src/Pure/term.ML
author wenzelm
Thu Jun 09 12:03:25 2005 +0200 (2005-06-09)
changeset 16338 3d1851acb4d0
parent 16294 97c9f2c1de3d
child 16537 954495db0f07
permissions -rw-r--r--
map_typ and map_term no longer global;
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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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  val --> : typ * typ -> typ
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  val ---> : typ list * typ -> typ
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  val is_TVar: typ -> bool
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  val is_funtype: typ -> bool
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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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  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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  structure Vartab : TABLE
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  structure Typtab : TABLE
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  structure Termtab : TABLE
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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 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_first_order: term -> bool
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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 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 type_of: term -> typ
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  val type_of1: typ list * term -> typ
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  val fastype_of: term -> typ
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  val fastype_of1: typ list * term -> typ
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  val list_abs: (string * typ) list * term -> 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_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 it_term_types: (typ * 'a -> 'a) -> term * 'a -> 'a
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  val foldl_atyps: ('a * typ -> 'a) -> 'a * typ -> 'a
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  val foldl_term_types: (term -> 'a * typ -> 'a) -> 'a * term -> 'a
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  val foldl_types: ('a * typ -> 'a) -> 'a * term -> 'a
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  val foldl_aterms: ('a * term -> 'a) -> 'a * term -> 'a
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  val foldl_map_aterms: ('a * term -> 'a * term) -> 'a * term -> 'a * term
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  val add_term_varnames: indexname list * term -> indexname list
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  val term_varnames: term -> indexname list
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  val dummyT: typ
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  val itselfT: typ -> typ
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  val a_itselfT: typ
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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 subst_TVars: (indexname * typ) list -> term -> term
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  val betapply: term * term -> term
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  val eq_ix: indexname * indexname -> bool
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  val ins_ix: indexname * indexname list -> indexname list
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  val mem_ix: indexname * indexname list -> bool
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  val aconv: term * term -> bool
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  val aconvs: term list * term list -> bool
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  val mem_term: term * term list -> bool
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  val subset_term: term list * term list -> bool
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  val eq_set_term: term list * term list -> bool
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  val ins_term: term * term list -> term list
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  val union_term: term list * term list -> term list
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  val inter_term: term list * term list -> term list
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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 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_vars: (indexname * typ) list * (indexname * term) list -> term -> term
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  val typ_subst_TVars: (indexname * typ) list -> typ -> typ
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  val subst_Vars: (indexname * term) list -> term -> term
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  val incr_tvar: int -> typ -> typ
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  val xless: (string * int) * indexname -> bool
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  val atless: term * term -> bool
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  val insert_aterm: term * term list -> term list
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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 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 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 maxidx_of_terms: term list -> int
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  val variant: string list -> string -> string
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  val variantlist: string list * string list -> string list
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        (* note reversed order of args wrt. variant! *)
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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 add_new_id: string list * string -> string list
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  val add_typ_classes: typ * class list -> class list
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  val add_typ_ixns: indexname list * typ -> indexname 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 typ_tfrees: typ -> (string * sort) list
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  val add_typ_tvars: typ * (indexname * sort) list -> (indexname * sort) list
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  val typ_tvars: typ -> (indexname * sort) list
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  val add_typ_tycons: typ * string list -> string list
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  val add_typ_varnames: typ * string list -> string list
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  val add_term_classes: term * class list -> class list
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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 term_constsT: term -> (string * typ) 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 add_term_free_names: term * string list -> string list
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  val add_term_names: term * string list -> string list
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  val add_term_tfree_names: term * string list -> string list
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  val add_term_tfrees: term * (string * sort) list -> (string * sort) list
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  val term_tfrees: term -> (string * sort) list
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  val add_term_tvar_ixns: term * indexname list -> indexname list
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  val add_term_tvarnames: term * string list -> string list
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  val add_term_tvars: term * (indexname * sort) list -> (indexname * sort) list
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  val term_tvars: term -> (indexname * sort) list
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  val add_term_tycons: term * string list -> string 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 exists_Const: (string * typ -> bool) -> term -> bool
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  val exists_subterm: (term -> bool) -> term -> bool
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  val compress_type: typ -> typ
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  val compress_term: term -> term
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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 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 invent_names: string list -> string -> int -> string list
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  val map_typ: (string -> string) -> (string -> string) -> typ -> typ
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  val map_term: (string -> string) -> (string -> string) -> (string -> string) -> term -> term
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  val add_tvarsT: (indexname * sort) list * typ -> (indexname * sort) list
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  val add_tvars: (indexname * sort) list * term -> (indexname * sort) list
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  val add_vars: (indexname * typ) list * term -> (indexname * typ) list
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  val add_frees: (string * typ) list * term -> (string * typ) list
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  val indexname_ord: indexname * indexname -> order
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  val typ_ord: typ * typ -> order
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  val typs_ord: typ list * typ list -> order
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  val term_ord: term * term -> order
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  val terms_ord: term list * term list -> 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 no_dummyT: typ -> typ
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  val dummy_patternN: string
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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 adhoc_freeze_vars: term -> term * string list
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  val string_of_vname: indexname -> string
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  val string_of_vname': indexname -> string
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  val string_of_term: term -> 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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(*For errors involving type mismatches*)
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exception TYPE of string * typ list * term list;
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(*For system 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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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]*)
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fun binder_types (Type("fun",[S,T])) = S :: binder_types T
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  | binder_types _   =  [];
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(* maps  [T1,...,Tn]--->T  to T*)
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fun body_type (Type("fun",[S,T])) = body_type T
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  | body_type T   =  T;
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(* maps  [T1,...,Tn]--->T  to   ([T1,T2,...,Tn], T)  *)
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fun strip_type T : typ list * typ =
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  (binder_types T, body_type T);
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(*Compute the type of the term, checking that combinations are well-typed
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  Ts = [T0,T1,...] holds types of bound variables 0, 1, ...*)
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fun type_of1 (Ts, Const (_,T)) = T
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  | type_of1 (Ts, Free  (_,T)) = T
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  | type_of1 (Ts, Bound i) = (List.nth (Ts,i)
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        handle Subscript => raise TYPE("type_of: bound variable", [], [Bound i]))
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  | type_of1 (Ts, Var (_,T)) = T
clasohm@0
   327
  | type_of1 (Ts, Abs (_,T,body)) = T --> type_of1(T::Ts, body)
wenzelm@13000
   328
  | type_of1 (Ts, f$u) =
clasohm@0
   329
      let val U = type_of1(Ts,u)
clasohm@0
   330
          and T = type_of1(Ts,f)
clasohm@0
   331
      in case T of
wenzelm@9536
   332
            Type("fun",[T1,T2]) =>
wenzelm@9536
   333
              if T1=U then T2  else raise TYPE
wenzelm@9536
   334
                    ("type_of: type mismatch in application", [T1,U], [f$u])
wenzelm@13000
   335
          | _ => raise TYPE
wenzelm@9536
   336
                    ("type_of: function type is expected in application",
wenzelm@9536
   337
                     [T,U], [f$u])
clasohm@0
   338
      end;
clasohm@0
   339
clasohm@0
   340
fun type_of t : typ = type_of1 ([],t);
clasohm@0
   341
clasohm@0
   342
(*Determines the type of a term, with minimal checking*)
wenzelm@13000
   343
fun fastype_of1 (Ts, f$u) =
lcp@61
   344
    (case fastype_of1 (Ts,f) of
wenzelm@9536
   345
        Type("fun",[_,T]) => T
wenzelm@9536
   346
        | _ => raise TERM("fastype_of: expected function type", [f$u]))
lcp@61
   347
  | fastype_of1 (_, Const (_,T)) = T
lcp@61
   348
  | fastype_of1 (_, Free (_,T)) = T
skalberg@15570
   349
  | fastype_of1 (Ts, Bound i) = (List.nth(Ts,i)
skalberg@15570
   350
         handle Subscript => raise TERM("fastype_of: Bound", [Bound i]))
wenzelm@13000
   351
  | fastype_of1 (_, Var (_,T)) = T
lcp@61
   352
  | fastype_of1 (Ts, Abs (_,T,u)) = T --> fastype_of1 (T::Ts, u);
lcp@61
   353
lcp@61
   354
fun fastype_of t : typ = fastype_of1 ([],t);
clasohm@0
   355
clasohm@0
   356
skalberg@15570
   357
val list_abs = Library.foldr (fn ((x, T), t) => Abs (x, T, t));
wenzelm@10806
   358
clasohm@0
   359
(* maps  (x1,...,xn)t   to   t  *)
wenzelm@13000
   360
fun strip_abs_body (Abs(_,_,t))  =  strip_abs_body t
clasohm@0
   361
  | strip_abs_body u  =  u;
clasohm@0
   362
clasohm@0
   363
(* maps  (x1,...,xn)t   to   [x1, ..., xn]  *)
wenzelm@13000
   364
fun strip_abs_vars (Abs(a,T,t))  =  (a,T) :: strip_abs_vars t
clasohm@0
   365
  | strip_abs_vars u  =  [] : (string*typ) list;
clasohm@0
   366
clasohm@0
   367
clasohm@0
   368
fun strip_qnt_body qnt =
clasohm@0
   369
let fun strip(tm as Const(c,_)$Abs(_,_,t)) = if c=qnt then strip t else tm
clasohm@0
   370
      | strip t = t
clasohm@0
   371
in strip end;
clasohm@0
   372
clasohm@0
   373
fun strip_qnt_vars qnt =
clasohm@0
   374
let fun strip(Const(c,_)$Abs(a,T,t)) = if c=qnt then (a,T)::strip t else []
clasohm@0
   375
      | strip t  =  [] : (string*typ) list
clasohm@0
   376
in strip end;
clasohm@0
   377
clasohm@0
   378
clasohm@0
   379
(* maps   (f, [t1,...,tn])  to  f(t1,...,tn) *)
skalberg@15570
   380
val list_comb : term * term list -> term = Library.foldl (op $);
clasohm@0
   381
clasohm@0
   382
clasohm@0
   383
(* maps   f(t1,...,tn)  to  (f, [t1,...,tn]) ; naturally tail-recursive*)
wenzelm@13000
   384
fun strip_comb u : term * term list =
clasohm@0
   385
    let fun stripc (f$t, ts) = stripc (f, t::ts)
wenzelm@13000
   386
        |   stripc  x =  x
clasohm@0
   387
    in  stripc(u,[])  end;
clasohm@0
   388
clasohm@0
   389
clasohm@0
   390
(* maps   f(t1,...,tn)  to  f , which is never a combination *)
clasohm@0
   391
fun head_of (f$t) = head_of f
clasohm@0
   392
  | head_of u = u;
clasohm@0
   393
clasohm@0
   394
clasohm@0
   395
(*Number of atoms and abstractions in a term*)
clasohm@0
   396
fun size_of_term (Abs (_,_,body)) = 1 + size_of_term body
clasohm@0
   397
  | size_of_term (f$t) = size_of_term f  +  size_of_term t
clasohm@0
   398
  | size_of_term _ = 1;
clasohm@0
   399
nipkow@949
   400
fun map_type_tvar f (Type(a,Ts)) = Type(a, map (map_type_tvar f) Ts)
nipkow@949
   401
  | map_type_tvar f (T as TFree _) = T
nipkow@949
   402
  | map_type_tvar f (TVar x) = f x;
nipkow@949
   403
nipkow@949
   404
fun map_type_tfree f (Type(a,Ts)) = Type(a, map (map_type_tfree f) Ts)
nipkow@949
   405
  | map_type_tfree f (TFree x) = f x
nipkow@949
   406
  | map_type_tfree f (T as TVar _) = T;
nipkow@949
   407
clasohm@0
   408
(* apply a function to all types in a term *)
clasohm@0
   409
fun map_term_types f =
clasohm@0
   410
let fun map(Const(a,T)) = Const(a, f T)
clasohm@0
   411
      | map(Free(a,T)) = Free(a, f T)
clasohm@0
   412
      | map(Var(v,T)) = Var(v, f T)
clasohm@0
   413
      | map(t as Bound _)  = t
clasohm@0
   414
      | map(Abs(a,T,t)) = Abs(a, f T, map t)
clasohm@0
   415
      | map(f$t) = map f $ map t;
clasohm@0
   416
in map end;
clasohm@0
   417
clasohm@0
   418
(* iterate a function over all types in a term *)
clasohm@0
   419
fun it_term_types f =
clasohm@0
   420
let fun iter(Const(_,T), a) = f(T,a)
clasohm@0
   421
      | iter(Free(_,T), a) = f(T,a)
clasohm@0
   422
      | iter(Var(_,T), a) = f(T,a)
clasohm@0
   423
      | iter(Abs(_,T,t), a) = iter(t,f(T,a))
clasohm@0
   424
      | iter(f$u, a) = iter(f, iter(u, a))
clasohm@0
   425
      | iter(Bound _, a) = a
clasohm@0
   426
in iter end
clasohm@0
   427
clasohm@0
   428
clasohm@0
   429
(** Connectives of higher order logic **)
clasohm@0
   430
wenzelm@375
   431
fun itselfT ty = Type ("itself", [ty]);
wenzelm@14854
   432
val a_itselfT = itselfT (TFree ("'a", []));
wenzelm@375
   433
clasohm@0
   434
val propT : typ = Type("prop",[]);
clasohm@0
   435
clasohm@0
   436
val implies = Const("==>", propT-->propT-->propT);
clasohm@0
   437
clasohm@0
   438
fun all T = Const("all", (T-->propT)-->propT);
clasohm@0
   439
clasohm@0
   440
fun equals T = Const("==", T-->T-->propT);
clasohm@0
   441
clasohm@0
   442
(* maps  !!x1...xn. t   to   t  *)
wenzelm@13000
   443
fun strip_all_body (Const("all",_)$Abs(_,_,t))  =  strip_all_body t
clasohm@0
   444
  | strip_all_body t  =  t;
clasohm@0
   445
clasohm@0
   446
(* maps  !!x1...xn. t   to   [x1, ..., xn]  *)
clasohm@0
   447
fun strip_all_vars (Const("all",_)$Abs(a,T,t))  =
wenzelm@13000
   448
                (a,T) :: strip_all_vars t
clasohm@0
   449
  | strip_all_vars t  =  [] : (string*typ) list;
clasohm@0
   450
clasohm@0
   451
(*increments a term's non-local bound variables
clasohm@0
   452
  required when moving a term within abstractions
clasohm@0
   453
     inc is  increment for bound variables
clasohm@0
   454
     lev is  level at which a bound variable is considered 'loose'*)
wenzelm@13000
   455
fun incr_bv (inc, lev, u as Bound i) = if i>=lev then Bound(i+inc) else u
clasohm@0
   456
  | incr_bv (inc, lev, Abs(a,T,body)) =
wenzelm@9536
   457
        Abs(a, T, incr_bv(inc,lev+1,body))
wenzelm@13000
   458
  | incr_bv (inc, lev, f$t) =
clasohm@0
   459
      incr_bv(inc,lev,f) $ incr_bv(inc,lev,t)
clasohm@0
   460
  | incr_bv (inc, lev, u) = u;
clasohm@0
   461
clasohm@0
   462
fun incr_boundvars  0  t = t
clasohm@0
   463
  | incr_boundvars inc t = incr_bv(inc,0,t);
clasohm@0
   464
wenzelm@12981
   465
(*Scan a pair of terms; while they are similar,
wenzelm@12981
   466
  accumulate corresponding bound vars in "al"*)
wenzelm@12981
   467
fun match_bvs(Abs(x,_,s),Abs(y,_,t), al) =
wenzelm@12981
   468
      match_bvs(s, t, if x="" orelse y="" then al
wenzelm@12981
   469
                                          else (x,y)::al)
wenzelm@12981
   470
  | match_bvs(f$s, g$t, al) = match_bvs(f,g,match_bvs(s,t,al))
wenzelm@12981
   471
  | match_bvs(_,_,al) = al;
wenzelm@12981
   472
wenzelm@12981
   473
(* strip abstractions created by parameters *)
wenzelm@12981
   474
fun match_bvars((s,t),al) = match_bvs(strip_abs_body s, strip_abs_body t, al);
wenzelm@12981
   475
wenzelm@12981
   476
fun rename_abs pat obj t =
wenzelm@12981
   477
  let
wenzelm@12981
   478
    val ren = match_bvs (pat, obj, []);
wenzelm@12981
   479
    fun ren_abs (Abs (x, T, b)) =
skalberg@15570
   480
          Abs (getOpt (assoc_string (ren, x), x), T, ren_abs b)
wenzelm@12981
   481
      | ren_abs (f $ t) = ren_abs f $ ren_abs t
wenzelm@12981
   482
      | ren_abs t = t
skalberg@15531
   483
  in if null ren then NONE else SOME (ren_abs t) end;
clasohm@0
   484
clasohm@0
   485
(*Accumulate all 'loose' bound vars referring to level 'lev' or beyond.
clasohm@0
   486
   (Bound 0) is loose at level 0 *)
wenzelm@13000
   487
fun add_loose_bnos (Bound i, lev, js) =
wenzelm@9536
   488
        if i<lev then js  else  (i-lev) ins_int js
clasohm@0
   489
  | add_loose_bnos (Abs (_,_,t), lev, js) = add_loose_bnos (t, lev+1, js)
clasohm@0
   490
  | add_loose_bnos (f$t, lev, js) =
wenzelm@13000
   491
        add_loose_bnos (f, lev, add_loose_bnos (t, lev, js))
clasohm@0
   492
  | add_loose_bnos (_, _, js) = js;
clasohm@0
   493
clasohm@0
   494
fun loose_bnos t = add_loose_bnos (t, 0, []);
clasohm@0
   495
clasohm@0
   496
(* loose_bvar(t,k) iff t contains a 'loose' bound variable referring to
clasohm@0
   497
   level k or beyond. *)
clasohm@0
   498
fun loose_bvar(Bound i,k) = i >= k
clasohm@0
   499
  | loose_bvar(f$t, k) = loose_bvar(f,k) orelse loose_bvar(t,k)
clasohm@0
   500
  | loose_bvar(Abs(_,_,t),k) = loose_bvar(t,k+1)
clasohm@0
   501
  | loose_bvar _ = false;
clasohm@0
   502
nipkow@2792
   503
fun loose_bvar1(Bound i,k) = i = k
nipkow@2792
   504
  | loose_bvar1(f$t, k) = loose_bvar1(f,k) orelse loose_bvar1(t,k)
nipkow@2792
   505
  | loose_bvar1(Abs(_,_,t),k) = loose_bvar1(t,k+1)
nipkow@2792
   506
  | loose_bvar1 _ = false;
clasohm@0
   507
clasohm@0
   508
(*Substitute arguments for loose bound variables.
clasohm@0
   509
  Beta-reduction of arg(n-1)...arg0 into t replacing (Bound i) with (argi).
wenzelm@4626
   510
  Note that for ((%x y. c) a b), the bound vars in c are x=1 and y=0
wenzelm@9536
   511
        and the appropriate call is  subst_bounds([b,a], c) .
clasohm@0
   512
  Loose bound variables >=n are reduced by "n" to
clasohm@0
   513
     compensate for the disappearance of lambdas.
clasohm@0
   514
*)
wenzelm@13000
   515
fun subst_bounds (args: term list, t) : term =
clasohm@0
   516
  let val n = length args;
clasohm@0
   517
      fun subst (t as Bound i, lev) =
wenzelm@9536
   518
           (if i<lev then  t    (*var is locally bound*)
wenzelm@9536
   519
            else  incr_boundvars lev (List.nth(args, i-lev))
wenzelm@9536
   520
                    handle Subscript => Bound(i-n)  (*loose: change it*))
wenzelm@9536
   521
        | subst (Abs(a,T,body), lev) = Abs(a, T,  subst(body,lev+1))
wenzelm@9536
   522
        | subst (f$t, lev) =  subst(f,lev)  $  subst(t,lev)
wenzelm@9536
   523
        | subst (t,lev) = t
clasohm@0
   524
  in   case args of [] => t  | _ => subst (t,0)  end;
clasohm@0
   525
paulson@2192
   526
(*Special case: one argument*)
wenzelm@13000
   527
fun subst_bound (arg, t) : term =
paulson@2192
   528
  let fun subst (t as Bound i, lev) =
wenzelm@9536
   529
            if i<lev then  t    (*var is locally bound*)
wenzelm@9536
   530
            else  if i=lev then incr_boundvars lev arg
wenzelm@9536
   531
                           else Bound(i-1)  (*loose: change it*)
wenzelm@9536
   532
        | subst (Abs(a,T,body), lev) = Abs(a, T,  subst(body,lev+1))
wenzelm@9536
   533
        | subst (f$t, lev) =  subst(f,lev)  $  subst(t,lev)
wenzelm@9536
   534
        | subst (t,lev) = t
paulson@2192
   535
  in  subst (t,0)  end;
paulson@2192
   536
clasohm@0
   537
(*beta-reduce if possible, else form application*)
paulson@2192
   538
fun betapply (Abs(_,_,t), u) = subst_bound (u,t)
clasohm@0
   539
  | betapply (f,u) = f$u;
clasohm@0
   540
wenzelm@14786
   541
paulson@2192
   542
(** Equality, membership and insertion of indexnames (string*ints) **)
paulson@2192
   543
paulson@2192
   544
(*optimized equality test for indexnames.  Yields a huge gain under Poly/ML*)
wenzelm@2959
   545
fun eq_ix ((a, i):indexname, (a',i'):indexname) = (a=a') andalso i=i';
paulson@2192
   546
paulson@2192
   547
(*membership in a list, optimized version for indexnames*)
wenzelm@2959
   548
fun mem_ix (_, []) = false
paulson@2192
   549
  | mem_ix (x, y :: ys) = eq_ix(x,y) orelse mem_ix (x, ys);
paulson@2192
   550
paulson@2192
   551
(*insertion into list, optimized version for indexnames*)
paulson@2192
   552
fun ins_ix (x,xs) = if mem_ix (x, xs) then xs else x :: xs;
paulson@2192
   553
clasohm@0
   554
(*Tests whether 2 terms are alpha-convertible and have same type.
wenzelm@4626
   555
  Note that constants may have more than one type.*)
clasohm@0
   556
fun (Const(a,T)) aconv (Const(b,U)) = a=b  andalso  T=U
paulson@2752
   557
  | (Free(a,T))  aconv (Free(b,U))  = a=b  andalso  T=U
paulson@2752
   558
  | (Var(v,T))   aconv (Var(w,U))   = eq_ix(v,w)  andalso  T=U
paulson@2752
   559
  | (Bound i)    aconv (Bound j)    = i=j
clasohm@0
   560
  | (Abs(_,T,t)) aconv (Abs(_,U,u)) = t aconv u  andalso  T=U
paulson@2752
   561
  | (f$t)        aconv (g$u)        = (f aconv g) andalso (t aconv u)
clasohm@0
   562
  | _ aconv _  =  false;
clasohm@0
   563
paulson@2176
   564
(** Membership, insertion, union for terms **)
paulson@2176
   565
paulson@2176
   566
fun mem_term (_, []) = false
paulson@2176
   567
  | mem_term (t, t'::ts) = t aconv t' orelse mem_term(t,ts);
paulson@2176
   568
paulson@2182
   569
fun subset_term ([], ys) = true
paulson@2182
   570
  | subset_term (x :: xs, ys) = mem_term (x, ys) andalso subset_term(xs, ys);
paulson@2182
   571
paulson@2182
   572
fun eq_set_term (xs, ys) =
paulson@2182
   573
    xs = ys orelse (subset_term (xs, ys) andalso subset_term (ys, xs));
paulson@2182
   574
paulson@2176
   575
fun ins_term(t,ts) = if mem_term(t,ts) then ts else t :: ts;
paulson@2176
   576
paulson@2176
   577
fun union_term (xs, []) = xs
paulson@2176
   578
  | union_term ([], ys) = ys
paulson@2176
   579
  | union_term ((x :: xs), ys) = union_term (xs, ins_term (x, ys));
paulson@2176
   580
paulson@5585
   581
fun inter_term ([], ys) = []
paulson@5585
   582
  | inter_term (x::xs, ys) =
paulson@5585
   583
      if mem_term (x,ys) then x :: inter_term(xs,ys) else inter_term(xs,ys);
paulson@5585
   584
clasohm@0
   585
(*are two term lists alpha-convertible in corresponding elements?*)
clasohm@0
   586
fun aconvs ([],[]) = true
clasohm@0
   587
  | aconvs (t::ts, u::us) = t aconv u andalso aconvs(ts,us)
clasohm@0
   588
  | aconvs _ = false;
clasohm@0
   589
wenzelm@13000
   590
(*A fast unification filter: true unless the two terms cannot be unified.
clasohm@0
   591
  Terms must be NORMAL.  Treats all Vars as distinct. *)
clasohm@0
   592
fun could_unify (t,u) =
clasohm@0
   593
  let fun matchrands (f$t, g$u) = could_unify(t,u) andalso  matchrands(f,g)
wenzelm@9536
   594
        | matchrands _ = true
clasohm@0
   595
  in case (head_of t , head_of u) of
wenzelm@9536
   596
        (_, Var _) => true
clasohm@0
   597
      | (Var _, _) => true
clasohm@0
   598
      | (Const(a,_), Const(b,_)) =>  a=b andalso matchrands(t,u)
clasohm@0
   599
      | (Free(a,_), Free(b,_)) =>  a=b andalso matchrands(t,u)
clasohm@0
   600
      | (Bound i, Bound j) =>  i=j andalso matchrands(t,u)
clasohm@0
   601
      | (Abs _, _) =>  true   (*because of possible eta equality*)
clasohm@0
   602
      | (_, Abs _) =>  true
clasohm@0
   603
      | _ => false
clasohm@0
   604
  end;
clasohm@0
   605
clasohm@0
   606
(*Substitute new for free occurrences of old in a term*)
clasohm@0
   607
fun subst_free [] = (fn t=>t)
clasohm@0
   608
  | subst_free pairs =
wenzelm@13000
   609
      let fun substf u =
wenzelm@9536
   610
            case gen_assoc (op aconv) (pairs, u) of
skalberg@15531
   611
                SOME u' => u'
skalberg@15531
   612
              | NONE => (case u of Abs(a,T,t) => Abs(a, T, substf t)
wenzelm@9536
   613
                                 | t$u' => substf t $ substf u'
wenzelm@9536
   614
                                 | _ => u)
clasohm@0
   615
      in  substf  end;
clasohm@0
   616
clasohm@0
   617
(*a total, irreflexive ordering on index names*)
clasohm@0
   618
fun xless ((a,i), (b,j): indexname) = i<j  orelse  (i=j andalso a<b);
clasohm@0
   619
clasohm@0
   620
wenzelm@13000
   621
(*Abstraction of the term "body" over its occurrences of v,
clasohm@0
   622
    which must contain no loose bound variables.
clasohm@0
   623
  The resulting term is ready to become the body of an Abs.*)
clasohm@0
   624
fun abstract_over (v,body) =
clasohm@0
   625
  let fun abst (lev,u) = if (v aconv u) then (Bound lev) else
clasohm@0
   626
      (case u of
clasohm@0
   627
          Abs(a,T,t) => Abs(a, T, abst(lev+1, t))
wenzelm@9536
   628
        | f$rand => abst(lev,f) $ abst(lev,rand)
wenzelm@9536
   629
        | _ => u)
clasohm@0
   630
  in  abst(0,body)  end;
clasohm@0
   631
berghofe@13665
   632
fun lambda (v as Free (x, T)) t = Abs (x, T, abstract_over (v, t))
berghofe@13665
   633
  | lambda (v as Var ((x, _), T)) t = Abs (x, T, abstract_over (v, t))
berghofe@13665
   634
  | lambda v t = raise TERM ("lambda", [v, t]);
clasohm@0
   635
clasohm@0
   636
(*Form an abstraction over a free variable.*)
clasohm@0
   637
fun absfree (a,T,body) = Abs(a, T, abstract_over (Free(a,T), body));
clasohm@0
   638
clasohm@0
   639
(*Abstraction over a list of free variables*)
clasohm@0
   640
fun list_abs_free ([ ] ,     t) = t
wenzelm@13000
   641
  | list_abs_free ((a,T)::vars, t) =
clasohm@0
   642
      absfree(a, T, list_abs_free(vars,t));
clasohm@0
   643
clasohm@0
   644
(*Quantification over a list of free variables*)
clasohm@0
   645
fun list_all_free ([], t: term) = t
wenzelm@13000
   646
  | list_all_free ((a,T)::vars, t) =
clasohm@0
   647
        (all T) $ (absfree(a, T, list_all_free(vars,t)));
clasohm@0
   648
clasohm@0
   649
(*Quantification over a list of variables (already bound in body) *)
clasohm@0
   650
fun list_all ([], t) = t
wenzelm@13000
   651
  | list_all ((a,T)::vars, t) =
clasohm@0
   652
        (all T) $ (Abs(a, T, list_all(vars,t)));
clasohm@0
   653
wenzelm@13000
   654
(*Replace the ATOMIC term ti by ui;    instl = [(t1,u1), ..., (tn,un)].
clasohm@0
   655
  A simultaneous substitution:  [ (a,b), (b,a) ] swaps a and b.  *)
clasohm@0
   656
fun subst_atomic [] t = t : term
clasohm@0
   657
  | subst_atomic (instl: (term*term) list) t =
clasohm@0
   658
      let fun subst (Abs(a,T,body)) = Abs(a, T, subst body)
wenzelm@9536
   659
            | subst (f$t') = subst f $ subst t'
skalberg@15570
   660
            | subst t = getOpt (assoc(instl,t),t)
clasohm@0
   661
      in  subst t  end;
clasohm@0
   662
berghofe@15797
   663
(*Replace the ATOMIC type Ti by Ui;    instl = [(T1,U1), ..., (Tn,Un)].*)
berghofe@15797
   664
fun typ_subst_atomic [] T = T
berghofe@15797
   665
  | typ_subst_atomic instl (Type (s, Ts)) =
berghofe@15797
   666
      Type (s, map (typ_subst_atomic instl) Ts)
berghofe@15797
   667
  | typ_subst_atomic instl T = getOpt (assoc (instl, T), T);
berghofe@15797
   668
lcp@728
   669
(*Substitute for type Vars in a type*)
clasohm@0
   670
fun typ_subst_TVars iTs T = if null iTs then T else
clasohm@0
   671
  let fun subst(Type(a,Ts)) = Type(a, map subst Ts)
wenzelm@9536
   672
        | subst(T as TFree _) = T
skalberg@15570
   673
        | subst(T as TVar(ixn,_)) = getOpt (assoc(iTs,ixn),T)
clasohm@0
   674
  in subst T end;
clasohm@0
   675
lcp@728
   676
(*Substitute for type Vars in a term*)
clasohm@0
   677
val subst_TVars = map_term_types o typ_subst_TVars;
clasohm@0
   678
lcp@728
   679
(*Substitute for Vars in a term; see also envir/norm_term*)
clasohm@0
   680
fun subst_Vars itms t = if null itms then t else
skalberg@15570
   681
  let fun subst(v as Var(ixn,_)) = getOpt (assoc(itms,ixn),v)
clasohm@0
   682
        | subst(Abs(a,T,t)) = Abs(a,T,subst t)
clasohm@0
   683
        | subst(f$t) = subst f $ subst t
clasohm@0
   684
        | subst(t) = t
clasohm@0
   685
  in subst t end;
clasohm@0
   686
lcp@728
   687
(*Substitute for type/term Vars in a term; see also envir/norm_term*)
clasohm@0
   688
fun subst_vars(iTs,itms) = if null iTs then subst_Vars itms else
clasohm@0
   689
  let fun subst(Const(a,T)) = Const(a,typ_subst_TVars iTs T)
clasohm@0
   690
        | subst(Free(a,T)) = Free(a,typ_subst_TVars iTs T)
clasohm@0
   691
        | subst(v as Var(ixn,T)) = (case assoc(itms,ixn) of
skalberg@15531
   692
            NONE   => Var(ixn,typ_subst_TVars iTs T)
skalberg@15531
   693
          | SOME t => t)
clasohm@0
   694
        | subst(b as Bound _) = b
clasohm@0
   695
        | subst(Abs(a,T,t)) = Abs(a,typ_subst_TVars iTs T,subst t)
clasohm@0
   696
        | subst(f$t) = subst f $ subst t
clasohm@0
   697
  in subst end;
clasohm@0
   698
clasohm@0
   699
paulson@15573
   700
(** Identifying first-order terms **)
paulson@15573
   701
paulson@15573
   702
(*Argument Ts is a reverse list of binder types, needed if term t contains Bound vars*)
paulson@15573
   703
fun has_not_funtype Ts t = not (is_funtype (fastype_of1 (Ts,t)));
paulson@15573
   704
kleing@15962
   705
(*First order means in all terms of the form f(t1,...,tn) no argument has a 
kleing@15962
   706
  function type. The meta-quantifier "all" is excluded--its argument always 
kleing@15962
   707
  has a function type--through a recursive call into its body.*)
paulson@15573
   708
fun first_order1 Ts (Abs (_,T,body)) = first_order1 (T::Ts) body
paulson@15954
   709
  | first_order1 Ts (Const("all",_)$Abs(a,T,body)) = 
paulson@15954
   710
      not (is_funtype T) andalso first_order1 (T::Ts) body
paulson@15573
   711
  | first_order1 Ts t =
paulson@15573
   712
      case strip_comb t of
paulson@15573
   713
	       (Var _, ts) => forall (first_order1 Ts andf has_not_funtype Ts) ts
paulson@15573
   714
	     | (Free _, ts) => forall (first_order1 Ts andf has_not_funtype Ts) ts
paulson@15573
   715
	     | (Const _, ts) => forall (first_order1 Ts andf has_not_funtype Ts) ts
paulson@15573
   716
	     | (Bound _, ts) => forall (first_order1 Ts andf has_not_funtype Ts) ts
paulson@15573
   717
	     | (Abs _, ts) => false (*not in beta-normal form*)
paulson@15573
   718
	     | _ => error "first_order: unexpected case";
paulson@15573
   719
paulson@15573
   720
val is_first_order = first_order1 [];
paulson@15573
   721
clasohm@0
   722
(*Computing the maximum index of a typ*)
paulson@2146
   723
fun maxidx_of_typ(Type(_,Ts)) = maxidx_of_typs Ts
clasohm@0
   724
  | maxidx_of_typ(TFree _) = ~1
paulson@2146
   725
  | maxidx_of_typ(TVar((_,i),_)) = i
paulson@2146
   726
and maxidx_of_typs [] = ~1
paulson@2146
   727
  | maxidx_of_typs (T::Ts) = Int.max(maxidx_of_typ T, maxidx_of_typs Ts);
clasohm@0
   728
clasohm@0
   729
clasohm@0
   730
(*Computing the maximum index of a term*)
clasohm@0
   731
fun maxidx_of_term (Const(_,T)) = maxidx_of_typ T
clasohm@0
   732
  | maxidx_of_term (Bound _) = ~1
clasohm@0
   733
  | maxidx_of_term (Free(_,T)) = maxidx_of_typ T
paulson@2146
   734
  | maxidx_of_term (Var ((_,i), T)) = Int.max(i, maxidx_of_typ T)
paulson@2146
   735
  | maxidx_of_term (Abs (_,T,u)) = Int.max(maxidx_of_term u, maxidx_of_typ T)
paulson@2146
   736
  | maxidx_of_term (f$t) = Int.max(maxidx_of_term f,  maxidx_of_term t);
clasohm@0
   737
skalberg@15570
   738
fun maxidx_of_terms ts = Library.foldl Int.max (~1, map maxidx_of_term ts);
berghofe@13665
   739
clasohm@0
   740
clasohm@0
   741
(* Increment the index of all Poly's in T by k *)
nipkow@949
   742
fun incr_tvar k = map_type_tvar (fn ((a,i),S) => TVar((a,i+k),S));
clasohm@0
   743
clasohm@0
   744
clasohm@0
   745
(**** Syntax-related declarations ****)
clasohm@0
   746
clasohm@0
   747
wenzelm@4626
   748
(*Dummy type for parsing and printing.  Will be replaced during type inference. *)
clasohm@0
   749
val dummyT = Type("dummy",[]);
clasohm@0
   750
wenzelm@14786
   751
fun no_dummyT typ =
wenzelm@14786
   752
  let
wenzelm@14786
   753
    fun check (T as Type ("dummy", _)) =
wenzelm@14786
   754
          raise TYPE ("Illegal occurrence of '_' dummy type", [T], [])
skalberg@15570
   755
      | check (Type (_, Ts)) = List.app check Ts
wenzelm@14786
   756
      | check _ = ();
wenzelm@14786
   757
  in check typ; typ end;
wenzelm@14786
   758
clasohm@0
   759
clasohm@0
   760
(*** Printing ***)
clasohm@0
   761
wenzelm@14676
   762
(*Makes a variant of a name distinct from the names in bs.
wenzelm@14676
   763
  First attaches the suffix and then increments this;
wenzelm@12306
   764
  preserves a suffix of underscores "_". *)
wenzelm@12306
   765
fun variant bs name =
wenzelm@12306
   766
  let
wenzelm@12306
   767
    val (c, u) = pairself implode (Library.take_suffix (equal "_") (Symbol.explode name));
wenzelm@12902
   768
    fun vary2 c = if ((c ^ u) mem_string bs) then vary2 (Symbol.bump_string c) else c;
wenzelm@14676
   769
    fun vary1 c = if ((c ^ u) mem_string bs) then vary2 (Symbol.bump_init c) else c;
wenzelm@12306
   770
  in vary1 (if c = "" then "u" else c) ^ u end;
clasohm@0
   771
clasohm@0
   772
(*Create variants of the list of names, with priority to the first ones*)
clasohm@0
   773
fun variantlist ([], used) = []
wenzelm@13000
   774
  | variantlist(b::bs, used) =
clasohm@0
   775
      let val b' = variant used b
clasohm@0
   776
      in  b' :: variantlist (bs, b'::used)  end;
clasohm@0
   777
wenzelm@14695
   778
(*Invent fresh names*)
wenzelm@14695
   779
fun invent_names _ _ 0 = []
wenzelm@14695
   780
  | invent_names used a n =
wenzelm@14695
   781
      let val b = Symbol.bump_string a in
wenzelm@14695
   782
        if a mem_string used then invent_names used b n
wenzelm@14695
   783
        else a :: invent_names used b (n - 1)
wenzelm@14695
   784
      end;
wenzelm@11353
   785
wenzelm@4017
   786
(** Consts etc. **)
wenzelm@4017
   787
skalberg@15574
   788
fun add_typ_classes (Type (_, Ts), cs) = foldr add_typ_classes cs Ts
wenzelm@4017
   789
  | add_typ_classes (TFree (_, S), cs) = S union cs
wenzelm@4017
   790
  | add_typ_classes (TVar (_, S), cs) = S union cs;
wenzelm@4017
   791
wenzelm@16294
   792
fun add_typ_tycons (Type (c, Ts), cs) = foldr add_typ_tycons (c ins_string cs) Ts
wenzelm@4017
   793
  | add_typ_tycons (_, cs) = cs;
wenzelm@4017
   794
wenzelm@4017
   795
val add_term_classes = it_term_types add_typ_classes;
wenzelm@4017
   796
val add_term_tycons = it_term_types add_typ_tycons;
wenzelm@4017
   797
wenzelm@9319
   798
fun add_term_consts (Const (c, _), cs) = c ins_string cs
wenzelm@4017
   799
  | add_term_consts (t $ u, cs) = add_term_consts (t, add_term_consts (u, cs))
wenzelm@4017
   800
  | add_term_consts (Abs (_, _, t), cs) = add_term_consts (t, cs)
wenzelm@4017
   801
  | add_term_consts (_, cs) = cs;
wenzelm@4017
   802
obua@16108
   803
fun add_term_constsT (Const c, cs) = c::cs
obua@16108
   804
  | add_term_constsT (t $ u, cs) = add_term_constsT (t, add_term_constsT (u, cs))
obua@16108
   805
  | add_term_constsT (Abs (_, _, t), cs) = add_term_constsT (t, cs)
obua@16108
   806
  | add_term_constsT (_, cs) = cs;
obua@16108
   807
nipkow@13646
   808
fun term_consts t = add_term_consts(t,[]);
nipkow@13646
   809
obua@16108
   810
fun term_constsT t = add_term_constsT(t,[]);
obua@16108
   811
oheimb@4185
   812
fun exists_Const P t = let
wenzelm@9536
   813
        fun ex (Const c      ) = P c
wenzelm@9536
   814
        |   ex (t $ u        ) = ex t orelse ex u
wenzelm@9536
   815
        |   ex (Abs (_, _, t)) = ex t
wenzelm@9536
   816
        |   ex _               = false
oheimb@4185
   817
    in ex t end;
wenzelm@4017
   818
nipkow@4631
   819
fun exists_subterm P =
nipkow@4631
   820
  let fun ex t = P t orelse
nipkow@4631
   821
                 (case t of
nipkow@4631
   822
                    u $ v        => ex u orelse ex v
nipkow@4631
   823
                  | Abs(_, _, u) => ex u
nipkow@4631
   824
                  | _            => false)
nipkow@4631
   825
  in ex end;
nipkow@4631
   826
wenzelm@4017
   827
(*map classes, tycons*)
wenzelm@4017
   828
fun map_typ f g (Type (c, Ts)) = Type (g c, map (map_typ f g) Ts)
wenzelm@4017
   829
  | map_typ f _ (TFree (x, S)) = TFree (x, map f S)
wenzelm@4017
   830
  | map_typ f _ (TVar (xi, S)) = TVar (xi, map f S);
wenzelm@4017
   831
wenzelm@4017
   832
(*map classes, tycons, consts*)
wenzelm@4017
   833
fun map_term f g h (Const (c, T)) = Const (h c, map_typ f g T)
wenzelm@4017
   834
  | map_term f g _ (Free (x, T)) = Free (x, map_typ f g T)
wenzelm@4017
   835
  | map_term f g _ (Var (xi, T)) = Var (xi, map_typ f g T)
wenzelm@4017
   836
  | map_term _ _ _ (t as Bound _) = t
wenzelm@4017
   837
  | map_term f g h (Abs (x, T, t)) = Abs (x, map_typ f g T, map_term f g h t)
wenzelm@4017
   838
  | map_term f g h (t $ u) = map_term f g h t $ map_term f g h u;
wenzelm@4017
   839
wenzelm@4017
   840
clasohm@0
   841
(** TFrees and TVars **)
clasohm@0
   842
clasohm@0
   843
(*maps  (bs,v)  to   v'::bs    this reverses the identifiers bs*)
clasohm@0
   844
fun add_new_id (bs, c) : string list =  variant bs c  ::  bs;
clasohm@0
   845
wenzelm@12802
   846
(*Accumulates the names of Frees in the term, suppressing duplicates.*)
wenzelm@12802
   847
fun add_term_free_names (Free(a,_), bs) = a ins_string bs
wenzelm@12802
   848
  | add_term_free_names (f$u, bs) = add_term_free_names (f, add_term_free_names(u, bs))
wenzelm@12802
   849
  | add_term_free_names (Abs(_,_,t), bs) = add_term_free_names(t,bs)
wenzelm@12802
   850
  | add_term_free_names (_, bs) = bs;
wenzelm@12802
   851
clasohm@0
   852
(*Accumulates the names in the term, suppressing duplicates.
clasohm@0
   853
  Includes Frees and Consts.  For choosing unambiguous bound var names.*)
wenzelm@10666
   854
fun add_term_names (Const(a,_), bs) = NameSpace.base a ins_string bs
paulson@2176
   855
  | add_term_names (Free(a,_), bs) = a ins_string bs
clasohm@0
   856
  | add_term_names (f$u, bs) = add_term_names (f, add_term_names(u, bs))
clasohm@0
   857
  | add_term_names (Abs(_,_,t), bs) = add_term_names(t,bs)
clasohm@0
   858
  | add_term_names (_, bs) = bs;
clasohm@0
   859
clasohm@0
   860
(*Accumulates the TVars in a type, suppressing duplicates. *)
skalberg@15574
   861
fun add_typ_tvars(Type(_,Ts),vs) = foldr add_typ_tvars vs Ts
clasohm@0
   862
  | add_typ_tvars(TFree(_),vs) = vs
wenzelm@16294
   863
  | add_typ_tvars(TVar(v),vs) = insert (op =) v vs;
clasohm@0
   864
clasohm@0
   865
(*Accumulates the TFrees in a type, suppressing duplicates. *)
skalberg@15574
   866
fun add_typ_tfree_names(Type(_,Ts),fs) = foldr add_typ_tfree_names fs Ts
paulson@2176
   867
  | add_typ_tfree_names(TFree(f,_),fs) = f ins_string fs
clasohm@0
   868
  | add_typ_tfree_names(TVar(_),fs) = fs;
clasohm@0
   869
skalberg@15574
   870
fun add_typ_tfrees(Type(_,Ts),fs) = foldr add_typ_tfrees fs Ts
wenzelm@16294
   871
  | add_typ_tfrees(TFree(f),fs) = insert (op =) f fs
clasohm@0
   872
  | add_typ_tfrees(TVar(_),fs) = fs;
clasohm@0
   873
skalberg@15574
   874
fun add_typ_varnames(Type(_,Ts),nms) = foldr add_typ_varnames nms Ts
paulson@2176
   875
  | add_typ_varnames(TFree(nm,_),nms) = nm ins_string nms
paulson@2176
   876
  | add_typ_varnames(TVar((nm,_),_),nms) = nm ins_string nms;
nipkow@949
   877
clasohm@0
   878
(*Accumulates the TVars in a term, suppressing duplicates. *)
clasohm@0
   879
val add_term_tvars = it_term_types add_typ_tvars;
clasohm@0
   880
clasohm@0
   881
(*Accumulates the TFrees in a term, suppressing duplicates. *)
clasohm@0
   882
val add_term_tfrees = it_term_types add_typ_tfrees;
clasohm@0
   883
val add_term_tfree_names = it_term_types add_typ_tfree_names;
clasohm@0
   884
nipkow@949
   885
val add_term_tvarnames = it_term_types add_typ_varnames;
nipkow@949
   886
clasohm@0
   887
(*Non-list versions*)
clasohm@0
   888
fun typ_tfrees T = add_typ_tfrees(T,[]);
clasohm@0
   889
fun typ_tvars T = add_typ_tvars(T,[]);
clasohm@0
   890
fun term_tfrees t = add_term_tfrees(t,[]);
clasohm@0
   891
fun term_tvars t = add_term_tvars(t,[]);
clasohm@0
   892
nipkow@949
   893
(*special code to enforce left-to-right collection of TVar-indexnames*)
nipkow@949
   894
skalberg@15570
   895
fun add_typ_ixns(ixns,Type(_,Ts)) = Library.foldl add_typ_ixns (ixns,Ts)
wenzelm@13000
   896
  | add_typ_ixns(ixns,TVar(ixn,_)) = if mem_ix (ixn, ixns) then ixns
wenzelm@9536
   897
                                     else ixns@[ixn]
nipkow@949
   898
  | add_typ_ixns(ixns,TFree(_)) = ixns;
nipkow@949
   899
nipkow@949
   900
fun add_term_tvar_ixns(Const(_,T),ixns) = add_typ_ixns(ixns,T)
nipkow@949
   901
  | add_term_tvar_ixns(Free(_,T),ixns) = add_typ_ixns(ixns,T)
nipkow@949
   902
  | add_term_tvar_ixns(Var(_,T),ixns) = add_typ_ixns(ixns,T)
nipkow@949
   903
  | add_term_tvar_ixns(Bound _,ixns) = ixns
nipkow@949
   904
  | add_term_tvar_ixns(Abs(_,T,t),ixns) =
nipkow@949
   905
      add_term_tvar_ixns(t,add_typ_ixns(ixns,T))
nipkow@949
   906
  | add_term_tvar_ixns(f$t,ixns) =
nipkow@949
   907
      add_term_tvar_ixns(t,add_term_tvar_ixns(f,ixns));
nipkow@949
   908
clasohm@0
   909
(** Frees and Vars **)
clasohm@0
   910
clasohm@0
   911
(*a partial ordering (not reflexive) for atomic terms*)
clasohm@0
   912
fun atless (Const (a,_), Const (b,_))  =  a<b
clasohm@0
   913
  | atless (Free (a,_), Free (b,_)) =  a<b
clasohm@0
   914
  | atless (Var(v,_), Var(w,_))  =  xless(v,w)
clasohm@0
   915
  | atless (Bound i, Bound j)  =   i<j
clasohm@0
   916
  | atless _  =  false;
clasohm@0
   917
clasohm@0
   918
(*insert atomic term into partially sorted list, suppressing duplicates (?)*)
clasohm@0
   919
fun insert_aterm (t,us) =
clasohm@0
   920
  let fun inserta [] = [t]
wenzelm@13000
   921
        | inserta (us as u::us') =
wenzelm@9536
   922
              if atless(t,u) then t::us
wenzelm@9536
   923
              else if t=u then us (*duplicate*)
wenzelm@9536
   924
              else u :: inserta(us')
clasohm@0
   925
  in  inserta us  end;
clasohm@0
   926
clasohm@0
   927
(*Accumulates the Vars in the term, suppressing duplicates*)
clasohm@0
   928
fun add_term_vars (t, vars: term list) = case t of
clasohm@0
   929
    Var   _ => insert_aterm(t,vars)
clasohm@0
   930
  | Abs (_,_,body) => add_term_vars(body,vars)
clasohm@0
   931
  | f$t =>  add_term_vars (f, add_term_vars(t, vars))
clasohm@0
   932
  | _ => vars;
clasohm@0
   933
clasohm@0
   934
fun term_vars t = add_term_vars(t,[]);
clasohm@0
   935
clasohm@0
   936
(*Accumulates the Frees in the term, suppressing duplicates*)
clasohm@0
   937
fun add_term_frees (t, frees: term list) = case t of
clasohm@0
   938
    Free   _ => insert_aterm(t,frees)
clasohm@0
   939
  | Abs (_,_,body) => add_term_frees(body,frees)
clasohm@0
   940
  | f$t =>  add_term_frees (f, add_term_frees(t, frees))
clasohm@0
   941
  | _ => frees;
clasohm@0
   942
clasohm@0
   943
fun term_frees t = add_term_frees(t,[]);
clasohm@0
   944
clasohm@0
   945
(*Given an abstraction over P, replaces the bound variable by a Free variable
clasohm@0
   946
  having a unique name. *)
clasohm@0
   947
fun variant_abs (a,T,P) =
clasohm@0
   948
  let val b = variant (add_term_names(P,[])) a
paulson@2192
   949
  in  (b,  subst_bound (Free(b,T), P))  end;
clasohm@0
   950
clasohm@0
   951
(* renames and reverses the strings in vars away from names *)
clasohm@0
   952
fun rename_aTs names vars : (string*typ)list =
clasohm@0
   953
  let fun rename_aT (vars,(a,T)) =
wenzelm@9536
   954
                (variant (map #1 vars @ names) a, T) :: vars
skalberg@15570
   955
  in Library.foldl rename_aT ([],vars) end;
clasohm@0
   956
clasohm@0
   957
fun rename_wrt_term t = rename_aTs (add_term_names(t,[]));
clasohm@1364
   958
paulson@1417
   959
wenzelm@4286
   960
(* left-ro-right traversal *)
wenzelm@4286
   961
wenzelm@4286
   962
(*foldl atoms of type*)
skalberg@15570
   963
fun foldl_atyps f (x, Type (_, Ts)) = Library.foldl (foldl_atyps f) (x, Ts)
wenzelm@4286
   964
  | foldl_atyps f x_atom = f x_atom;
wenzelm@4286
   965
wenzelm@4286
   966
(*foldl atoms of term*)
wenzelm@4286
   967
fun foldl_aterms f (x, t $ u) = foldl_aterms f (foldl_aterms f (x, t), u)
wenzelm@4286
   968
  | foldl_aterms f (x, Abs (_, _, t)) = foldl_aterms f (x, t)
wenzelm@4286
   969
  | foldl_aterms f x_atom = f x_atom;
wenzelm@4286
   970
wenzelm@6548
   971
fun foldl_map_aterms f (x, t $ u) =
wenzelm@6548
   972
      let val (x', t') = foldl_map_aterms f (x, t); val (x'', u') = foldl_map_aterms f (x', u);
wenzelm@6548
   973
      in (x'', t' $ u') end
wenzelm@6548
   974
  | foldl_map_aterms f (x, Abs (a, T, t)) =
wenzelm@6548
   975
      let val (x', t') = foldl_map_aterms f (x, t) in (x', Abs (a, T, t')) end
wenzelm@6548
   976
  | foldl_map_aterms f x_atom = f x_atom;
wenzelm@6548
   977
wenzelm@4286
   978
(*foldl types of term*)
wenzelm@8609
   979
fun foldl_term_types f (x, t as Const (_, T)) = f t (x, T)
wenzelm@8609
   980
  | foldl_term_types f (x, t as Free (_, T)) = f t (x, T)
wenzelm@8609
   981
  | foldl_term_types f (x, t as Var (_, T)) = f t (x, T)
wenzelm@8609
   982
  | foldl_term_types f (x, Bound _) = x
wenzelm@8609
   983
  | foldl_term_types f (x, t as Abs (_, T, b)) = foldl_term_types f (f t (x, T), b)
wenzelm@8609
   984
  | foldl_term_types f (x, t $ u) = foldl_term_types f (foldl_term_types f (x, t), u);
wenzelm@8609
   985
wenzelm@8609
   986
fun foldl_types f = foldl_term_types (fn _ => f);
wenzelm@4286
   987
wenzelm@12499
   988
(*collect variables*)
wenzelm@16294
   989
val add_tvarsT = foldl_atyps (fn (vs, TVar v) => insert (op =) v vs | (vs, _) => vs);
wenzelm@12499
   990
val add_tvars = foldl_types add_tvarsT;
wenzelm@16294
   991
val add_vars = foldl_aterms (fn (vs, Var v) => insert (op =) v vs | (vs, _) => vs);
wenzelm@16294
   992
val add_frees = foldl_aterms (fn (vs, Free v) => insert (op =) v vs | (vs, _) => vs);
wenzelm@12499
   993
wenzelm@15025
   994
(*collect variable names*)
wenzelm@15025
   995
val add_term_varnames = foldl_aterms (fn (xs, Var (x, _)) => ins_ix (x, xs) | (xs, _) => xs);
wenzelm@15025
   996
fun term_varnames t = add_term_varnames ([], t);
wenzelm@4286
   997
paulson@1417
   998
wenzelm@4444
   999
(** type and term orders **)
wenzelm@4444
  1000
wenzelm@4444
  1001
fun indexname_ord ((x, i), (y, j)) =
paulson@14472
  1002
  (case Int.compare (i, j) of EQUAL => String.compare (x, y) | ord => ord);
wenzelm@4444
  1003
paulson@14472
  1004
val sort_ord = list_ord String.compare;
wenzelm@13000
  1005
wenzelm@4444
  1006
wenzelm@4444
  1007
(* typ_ord *)
wenzelm@4444
  1008
paulson@14472
  1009
fun typ_ord (Type x, Type y) = prod_ord String.compare typs_ord (x, y)
wenzelm@4444
  1010
  | typ_ord (Type _, _) = GREATER
wenzelm@4444
  1011
  | typ_ord (TFree _, Type _) = LESS
paulson@14472
  1012
  | typ_ord (TFree x, TFree y) = prod_ord String.compare sort_ord (x, y)
wenzelm@4444
  1013
  | typ_ord (TFree _, TVar _) = GREATER
wenzelm@4444
  1014
  | typ_ord (TVar _, Type _) = LESS
wenzelm@4444
  1015
  | typ_ord (TVar _, TFree _) = LESS
wenzelm@13000
  1016
  | typ_ord (TVar x, TVar y) = prod_ord indexname_ord sort_ord (x, y)
wenzelm@4444
  1017
and typs_ord Ts_Us = list_ord typ_ord Ts_Us;
wenzelm@4444
  1018
wenzelm@4444
  1019
wenzelm@4444
  1020
(* term_ord *)
wenzelm@4444
  1021
wenzelm@4444
  1022
(*a linear well-founded AC-compatible ordering for terms:
wenzelm@4444
  1023
  s < t <=> 1. size(s) < size(t) or
wenzelm@4444
  1024
            2. size(s) = size(t) and s=f(...) and t=g(...) and f<g or
wenzelm@4444
  1025
            3. size(s) = size(t) and s=f(s1..sn) and t=f(t1..tn) and
wenzelm@4444
  1026
               (s1..sn) < (t1..tn) (lexicographically)*)
wenzelm@4444
  1027
wenzelm@4444
  1028
fun dest_hd (Const (a, T)) = (((a, 0), T), 0)
wenzelm@4444
  1029
  | dest_hd (Free (a, T)) = (((a, 0), T), 1)
wenzelm@4444
  1030
  | dest_hd (Var v) = (v, 2)
wenzelm@4444
  1031
  | dest_hd (Bound i) = ((("", i), dummyT), 3)
wenzelm@4444
  1032
  | dest_hd (Abs (_, T, _)) = ((("", 0), T), 4);
wenzelm@4444
  1033
wenzelm@4444
  1034
fun term_ord (Abs (_, T, t), Abs(_, U, u)) =
wenzelm@4444
  1035
      (case term_ord (t, u) of EQUAL => typ_ord (T, U) | ord => ord)
wenzelm@4444
  1036
  | term_ord (t, u) =
paulson@14472
  1037
      (case Int.compare (size_of_term t, size_of_term u) of
wenzelm@4444
  1038
        EQUAL =>
wenzelm@4444
  1039
          let val (f, ts) = strip_comb t and (g, us) = strip_comb u in
wenzelm@4444
  1040
            (case hd_ord (f, g) of EQUAL => terms_ord (ts, us) | ord => ord)
wenzelm@4444
  1041
          end
wenzelm@4444
  1042
      | ord => ord)
wenzelm@4444
  1043
and hd_ord (f, g) =
paulson@14472
  1044
  prod_ord (prod_ord indexname_ord typ_ord) Int.compare (dest_hd f, dest_hd g)
wenzelm@4444
  1045
and terms_ord (ts, us) = list_ord term_ord (ts, us);
wenzelm@4444
  1046
wenzelm@4444
  1047
fun termless tu = (term_ord tu = LESS);
wenzelm@4444
  1048
berghofe@8408
  1049
structure Vartab = TableFun(type key = indexname val ord = indexname_ord);
wenzelm@13000
  1050
structure Typtab = TableFun(type key = typ val ord = typ_ord);
berghofe@8408
  1051
structure Termtab = TableFun(type key = term val ord = term_ord);
berghofe@8408
  1052
wenzelm@4444
  1053
wenzelm@13000
  1054
(*** Compression of terms and types by sharing common subtrees.
wenzelm@13000
  1055
     Saves 50-75% on storage requirements.  As it is a bit slow,
wenzelm@13000
  1056
     it should be called only for axioms, stored theorems, etc.
wenzelm@13000
  1057
     Recorded term and type fragments are never disposed. ***)
paulson@1417
  1058
wenzelm@16338
  1059
paulson@1417
  1060
(** Sharing of types **)
paulson@1417
  1061
wenzelm@13000
  1062
val memo_types = ref (Typtab.empty: typ Typtab.table);
paulson@1417
  1063
paulson@1417
  1064
fun compress_type T =
wenzelm@13000
  1065
  (case Typtab.lookup (! memo_types, T) of
skalberg@15531
  1066
    SOME T' => T'
skalberg@15531
  1067
  | NONE =>
wenzelm@13000
  1068
      let val T' = (case T of Type (a, Ts) => Type (a, map compress_type Ts) | _ => T)
wenzelm@13000
  1069
      in memo_types := Typtab.update ((T', T'), ! memo_types); T' end);
wenzelm@13000
  1070
paulson@1417
  1071
paulson@1417
  1072
(** Sharing of atomic terms **)
paulson@1417
  1073
wenzelm@13000
  1074
val memo_terms = ref (Termtab.empty : term Termtab.table);
paulson@1417
  1075
paulson@1417
  1076
fun share_term (t $ u) = share_term t $ share_term u
wenzelm@13000
  1077
  | share_term (Abs (a, T, u)) = Abs (a, T, share_term u)
paulson@1417
  1078
  | share_term t =
wenzelm@13000
  1079
      (case Termtab.lookup (! memo_terms, t) of
skalberg@15531
  1080
        SOME t' => t'
skalberg@15531
  1081
      | NONE => (memo_terms := Termtab.update ((t, t), ! memo_terms); t));
paulson@1417
  1082
paulson@1417
  1083
val compress_term = share_term o map_term_types compress_type;
paulson@1417
  1084
wenzelm@4444
  1085
wenzelm@9536
  1086
(* dummy patterns *)
wenzelm@9536
  1087
wenzelm@9536
  1088
val dummy_patternN = "dummy_pattern";
wenzelm@9536
  1089
wenzelm@9536
  1090
fun is_dummy_pattern (Const ("dummy_pattern", _)) = true
wenzelm@9536
  1091
  | is_dummy_pattern _ = false;
wenzelm@9536
  1092
wenzelm@9536
  1093
fun no_dummy_patterns tm =
wenzelm@9536
  1094
  if not (foldl_aterms (fn (b, t) => b orelse is_dummy_pattern t) (false, tm)) then tm
wenzelm@9536
  1095
  else raise TERM ("Illegal occurrence of '_' dummy pattern", [tm]);
wenzelm@9536
  1096
wenzelm@11903
  1097
fun replace_dummy Ts (i, Const ("dummy_pattern", T)) =
wenzelm@11903
  1098
      (i + 1, list_comb (Var (("_dummy_", i), Ts ---> T), map Bound (0 upto length Ts - 1)))
wenzelm@11903
  1099
  | replace_dummy Ts (i, Abs (x, T, t)) =
wenzelm@11903
  1100
      let val (i', t') = replace_dummy (T :: Ts) (i, t)
wenzelm@11903
  1101
      in (i', Abs (x, T, t')) end
wenzelm@11903
  1102
  | replace_dummy Ts (i, t $ u) =
wenzelm@11903
  1103
      let val (i', t') = replace_dummy Ts (i, t); val (i'', u') = replace_dummy Ts (i', u)
wenzelm@11903
  1104
      in (i'', t' $ u') end
wenzelm@11903
  1105
  | replace_dummy _ (i, a) = (i, a);
wenzelm@11903
  1106
wenzelm@11903
  1107
val replace_dummy_patterns = replace_dummy [];
wenzelm@9536
  1108
wenzelm@10552
  1109
fun is_replaced_dummy_pattern ("_dummy_", _) = true
wenzelm@10552
  1110
  | is_replaced_dummy_pattern _ = false;
wenzelm@9536
  1111
wenzelm@16035
  1112
fun show_dummy_patterns (Var (("_dummy_", _), T)) = Const ("dummy_pattern", T)
wenzelm@16035
  1113
  | show_dummy_patterns (t $ u) = show_dummy_patterns t $ show_dummy_patterns u
wenzelm@16035
  1114
  | show_dummy_patterns (Abs (x, T, t)) = Abs (x, T, show_dummy_patterns t)
wenzelm@16035
  1115
  | show_dummy_patterns a = a;
wenzelm@16035
  1116
wenzelm@13484
  1117
wenzelm@13484
  1118
(* adhoc freezing *)
wenzelm@13484
  1119
wenzelm@13484
  1120
fun adhoc_freeze_vars tm =
wenzelm@13484
  1121
  let
wenzelm@13484
  1122
    fun mk_inst (var as Var ((a, i), T)) =
wenzelm@13484
  1123
      let val x = a ^ Library.gensym "_" ^ string_of_int i
wenzelm@13484
  1124
      in ((var,  Free(x, T)), x) end;
wenzelm@13484
  1125
    val (insts, xs) = split_list (map mk_inst (term_vars tm));
wenzelm@13484
  1126
  in (subst_atomic insts tm, xs) end;
wenzelm@13484
  1127
wenzelm@13484
  1128
wenzelm@14786
  1129
(* string_of_vname *)
wenzelm@14786
  1130
wenzelm@15986
  1131
val show_question_marks = ref true;
berghofe@15472
  1132
wenzelm@14786
  1133
fun string_of_vname (x, i) =
wenzelm@14786
  1134
  let
wenzelm@15986
  1135
    val question_mark = if ! show_question_marks then "?" else "";
wenzelm@15986
  1136
    val idx = string_of_int i;
wenzelm@15986
  1137
    val dot =
wenzelm@15986
  1138
      (case rev (Symbol.explode x) of
wenzelm@15986
  1139
        _ :: "\\<^isub>" :: _ => false
wenzelm@15986
  1140
      | _ :: "\\<^isup>" :: _ => false
wenzelm@15986
  1141
      | c :: _ => Symbol.is_digit c
wenzelm@15986
  1142
      | _ => true);
wenzelm@14786
  1143
  in
wenzelm@15986
  1144
    if dot then question_mark ^ x ^ "." ^ idx
wenzelm@15986
  1145
    else if i <> 0 then question_mark ^ x ^ idx
wenzelm@15986
  1146
    else question_mark ^ x
wenzelm@14786
  1147
  end;
wenzelm@14786
  1148
wenzelm@14786
  1149
fun string_of_vname' (x, ~1) = x
wenzelm@14786
  1150
  | string_of_vname' xi = string_of_vname xi;
wenzelm@14786
  1151
nipkow@15612
  1152
fun string_of_term (Const(s,_)) = s
nipkow@15612
  1153
  | string_of_term (Free(s,_)) = s
nipkow@15612
  1154
  | string_of_term (Var(ix,_)) = string_of_vname ix
nipkow@15612
  1155
  | string_of_term (Bound i) = string_of_int i
nipkow@15612
  1156
  | string_of_term (Abs(x,_,t)) = "%" ^ x ^ ". " ^ string_of_term t
nipkow@15612
  1157
  | string_of_term (s $ t) =
nipkow@15612
  1158
      "(" ^ string_of_term s ^ " " ^ string_of_term t ^ ")"
nipkow@15612
  1159
clasohm@1364
  1160
end;
clasohm@1364
  1161
wenzelm@4444
  1162
structure BasicTerm: BASIC_TERM = Term;
wenzelm@4444
  1163
open BasicTerm;