src/Pure/term.ML
author berghofe
Wed Oct 31 19:37:04 2001 +0100 (2001-10-31)
changeset 11998 b14e7686ce84
parent 11922 78857e6107cb
child 12306 749a04f0cfb0
permissions -rw-r--r--
- enter_thmx -> enter_thms
- improved naming of theorems: enter_thms now takes functions pre_name and post_name
as arguments
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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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  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 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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    $ of term * term
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  structure Vartab : 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 dest_Type: typ -> string * typ list
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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 map_typ: (class -> class) -> (string -> string) -> typ -> typ
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  val map_term:
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     (class -> class) ->
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     (string -> string) -> (string -> string) -> term -> term
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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 dummyT: typ
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  val logicC: class
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  val logicS: sort
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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 flexpair: 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 subst_TVars_Vartab: typ Vartab.table -> 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 eq_sort: sort * class list -> bool
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  val mem_sort: sort * class list list -> bool
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  val subset_sort: sort list * class list list -> bool
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  val eq_set_sort: sort list * sort list -> bool
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  val ins_sort: sort * class list list -> class list list
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  val union_sort: sort list * sort list -> sort list
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  val rems_sort: sort list * sort list -> sort list
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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 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 typ_subst_TVars_Vartab : typ Vartab.table -> 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 read_radixint: int * string list -> int * string list
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  val read_int: string list -> int * string list
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  val oct_char: string -> string
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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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  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 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_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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end;
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signature TERM =
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sig
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  include BASIC_TERM
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  val invent_names: int -> string -> string 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 termless: term * term -> bool
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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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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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(* 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 ---> = 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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(** 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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(** 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) = (nth_elem (i,Ts)  
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        handle LIST _ => raise TYPE("type_of: bound variable", [], [Bound i]))
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  | type_of1 (Ts, Var (_,T)) = T
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  | type_of1 (Ts, Abs (_,T,body)) = T --> type_of1(T::Ts, body)
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  | type_of1 (Ts, f$u) = 
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      let val U = type_of1(Ts,u)
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          and T = type_of1(Ts,f)
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      in case T of
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            Type("fun",[T1,T2]) =>
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              if T1=U then T2  else raise TYPE
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                    ("type_of: type mismatch in application", [T1,U], [f$u])
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          | _ => raise TYPE 
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                    ("type_of: function type is expected in application",
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                     [T,U], [f$u])
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      end;
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fun type_of t : typ = type_of1 ([],t);
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(*Determines the type of a term, with minimal checking*)
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fun fastype_of1 (Ts, f$u) = 
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    (case fastype_of1 (Ts,f) of
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        Type("fun",[_,T]) => T
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        | _ => raise TERM("fastype_of: expected function type", [f$u]))
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  | fastype_of1 (_, Const (_,T)) = T
lcp@61
   329
  | fastype_of1 (_, Free (_,T)) = T
lcp@61
   330
  | fastype_of1 (Ts, Bound i) = (nth_elem(i,Ts)
wenzelm@9536
   331
         handle LIST _ => raise TERM("fastype_of: Bound", [Bound i]))
lcp@61
   332
  | fastype_of1 (_, Var (_,T)) = T 
lcp@61
   333
  | fastype_of1 (Ts, Abs (_,T,u)) = T --> fastype_of1 (T::Ts, u);
lcp@61
   334
lcp@61
   335
fun fastype_of t : typ = fastype_of1 ([],t);
clasohm@0
   336
clasohm@0
   337
wenzelm@10806
   338
val list_abs = foldr (fn ((x, T), t) => Abs (x, T, t));
wenzelm@10806
   339
clasohm@0
   340
(* maps  (x1,...,xn)t   to   t  *)
clasohm@0
   341
fun strip_abs_body (Abs(_,_,t))  =  strip_abs_body t  
clasohm@0
   342
  | strip_abs_body u  =  u;
clasohm@0
   343
clasohm@0
   344
(* maps  (x1,...,xn)t   to   [x1, ..., xn]  *)
clasohm@0
   345
fun strip_abs_vars (Abs(a,T,t))  =  (a,T) :: strip_abs_vars t 
clasohm@0
   346
  | strip_abs_vars u  =  [] : (string*typ) list;
clasohm@0
   347
clasohm@0
   348
clasohm@0
   349
fun strip_qnt_body qnt =
clasohm@0
   350
let fun strip(tm as Const(c,_)$Abs(_,_,t)) = if c=qnt then strip t else tm
clasohm@0
   351
      | strip t = t
clasohm@0
   352
in strip end;
clasohm@0
   353
clasohm@0
   354
fun strip_qnt_vars qnt =
clasohm@0
   355
let fun strip(Const(c,_)$Abs(a,T,t)) = if c=qnt then (a,T)::strip t else []
clasohm@0
   356
      | strip t  =  [] : (string*typ) list
clasohm@0
   357
in strip end;
clasohm@0
   358
clasohm@0
   359
clasohm@0
   360
(* maps   (f, [t1,...,tn])  to  f(t1,...,tn) *)
clasohm@0
   361
val list_comb : term * term list -> term = foldl (op $);
clasohm@0
   362
clasohm@0
   363
clasohm@0
   364
(* maps   f(t1,...,tn)  to  (f, [t1,...,tn]) ; naturally tail-recursive*)
clasohm@0
   365
fun strip_comb u : term * term list = 
clasohm@0
   366
    let fun stripc (f$t, ts) = stripc (f, t::ts)
clasohm@0
   367
        |   stripc  x =  x 
clasohm@0
   368
    in  stripc(u,[])  end;
clasohm@0
   369
clasohm@0
   370
clasohm@0
   371
(* maps   f(t1,...,tn)  to  f , which is never a combination *)
clasohm@0
   372
fun head_of (f$t) = head_of f
clasohm@0
   373
  | head_of u = u;
clasohm@0
   374
clasohm@0
   375
clasohm@0
   376
(*Number of atoms and abstractions in a term*)
clasohm@0
   377
fun size_of_term (Abs (_,_,body)) = 1 + size_of_term body
clasohm@0
   378
  | size_of_term (f$t) = size_of_term f  +  size_of_term t
clasohm@0
   379
  | size_of_term _ = 1;
clasohm@0
   380
nipkow@949
   381
fun map_type_tvar f (Type(a,Ts)) = Type(a, map (map_type_tvar f) Ts)
nipkow@949
   382
  | map_type_tvar f (T as TFree _) = T
nipkow@949
   383
  | map_type_tvar f (TVar x) = f x;
nipkow@949
   384
nipkow@949
   385
fun map_type_tfree f (Type(a,Ts)) = Type(a, map (map_type_tfree f) Ts)
nipkow@949
   386
  | map_type_tfree f (TFree x) = f x
nipkow@949
   387
  | map_type_tfree f (T as TVar _) = T;
nipkow@949
   388
clasohm@0
   389
(* apply a function to all types in a term *)
clasohm@0
   390
fun map_term_types f =
clasohm@0
   391
let fun map(Const(a,T)) = Const(a, f T)
clasohm@0
   392
      | map(Free(a,T)) = Free(a, f T)
clasohm@0
   393
      | map(Var(v,T)) = Var(v, f T)
clasohm@0
   394
      | map(t as Bound _)  = t
clasohm@0
   395
      | map(Abs(a,T,t)) = Abs(a, f T, map t)
clasohm@0
   396
      | map(f$t) = map f $ map t;
clasohm@0
   397
in map end;
clasohm@0
   398
clasohm@0
   399
(* iterate a function over all types in a term *)
clasohm@0
   400
fun it_term_types f =
clasohm@0
   401
let fun iter(Const(_,T), a) = f(T,a)
clasohm@0
   402
      | iter(Free(_,T), a) = f(T,a)
clasohm@0
   403
      | iter(Var(_,T), a) = f(T,a)
clasohm@0
   404
      | iter(Abs(_,T,t), a) = iter(t,f(T,a))
clasohm@0
   405
      | iter(f$u, a) = iter(f, iter(u, a))
clasohm@0
   406
      | iter(Bound _, a) = a
clasohm@0
   407
in iter end
clasohm@0
   408
clasohm@0
   409
clasohm@0
   410
(** Connectives of higher order logic **)
clasohm@0
   411
wenzelm@375
   412
val logicC: class = "logic";
wenzelm@375
   413
val logicS: sort = [logicC];
wenzelm@375
   414
wenzelm@375
   415
fun itselfT ty = Type ("itself", [ty]);
wenzelm@375
   416
val a_itselfT = itselfT (TFree ("'a", logicS));
wenzelm@375
   417
clasohm@0
   418
val propT : typ = Type("prop",[]);
clasohm@0
   419
clasohm@0
   420
val implies = Const("==>", propT-->propT-->propT);
clasohm@0
   421
clasohm@0
   422
fun all T = Const("all", (T-->propT)-->propT);
clasohm@0
   423
clasohm@0
   424
fun equals T = Const("==", T-->T-->propT);
clasohm@0
   425
clasohm@0
   426
fun flexpair T = Const("=?=", T-->T-->propT);
clasohm@0
   427
clasohm@0
   428
(* maps  !!x1...xn. t   to   t  *)
clasohm@0
   429
fun strip_all_body (Const("all",_)$Abs(_,_,t))  =  strip_all_body t  
clasohm@0
   430
  | strip_all_body t  =  t;
clasohm@0
   431
clasohm@0
   432
(* maps  !!x1...xn. t   to   [x1, ..., xn]  *)
clasohm@0
   433
fun strip_all_vars (Const("all",_)$Abs(a,T,t))  =
wenzelm@9536
   434
                (a,T) :: strip_all_vars t 
clasohm@0
   435
  | strip_all_vars t  =  [] : (string*typ) list;
clasohm@0
   436
clasohm@0
   437
(*increments a term's non-local bound variables
clasohm@0
   438
  required when moving a term within abstractions
clasohm@0
   439
     inc is  increment for bound variables
clasohm@0
   440
     lev is  level at which a bound variable is considered 'loose'*)
clasohm@0
   441
fun incr_bv (inc, lev, u as Bound i) = if i>=lev then Bound(i+inc) else u 
clasohm@0
   442
  | incr_bv (inc, lev, Abs(a,T,body)) =
wenzelm@9536
   443
        Abs(a, T, incr_bv(inc,lev+1,body))
clasohm@0
   444
  | incr_bv (inc, lev, f$t) = 
clasohm@0
   445
      incr_bv(inc,lev,f) $ incr_bv(inc,lev,t)
clasohm@0
   446
  | incr_bv (inc, lev, u) = u;
clasohm@0
   447
clasohm@0
   448
fun incr_boundvars  0  t = t
clasohm@0
   449
  | incr_boundvars inc t = incr_bv(inc,0,t);
clasohm@0
   450
clasohm@0
   451
clasohm@0
   452
(*Accumulate all 'loose' bound vars referring to level 'lev' or beyond.
clasohm@0
   453
   (Bound 0) is loose at level 0 *)
clasohm@0
   454
fun add_loose_bnos (Bound i, lev, js) = 
wenzelm@9536
   455
        if i<lev then js  else  (i-lev) ins_int js
clasohm@0
   456
  | add_loose_bnos (Abs (_,_,t), lev, js) = add_loose_bnos (t, lev+1, js)
clasohm@0
   457
  | add_loose_bnos (f$t, lev, js) =
wenzelm@9536
   458
        add_loose_bnos (f, lev, add_loose_bnos (t, lev, js)) 
clasohm@0
   459
  | add_loose_bnos (_, _, js) = js;
clasohm@0
   460
clasohm@0
   461
fun loose_bnos t = add_loose_bnos (t, 0, []);
clasohm@0
   462
clasohm@0
   463
(* loose_bvar(t,k) iff t contains a 'loose' bound variable referring to
clasohm@0
   464
   level k or beyond. *)
clasohm@0
   465
fun loose_bvar(Bound i,k) = i >= k
clasohm@0
   466
  | loose_bvar(f$t, k) = loose_bvar(f,k) orelse loose_bvar(t,k)
clasohm@0
   467
  | loose_bvar(Abs(_,_,t),k) = loose_bvar(t,k+1)
clasohm@0
   468
  | loose_bvar _ = false;
clasohm@0
   469
nipkow@2792
   470
fun loose_bvar1(Bound i,k) = i = k
nipkow@2792
   471
  | loose_bvar1(f$t, k) = loose_bvar1(f,k) orelse loose_bvar1(t,k)
nipkow@2792
   472
  | loose_bvar1(Abs(_,_,t),k) = loose_bvar1(t,k+1)
nipkow@2792
   473
  | loose_bvar1 _ = false;
clasohm@0
   474
clasohm@0
   475
(*Substitute arguments for loose bound variables.
clasohm@0
   476
  Beta-reduction of arg(n-1)...arg0 into t replacing (Bound i) with (argi).
wenzelm@4626
   477
  Note that for ((%x y. c) a b), the bound vars in c are x=1 and y=0
wenzelm@9536
   478
        and the appropriate call is  subst_bounds([b,a], c) .
clasohm@0
   479
  Loose bound variables >=n are reduced by "n" to
clasohm@0
   480
     compensate for the disappearance of lambdas.
clasohm@0
   481
*)
clasohm@0
   482
fun subst_bounds (args: term list, t) : term = 
clasohm@0
   483
  let val n = length args;
clasohm@0
   484
      fun subst (t as Bound i, lev) =
wenzelm@9536
   485
           (if i<lev then  t    (*var is locally bound*)
wenzelm@9536
   486
            else  incr_boundvars lev (List.nth(args, i-lev))
wenzelm@9536
   487
                    handle Subscript => Bound(i-n)  (*loose: change it*))
wenzelm@9536
   488
        | subst (Abs(a,T,body), lev) = Abs(a, T,  subst(body,lev+1))
wenzelm@9536
   489
        | subst (f$t, lev) =  subst(f,lev)  $  subst(t,lev)
wenzelm@9536
   490
        | subst (t,lev) = t
clasohm@0
   491
  in   case args of [] => t  | _ => subst (t,0)  end;
clasohm@0
   492
paulson@2192
   493
(*Special case: one argument*)
paulson@2192
   494
fun subst_bound (arg, t) : term = 
paulson@2192
   495
  let fun subst (t as Bound i, lev) =
wenzelm@9536
   496
            if i<lev then  t    (*var is locally bound*)
wenzelm@9536
   497
            else  if i=lev then incr_boundvars lev arg
wenzelm@9536
   498
                           else Bound(i-1)  (*loose: change it*)
wenzelm@9536
   499
        | subst (Abs(a,T,body), lev) = Abs(a, T,  subst(body,lev+1))
wenzelm@9536
   500
        | subst (f$t, lev) =  subst(f,lev)  $  subst(t,lev)
wenzelm@9536
   501
        | subst (t,lev) = t
paulson@2192
   502
  in  subst (t,0)  end;
paulson@2192
   503
clasohm@0
   504
(*beta-reduce if possible, else form application*)
paulson@2192
   505
fun betapply (Abs(_,_,t), u) = subst_bound (u,t)
clasohm@0
   506
  | betapply (f,u) = f$u;
clasohm@0
   507
paulson@2192
   508
(** Equality, membership and insertion of indexnames (string*ints) **)
paulson@2192
   509
paulson@2192
   510
(*optimized equality test for indexnames.  Yields a huge gain under Poly/ML*)
wenzelm@2959
   511
fun eq_ix ((a, i):indexname, (a',i'):indexname) = (a=a') andalso i=i';
paulson@2192
   512
paulson@2192
   513
(*membership in a list, optimized version for indexnames*)
wenzelm@2959
   514
fun mem_ix (_, []) = false
paulson@2192
   515
  | mem_ix (x, y :: ys) = eq_ix(x,y) orelse mem_ix (x, ys);
paulson@2192
   516
paulson@2192
   517
(*insertion into list, optimized version for indexnames*)
paulson@2192
   518
fun ins_ix (x,xs) = if mem_ix (x, xs) then xs else x :: xs;
paulson@2192
   519
clasohm@0
   520
(*Tests whether 2 terms are alpha-convertible and have same type.
wenzelm@4626
   521
  Note that constants may have more than one type.*)
clasohm@0
   522
fun (Const(a,T)) aconv (Const(b,U)) = a=b  andalso  T=U
paulson@2752
   523
  | (Free(a,T))  aconv (Free(b,U))  = a=b  andalso  T=U
paulson@2752
   524
  | (Var(v,T))   aconv (Var(w,U))   = eq_ix(v,w)  andalso  T=U
paulson@2752
   525
  | (Bound i)    aconv (Bound j)    = i=j
clasohm@0
   526
  | (Abs(_,T,t)) aconv (Abs(_,U,u)) = t aconv u  andalso  T=U
paulson@2752
   527
  | (f$t)        aconv (g$u)        = (f aconv g) andalso (t aconv u)
clasohm@0
   528
  | _ aconv _  =  false;
clasohm@0
   529
paulson@2176
   530
(** Membership, insertion, union for terms **)
paulson@2176
   531
paulson@2176
   532
fun mem_term (_, []) = false
paulson@2176
   533
  | mem_term (t, t'::ts) = t aconv t' orelse mem_term(t,ts);
paulson@2176
   534
paulson@2182
   535
fun subset_term ([], ys) = true
paulson@2182
   536
  | subset_term (x :: xs, ys) = mem_term (x, ys) andalso subset_term(xs, ys);
paulson@2182
   537
paulson@2182
   538
fun eq_set_term (xs, ys) =
paulson@2182
   539
    xs = ys orelse (subset_term (xs, ys) andalso subset_term (ys, xs));
paulson@2182
   540
paulson@2176
   541
fun ins_term(t,ts) = if mem_term(t,ts) then ts else t :: ts;
paulson@2176
   542
paulson@2176
   543
fun union_term (xs, []) = xs
paulson@2176
   544
  | union_term ([], ys) = ys
paulson@2176
   545
  | union_term ((x :: xs), ys) = union_term (xs, ins_term (x, ys));
paulson@2176
   546
paulson@5585
   547
fun inter_term ([], ys) = []
paulson@5585
   548
  | inter_term (x::xs, ys) =
paulson@5585
   549
      if mem_term (x,ys) then x :: inter_term(xs,ys) else inter_term(xs,ys);
paulson@5585
   550
paulson@2176
   551
(** Equality, membership and insertion of sorts (string lists) **)
paulson@2176
   552
paulson@2176
   553
fun eq_sort ([]:sort, []) = true
paulson@2176
   554
  | eq_sort ((s::ss), (t::ts)) = s=t andalso eq_sort(ss,ts)
paulson@2176
   555
  | eq_sort (_, _) = false;
paulson@2176
   556
paulson@2176
   557
fun mem_sort (_:sort, []) = false
paulson@2176
   558
  | mem_sort (S, S'::Ss) = eq_sort (S, S') orelse mem_sort(S,Ss);
paulson@2176
   559
paulson@2176
   560
fun ins_sort(S,Ss) = if mem_sort(S,Ss) then Ss else S :: Ss;
paulson@2176
   561
paulson@2176
   562
fun union_sort (xs, []) = xs
paulson@2176
   563
  | union_sort ([], ys) = ys
paulson@2176
   564
  | union_sort ((x :: xs), ys) = union_sort (xs, ins_sort (x, ys));
paulson@2176
   565
paulson@2182
   566
fun subset_sort ([], ys) = true
paulson@2182
   567
  | subset_sort (x :: xs, ys) = mem_sort (x, ys) andalso subset_sort(xs, ys);
paulson@2182
   568
paulson@2182
   569
fun eq_set_sort (xs, ys) =
paulson@2182
   570
    xs = ys orelse (subset_sort (xs, ys) andalso subset_sort (ys, xs));
paulson@2182
   571
wenzelm@7638
   572
val rems_sort = gen_rems eq_sort;
wenzelm@7638
   573
clasohm@0
   574
(*are two term lists alpha-convertible in corresponding elements?*)
clasohm@0
   575
fun aconvs ([],[]) = true
clasohm@0
   576
  | aconvs (t::ts, u::us) = t aconv u andalso aconvs(ts,us)
clasohm@0
   577
  | aconvs _ = false;
clasohm@0
   578
clasohm@0
   579
(*A fast unification filter: true unless the two terms cannot be unified. 
clasohm@0
   580
  Terms must be NORMAL.  Treats all Vars as distinct. *)
clasohm@0
   581
fun could_unify (t,u) =
clasohm@0
   582
  let fun matchrands (f$t, g$u) = could_unify(t,u) andalso  matchrands(f,g)
wenzelm@9536
   583
        | matchrands _ = true
clasohm@0
   584
  in case (head_of t , head_of u) of
wenzelm@9536
   585
        (_, Var _) => true
clasohm@0
   586
      | (Var _, _) => true
clasohm@0
   587
      | (Const(a,_), Const(b,_)) =>  a=b andalso matchrands(t,u)
clasohm@0
   588
      | (Free(a,_), Free(b,_)) =>  a=b andalso matchrands(t,u)
clasohm@0
   589
      | (Bound i, Bound j) =>  i=j andalso matchrands(t,u)
clasohm@0
   590
      | (Abs _, _) =>  true   (*because of possible eta equality*)
clasohm@0
   591
      | (_, Abs _) =>  true
clasohm@0
   592
      | _ => false
clasohm@0
   593
  end;
clasohm@0
   594
clasohm@0
   595
(*Substitute new for free occurrences of old in a term*)
clasohm@0
   596
fun subst_free [] = (fn t=>t)
clasohm@0
   597
  | subst_free pairs =
clasohm@0
   598
      let fun substf u = 
wenzelm@9536
   599
            case gen_assoc (op aconv) (pairs, u) of
wenzelm@9536
   600
                Some u' => u'
wenzelm@9536
   601
              | None => (case u of Abs(a,T,t) => Abs(a, T, substf t)
wenzelm@9536
   602
                                 | t$u' => substf t $ substf u'
wenzelm@9536
   603
                                 | _ => u)
clasohm@0
   604
      in  substf  end;
clasohm@0
   605
clasohm@0
   606
(*a total, irreflexive ordering on index names*)
clasohm@0
   607
fun xless ((a,i), (b,j): indexname) = i<j  orelse  (i=j andalso a<b);
clasohm@0
   608
clasohm@0
   609
clasohm@0
   610
(*Abstraction of the term "body" over its occurrences of v, 
clasohm@0
   611
    which must contain no loose bound variables.
clasohm@0
   612
  The resulting term is ready to become the body of an Abs.*)
clasohm@0
   613
fun abstract_over (v,body) =
clasohm@0
   614
  let fun abst (lev,u) = if (v aconv u) then (Bound lev) else
clasohm@0
   615
      (case u of
clasohm@0
   616
          Abs(a,T,t) => Abs(a, T, abst(lev+1, t))
wenzelm@9536
   617
        | f$rand => abst(lev,f) $ abst(lev,rand)
wenzelm@9536
   618
        | _ => u)
clasohm@0
   619
  in  abst(0,body)  end;
clasohm@0
   620
wenzelm@11922
   621
fun lambda v t =
wenzelm@11922
   622
  let val (x, T) = dest_Free v
wenzelm@11922
   623
  in Abs (x, T, abstract_over (v, t)) end;
clasohm@0
   624
clasohm@0
   625
(*Form an abstraction over a free variable.*)
clasohm@0
   626
fun absfree (a,T,body) = Abs(a, T, abstract_over (Free(a,T), body));
clasohm@0
   627
clasohm@0
   628
(*Abstraction over a list of free variables*)
clasohm@0
   629
fun list_abs_free ([ ] ,     t) = t
clasohm@0
   630
  | list_abs_free ((a,T)::vars, t) = 
clasohm@0
   631
      absfree(a, T, list_abs_free(vars,t));
clasohm@0
   632
clasohm@0
   633
(*Quantification over a list of free variables*)
clasohm@0
   634
fun list_all_free ([], t: term) = t
clasohm@0
   635
  | list_all_free ((a,T)::vars, t) = 
clasohm@0
   636
        (all T) $ (absfree(a, T, list_all_free(vars,t)));
clasohm@0
   637
clasohm@0
   638
(*Quantification over a list of variables (already bound in body) *)
clasohm@0
   639
fun list_all ([], t) = t
clasohm@0
   640
  | list_all ((a,T)::vars, t) = 
clasohm@0
   641
        (all T) $ (Abs(a, T, list_all(vars,t)));
clasohm@0
   642
clasohm@0
   643
(*Replace the ATOMIC term ti by ui;    instl = [(t1,u1), ..., (tn,un)]. 
clasohm@0
   644
  A simultaneous substitution:  [ (a,b), (b,a) ] swaps a and b.  *)
clasohm@0
   645
fun subst_atomic [] t = t : term
clasohm@0
   646
  | subst_atomic (instl: (term*term) list) t =
clasohm@0
   647
      let fun subst (Abs(a,T,body)) = Abs(a, T, subst body)
wenzelm@9536
   648
            | subst (f$t') = subst f $ subst t'
nipkow@9721
   649
            | subst t = if_none (assoc(instl,t)) t
clasohm@0
   650
      in  subst t  end;
clasohm@0
   651
lcp@728
   652
(*Substitute for type Vars in a type*)
clasohm@0
   653
fun typ_subst_TVars iTs T = if null iTs then T else
clasohm@0
   654
  let fun subst(Type(a,Ts)) = Type(a, map subst Ts)
wenzelm@9536
   655
        | subst(T as TFree _) = T
nipkow@9721
   656
        | subst(T as TVar(ixn,_)) = if_none (assoc(iTs,ixn)) T
clasohm@0
   657
  in subst T end;
clasohm@0
   658
lcp@728
   659
(*Substitute for type Vars in a term*)
clasohm@0
   660
val subst_TVars = map_term_types o typ_subst_TVars;
clasohm@0
   661
lcp@728
   662
(*Substitute for Vars in a term; see also envir/norm_term*)
clasohm@0
   663
fun subst_Vars itms t = if null itms then t else
nipkow@9721
   664
  let fun subst(v as Var(ixn,_)) = if_none (assoc(itms,ixn)) v
clasohm@0
   665
        | subst(Abs(a,T,t)) = Abs(a,T,subst t)
clasohm@0
   666
        | subst(f$t) = subst f $ subst t
clasohm@0
   667
        | subst(t) = t
clasohm@0
   668
  in subst t end;
clasohm@0
   669
lcp@728
   670
(*Substitute for type/term Vars in a term; see also envir/norm_term*)
clasohm@0
   671
fun subst_vars(iTs,itms) = if null iTs then subst_Vars itms else
clasohm@0
   672
  let fun subst(Const(a,T)) = Const(a,typ_subst_TVars iTs T)
clasohm@0
   673
        | subst(Free(a,T)) = Free(a,typ_subst_TVars iTs T)
clasohm@0
   674
        | subst(v as Var(ixn,T)) = (case assoc(itms,ixn) of
clasohm@0
   675
            None   => Var(ixn,typ_subst_TVars iTs T)
clasohm@0
   676
          | Some t => t)
clasohm@0
   677
        | subst(b as Bound _) = b
clasohm@0
   678
        | subst(Abs(a,T,t)) = Abs(a,typ_subst_TVars iTs T,subst t)
clasohm@0
   679
        | subst(f$t) = subst f $ subst t
clasohm@0
   680
  in subst end;
clasohm@0
   681
clasohm@0
   682
clasohm@0
   683
(*Computing the maximum index of a typ*)
paulson@2146
   684
fun maxidx_of_typ(Type(_,Ts)) = maxidx_of_typs Ts
clasohm@0
   685
  | maxidx_of_typ(TFree _) = ~1
paulson@2146
   686
  | maxidx_of_typ(TVar((_,i),_)) = i
paulson@2146
   687
and maxidx_of_typs [] = ~1
paulson@2146
   688
  | maxidx_of_typs (T::Ts) = Int.max(maxidx_of_typ T, maxidx_of_typs Ts);
clasohm@0
   689
clasohm@0
   690
clasohm@0
   691
(*Computing the maximum index of a term*)
clasohm@0
   692
fun maxidx_of_term (Const(_,T)) = maxidx_of_typ T
clasohm@0
   693
  | maxidx_of_term (Bound _) = ~1
clasohm@0
   694
  | maxidx_of_term (Free(_,T)) = maxidx_of_typ T
paulson@2146
   695
  | maxidx_of_term (Var ((_,i), T)) = Int.max(i, maxidx_of_typ T)
paulson@2146
   696
  | maxidx_of_term (Abs (_,T,u)) = Int.max(maxidx_of_term u, maxidx_of_typ T)
paulson@2146
   697
  | maxidx_of_term (f$t) = Int.max(maxidx_of_term f,  maxidx_of_term t);
clasohm@0
   698
clasohm@0
   699
clasohm@0
   700
(* Increment the index of all Poly's in T by k *)
nipkow@949
   701
fun incr_tvar k = map_type_tvar (fn ((a,i),S) => TVar((a,i+k),S));
clasohm@0
   702
clasohm@0
   703
clasohm@0
   704
(**** Syntax-related declarations ****)
clasohm@0
   705
clasohm@0
   706
wenzelm@4626
   707
(*Dummy type for parsing and printing.  Will be replaced during type inference. *)
clasohm@0
   708
val dummyT = Type("dummy",[]);
clasohm@0
   709
wenzelm@4694
   710
(*read a numeral of the given radix, normally 10*)
wenzelm@4694
   711
fun read_radixint (radix: int, cs) : int * string list =
clasohm@0
   712
  let val zero = ord"0"
clasohm@0
   713
      val limit = zero+radix
clasohm@0
   714
      fun scan (num,[]) = (num,[])
wenzelm@9536
   715
        | scan (num, c::cs) =
wenzelm@9536
   716
              if  zero <= ord c  andalso  ord c < limit
wenzelm@9536
   717
              then scan(radix*num + ord c - zero, cs)
wenzelm@9536
   718
              else (num, c::cs)
clasohm@0
   719
  in  scan(0,cs)  end;
clasohm@0
   720
wenzelm@5986
   721
fun read_int cs = read_radixint (10, cs);
wenzelm@5986
   722
wenzelm@5986
   723
fun octal s = #1 (read_radixint (8, explode s));
wenzelm@5986
   724
val oct_char = chr o octal;
clasohm@0
   725
clasohm@0
   726
clasohm@0
   727
(*** Printing ***)
clasohm@0
   728
clasohm@0
   729
clasohm@0
   730
(*Makes a variant of the name c distinct from the names in bs.
clasohm@0
   731
  First attaches the suffix "a" and then increments this. *)
clasohm@0
   732
fun variant bs c : string =
paulson@2138
   733
  let fun vary2 c = if (c mem_string bs) then  vary2 (bump_string c)  else  c
paulson@2138
   734
      fun vary1 c = if (c mem_string bs) then  vary2 (c ^ "a")  else  c
clasohm@0
   735
  in  vary1 (if c="" then "u" else c)  end;
clasohm@0
   736
clasohm@0
   737
(*Create variants of the list of names, with priority to the first ones*)
clasohm@0
   738
fun variantlist ([], used) = []
clasohm@0
   739
  | variantlist(b::bs, used) = 
clasohm@0
   740
      let val b' = variant used b
clasohm@0
   741
      in  b' :: variantlist (bs, b'::used)  end;
clasohm@0
   742
wenzelm@11353
   743
fun invent_names n prfx = Library.tl (variantlist (Library.replicate (n + 1) prfx, []));
wenzelm@11353
   744
wenzelm@4017
   745
wenzelm@4017
   746
wenzelm@4017
   747
(** Consts etc. **)
wenzelm@4017
   748
wenzelm@4017
   749
fun add_typ_classes (Type (_, Ts), cs) = foldr add_typ_classes (Ts, cs)
wenzelm@4017
   750
  | add_typ_classes (TFree (_, S), cs) = S union cs
wenzelm@4017
   751
  | add_typ_classes (TVar (_, S), cs) = S union cs;
wenzelm@4017
   752
wenzelm@4017
   753
fun add_typ_tycons (Type (c, Ts), cs) = foldr add_typ_tycons (Ts, c ins cs)
wenzelm@4017
   754
  | add_typ_tycons (_, cs) = cs;
wenzelm@4017
   755
wenzelm@4017
   756
val add_term_classes = it_term_types add_typ_classes;
wenzelm@4017
   757
val add_term_tycons = it_term_types add_typ_tycons;
wenzelm@4017
   758
wenzelm@9319
   759
fun add_term_consts (Const (c, _), cs) = c ins_string cs
wenzelm@4017
   760
  | add_term_consts (t $ u, cs) = add_term_consts (t, add_term_consts (u, cs))
wenzelm@4017
   761
  | add_term_consts (Abs (_, _, t), cs) = add_term_consts (t, cs)
wenzelm@4017
   762
  | add_term_consts (_, cs) = cs;
wenzelm@4017
   763
oheimb@4185
   764
fun exists_Const P t = let
wenzelm@9536
   765
        fun ex (Const c      ) = P c
wenzelm@9536
   766
        |   ex (t $ u        ) = ex t orelse ex u
wenzelm@9536
   767
        |   ex (Abs (_, _, t)) = ex t
wenzelm@9536
   768
        |   ex _               = false
oheimb@4185
   769
    in ex t end;
wenzelm@4017
   770
nipkow@4631
   771
fun exists_subterm P =
nipkow@4631
   772
  let fun ex t = P t orelse
nipkow@4631
   773
                 (case t of
nipkow@4631
   774
                    u $ v        => ex u orelse ex v
nipkow@4631
   775
                  | Abs(_, _, u) => ex u
nipkow@4631
   776
                  | _            => false)
nipkow@4631
   777
  in ex end;
nipkow@4631
   778
wenzelm@4017
   779
(*map classes, tycons*)
wenzelm@4017
   780
fun map_typ f g (Type (c, Ts)) = Type (g c, map (map_typ f g) Ts)
wenzelm@4017
   781
  | map_typ f _ (TFree (x, S)) = TFree (x, map f S)
wenzelm@4017
   782
  | map_typ f _ (TVar (xi, S)) = TVar (xi, map f S);
wenzelm@4017
   783
wenzelm@4017
   784
(*map classes, tycons, consts*)
wenzelm@4017
   785
fun map_term f g h (Const (c, T)) = Const (h c, map_typ f g T)
wenzelm@4017
   786
  | map_term f g _ (Free (x, T)) = Free (x, map_typ f g T)
wenzelm@4017
   787
  | map_term f g _ (Var (xi, T)) = Var (xi, map_typ f g T)
wenzelm@4017
   788
  | map_term _ _ _ (t as Bound _) = t
wenzelm@4017
   789
  | map_term f g h (Abs (x, T, t)) = Abs (x, map_typ f g T, map_term f g h t)
wenzelm@4017
   790
  | map_term f g h (t $ u) = map_term f g h t $ map_term f g h u;
wenzelm@4017
   791
wenzelm@4017
   792
wenzelm@4017
   793
clasohm@0
   794
(** TFrees and TVars **)
clasohm@0
   795
clasohm@0
   796
(*maps  (bs,v)  to   v'::bs    this reverses the identifiers bs*)
clasohm@0
   797
fun add_new_id (bs, c) : string list =  variant bs c  ::  bs;
clasohm@0
   798
clasohm@0
   799
(*Accumulates the names in the term, suppressing duplicates.
clasohm@0
   800
  Includes Frees and Consts.  For choosing unambiguous bound var names.*)
wenzelm@10666
   801
fun add_term_names (Const(a,_), bs) = NameSpace.base a ins_string bs
paulson@2176
   802
  | add_term_names (Free(a,_), bs) = a ins_string bs
clasohm@0
   803
  | add_term_names (f$u, bs) = add_term_names (f, add_term_names(u, bs))
clasohm@0
   804
  | add_term_names (Abs(_,_,t), bs) = add_term_names(t,bs)
clasohm@0
   805
  | add_term_names (_, bs) = bs;
clasohm@0
   806
clasohm@0
   807
(*Accumulates the TVars in a type, suppressing duplicates. *)
clasohm@0
   808
fun add_typ_tvars(Type(_,Ts),vs) = foldr add_typ_tvars (Ts,vs)
clasohm@0
   809
  | add_typ_tvars(TFree(_),vs) = vs
clasohm@0
   810
  | add_typ_tvars(TVar(v),vs) = v ins vs;
clasohm@0
   811
clasohm@0
   812
(*Accumulates the TFrees in a type, suppressing duplicates. *)
clasohm@0
   813
fun add_typ_tfree_names(Type(_,Ts),fs) = foldr add_typ_tfree_names (Ts,fs)
paulson@2176
   814
  | add_typ_tfree_names(TFree(f,_),fs) = f ins_string fs
clasohm@0
   815
  | add_typ_tfree_names(TVar(_),fs) = fs;
clasohm@0
   816
clasohm@0
   817
fun add_typ_tfrees(Type(_,Ts),fs) = foldr add_typ_tfrees (Ts,fs)
clasohm@0
   818
  | add_typ_tfrees(TFree(f),fs) = f ins fs
clasohm@0
   819
  | add_typ_tfrees(TVar(_),fs) = fs;
clasohm@0
   820
nipkow@949
   821
fun add_typ_varnames(Type(_,Ts),nms) = foldr add_typ_varnames (Ts,nms)
paulson@2176
   822
  | add_typ_varnames(TFree(nm,_),nms) = nm ins_string nms
paulson@2176
   823
  | add_typ_varnames(TVar((nm,_),_),nms) = nm ins_string nms;
nipkow@949
   824
clasohm@0
   825
(*Accumulates the TVars in a term, suppressing duplicates. *)
clasohm@0
   826
val add_term_tvars = it_term_types add_typ_tvars;
clasohm@0
   827
clasohm@0
   828
(*Accumulates the TFrees in a term, suppressing duplicates. *)
clasohm@0
   829
val add_term_tfrees = it_term_types add_typ_tfrees;
clasohm@0
   830
val add_term_tfree_names = it_term_types add_typ_tfree_names;
clasohm@0
   831
nipkow@949
   832
val add_term_tvarnames = it_term_types add_typ_varnames;
nipkow@949
   833
clasohm@0
   834
(*Non-list versions*)
clasohm@0
   835
fun typ_tfrees T = add_typ_tfrees(T,[]);
clasohm@0
   836
fun typ_tvars T = add_typ_tvars(T,[]);
clasohm@0
   837
fun term_tfrees t = add_term_tfrees(t,[]);
clasohm@0
   838
fun term_tvars t = add_term_tvars(t,[]);
clasohm@0
   839
nipkow@949
   840
(*special code to enforce left-to-right collection of TVar-indexnames*)
nipkow@949
   841
nipkow@949
   842
fun add_typ_ixns(ixns,Type(_,Ts)) = foldl add_typ_ixns (ixns,Ts)
paulson@2176
   843
  | add_typ_ixns(ixns,TVar(ixn,_)) = if mem_ix (ixn, ixns) then ixns 
wenzelm@9536
   844
                                     else ixns@[ixn]
nipkow@949
   845
  | add_typ_ixns(ixns,TFree(_)) = ixns;
nipkow@949
   846
nipkow@949
   847
fun add_term_tvar_ixns(Const(_,T),ixns) = add_typ_ixns(ixns,T)
nipkow@949
   848
  | add_term_tvar_ixns(Free(_,T),ixns) = add_typ_ixns(ixns,T)
nipkow@949
   849
  | add_term_tvar_ixns(Var(_,T),ixns) = add_typ_ixns(ixns,T)
nipkow@949
   850
  | add_term_tvar_ixns(Bound _,ixns) = ixns
nipkow@949
   851
  | add_term_tvar_ixns(Abs(_,T,t),ixns) =
nipkow@949
   852
      add_term_tvar_ixns(t,add_typ_ixns(ixns,T))
nipkow@949
   853
  | add_term_tvar_ixns(f$t,ixns) =
nipkow@949
   854
      add_term_tvar_ixns(t,add_term_tvar_ixns(f,ixns));
nipkow@949
   855
clasohm@0
   856
(** Frees and Vars **)
clasohm@0
   857
clasohm@0
   858
(*a partial ordering (not reflexive) for atomic terms*)
clasohm@0
   859
fun atless (Const (a,_), Const (b,_))  =  a<b
clasohm@0
   860
  | atless (Free (a,_), Free (b,_)) =  a<b
clasohm@0
   861
  | atless (Var(v,_), Var(w,_))  =  xless(v,w)
clasohm@0
   862
  | atless (Bound i, Bound j)  =   i<j
clasohm@0
   863
  | atless _  =  false;
clasohm@0
   864
clasohm@0
   865
(*insert atomic term into partially sorted list, suppressing duplicates (?)*)
clasohm@0
   866
fun insert_aterm (t,us) =
clasohm@0
   867
  let fun inserta [] = [t]
clasohm@0
   868
        | inserta (us as u::us') = 
wenzelm@9536
   869
              if atless(t,u) then t::us
wenzelm@9536
   870
              else if t=u then us (*duplicate*)
wenzelm@9536
   871
              else u :: inserta(us')
clasohm@0
   872
  in  inserta us  end;
clasohm@0
   873
clasohm@0
   874
(*Accumulates the Vars in the term, suppressing duplicates*)
clasohm@0
   875
fun add_term_vars (t, vars: term list) = case t of
clasohm@0
   876
    Var   _ => insert_aterm(t,vars)
clasohm@0
   877
  | Abs (_,_,body) => add_term_vars(body,vars)
clasohm@0
   878
  | f$t =>  add_term_vars (f, add_term_vars(t, vars))
clasohm@0
   879
  | _ => vars;
clasohm@0
   880
clasohm@0
   881
fun term_vars t = add_term_vars(t,[]);
clasohm@0
   882
clasohm@0
   883
(*Accumulates the Frees in the term, suppressing duplicates*)
clasohm@0
   884
fun add_term_frees (t, frees: term list) = case t of
clasohm@0
   885
    Free   _ => insert_aterm(t,frees)
clasohm@0
   886
  | Abs (_,_,body) => add_term_frees(body,frees)
clasohm@0
   887
  | f$t =>  add_term_frees (f, add_term_frees(t, frees))
clasohm@0
   888
  | _ => frees;
clasohm@0
   889
clasohm@0
   890
fun term_frees t = add_term_frees(t,[]);
clasohm@0
   891
clasohm@0
   892
(*Given an abstraction over P, replaces the bound variable by a Free variable
clasohm@0
   893
  having a unique name. *)
clasohm@0
   894
fun variant_abs (a,T,P) =
clasohm@0
   895
  let val b = variant (add_term_names(P,[])) a
paulson@2192
   896
  in  (b,  subst_bound (Free(b,T), P))  end;
clasohm@0
   897
clasohm@0
   898
(* renames and reverses the strings in vars away from names *)
clasohm@0
   899
fun rename_aTs names vars : (string*typ)list =
clasohm@0
   900
  let fun rename_aT (vars,(a,T)) =
wenzelm@9536
   901
                (variant (map #1 vars @ names) a, T) :: vars
clasohm@0
   902
  in foldl rename_aT ([],vars) end;
clasohm@0
   903
clasohm@0
   904
fun rename_wrt_term t = rename_aTs (add_term_names(t,[]));
clasohm@1364
   905
paulson@1417
   906
wenzelm@4286
   907
(* left-ro-right traversal *)
wenzelm@4286
   908
wenzelm@4286
   909
(*foldl atoms of type*)
wenzelm@4286
   910
fun foldl_atyps f (x, Type (_, Ts)) = foldl (foldl_atyps f) (x, Ts)
wenzelm@4286
   911
  | foldl_atyps f x_atom = f x_atom;
wenzelm@4286
   912
wenzelm@4286
   913
(*foldl atoms of term*)
wenzelm@4286
   914
fun foldl_aterms f (x, t $ u) = foldl_aterms f (foldl_aterms f (x, t), u)
wenzelm@4286
   915
  | foldl_aterms f (x, Abs (_, _, t)) = foldl_aterms f (x, t)
wenzelm@4286
   916
  | foldl_aterms f x_atom = f x_atom;
wenzelm@4286
   917
wenzelm@6548
   918
fun foldl_map_aterms f (x, t $ u) =
wenzelm@6548
   919
      let val (x', t') = foldl_map_aterms f (x, t); val (x'', u') = foldl_map_aterms f (x', u);
wenzelm@6548
   920
      in (x'', t' $ u') end
wenzelm@6548
   921
  | foldl_map_aterms f (x, Abs (a, T, t)) =
wenzelm@6548
   922
      let val (x', t') = foldl_map_aterms f (x, t) in (x', Abs (a, T, t')) end
wenzelm@6548
   923
  | foldl_map_aterms f x_atom = f x_atom;
wenzelm@6548
   924
wenzelm@4286
   925
(*foldl types of term*)
wenzelm@8609
   926
fun foldl_term_types f (x, t as Const (_, T)) = f t (x, T)
wenzelm@8609
   927
  | foldl_term_types f (x, t as Free (_, T)) = f t (x, T)
wenzelm@8609
   928
  | foldl_term_types f (x, t as Var (_, T)) = f t (x, T)
wenzelm@8609
   929
  | foldl_term_types f (x, Bound _) = x
wenzelm@8609
   930
  | foldl_term_types f (x, t as Abs (_, T, b)) = foldl_term_types f (f t (x, T), b)
wenzelm@8609
   931
  | foldl_term_types f (x, t $ u) = foldl_term_types f (foldl_term_types f (x, t), u);
wenzelm@8609
   932
wenzelm@8609
   933
fun foldl_types f = foldl_term_types (fn _ => f);
wenzelm@4286
   934
wenzelm@4286
   935
paulson@1417
   936
wenzelm@4444
   937
(** type and term orders **)
wenzelm@4444
   938
wenzelm@4444
   939
fun indexname_ord ((x, i), (y, j)) =
wenzelm@4444
   940
  (case int_ord (i, j) of EQUAL => string_ord (x, y) | ord => ord);
wenzelm@4444
   941
wenzelm@4444
   942
wenzelm@4444
   943
(* typ_ord *)
wenzelm@4444
   944
wenzelm@4444
   945
(*assumes that TFrees / TVars with the same name have same sorts*)
wenzelm@4444
   946
fun typ_ord (Type (a, Ts), Type (b, Us)) =
wenzelm@4444
   947
      (case string_ord (a, b) of EQUAL => typs_ord (Ts, Us) | ord => ord)
wenzelm@4444
   948
  | typ_ord (Type _, _) = GREATER
wenzelm@4444
   949
  | typ_ord (TFree _, Type _) = LESS
wenzelm@4444
   950
  | typ_ord (TFree (a, _), TFree (b, _)) = string_ord (a, b)
wenzelm@4444
   951
  | typ_ord (TFree _, TVar _) = GREATER
wenzelm@4444
   952
  | typ_ord (TVar _, Type _) = LESS
wenzelm@4444
   953
  | typ_ord (TVar _, TFree _) = LESS
wenzelm@4444
   954
  | typ_ord (TVar (xi, _), TVar (yj, _)) = indexname_ord (xi, yj)
wenzelm@4444
   955
and typs_ord Ts_Us = list_ord typ_ord Ts_Us;
wenzelm@4444
   956
wenzelm@4444
   957
wenzelm@4444
   958
(* term_ord *)
wenzelm@4444
   959
wenzelm@4444
   960
(*a linear well-founded AC-compatible ordering for terms:
wenzelm@4444
   961
  s < t <=> 1. size(s) < size(t) or
wenzelm@4444
   962
            2. size(s) = size(t) and s=f(...) and t=g(...) and f<g or
wenzelm@4444
   963
            3. size(s) = size(t) and s=f(s1..sn) and t=f(t1..tn) and
wenzelm@4444
   964
               (s1..sn) < (t1..tn) (lexicographically)*)
wenzelm@4444
   965
wenzelm@4444
   966
fun dest_hd (Const (a, T)) = (((a, 0), T), 0)
wenzelm@4444
   967
  | dest_hd (Free (a, T)) = (((a, 0), T), 1)
wenzelm@4444
   968
  | dest_hd (Var v) = (v, 2)
wenzelm@4444
   969
  | dest_hd (Bound i) = ((("", i), dummyT), 3)
wenzelm@4444
   970
  | dest_hd (Abs (_, T, _)) = ((("", 0), T), 4);
wenzelm@4444
   971
wenzelm@4444
   972
fun term_ord (Abs (_, T, t), Abs(_, U, u)) =
wenzelm@4444
   973
      (case term_ord (t, u) of EQUAL => typ_ord (T, U) | ord => ord)
wenzelm@4444
   974
  | term_ord (t, u) =
wenzelm@4444
   975
      (case int_ord (size_of_term t, size_of_term u) of
wenzelm@4444
   976
        EQUAL =>
wenzelm@4444
   977
          let val (f, ts) = strip_comb t and (g, us) = strip_comb u in
wenzelm@4444
   978
            (case hd_ord (f, g) of EQUAL => terms_ord (ts, us) | ord => ord)
wenzelm@4444
   979
          end
wenzelm@4444
   980
      | ord => ord)
wenzelm@4444
   981
and hd_ord (f, g) =
wenzelm@4444
   982
  prod_ord (prod_ord indexname_ord typ_ord) int_ord (dest_hd f, dest_hd g)
wenzelm@4444
   983
and terms_ord (ts, us) = list_ord term_ord (ts, us);
wenzelm@4444
   984
wenzelm@4444
   985
fun termless tu = (term_ord tu = LESS);
wenzelm@4444
   986
berghofe@8408
   987
structure Vartab = TableFun(type key = indexname val ord = indexname_ord);
berghofe@8408
   988
structure Termtab = TableFun(type key = term val ord = term_ord);
berghofe@8408
   989
berghofe@8408
   990
(*Substitute for type Vars in a type, version using Vartab*)
berghofe@8408
   991
fun typ_subst_TVars_Vartab iTs T = if Vartab.is_empty iTs then T else
berghofe@8408
   992
  let fun subst(Type(a, Ts)) = Type(a, map subst Ts)
wenzelm@9536
   993
        | subst(T as TFree _) = T
wenzelm@9536
   994
        | subst(T as TVar(ixn, _)) =
berghofe@8408
   995
            (case Vartab.lookup (iTs, ixn) of None => T | Some(U) => U)
berghofe@8408
   996
  in subst T end;
berghofe@8408
   997
berghofe@8408
   998
(*Substitute for type Vars in a term, version using Vartab*)
berghofe@8408
   999
val subst_TVars_Vartab = map_term_types o typ_subst_TVars_Vartab;
wenzelm@4444
  1000
wenzelm@4444
  1001
paulson@1426
  1002
(*** Compression of terms and types by sharing common subtrees.  
paulson@1426
  1003
     Saves 50-75% on storage requirements.  As it is fairly slow, 
paulson@1426
  1004
     it is called only for axioms, stored theorems, etc. ***)
paulson@1417
  1005
paulson@1417
  1006
(** Sharing of types **)
paulson@1417
  1007
paulson@1417
  1008
fun atomic_tag (Type (a,_)) = if a<>"fun" then a else raise Match
paulson@1417
  1009
  | atomic_tag (TFree (a,_)) = a
paulson@1417
  1010
  | atomic_tag (TVar ((a,_),_)) = a;
paulson@1417
  1011
paulson@1417
  1012
fun type_tag (Type("fun",[S,T])) = atomic_tag S ^ type_tag T
paulson@1417
  1013
  | type_tag T = atomic_tag T;
paulson@1417
  1014
wenzelm@4487
  1015
val memo_types = ref (Symtab.empty : typ list Symtab.table);
paulson@1417
  1016
oheimb@4188
  1017
(* special case of library/find_first *)
paulson@1417
  1018
fun find_type (T, []: typ list) = None
paulson@1417
  1019
  | find_type (T, T'::Ts) =
paulson@1417
  1020
       if T=T' then Some T'
paulson@1417
  1021
       else find_type (T, Ts);
paulson@1417
  1022
paulson@1417
  1023
fun compress_type T =
paulson@1417
  1024
  let val tag = type_tag T
wenzelm@6963
  1025
      val tylist = Symtab.lookup_multi (!memo_types, tag)
paulson@1417
  1026
  in  
paulson@1417
  1027
      case find_type (T,tylist) of
wenzelm@9536
  1028
        Some T' => T'
paulson@1417
  1029
      | None => 
wenzelm@9536
  1030
            let val T' =
wenzelm@9536
  1031
                case T of
wenzelm@9536
  1032
                    Type (a,Ts) => Type (a, map compress_type Ts)
wenzelm@9536
  1033
                  | _ => T
wenzelm@9536
  1034
            in  memo_types := Symtab.update ((tag, T'::tylist), !memo_types);
wenzelm@9536
  1035
                T
wenzelm@9536
  1036
            end
paulson@1417
  1037
  end
paulson@1417
  1038
  handle Match =>
paulson@1417
  1039
      let val Type (a,Ts) = T
paulson@1417
  1040
      in  Type (a, map compress_type Ts)  end;
paulson@1417
  1041
paulson@1417
  1042
(** Sharing of atomic terms **)
paulson@1417
  1043
wenzelm@4487
  1044
val memo_terms = ref (Symtab.empty : term list Symtab.table);
paulson@1417
  1045
oheimb@4188
  1046
(* special case of library/find_first *)
paulson@1417
  1047
fun find_term (t, []: term list) = None
paulson@1417
  1048
  | find_term (t, t'::ts) =
paulson@1417
  1049
       if t=t' then Some t'
paulson@1417
  1050
       else find_term (t, ts);
paulson@1417
  1051
paulson@1417
  1052
fun const_tag (Const (a,_)) = a
paulson@1417
  1053
  | const_tag (Free (a,_))  = a
paulson@1417
  1054
  | const_tag (Var ((a,i),_)) = a
paulson@1417
  1055
  | const_tag (t as Bound _)  = ".B.";
paulson@1417
  1056
paulson@1417
  1057
fun share_term (t $ u) = share_term t $ share_term u
paulson@1417
  1058
  | share_term (Abs (a,T,u)) = Abs (a, T, share_term u)
paulson@1417
  1059
  | share_term t =
paulson@1417
  1060
      let val tag = const_tag t
wenzelm@9536
  1061
          val ts = Symtab.lookup_multi (!memo_terms, tag)
paulson@1417
  1062
      in 
wenzelm@9536
  1063
          case find_term (t,ts) of
wenzelm@9536
  1064
              Some t' => t'
wenzelm@9536
  1065
            | None => (memo_terms := Symtab.update ((tag, t::ts), !memo_terms);
wenzelm@9536
  1066
                       t)
paulson@1417
  1067
      end;
paulson@1417
  1068
paulson@1417
  1069
val compress_term = share_term o map_term_types compress_type;
paulson@1417
  1070
wenzelm@4444
  1071
wenzelm@9536
  1072
(* dummy patterns *)
wenzelm@9536
  1073
wenzelm@9536
  1074
val dummy_patternN = "dummy_pattern";
wenzelm@9536
  1075
wenzelm@9536
  1076
fun is_dummy_pattern (Const ("dummy_pattern", _)) = true
wenzelm@9536
  1077
  | is_dummy_pattern _ = false;
wenzelm@9536
  1078
wenzelm@9536
  1079
fun no_dummy_patterns tm =
wenzelm@9536
  1080
  if not (foldl_aterms (fn (b, t) => b orelse is_dummy_pattern t) (false, tm)) then tm
wenzelm@9536
  1081
  else raise TERM ("Illegal occurrence of '_' dummy pattern", [tm]);
wenzelm@9536
  1082
wenzelm@11903
  1083
fun replace_dummy Ts (i, Const ("dummy_pattern", T)) =
wenzelm@11903
  1084
      (i + 1, list_comb (Var (("_dummy_", i), Ts ---> T), map Bound (0 upto length Ts - 1)))
wenzelm@11903
  1085
  | replace_dummy Ts (i, Abs (x, T, t)) =
wenzelm@11903
  1086
      let val (i', t') = replace_dummy (T :: Ts) (i, t)
wenzelm@11903
  1087
      in (i', Abs (x, T, t')) end
wenzelm@11903
  1088
  | replace_dummy Ts (i, t $ u) =
wenzelm@11903
  1089
      let val (i', t') = replace_dummy Ts (i, t); val (i'', u') = replace_dummy Ts (i', u)
wenzelm@11903
  1090
      in (i'', t' $ u') end
wenzelm@11903
  1091
  | replace_dummy _ (i, a) = (i, a);
wenzelm@11903
  1092
wenzelm@11903
  1093
val replace_dummy_patterns = replace_dummy [];
wenzelm@9536
  1094
wenzelm@10552
  1095
fun is_replaced_dummy_pattern ("_dummy_", _) = true
wenzelm@10552
  1096
  | is_replaced_dummy_pattern _ = false;
wenzelm@9536
  1097
clasohm@1364
  1098
end;
clasohm@1364
  1099
wenzelm@4444
  1100
wenzelm@4444
  1101
structure BasicTerm: BASIC_TERM = Term;
wenzelm@4444
  1102
open BasicTerm;