, T, t)) (k, used) =
haftmann@20109
   822
          let
haftmann@20109
   823
            val v' = Name.variant used v;
haftmann@20109
   824
            val t' = subst_bound (Free (v, T), t);
haftmann@20109
   825
            val ((vs, t''), (k', used')) = strip_abs t' (k - 1, v' :: used);
haftmann@20109
   826
          in (((v', T) :: vs, t''), (k', used')) end
haftmann@20109
   827
      | strip_abs t (k, used) = (([], t), (k, used));
haftmann@20109
   828
    fun expand_eta [] t _ = ([], t)
haftmann@20109
   829
      | expand_eta (T::Ts) t used =
haftmann@20109
   830
          let
haftmann@20109
   831
            val v = hd (Name.invent_list used "a" 1)
haftmann@20109
   832
            val (vs, t') = expand_eta Ts (t $ Free (v, T)) (v :: used);
haftmann@20109
   833
          in ((v, T) :: vs, t') end;
haftmann@20109
   834
    val ((vs1, t'), (k', used')) = strip_abs t (k, used);
haftmann@20109
   835
    val Ts = (fst o chop k' o fst o strip_type o fastype_of) t';
haftmann@20109
   836
    val (vs2, t'') = expand_eta Ts t' used';
haftmann@20109
   837
  in (vs1 @ vs2, t'') end;
haftmann@20109
   838
haftmann@20109
   839
wenzelm@16882
   840
(** Specialized equality, membership, insertion etc. **)
paulson@2192
   841
wenzelm@20082
   842
(* variables *)
wenzelm@16882
   843
wenzelm@16724
   844
fun eq_ix ((x, i): indexname, (y, j)) = i = j andalso x = y;
paulson@2192
   845
wenzelm@16943
   846
fun eq_tvar ((xi, S: sort), (xi', S')) = eq_ix (xi, xi') andalso S = S';
wenzelm@16943
   847
fun eq_var ((xi, T: typ), (xi', T')) = eq_ix (xi, xi') andalso T = T';
wenzelm@16943
   848
wenzelm@16943
   849
val tvar_ord = prod_ord indexname_ord sort_ord;
wenzelm@16943
   850
val var_ord = prod_ord indexname_ord typ_ord;
wenzelm@16882
   851
wenzelm@16882
   852
wenzelm@13000
   853
(*A fast unification filter: true unless the two terms cannot be unified.
clasohm@0
   854
  Terms must be NORMAL.  Treats all Vars as distinct. *)
clasohm@0
   855
fun could_unify (t,u) =
clasohm@0
   856
  let fun matchrands (f$t, g$u) = could_unify(t,u) andalso  matchrands(f,g)
wenzelm@9536
   857
        | matchrands _ = true
clasohm@0
   858
  in case (head_of t , head_of u) of
wenzelm@9536
   859
        (_, Var _) => true
clasohm@0
   860
      | (Var _, _) => true
clasohm@0
   861
      | (Const(a,_), Const(b,_)) =>  a=b andalso matchrands(t,u)
clasohm@0
   862
      | (Free(a,_), Free(b,_)) =>  a=b andalso matchrands(t,u)
clasohm@0
   863
      | (Bound i, Bound j) =>  i=j andalso matchrands(t,u)
clasohm@0
   864
      | (Abs _, _) =>  true   (*because of possible eta equality*)
clasohm@0
   865
      | (_, Abs _) =>  true
clasohm@0
   866
      | _ => false
clasohm@0
   867
  end;
clasohm@0
   868
clasohm@0
   869
(*Substitute new for free occurrences of old in a term*)
clasohm@0
   870
fun subst_free [] = (fn t=>t)
clasohm@0
   871
  | subst_free pairs =
wenzelm@13000
   872
      let fun substf u =
haftmann@17314
   873
            case AList.lookup (op aconv) pairs u of
skalberg@15531
   874
                SOME u' => u'
skalberg@15531
   875
              | NONE => (case u of Abs(a,T,t) => Abs(a, T, substf t)
wenzelm@9536
   876
                                 | t$u' => substf t $ substf u'
wenzelm@9536
   877
                                 | _ => u)
clasohm@0
   878
      in  substf  end;
clasohm@0
   879
wenzelm@13000
   880
(*Abstraction of the term "body" over its occurrences of v,
clasohm@0
   881
    which must contain no loose bound variables.
clasohm@0
   882
  The resulting term is ready to become the body of an Abs.*)
wenzelm@16882
   883
fun abstract_over (v, body) =
wenzelm@16882
   884
  let
wenzelm@16990
   885
    exception SAME;
wenzelm@16990
   886
    fun abs lev tm =
wenzelm@16990
   887
      if v aconv tm then Bound lev
wenzelm@16882
   888
      else
wenzelm@16990
   889
        (case tm of
wenzelm@16990
   890
          Abs (a, T, t) => Abs (a, T, abs (lev + 1) t)
wenzelm@16990
   891
        | t $ u => (abs lev t $ (abs lev u handle SAME => u) handle SAME => t $ abs lev u)
wenzelm@16990
   892
        | _ => raise SAME);
wenzelm@16990
   893
  in abs 0 body handle SAME => body end;
clasohm@0
   894
wenzelm@18975
   895
fun lambda (v as Const (x, T)) t = Abs (NameSpace.base x, T, abstract_over (v, t))
wenzelm@18942
   896
  | lambda (v as Free (x, T)) t = Abs (x, T, abstract_over (v, t))
berghofe@13665
   897
  | lambda (v as Var ((x, _), T)) t = Abs (x, T, abstract_over (v, t))
berghofe@13665
   898
  | lambda v t = raise TERM ("lambda", [v, t]);
clasohm@0
   899
clasohm@0
   900
(*Form an abstraction over a free variable.*)
clasohm@0
   901
fun absfree (a,T,body) = Abs(a, T, abstract_over (Free(a,T), body));
wenzelm@17786
   902
fun absdummy (T, body) = Abs ("uu", T, body);
clasohm@0
   903
clasohm@0
   904
(*Abstraction over a list of free variables*)
clasohm@0
   905
fun list_abs_free ([ ] ,     t) = t
wenzelm@13000
   906
  | list_abs_free ((a,T)::vars, t) =
clasohm@0
   907
      absfree(a, T, list_abs_free(vars,t));
clasohm@0
   908
clasohm@0
   909
(*Quantification over a list of free variables*)
clasohm@0
   910
fun list_all_free ([], t: term) = t
wenzelm@13000
   911
  | list_all_free ((a,T)::vars, t) =
clasohm@0
   912
        (all T) $ (absfree(a, T, list_all_free(vars,t)));
clasohm@0
   913
clasohm@0
   914
(*Quantification over a list of variables (already bound in body) *)
clasohm@0
   915
fun list_all ([], t) = t
wenzelm@13000
   916
  | list_all ((a,T)::vars, t) =
clasohm@0
   917
        (all T) $ (Abs(a, T, list_all(vars,t)));
clasohm@0
   918
wenzelm@16678
   919
(*Replace the ATOMIC term ti by ui;    inst = [(t1,u1), ..., (tn,un)].
clasohm@0
   920
  A simultaneous substitution:  [ (a,b), (b,a) ] swaps a and b.  *)
wenzelm@16678
   921
fun subst_atomic [] tm = tm
wenzelm@16678
   922
  | subst_atomic inst tm =
wenzelm@16678
   923
      let
wenzelm@16678
   924
        fun subst (Abs (a, T, body)) = Abs (a, T, subst body)
wenzelm@16678
   925
          | subst (t $ u) = subst t $ subst u
wenzelm@18942
   926
          | subst t = the_default t (AList.lookup (op aconv) inst t);
wenzelm@16678
   927
      in subst tm end;
clasohm@0
   928
wenzelm@16678
   929
(*Replace the ATOMIC type Ti by Ui;    inst = [(T1,U1), ..., (Tn,Un)].*)
wenzelm@16678
   930
fun typ_subst_atomic [] ty = ty
wenzelm@16678
   931
  | typ_subst_atomic inst ty =
wenzelm@16678
   932
      let
wenzelm@16678
   933
        fun subst (Type (a, Ts)) = Type (a, map subst Ts)
wenzelm@18942
   934
          | subst T = the_default T (AList.lookup (op = : typ * typ -> bool) inst T);
wenzelm@16678
   935
      in subst ty end;
berghofe@15797
   936
wenzelm@16678
   937
fun subst_atomic_types [] tm = tm
wenzelm@16678
   938
  | subst_atomic_types inst tm = map_term_types (typ_subst_atomic inst) tm;
wenzelm@16678
   939
wenzelm@16678
   940
fun typ_subst_TVars [] ty = ty
wenzelm@16678
   941
  | typ_subst_TVars inst ty =
wenzelm@16678
   942
      let
wenzelm@16678
   943
        fun subst (Type (a, Ts)) = Type (a, map subst Ts)
wenzelm@18942
   944
          | subst (T as TVar (xi, _)) = the_default T (AList.lookup (op =) inst xi)
wenzelm@16678
   945
          | subst T = T;
wenzelm@16678
   946
      in subst ty end;
clasohm@0
   947
wenzelm@16678
   948
fun subst_TVars [] tm = tm
wenzelm@16678
   949
  | subst_TVars inst tm = map_term_types (typ_subst_TVars inst) tm;
clasohm@0
   950
wenzelm@16678
   951
fun subst_Vars [] tm = tm
wenzelm@16678
   952
  | subst_Vars inst tm =
wenzelm@16678
   953
      let
wenzelm@18942
   954
        fun subst (t as Var (xi, _)) = the_default t (AList.lookup (op =) inst xi)
wenzelm@16678
   955
          | subst (Abs (a, T, t)) = Abs (a, T, subst t)
wenzelm@16678
   956
          | subst (t $ u) = subst t $ subst u
wenzelm@16678
   957
          | subst t = t;
wenzelm@16678
   958
      in subst tm end;
clasohm@0
   959
wenzelm@16678
   960
fun subst_vars ([], []) tm = tm
wenzelm@16678
   961
  | subst_vars ([], inst) tm = subst_Vars inst tm
wenzelm@16678
   962
  | subst_vars (instT, inst) tm =
wenzelm@16678
   963
      let
wenzelm@16678
   964
        fun subst (Const (a, T)) = Const (a, typ_subst_TVars instT T)
wenzelm@16678
   965
          | subst (Free (a, T)) = Free (a, typ_subst_TVars instT T)
wenzelm@16678
   966
          | subst (t as Var (xi, T)) =
haftmann@17271
   967
              (case AList.lookup (op =) inst xi of
wenzelm@16678
   968
                NONE => Var (xi, typ_subst_TVars instT T)
wenzelm@16678
   969
              | SOME t => t)
wenzelm@16678
   970
          | subst (t as Bound _) = t
wenzelm@16678
   971
          | subst (Abs (a, T, t)) = Abs (a, typ_subst_TVars instT T, subst t)
wenzelm@16678
   972
          | subst (t $ u) = subst t $ subst u;
wenzelm@16678
   973
      in subst tm end;
clasohm@0
   974
clasohm@0
   975
wenzelm@19909
   976
(* generalization of fixed variables *)
wenzelm@19909
   977
wenzelm@19909
   978
local exception SAME in
wenzelm@19909
   979
wenzelm@19909
   980
fun generalizeT_same [] _ _ = raise SAME
wenzelm@19909
   981
  | generalizeT_same tfrees idx ty =
wenzelm@19909
   982
      let
wenzelm@19909
   983
        fun gen_typ (Type (a, Ts)) = Type (a, gen_typs Ts)
wenzelm@19909
   984
          | gen_typ (TFree (a, S)) =
wenzelm@19909
   985
              if member (op =) tfrees a then TVar ((a, idx), S)
wenzelm@19909
   986
              else raise SAME
wenzelm@19909
   987
          | gen_typ _ = raise SAME
wenzelm@19909
   988
        and gen_typs (T :: Ts) =
wenzelm@19909
   989
            (gen_typ T :: (gen_typs Ts handle SAME => Ts)
wenzelm@19909
   990
              handle SAME => T :: gen_typs Ts)
wenzelm@19909
   991
          | gen_typs [] = raise SAME;
wenzelm@19909
   992
      in gen_typ ty end;
wenzelm@19909
   993
wenzelm@20001
   994
fun generalize_same ([], []) _ _ = raise SAME
wenzelm@20001
   995
  | generalize_same (tfrees, frees) idx tm =
wenzelm@19909
   996
      let
wenzelm@19909
   997
        val genT = generalizeT_same tfrees idx;
wenzelm@19909
   998
        fun gen (Free (x, T)) =
wenzelm@20082
   999
              if member (op =) frees x then
wenzelm@20082
  1000
                Var (Name.clean_index (x, idx), genT T handle SAME => T)
wenzelm@19909
  1001
              else Free (x, genT T)
wenzelm@19909
  1002
          | gen (Var (xi, T)) = Var (xi, genT T)
wenzelm@19909
  1003
          | gen (Const (c, T)) = Const (c, genT T)
wenzelm@19909
  1004
          | gen (Bound _) = raise SAME
wenzelm@19909
  1005
          | gen (Abs (x, T, t)) =
wenzelm@19909
  1006
              (Abs (x, genT T, gen t handle SAME => t)
wenzelm@19909
  1007
                handle SAME => Abs (x, T, gen t))
wenzelm@19909
  1008
          | gen (t $ u) = (gen t $ (gen u handle SAME => u) handle SAME => t $ gen u);
wenzelm@20001
  1009
      in gen tm end;
wenzelm@19909
  1010
wenzelm@20001
  1011
fun generalize names i tm = generalize_same names i tm handle SAME => tm;
wenzelm@20001
  1012
fun generalizeT names i ty = generalizeT_same names i ty handle SAME => ty;
wenzelm@20001
  1013
wenzelm@20001
  1014
fun generalize_option names i tm = SOME (generalize_same names i tm) handle SAME => NONE;
wenzelm@20001
  1015
fun generalizeT_option names i ty = SOME (generalizeT_same names i ty) handle SAME => NONE;
wenzelm@19909
  1016
wenzelm@19909
  1017
end;
wenzelm@19909
  1018
wenzelm@19909
  1019
wenzelm@16943
  1020
(* instantiation of schematic variables (types before terms) *)
wenzelm@16882
  1021
wenzelm@16882
  1022
local exception SAME in
wenzelm@16882
  1023
wenzelm@16943
  1024
fun instantiateT_same [] _ = raise SAME
wenzelm@16943
  1025
  | instantiateT_same instT ty =
wenzelm@16882
  1026
      let
wenzelm@16882
  1027
        fun subst_typ (Type (a, Ts)) = Type (a, subst_typs Ts)
wenzelm@16882
  1028
          | subst_typ (TVar v) =
haftmann@17314
  1029
              (case AList.lookup eq_tvar instT v of
wenzelm@16882
  1030
                SOME T => T
wenzelm@16882
  1031
              | NONE => raise SAME)
wenzelm@16882
  1032
          | subst_typ _ = raise SAME
wenzelm@16882
  1033
        and subst_typs (T :: Ts) =
wenzelm@16882
  1034
            (subst_typ T :: (subst_typs Ts handle SAME => Ts)
wenzelm@16882
  1035
              handle SAME => T :: subst_typs Ts)
wenzelm@16882
  1036
          | subst_typs [] = raise SAME;
wenzelm@16882
  1037
      in subst_typ ty end;
wenzelm@16882
  1038
wenzelm@20001
  1039
fun instantiate_same ([], []) _ = raise SAME
wenzelm@20001
  1040
  | instantiate_same (instT, inst) tm =
wenzelm@16882
  1041
      let
wenzelm@16943
  1042
        val substT = instantiateT_same instT;
wenzelm@16943
  1043
        fun subst (Const (c, T)) = Const (c, substT T)
wenzelm@16943
  1044
          | subst (Free (x, T)) = Free (x, substT T)
wenzelm@16882
  1045
          | subst (Var (xi, T)) =
wenzelm@16943
  1046
              let val (T', same) = (substT T, false) handle SAME => (T, true) in
haftmann@17314
  1047
                (case AList.lookup eq_var inst (xi, T') of
wenzelm@16882
  1048
                   SOME t => t
wenzelm@16882
  1049
                 | NONE => if same then raise SAME else Var (xi, T'))
wenzelm@16882
  1050
              end
wenzelm@16882
  1051
          | subst (Bound _) = raise SAME
wenzelm@16882
  1052
          | subst (Abs (x, T, t)) =
wenzelm@16943
  1053
              (Abs (x, substT T, subst t handle SAME => t)
wenzelm@16882
  1054
                handle SAME => Abs (x, T, subst t))
wenzelm@16882
  1055
          | subst (t $ u) = (subst t $ (subst u handle SAME => u) handle SAME => t $ subst u);
wenzelm@20001
  1056
      in subst tm end;
wenzelm@16882
  1057
wenzelm@20001
  1058
fun instantiate insts tm = instantiate_same insts tm handle SAME => tm;
wenzelm@20001
  1059
fun instantiateT insts ty = instantiateT_same insts ty handle SAME => ty;
wenzelm@20001
  1060
wenzelm@20001
  1061
fun instantiate_option insts tm = SOME (instantiate_same insts tm) handle SAME => NONE;
wenzelm@20001
  1062
fun instantiateT_option insts ty = SOME (instantiateT_same insts ty) handle SAME => NONE;
wenzelm@16882
  1063
wenzelm@16882
  1064
end;
wenzelm@16882
  1065
wenzelm@16882
  1066
paulson@15573
  1067
(** Identifying first-order terms **)
paulson@15573
  1068
paulson@15573
  1069
(*Argument Ts is a reverse list of binder types, needed if term t contains Bound vars*)
paulson@15573
  1070
fun has_not_funtype Ts t = not (is_funtype (fastype_of1 (Ts,t)));
paulson@15573
  1071
wenzelm@16537
  1072
(*First order means in all terms of the form f(t1,...,tn) no argument has a
paulson@16589
  1073
  function type. The supplied quantifiers are excluded: their argument always
paulson@16589
  1074
  has a function type through a recursive call into its body.*)
wenzelm@16667
  1075
fun is_first_order quants =
paulson@16589
  1076
  let fun first_order1 Ts (Abs (_,T,body)) = first_order1 (T::Ts) body
wenzelm@16667
  1077
        | first_order1 Ts (Const(q,_) $ Abs(a,T,body)) =
wenzelm@16667
  1078
            q mem_string quants  andalso   (*it is a known quantifier*)
paulson@16589
  1079
            not (is_funtype T)   andalso first_order1 (T::Ts) body
wenzelm@16667
  1080
        | first_order1 Ts t =
wenzelm@16667
  1081
            case strip_comb t of
wenzelm@16667
  1082
                 (Var _, ts) => forall (first_order1 Ts andf has_not_funtype Ts) ts
wenzelm@16667
  1083
               | (Free _, ts) => forall (first_order1 Ts andf has_not_funtype Ts) ts
wenzelm@16667
  1084
               | (Const _, ts) => forall (first_order1 Ts andf has_not_funtype Ts) ts
wenzelm@16667
  1085
               | (Bound _, ts) => forall (first_order1 Ts andf has_not_funtype Ts) ts
wenzelm@16667
  1086
               | (Abs _, ts) => false (*not in beta-normal form*)
wenzelm@16667
  1087
               | _ => error "first_order: unexpected case"
paulson@16589
  1088
    in  first_order1 []  end;
paulson@15573
  1089
wenzelm@16710
  1090
wenzelm@16990
  1091
(* maximum index of typs and terms *)
clasohm@0
  1092
wenzelm@16710
  1093
fun maxidx_typ (TVar ((_, j), _)) i = Int.max (i, j)
wenzelm@16710
  1094
  | maxidx_typ (Type (_, Ts)) i = maxidx_typs Ts i
wenzelm@16710
  1095
  | maxidx_typ (TFree _) i = i
wenzelm@16710
  1096
and maxidx_typs [] i = i
wenzelm@16710
  1097
  | maxidx_typs (T :: Ts) i = maxidx_typs Ts (maxidx_typ T i);
clasohm@0
  1098
wenzelm@16710
  1099
fun maxidx_term (Var ((_, j), T)) i = maxidx_typ T (Int.max (i, j))
wenzelm@16710
  1100
  | maxidx_term (Const (_, T)) i = maxidx_typ T i
wenzelm@16710
  1101
  | maxidx_term (Free (_, T)) i = maxidx_typ T i
wenzelm@16710
  1102
  | maxidx_term (Bound _) i = i
wenzelm@16710
  1103
  | maxidx_term (Abs (_, T, t)) i = maxidx_term t (maxidx_typ T i)
wenzelm@16710
  1104
  | maxidx_term (t $ u) i = maxidx_term u (maxidx_term t i);
clasohm@0
  1105
wenzelm@16710
  1106
fun maxidx_of_typ T = maxidx_typ T ~1;
wenzelm@16710
  1107
fun maxidx_of_typs Ts = maxidx_typs Ts ~1;
wenzelm@16710
  1108
fun maxidx_of_term t = maxidx_term t ~1;
berghofe@13665
  1109
clasohm@0
  1110
clasohm@0
  1111
clasohm@0
  1112
(**** Syntax-related declarations ****)
clasohm@0
  1113
wenzelm@19909
  1114
(* substructure *)
wenzelm@4017
  1115
wenzelm@19909
  1116
fun exists_subtype P =
wenzelm@19909
  1117
  let
wenzelm@19909
  1118
    fun ex ty = P ty orelse
wenzelm@19909
  1119
      (case ty of Type (_, Ts) => exists ex Ts | _ => false);
wenzelm@19909
  1120
  in ex end;
nipkow@13646
  1121
wenzelm@16943
  1122
fun exists_subterm P =
wenzelm@16943
  1123
  let
wenzelm@16943
  1124
    fun ex tm = P tm orelse
wenzelm@16943
  1125
      (case tm of
wenzelm@16943
  1126
        t $ u => ex t orelse ex u
wenzelm@16943
  1127
      | Abs (_, _, t) => ex t
wenzelm@16943
  1128
      | _ => false);
wenzelm@16943
  1129
  in ex end;
obua@16108
  1130
wenzelm@19909
  1131
wenzelm@19909
  1132
(** Consts etc. **)
wenzelm@19909
  1133
wenzelm@19909
  1134
fun add_term_consts (Const (c, _), cs) = insert (op =) c cs
wenzelm@19909
  1135
  | add_term_consts (t $ u, cs) = add_term_consts (t, add_term_consts (u, cs))
wenzelm@19909
  1136
  | add_term_consts (Abs (_, _, t), cs) = add_term_consts (t, cs)
wenzelm@19909
  1137
  | add_term_consts (_, cs) = cs;
wenzelm@19909
  1138
wenzelm@19909
  1139
fun term_consts t = add_term_consts(t,[]);
wenzelm@19909
  1140
wenzelm@16943
  1141
fun exists_Const P = exists_subterm (fn Const c => P c | _ => false);
nipkow@4631
  1142
wenzelm@4017
  1143
clasohm@0
  1144
(** TFrees and TVars **)
clasohm@0
  1145
wenzelm@12802
  1146
(*Accumulates the names of Frees in the term, suppressing duplicates.*)
wenzelm@12802
  1147
fun add_term_free_names (Free(a,_), bs) = a ins_string bs
wenzelm@12802
  1148
  | add_term_free_names (f$u, bs) = add_term_free_names (f, add_term_free_names(u, bs))
wenzelm@12802
  1149
  | add_term_free_names (Abs(_,_,t), bs) = add_term_free_names(t,bs)
wenzelm@12802
  1150
  | add_term_free_names (_, bs) = bs;
wenzelm@12802
  1151
clasohm@0
  1152
(*Accumulates the names in the term, suppressing duplicates.
clasohm@0
  1153
  Includes Frees and Consts.  For choosing unambiguous bound var names.*)
wenzelm@10666
  1154
fun add_term_names (Const(a,_), bs) = NameSpace.base a ins_string bs
paulson@2176
  1155
  | add_term_names (Free(a,_), bs) = a ins_string bs
clasohm@0
  1156
  | add_term_names (f$u, bs) = add_term_names (f, add_term_names(u, bs))
clasohm@0
  1157
  | add_term_names (Abs(_,_,t), bs) = add_term_names(t,bs)
clasohm@0
  1158
  | add_term_names (_, bs) = bs;
clasohm@0
  1159
clasohm@0
  1160
(*Accumulates the TVars in a type, suppressing duplicates. *)
skalberg@15574
  1161
fun add_typ_tvars(Type(_,Ts),vs) = foldr add_typ_tvars vs Ts
clasohm@0
  1162
  | add_typ_tvars(TFree(_),vs) = vs
wenzelm@16294
  1163
  | add_typ_tvars(TVar(v),vs) = insert (op =) v vs;
clasohm@0
  1164
clasohm@0
  1165
(*Accumulates the TFrees in a type, suppressing duplicates. *)
skalberg@15574
  1166
fun add_typ_tfree_names(Type(_,Ts),fs) = foldr add_typ_tfree_names fs Ts
paulson@2176
  1167
  | add_typ_tfree_names(TFree(f,_),fs) = f ins_string fs
clasohm@0
  1168
  | add_typ_tfree_names(TVar(_),fs) = fs;
clasohm@0
  1169
skalberg@15574
  1170
fun add_typ_tfrees(Type(_,Ts),fs) = foldr add_typ_tfrees fs Ts
wenzelm@16294
  1171
  | add_typ_tfrees(TFree(f),fs) = insert (op =) f fs
clasohm@0
  1172
  | add_typ_tfrees(TVar(_),fs) = fs;
clasohm@0
  1173
skalberg@15574
  1174
fun add_typ_varnames(Type(_,Ts),nms) = foldr add_typ_varnames nms Ts
paulson@2176
  1175
  | add_typ_varnames(TFree(nm,_),nms) = nm ins_string nms
paulson@2176
  1176
  | add_typ_varnames(TVar((nm,_),_),nms) = nm ins_string nms;
nipkow@949
  1177
clasohm@0
  1178
(*Accumulates the TVars in a term, suppressing duplicates. *)
clasohm@0
  1179
val add_term_tvars = it_term_types add_typ_tvars;
clasohm@0
  1180
clasohm@0
  1181
(*Accumulates the TFrees in a term, suppressing duplicates. *)
clasohm@0
  1182
val add_term_tfrees = it_term_types add_typ_tfrees;
clasohm@0
  1183
val add_term_tfree_names = it_term_types add_typ_tfree_names;
clasohm@0
  1184
nipkow@949
  1185
val add_term_tvarnames = it_term_types add_typ_varnames;
nipkow@949
  1186
clasohm@0
  1187
(*Non-list versions*)
clasohm@0
  1188
fun typ_tfrees T = add_typ_tfrees(T,[]);
clasohm@0
  1189
fun typ_tvars T = add_typ_tvars(T,[]);
clasohm@0
  1190
fun term_tfrees t = add_term_tfrees(t,[]);
clasohm@0
  1191
fun term_tvars t = add_term_tvars(t,[]);
clasohm@0
  1192
nipkow@949
  1193
(*special code to enforce left-to-right collection of TVar-indexnames*)
nipkow@949
  1194
skalberg@15570
  1195
fun add_typ_ixns(ixns,Type(_,Ts)) = Library.foldl add_typ_ixns (ixns,Ts)
wenzelm@20082
  1196
  | add_typ_ixns(ixns,TVar(ixn,_)) = if member (op =) ixns ixn then ixns
wenzelm@9536
  1197
                                     else ixns@[ixn]
nipkow@949
  1198
  | add_typ_ixns(ixns,TFree(_)) = ixns;
nipkow@949
  1199
nipkow@949
  1200
fun add_term_tvar_ixns(Const(_,T),ixns) = add_typ_ixns(ixns,T)
nipkow@949
  1201
  | add_term_tvar_ixns(Free(_,T),ixns) = add_typ_ixns(ixns,T)
nipkow@949
  1202
  | add_term_tvar_ixns(Var(_,T),ixns) = add_typ_ixns(ixns,T)
nipkow@949
  1203
  | add_term_tvar_ixns(Bound _,ixns) = ixns
nipkow@949
  1204
  | add_term_tvar_ixns(Abs(_,T,t),ixns) =
nipkow@949
  1205
      add_term_tvar_ixns(t,add_typ_ixns(ixns,T))
nipkow@949
  1206
  | add_term_tvar_ixns(f$t,ixns) =
nipkow@949
  1207
      add_term_tvar_ixns(t,add_term_tvar_ixns(f,ixns));
nipkow@949
  1208
wenzelm@16537
  1209
clasohm@0
  1210
(** Frees and Vars **)
clasohm@0
  1211
clasohm@0
  1212
(*Accumulates the Vars in the term, suppressing duplicates*)
clasohm@0
  1213
fun add_term_vars (t, vars: term list) = case t of
wenzelm@16990
  1214
    Var   _ => OrdList.insert term_ord t vars
clasohm@0
  1215
  | Abs (_,_,body) => add_term_vars(body,vars)
clasohm@0
  1216
  | f$t =>  add_term_vars (f, add_term_vars(t, vars))
clasohm@0
  1217
  | _ => vars;
clasohm@0
  1218
clasohm@0
  1219
fun term_vars t = add_term_vars(t,[]);
clasohm@0
  1220
clasohm@0
  1221
(*Accumulates the Frees in the term, suppressing duplicates*)
clasohm@0
  1222
fun add_term_frees (t, frees: term list) = case t of
wenzelm@16990
  1223
    Free   _ => OrdList.insert term_ord t frees
clasohm@0
  1224
  | Abs (_,_,body) => add_term_frees(body,frees)
clasohm@0
  1225
  | f$t =>  add_term_frees (f, add_term_frees(t, frees))
clasohm@0
  1226
  | _ => frees;
clasohm@0
  1227
clasohm@0
  1228
fun term_frees t = add_term_frees(t,[]);
clasohm@0
  1229
clasohm@0
  1230
(*Given an abstraction over P, replaces the bound variable by a Free variable
wenzelm@17851
  1231
  having a unique name -- SLOW!*)
clasohm@0
  1232
fun variant_abs (a,T,P) =
wenzelm@20082
  1233
  let val b = Name.variant (add_term_names(P,[])) a
paulson@2192
  1234
  in  (b,  subst_bound (Free(b,T), P))  end;
clasohm@0
  1235
wenzelm@16678
  1236
fun dest_abs (x, T, body) =
wenzelm@16678
  1237
  let
wenzelm@16678
  1238
    fun name_clash (Free (y, _)) = (x = y)
wenzelm@16678
  1239
      | name_clash (t $ u) = name_clash t orelse name_clash u
wenzelm@16678
  1240
      | name_clash (Abs (_, _, t)) = name_clash t
wenzelm@16678
  1241
      | name_clash _ = false;
wenzelm@16678
  1242
  in
wenzelm@16678
  1243
    if name_clash body then
wenzelm@20082
  1244
      dest_abs (Name.variant [x] x, T, body)    (*potentially slow, but rarely happens*)
wenzelm@16678
  1245
    else (x, subst_bound (Free (x, T), body))
wenzelm@16678
  1246
  end;
wenzelm@16678
  1247
clasohm@0
  1248
(* renames and reverses the strings in vars away from names *)
clasohm@0
  1249
fun rename_aTs names vars : (string*typ)list =
clasohm@0
  1250
  let fun rename_aT (vars,(a,T)) =
wenzelm@20082
  1251
                (Name.variant (map #1 vars @ names) a, T) :: vars
skalberg@15570
  1252
  in Library.foldl rename_aT ([],vars) end;
clasohm@0
  1253
clasohm@0
  1254
fun rename_wrt_term t = rename_aTs (add_term_names(t,[]));
clasohm@1364
  1255
paulson@1417
  1256
wenzelm@16943
  1257
(* zero var indexes *)
wenzelm@4286
  1258
wenzelm@16943
  1259
fun zero_var_inst vars =
wenzelm@16943
  1260
  fold (fn v as ((x, i), X) => fn (used, inst) =>
wenzelm@16943
  1261
    let
wenzelm@20100
  1262
      val ([x'], used') = Name.variants [if Name.is_bound x then "u" else x] used;
wenzelm@16943
  1263
    in if x = x' andalso i = 0 then (used', inst) else (used', (v, ((x', 0), X)) :: inst) end)
wenzelm@20100
  1264
  vars (Name.context, []) |> #2;
wenzelm@4286
  1265
wenzelm@16943
  1266
fun zero_var_indexesT ty =
wenzelm@16943
  1267
  instantiateT (map (apsnd TVar) (zero_var_inst (sort tvar_ord (add_tvarsT ty [])))) ty;
haftmann@16790
  1268
wenzelm@16943
  1269
fun zero_var_indexes_inst tm =
wenzelm@16943
  1270
  let
wenzelm@16943
  1271
    val instT = map (apsnd TVar) (zero_var_inst (sort tvar_ord (fold_types add_tvarsT tm [])));
wenzelm@16943
  1272
    val inst =
wenzelm@16943
  1273
      add_vars tm [] |> map (apsnd (instantiateT instT))
wenzelm@16943
  1274
      |> sort var_ord |> zero_var_inst |> map (apsnd Var);
wenzelm@16943
  1275
  in (instT, inst) end;
wenzelm@12499
  1276
wenzelm@16943
  1277
fun zero_var_indexes tm = instantiate (zero_var_indexes_inst tm) tm;
wenzelm@4286
  1278
paulson@1417
  1279
wenzelm@9536
  1280
(* dummy patterns *)
wenzelm@9536
  1281
wenzelm@9536
  1282
val dummy_patternN = "dummy_pattern";
wenzelm@9536
  1283
wenzelm@18253
  1284
fun dummy_pattern T = Const (dummy_patternN, T);
wenzelm@18253
  1285
wenzelm@9536
  1286
fun is_dummy_pattern (Const ("dummy_pattern", _)) = true
wenzelm@9536
  1287
  | is_dummy_pattern _ = false;
wenzelm@9536
  1288
wenzelm@9536
  1289
fun no_dummy_patterns tm =
haftmann@16787
  1290
  if not (fold_aterms (fn t => fn b => b orelse is_dummy_pattern t) tm false) then tm
wenzelm@9536
  1291
  else raise TERM ("Illegal occurrence of '_' dummy pattern", [tm]);
wenzelm@9536
  1292
wenzelm@11903
  1293
fun replace_dummy Ts (i, Const ("dummy_pattern", T)) =
wenzelm@11903
  1294
      (i + 1, list_comb (Var (("_dummy_", i), Ts ---> T), map Bound (0 upto length Ts - 1)))
wenzelm@11903
  1295
  | replace_dummy Ts (i, Abs (x, T, t)) =
wenzelm@11903
  1296
      let val (i', t') = replace_dummy (T :: Ts) (i, t)
wenzelm@11903
  1297
      in (i', Abs (x, T, t')) end
wenzelm@11903
  1298
  | replace_dummy Ts (i, t $ u) =
wenzelm@11903
  1299
      let val (i', t') = replace_dummy Ts (i, t); val (i'', u') = replace_dummy Ts (i', u)
wenzelm@11903
  1300
      in (i'', t' $ u') end
wenzelm@11903
  1301
  | replace_dummy _ (i, a) = (i, a);
wenzelm@11903
  1302
wenzelm@11903
  1303
val replace_dummy_patterns = replace_dummy [];
wenzelm@9536
  1304
wenzelm@10552
  1305
fun is_replaced_dummy_pattern ("_dummy_", _) = true
wenzelm@10552
  1306
  | is_replaced_dummy_pattern _ = false;
wenzelm@9536
  1307
wenzelm@16035
  1308
fun show_dummy_patterns (Var (("_dummy_", _), T)) = Const ("dummy_pattern", T)
wenzelm@16035
  1309
  | show_dummy_patterns (t $ u) = show_dummy_patterns t $ show_dummy_patterns u
wenzelm@16035
  1310
  | show_dummy_patterns (Abs (x, T, t)) = Abs (x, T, show_dummy_patterns t)
wenzelm@16035
  1311
  | show_dummy_patterns a = a;
wenzelm@16035
  1312
wenzelm@13484
  1313
wenzelm@20100
  1314
(* display variables *)
wenzelm@20100
  1315
wenzelm@15986
  1316
val show_question_marks = ref true;
berghofe@15472
  1317
wenzelm@14786
  1318
fun string_of_vname (x, i) =
wenzelm@14786
  1319
  let
wenzelm@15986
  1320
    val question_mark = if ! show_question_marks then "?" else "";
wenzelm@15986
  1321
    val idx = string_of_int i;
wenzelm@15986
  1322
    val dot =
wenzelm@15986
  1323
      (case rev (Symbol.explode x) of
wenzelm@15986
  1324
        _ :: "\\<^isub>" :: _ => false
wenzelm@15986
  1325
      | _ :: "\\<^isup>" :: _ => false
wenzelm@15986
  1326
      | c :: _ => Symbol.is_digit c
wenzelm@15986
  1327
      | _ => true);
wenzelm@14786
  1328
  in
wenzelm@15986
  1329
    if dot then question_mark ^ x ^ "." ^ idx
wenzelm@15986
  1330
    else if i <> 0 then question_mark ^ x ^ idx
wenzelm@15986
  1331
    else question_mark ^ x
wenzelm@14786
  1332
  end;
wenzelm@14786
  1333
wenzelm@14786
  1334
fun string_of_vname' (x, ~1) = x
wenzelm@14786
  1335
  | string_of_vname' xi = string_of_vname xi;
wenzelm@14786
  1336
clasohm@1364
  1337
end;
clasohm@1364
  1338
wenzelm@4444
  1339
structure BasicTerm: BASIC_TERM = Term;
wenzelm@4444
  1340
open BasicTerm;