src/Pure/term.ML
author skalberg
Sun Feb 13 17:15:14 2005 +0100 (2005-02-13)
changeset 15531 08c8dad8e399
parent 15472 4674102737e9
child 15570 8d8c70b41bab
permissions -rw-r--r--
Deleted Library.option type.
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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 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 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 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 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 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 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 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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  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 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_var_qmarks: 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 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 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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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 ---> = 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$u])
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      end;
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   327
clasohm@0
   328
fun type_of t : typ = type_of1 ([],t);
clasohm@0
   329
clasohm@0
   330
(*Determines the type of a term, with minimal checking*)
wenzelm@13000
   331
fun fastype_of1 (Ts, f$u) =
lcp@61
   332
    (case fastype_of1 (Ts,f) of
wenzelm@9536
   333
        Type("fun",[_,T]) => T
wenzelm@9536
   334
        | _ => raise TERM("fastype_of: expected function type", [f$u]))
lcp@61
   335
  | fastype_of1 (_, Const (_,T)) = T
lcp@61
   336
  | fastype_of1 (_, Free (_,T)) = T
lcp@61
   337
  | fastype_of1 (Ts, Bound i) = (nth_elem(i,Ts)
wenzelm@9536
   338
         handle LIST _ => raise TERM("fastype_of: Bound", [Bound i]))
wenzelm@13000
   339
  | fastype_of1 (_, Var (_,T)) = T
lcp@61
   340
  | fastype_of1 (Ts, Abs (_,T,u)) = T --> fastype_of1 (T::Ts, u);
lcp@61
   341
lcp@61
   342
fun fastype_of t : typ = fastype_of1 ([],t);
clasohm@0
   343
clasohm@0
   344
wenzelm@10806
   345
val list_abs = foldr (fn ((x, T), t) => Abs (x, T, t));
wenzelm@10806
   346
clasohm@0
   347
(* maps  (x1,...,xn)t   to   t  *)
wenzelm@13000
   348
fun strip_abs_body (Abs(_,_,t))  =  strip_abs_body t
clasohm@0
   349
  | strip_abs_body u  =  u;
clasohm@0
   350
clasohm@0
   351
(* maps  (x1,...,xn)t   to   [x1, ..., xn]  *)
wenzelm@13000
   352
fun strip_abs_vars (Abs(a,T,t))  =  (a,T) :: strip_abs_vars t
clasohm@0
   353
  | strip_abs_vars u  =  [] : (string*typ) list;
clasohm@0
   354
clasohm@0
   355
clasohm@0
   356
fun strip_qnt_body qnt =
clasohm@0
   357
let fun strip(tm as Const(c,_)$Abs(_,_,t)) = if c=qnt then strip t else tm
clasohm@0
   358
      | strip t = t
clasohm@0
   359
in strip end;
clasohm@0
   360
clasohm@0
   361
fun strip_qnt_vars qnt =
clasohm@0
   362
let fun strip(Const(c,_)$Abs(a,T,t)) = if c=qnt then (a,T)::strip t else []
clasohm@0
   363
      | strip t  =  [] : (string*typ) list
clasohm@0
   364
in strip end;
clasohm@0
   365
clasohm@0
   366
clasohm@0
   367
(* maps   (f, [t1,...,tn])  to  f(t1,...,tn) *)
clasohm@0
   368
val list_comb : term * term list -> term = foldl (op $);
clasohm@0
   369
clasohm@0
   370
clasohm@0
   371
(* maps   f(t1,...,tn)  to  (f, [t1,...,tn]) ; naturally tail-recursive*)
wenzelm@13000
   372
fun strip_comb u : term * term list =
clasohm@0
   373
    let fun stripc (f$t, ts) = stripc (f, t::ts)
wenzelm@13000
   374
        |   stripc  x =  x
clasohm@0
   375
    in  stripc(u,[])  end;
clasohm@0
   376
clasohm@0
   377
clasohm@0
   378
(* maps   f(t1,...,tn)  to  f , which is never a combination *)
clasohm@0
   379
fun head_of (f$t) = head_of f
clasohm@0
   380
  | head_of u = u;
clasohm@0
   381
clasohm@0
   382
clasohm@0
   383
(*Number of atoms and abstractions in a term*)
clasohm@0
   384
fun size_of_term (Abs (_,_,body)) = 1 + size_of_term body
clasohm@0
   385
  | size_of_term (f$t) = size_of_term f  +  size_of_term t
clasohm@0
   386
  | size_of_term _ = 1;
clasohm@0
   387
nipkow@949
   388
fun map_type_tvar f (Type(a,Ts)) = Type(a, map (map_type_tvar f) Ts)
nipkow@949
   389
  | map_type_tvar f (T as TFree _) = T
nipkow@949
   390
  | map_type_tvar f (TVar x) = f x;
nipkow@949
   391
nipkow@949
   392
fun map_type_tfree f (Type(a,Ts)) = Type(a, map (map_type_tfree f) Ts)
nipkow@949
   393
  | map_type_tfree f (TFree x) = f x
nipkow@949
   394
  | map_type_tfree f (T as TVar _) = T;
nipkow@949
   395
clasohm@0
   396
(* apply a function to all types in a term *)
clasohm@0
   397
fun map_term_types f =
clasohm@0
   398
let fun map(Const(a,T)) = Const(a, f T)
clasohm@0
   399
      | map(Free(a,T)) = Free(a, f T)
clasohm@0
   400
      | map(Var(v,T)) = Var(v, f T)
clasohm@0
   401
      | map(t as Bound _)  = t
clasohm@0
   402
      | map(Abs(a,T,t)) = Abs(a, f T, map t)
clasohm@0
   403
      | map(f$t) = map f $ map t;
clasohm@0
   404
in map end;
clasohm@0
   405
clasohm@0
   406
(* iterate a function over all types in a term *)
clasohm@0
   407
fun it_term_types f =
clasohm@0
   408
let fun iter(Const(_,T), a) = f(T,a)
clasohm@0
   409
      | iter(Free(_,T), a) = f(T,a)
clasohm@0
   410
      | iter(Var(_,T), a) = f(T,a)
clasohm@0
   411
      | iter(Abs(_,T,t), a) = iter(t,f(T,a))
clasohm@0
   412
      | iter(f$u, a) = iter(f, iter(u, a))
clasohm@0
   413
      | iter(Bound _, a) = a
clasohm@0
   414
in iter end
clasohm@0
   415
clasohm@0
   416
clasohm@0
   417
(** Connectives of higher order logic **)
clasohm@0
   418
wenzelm@375
   419
fun itselfT ty = Type ("itself", [ty]);
wenzelm@14854
   420
val a_itselfT = itselfT (TFree ("'a", []));
wenzelm@375
   421
clasohm@0
   422
val propT : typ = Type("prop",[]);
clasohm@0
   423
clasohm@0
   424
val implies = Const("==>", propT-->propT-->propT);
clasohm@0
   425
clasohm@0
   426
fun all T = Const("all", (T-->propT)-->propT);
clasohm@0
   427
clasohm@0
   428
fun equals T = Const("==", T-->T-->propT);
clasohm@0
   429
clasohm@0
   430
(* maps  !!x1...xn. t   to   t  *)
wenzelm@13000
   431
fun strip_all_body (Const("all",_)$Abs(_,_,t))  =  strip_all_body t
clasohm@0
   432
  | strip_all_body t  =  t;
clasohm@0
   433
clasohm@0
   434
(* maps  !!x1...xn. t   to   [x1, ..., xn]  *)
clasohm@0
   435
fun strip_all_vars (Const("all",_)$Abs(a,T,t))  =
wenzelm@13000
   436
                (a,T) :: strip_all_vars t
clasohm@0
   437
  | strip_all_vars t  =  [] : (string*typ) list;
clasohm@0
   438
clasohm@0
   439
(*increments a term's non-local bound variables
clasohm@0
   440
  required when moving a term within abstractions
clasohm@0
   441
     inc is  increment for bound variables
clasohm@0
   442
     lev is  level at which a bound variable is considered 'loose'*)
wenzelm@13000
   443
fun incr_bv (inc, lev, u as Bound i) = if i>=lev then Bound(i+inc) else u
clasohm@0
   444
  | incr_bv (inc, lev, Abs(a,T,body)) =
wenzelm@9536
   445
        Abs(a, T, incr_bv(inc,lev+1,body))
wenzelm@13000
   446
  | incr_bv (inc, lev, f$t) =
clasohm@0
   447
      incr_bv(inc,lev,f) $ incr_bv(inc,lev,t)
clasohm@0
   448
  | incr_bv (inc, lev, u) = u;
clasohm@0
   449
clasohm@0
   450
fun incr_boundvars  0  t = t
clasohm@0
   451
  | incr_boundvars inc t = incr_bv(inc,0,t);
clasohm@0
   452
wenzelm@12981
   453
(*Scan a pair of terms; while they are similar,
wenzelm@12981
   454
  accumulate corresponding bound vars in "al"*)
wenzelm@12981
   455
fun match_bvs(Abs(x,_,s),Abs(y,_,t), al) =
wenzelm@12981
   456
      match_bvs(s, t, if x="" orelse y="" then al
wenzelm@12981
   457
                                          else (x,y)::al)
wenzelm@12981
   458
  | match_bvs(f$s, g$t, al) = match_bvs(f,g,match_bvs(s,t,al))
wenzelm@12981
   459
  | match_bvs(_,_,al) = al;
wenzelm@12981
   460
wenzelm@12981
   461
(* strip abstractions created by parameters *)
wenzelm@12981
   462
fun match_bvars((s,t),al) = match_bvs(strip_abs_body s, strip_abs_body t, al);
wenzelm@12981
   463
wenzelm@12981
   464
fun rename_abs pat obj t =
wenzelm@12981
   465
  let
wenzelm@12981
   466
    val ren = match_bvs (pat, obj, []);
wenzelm@12981
   467
    fun ren_abs (Abs (x, T, b)) =
wenzelm@12981
   468
          Abs (if_none (assoc_string (ren, x)) x, T, ren_abs b)
wenzelm@12981
   469
      | ren_abs (f $ t) = ren_abs f $ ren_abs t
wenzelm@12981
   470
      | ren_abs t = t
skalberg@15531
   471
  in if null ren then NONE else SOME (ren_abs t) end;
clasohm@0
   472
clasohm@0
   473
(*Accumulate all 'loose' bound vars referring to level 'lev' or beyond.
clasohm@0
   474
   (Bound 0) is loose at level 0 *)
wenzelm@13000
   475
fun add_loose_bnos (Bound i, lev, js) =
wenzelm@9536
   476
        if i<lev then js  else  (i-lev) ins_int js
clasohm@0
   477
  | add_loose_bnos (Abs (_,_,t), lev, js) = add_loose_bnos (t, lev+1, js)
clasohm@0
   478
  | add_loose_bnos (f$t, lev, js) =
wenzelm@13000
   479
        add_loose_bnos (f, lev, add_loose_bnos (t, lev, js))
clasohm@0
   480
  | add_loose_bnos (_, _, js) = js;
clasohm@0
   481
clasohm@0
   482
fun loose_bnos t = add_loose_bnos (t, 0, []);
clasohm@0
   483
clasohm@0
   484
(* loose_bvar(t,k) iff t contains a 'loose' bound variable referring to
clasohm@0
   485
   level k or beyond. *)
clasohm@0
   486
fun loose_bvar(Bound i,k) = i >= k
clasohm@0
   487
  | loose_bvar(f$t, k) = loose_bvar(f,k) orelse loose_bvar(t,k)
clasohm@0
   488
  | loose_bvar(Abs(_,_,t),k) = loose_bvar(t,k+1)
clasohm@0
   489
  | loose_bvar _ = false;
clasohm@0
   490
nipkow@2792
   491
fun loose_bvar1(Bound i,k) = i = k
nipkow@2792
   492
  | loose_bvar1(f$t, k) = loose_bvar1(f,k) orelse loose_bvar1(t,k)
nipkow@2792
   493
  | loose_bvar1(Abs(_,_,t),k) = loose_bvar1(t,k+1)
nipkow@2792
   494
  | loose_bvar1 _ = false;
clasohm@0
   495
clasohm@0
   496
(*Substitute arguments for loose bound variables.
clasohm@0
   497
  Beta-reduction of arg(n-1)...arg0 into t replacing (Bound i) with (argi).
wenzelm@4626
   498
  Note that for ((%x y. c) a b), the bound vars in c are x=1 and y=0
wenzelm@9536
   499
        and the appropriate call is  subst_bounds([b,a], c) .
clasohm@0
   500
  Loose bound variables >=n are reduced by "n" to
clasohm@0
   501
     compensate for the disappearance of lambdas.
clasohm@0
   502
*)
wenzelm@13000
   503
fun subst_bounds (args: term list, t) : term =
clasohm@0
   504
  let val n = length args;
clasohm@0
   505
      fun subst (t as Bound i, lev) =
wenzelm@9536
   506
           (if i<lev then  t    (*var is locally bound*)
wenzelm@9536
   507
            else  incr_boundvars lev (List.nth(args, i-lev))
wenzelm@9536
   508
                    handle Subscript => Bound(i-n)  (*loose: change it*))
wenzelm@9536
   509
        | subst (Abs(a,T,body), lev) = Abs(a, T,  subst(body,lev+1))
wenzelm@9536
   510
        | subst (f$t, lev) =  subst(f,lev)  $  subst(t,lev)
wenzelm@9536
   511
        | subst (t,lev) = t
clasohm@0
   512
  in   case args of [] => t  | _ => subst (t,0)  end;
clasohm@0
   513
paulson@2192
   514
(*Special case: one argument*)
wenzelm@13000
   515
fun subst_bound (arg, t) : term =
paulson@2192
   516
  let fun subst (t as Bound i, lev) =
wenzelm@9536
   517
            if i<lev then  t    (*var is locally bound*)
wenzelm@9536
   518
            else  if i=lev then incr_boundvars lev arg
wenzelm@9536
   519
                           else Bound(i-1)  (*loose: change it*)
wenzelm@9536
   520
        | subst (Abs(a,T,body), lev) = Abs(a, T,  subst(body,lev+1))
wenzelm@9536
   521
        | subst (f$t, lev) =  subst(f,lev)  $  subst(t,lev)
wenzelm@9536
   522
        | subst (t,lev) = t
paulson@2192
   523
  in  subst (t,0)  end;
paulson@2192
   524
clasohm@0
   525
(*beta-reduce if possible, else form application*)
paulson@2192
   526
fun betapply (Abs(_,_,t), u) = subst_bound (u,t)
clasohm@0
   527
  | betapply (f,u) = f$u;
clasohm@0
   528
wenzelm@14786
   529
paulson@2192
   530
(** Equality, membership and insertion of indexnames (string*ints) **)
paulson@2192
   531
paulson@2192
   532
(*optimized equality test for indexnames.  Yields a huge gain under Poly/ML*)
wenzelm@2959
   533
fun eq_ix ((a, i):indexname, (a',i'):indexname) = (a=a') andalso i=i';
paulson@2192
   534
paulson@2192
   535
(*membership in a list, optimized version for indexnames*)
wenzelm@2959
   536
fun mem_ix (_, []) = false
paulson@2192
   537
  | mem_ix (x, y :: ys) = eq_ix(x,y) orelse mem_ix (x, ys);
paulson@2192
   538
paulson@2192
   539
(*insertion into list, optimized version for indexnames*)
paulson@2192
   540
fun ins_ix (x,xs) = if mem_ix (x, xs) then xs else x :: xs;
paulson@2192
   541
clasohm@0
   542
(*Tests whether 2 terms are alpha-convertible and have same type.
wenzelm@4626
   543
  Note that constants may have more than one type.*)
clasohm@0
   544
fun (Const(a,T)) aconv (Const(b,U)) = a=b  andalso  T=U
paulson@2752
   545
  | (Free(a,T))  aconv (Free(b,U))  = a=b  andalso  T=U
paulson@2752
   546
  | (Var(v,T))   aconv (Var(w,U))   = eq_ix(v,w)  andalso  T=U
paulson@2752
   547
  | (Bound i)    aconv (Bound j)    = i=j
clasohm@0
   548
  | (Abs(_,T,t)) aconv (Abs(_,U,u)) = t aconv u  andalso  T=U
paulson@2752
   549
  | (f$t)        aconv (g$u)        = (f aconv g) andalso (t aconv u)
clasohm@0
   550
  | _ aconv _  =  false;
clasohm@0
   551
paulson@2176
   552
(** Membership, insertion, union for terms **)
paulson@2176
   553
paulson@2176
   554
fun mem_term (_, []) = false
paulson@2176
   555
  | mem_term (t, t'::ts) = t aconv t' orelse mem_term(t,ts);
paulson@2176
   556
paulson@2182
   557
fun subset_term ([], ys) = true
paulson@2182
   558
  | subset_term (x :: xs, ys) = mem_term (x, ys) andalso subset_term(xs, ys);
paulson@2182
   559
paulson@2182
   560
fun eq_set_term (xs, ys) =
paulson@2182
   561
    xs = ys orelse (subset_term (xs, ys) andalso subset_term (ys, xs));
paulson@2182
   562
paulson@2176
   563
fun ins_term(t,ts) = if mem_term(t,ts) then ts else t :: ts;
paulson@2176
   564
paulson@2176
   565
fun union_term (xs, []) = xs
paulson@2176
   566
  | union_term ([], ys) = ys
paulson@2176
   567
  | union_term ((x :: xs), ys) = union_term (xs, ins_term (x, ys));
paulson@2176
   568
paulson@5585
   569
fun inter_term ([], ys) = []
paulson@5585
   570
  | inter_term (x::xs, ys) =
paulson@5585
   571
      if mem_term (x,ys) then x :: inter_term(xs,ys) else inter_term(xs,ys);
paulson@5585
   572
clasohm@0
   573
(*are two term lists alpha-convertible in corresponding elements?*)
clasohm@0
   574
fun aconvs ([],[]) = true
clasohm@0
   575
  | aconvs (t::ts, u::us) = t aconv u andalso aconvs(ts,us)
clasohm@0
   576
  | aconvs _ = false;
clasohm@0
   577
wenzelm@13000
   578
(*A fast unification filter: true unless the two terms cannot be unified.
clasohm@0
   579
  Terms must be NORMAL.  Treats all Vars as distinct. *)
clasohm@0
   580
fun could_unify (t,u) =
clasohm@0
   581
  let fun matchrands (f$t, g$u) = could_unify(t,u) andalso  matchrands(f,g)
wenzelm@9536
   582
        | matchrands _ = true
clasohm@0
   583
  in case (head_of t , head_of u) of
wenzelm@9536
   584
        (_, Var _) => true
clasohm@0
   585
      | (Var _, _) => true
clasohm@0
   586
      | (Const(a,_), Const(b,_)) =>  a=b andalso matchrands(t,u)
clasohm@0
   587
      | (Free(a,_), Free(b,_)) =>  a=b andalso matchrands(t,u)
clasohm@0
   588
      | (Bound i, Bound j) =>  i=j andalso matchrands(t,u)
clasohm@0
   589
      | (Abs _, _) =>  true   (*because of possible eta equality*)
clasohm@0
   590
      | (_, Abs _) =>  true
clasohm@0
   591
      | _ => false
clasohm@0
   592
  end;
clasohm@0
   593
clasohm@0
   594
(*Substitute new for free occurrences of old in a term*)
clasohm@0
   595
fun subst_free [] = (fn t=>t)
clasohm@0
   596
  | subst_free pairs =
wenzelm@13000
   597
      let fun substf u =
wenzelm@9536
   598
            case gen_assoc (op aconv) (pairs, u) of
skalberg@15531
   599
                SOME u' => u'
skalberg@15531
   600
              | NONE => (case u of Abs(a,T,t) => Abs(a, T, substf t)
wenzelm@9536
   601
                                 | t$u' => substf t $ substf u'
wenzelm@9536
   602
                                 | _ => u)
clasohm@0
   603
      in  substf  end;
clasohm@0
   604
clasohm@0
   605
(*a total, irreflexive ordering on index names*)
clasohm@0
   606
fun xless ((a,i), (b,j): indexname) = i<j  orelse  (i=j andalso a<b);
clasohm@0
   607
clasohm@0
   608
wenzelm@13000
   609
(*Abstraction of the term "body" over its occurrences of v,
clasohm@0
   610
    which must contain no loose bound variables.
clasohm@0
   611
  The resulting term is ready to become the body of an Abs.*)
clasohm@0
   612
fun abstract_over (v,body) =
clasohm@0
   613
  let fun abst (lev,u) = if (v aconv u) then (Bound lev) else
clasohm@0
   614
      (case u of
clasohm@0
   615
          Abs(a,T,t) => Abs(a, T, abst(lev+1, t))
wenzelm@9536
   616
        | f$rand => abst(lev,f) $ abst(lev,rand)
wenzelm@9536
   617
        | _ => u)
clasohm@0
   618
  in  abst(0,body)  end;
clasohm@0
   619
berghofe@13665
   620
fun lambda (v as Free (x, T)) t = Abs (x, T, abstract_over (v, t))
berghofe@13665
   621
  | lambda (v as Var ((x, _), T)) t = Abs (x, T, abstract_over (v, t))
berghofe@13665
   622
  | lambda v t = raise TERM ("lambda", [v, t]);
clasohm@0
   623
clasohm@0
   624
(*Form an abstraction over a free variable.*)
clasohm@0
   625
fun absfree (a,T,body) = Abs(a, T, abstract_over (Free(a,T), body));
clasohm@0
   626
clasohm@0
   627
(*Abstraction over a list of free variables*)
clasohm@0
   628
fun list_abs_free ([ ] ,     t) = t
wenzelm@13000
   629
  | list_abs_free ((a,T)::vars, t) =
clasohm@0
   630
      absfree(a, T, list_abs_free(vars,t));
clasohm@0
   631
clasohm@0
   632
(*Quantification over a list of free variables*)
clasohm@0
   633
fun list_all_free ([], t: term) = t
wenzelm@13000
   634
  | list_all_free ((a,T)::vars, t) =
clasohm@0
   635
        (all T) $ (absfree(a, T, list_all_free(vars,t)));
clasohm@0
   636
clasohm@0
   637
(*Quantification over a list of variables (already bound in body) *)
clasohm@0
   638
fun list_all ([], t) = t
wenzelm@13000
   639
  | list_all ((a,T)::vars, t) =
clasohm@0
   640
        (all T) $ (Abs(a, T, list_all(vars,t)));
clasohm@0
   641
wenzelm@13000
   642
(*Replace the ATOMIC term ti by ui;    instl = [(t1,u1), ..., (tn,un)].
clasohm@0
   643
  A simultaneous substitution:  [ (a,b), (b,a) ] swaps a and b.  *)
clasohm@0
   644
fun subst_atomic [] t = t : term
clasohm@0
   645
  | subst_atomic (instl: (term*term) list) t =
clasohm@0
   646
      let fun subst (Abs(a,T,body)) = Abs(a, T, subst body)
wenzelm@9536
   647
            | subst (f$t') = subst f $ subst t'
nipkow@9721
   648
            | subst t = if_none (assoc(instl,t)) t
clasohm@0
   649
      in  subst t  end;
clasohm@0
   650
lcp@728
   651
(*Substitute for type Vars in a type*)
clasohm@0
   652
fun typ_subst_TVars iTs T = if null iTs then T else
clasohm@0
   653
  let fun subst(Type(a,Ts)) = Type(a, map subst Ts)
wenzelm@9536
   654
        | subst(T as TFree _) = T
nipkow@9721
   655
        | subst(T as TVar(ixn,_)) = if_none (assoc(iTs,ixn)) T
clasohm@0
   656
  in subst T end;
clasohm@0
   657
lcp@728
   658
(*Substitute for type Vars in a term*)
clasohm@0
   659
val subst_TVars = map_term_types o typ_subst_TVars;
clasohm@0
   660
lcp@728
   661
(*Substitute for Vars in a term; see also envir/norm_term*)
clasohm@0
   662
fun subst_Vars itms t = if null itms then t else
nipkow@9721
   663
  let fun subst(v as Var(ixn,_)) = if_none (assoc(itms,ixn)) v
clasohm@0
   664
        | subst(Abs(a,T,t)) = Abs(a,T,subst t)
clasohm@0
   665
        | subst(f$t) = subst f $ subst t
clasohm@0
   666
        | subst(t) = t
clasohm@0
   667
  in subst t end;
clasohm@0
   668
lcp@728
   669
(*Substitute for type/term Vars in a term; see also envir/norm_term*)
clasohm@0
   670
fun subst_vars(iTs,itms) = if null iTs then subst_Vars itms else
clasohm@0
   671
  let fun subst(Const(a,T)) = Const(a,typ_subst_TVars iTs T)
clasohm@0
   672
        | subst(Free(a,T)) = Free(a,typ_subst_TVars iTs T)
clasohm@0
   673
        | subst(v as Var(ixn,T)) = (case assoc(itms,ixn) of
skalberg@15531
   674
            NONE   => Var(ixn,typ_subst_TVars iTs T)
skalberg@15531
   675
          | SOME t => t)
clasohm@0
   676
        | subst(b as Bound _) = b
clasohm@0
   677
        | subst(Abs(a,T,t)) = Abs(a,typ_subst_TVars iTs T,subst t)
clasohm@0
   678
        | subst(f$t) = subst f $ subst t
clasohm@0
   679
  in subst end;
clasohm@0
   680
clasohm@0
   681
clasohm@0
   682
(*Computing the maximum index of a typ*)
paulson@2146
   683
fun maxidx_of_typ(Type(_,Ts)) = maxidx_of_typs Ts
clasohm@0
   684
  | maxidx_of_typ(TFree _) = ~1
paulson@2146
   685
  | maxidx_of_typ(TVar((_,i),_)) = i
paulson@2146
   686
and maxidx_of_typs [] = ~1
paulson@2146
   687
  | maxidx_of_typs (T::Ts) = Int.max(maxidx_of_typ T, maxidx_of_typs Ts);
clasohm@0
   688
clasohm@0
   689
clasohm@0
   690
(*Computing the maximum index of a term*)
clasohm@0
   691
fun maxidx_of_term (Const(_,T)) = maxidx_of_typ T
clasohm@0
   692
  | maxidx_of_term (Bound _) = ~1
clasohm@0
   693
  | maxidx_of_term (Free(_,T)) = maxidx_of_typ T
paulson@2146
   694
  | maxidx_of_term (Var ((_,i), T)) = Int.max(i, maxidx_of_typ T)
paulson@2146
   695
  | maxidx_of_term (Abs (_,T,u)) = Int.max(maxidx_of_term u, maxidx_of_typ T)
paulson@2146
   696
  | maxidx_of_term (f$t) = Int.max(maxidx_of_term f,  maxidx_of_term t);
clasohm@0
   697
berghofe@13665
   698
fun maxidx_of_terms ts = foldl Int.max (~1, map maxidx_of_term ts);
berghofe@13665
   699
clasohm@0
   700
clasohm@0
   701
(* Increment the index of all Poly's in T by k *)
nipkow@949
   702
fun incr_tvar k = map_type_tvar (fn ((a,i),S) => TVar((a,i+k),S));
clasohm@0
   703
clasohm@0
   704
clasohm@0
   705
(**** Syntax-related declarations ****)
clasohm@0
   706
clasohm@0
   707
wenzelm@4626
   708
(*Dummy type for parsing and printing.  Will be replaced during type inference. *)
clasohm@0
   709
val dummyT = Type("dummy",[]);
clasohm@0
   710
wenzelm@14786
   711
fun no_dummyT typ =
wenzelm@14786
   712
  let
wenzelm@14786
   713
    fun check (T as Type ("dummy", _)) =
wenzelm@14786
   714
          raise TYPE ("Illegal occurrence of '_' dummy type", [T], [])
wenzelm@14786
   715
      | check (Type (_, Ts)) = seq check Ts
wenzelm@14786
   716
      | check _ = ();
wenzelm@14786
   717
  in check typ; typ end;
wenzelm@14786
   718
clasohm@0
   719
clasohm@0
   720
(*** Printing ***)
clasohm@0
   721
wenzelm@14676
   722
(*Makes a variant of a name distinct from the names in bs.
wenzelm@14676
   723
  First attaches the suffix and then increments this;
wenzelm@12306
   724
  preserves a suffix of underscores "_". *)
wenzelm@12306
   725
fun variant bs name =
wenzelm@12306
   726
  let
wenzelm@12306
   727
    val (c, u) = pairself implode (Library.take_suffix (equal "_") (Symbol.explode name));
wenzelm@12902
   728
    fun vary2 c = if ((c ^ u) mem_string bs) then vary2 (Symbol.bump_string c) else c;
wenzelm@14676
   729
    fun vary1 c = if ((c ^ u) mem_string bs) then vary2 (Symbol.bump_init c) else c;
wenzelm@12306
   730
  in vary1 (if c = "" then "u" else c) ^ u end;
clasohm@0
   731
clasohm@0
   732
(*Create variants of the list of names, with priority to the first ones*)
clasohm@0
   733
fun variantlist ([], used) = []
wenzelm@13000
   734
  | variantlist(b::bs, used) =
clasohm@0
   735
      let val b' = variant used b
clasohm@0
   736
      in  b' :: variantlist (bs, b'::used)  end;
clasohm@0
   737
wenzelm@14695
   738
(*Invent fresh names*)
wenzelm@14695
   739
fun invent_names _ _ 0 = []
wenzelm@14695
   740
  | invent_names used a n =
wenzelm@14695
   741
      let val b = Symbol.bump_string a in
wenzelm@14695
   742
        if a mem_string used then invent_names used b n
wenzelm@14695
   743
        else a :: invent_names used b (n - 1)
wenzelm@14695
   744
      end;
wenzelm@11353
   745
wenzelm@4017
   746
wenzelm@4017
   747
wenzelm@4017
   748
(** Consts etc. **)
wenzelm@4017
   749
wenzelm@4017
   750
fun add_typ_classes (Type (_, Ts), cs) = foldr add_typ_classes (Ts, cs)
wenzelm@4017
   751
  | add_typ_classes (TFree (_, S), cs) = S union cs
wenzelm@4017
   752
  | add_typ_classes (TVar (_, S), cs) = S union cs;
wenzelm@4017
   753
wenzelm@4017
   754
fun add_typ_tycons (Type (c, Ts), cs) = foldr add_typ_tycons (Ts, c ins cs)
wenzelm@4017
   755
  | add_typ_tycons (_, cs) = cs;
wenzelm@4017
   756
wenzelm@4017
   757
val add_term_classes = it_term_types add_typ_classes;
wenzelm@4017
   758
val add_term_tycons = it_term_types add_typ_tycons;
wenzelm@4017
   759
wenzelm@9319
   760
fun add_term_consts (Const (c, _), cs) = c ins_string cs
wenzelm@4017
   761
  | add_term_consts (t $ u, cs) = add_term_consts (t, add_term_consts (u, cs))
wenzelm@4017
   762
  | add_term_consts (Abs (_, _, t), cs) = add_term_consts (t, cs)
wenzelm@4017
   763
  | add_term_consts (_, cs) = cs;
wenzelm@4017
   764
nipkow@13646
   765
fun term_consts t = add_term_consts(t,[]);
nipkow@13646
   766
oheimb@4185
   767
fun exists_Const P t = let
wenzelm@9536
   768
        fun ex (Const c      ) = P c
wenzelm@9536
   769
        |   ex (t $ u        ) = ex t orelse ex u
wenzelm@9536
   770
        |   ex (Abs (_, _, t)) = ex t
wenzelm@9536
   771
        |   ex _               = false
oheimb@4185
   772
    in ex t end;
wenzelm@4017
   773
nipkow@4631
   774
fun exists_subterm P =
nipkow@4631
   775
  let fun ex t = P t orelse
nipkow@4631
   776
                 (case t of
nipkow@4631
   777
                    u $ v        => ex u orelse ex v
nipkow@4631
   778
                  | Abs(_, _, u) => ex u
nipkow@4631
   779
                  | _            => false)
nipkow@4631
   780
  in ex end;
nipkow@4631
   781
wenzelm@4017
   782
(*map classes, tycons*)
wenzelm@4017
   783
fun map_typ f g (Type (c, Ts)) = Type (g c, map (map_typ f g) Ts)
wenzelm@4017
   784
  | map_typ f _ (TFree (x, S)) = TFree (x, map f S)
wenzelm@4017
   785
  | map_typ f _ (TVar (xi, S)) = TVar (xi, map f S);
wenzelm@4017
   786
wenzelm@4017
   787
(*map classes, tycons, consts*)
wenzelm@4017
   788
fun map_term f g h (Const (c, T)) = Const (h c, map_typ f g T)
wenzelm@4017
   789
  | map_term f g _ (Free (x, T)) = Free (x, map_typ f g T)
wenzelm@4017
   790
  | map_term f g _ (Var (xi, T)) = Var (xi, map_typ f g T)
wenzelm@4017
   791
  | map_term _ _ _ (t as Bound _) = t
wenzelm@4017
   792
  | map_term f g h (Abs (x, T, t)) = Abs (x, map_typ f g T, map_term f g h t)
wenzelm@4017
   793
  | map_term f g h (t $ u) = map_term f g h t $ map_term f g h u;
wenzelm@4017
   794
wenzelm@4017
   795
wenzelm@4017
   796
clasohm@0
   797
(** TFrees and TVars **)
clasohm@0
   798
clasohm@0
   799
(*maps  (bs,v)  to   v'::bs    this reverses the identifiers bs*)
clasohm@0
   800
fun add_new_id (bs, c) : string list =  variant bs c  ::  bs;
clasohm@0
   801
wenzelm@12802
   802
(*Accumulates the names of Frees in the term, suppressing duplicates.*)
wenzelm@12802
   803
fun add_term_free_names (Free(a,_), bs) = a ins_string bs
wenzelm@12802
   804
  | add_term_free_names (f$u, bs) = add_term_free_names (f, add_term_free_names(u, bs))
wenzelm@12802
   805
  | add_term_free_names (Abs(_,_,t), bs) = add_term_free_names(t,bs)
wenzelm@12802
   806
  | add_term_free_names (_, bs) = bs;
wenzelm@12802
   807
clasohm@0
   808
(*Accumulates the names in the term, suppressing duplicates.
clasohm@0
   809
  Includes Frees and Consts.  For choosing unambiguous bound var names.*)
wenzelm@10666
   810
fun add_term_names (Const(a,_), bs) = NameSpace.base a ins_string bs
paulson@2176
   811
  | add_term_names (Free(a,_), bs) = a ins_string bs
clasohm@0
   812
  | add_term_names (f$u, bs) = add_term_names (f, add_term_names(u, bs))
clasohm@0
   813
  | add_term_names (Abs(_,_,t), bs) = add_term_names(t,bs)
clasohm@0
   814
  | add_term_names (_, bs) = bs;
clasohm@0
   815
clasohm@0
   816
(*Accumulates the TVars in a type, suppressing duplicates. *)
clasohm@0
   817
fun add_typ_tvars(Type(_,Ts),vs) = foldr add_typ_tvars (Ts,vs)
clasohm@0
   818
  | add_typ_tvars(TFree(_),vs) = vs
clasohm@0
   819
  | add_typ_tvars(TVar(v),vs) = v ins vs;
clasohm@0
   820
clasohm@0
   821
(*Accumulates the TFrees in a type, suppressing duplicates. *)
clasohm@0
   822
fun add_typ_tfree_names(Type(_,Ts),fs) = foldr add_typ_tfree_names (Ts,fs)
paulson@2176
   823
  | add_typ_tfree_names(TFree(f,_),fs) = f ins_string fs
clasohm@0
   824
  | add_typ_tfree_names(TVar(_),fs) = fs;
clasohm@0
   825
clasohm@0
   826
fun add_typ_tfrees(Type(_,Ts),fs) = foldr add_typ_tfrees (Ts,fs)
clasohm@0
   827
  | add_typ_tfrees(TFree(f),fs) = f ins fs
clasohm@0
   828
  | add_typ_tfrees(TVar(_),fs) = fs;
clasohm@0
   829
nipkow@949
   830
fun add_typ_varnames(Type(_,Ts),nms) = foldr add_typ_varnames (Ts,nms)
paulson@2176
   831
  | add_typ_varnames(TFree(nm,_),nms) = nm ins_string nms
paulson@2176
   832
  | add_typ_varnames(TVar((nm,_),_),nms) = nm ins_string nms;
nipkow@949
   833
clasohm@0
   834
(*Accumulates the TVars in a term, suppressing duplicates. *)
clasohm@0
   835
val add_term_tvars = it_term_types add_typ_tvars;
clasohm@0
   836
clasohm@0
   837
(*Accumulates the TFrees in a term, suppressing duplicates. *)
clasohm@0
   838
val add_term_tfrees = it_term_types add_typ_tfrees;
clasohm@0
   839
val add_term_tfree_names = it_term_types add_typ_tfree_names;
clasohm@0
   840
nipkow@949
   841
val add_term_tvarnames = it_term_types add_typ_varnames;
nipkow@949
   842
clasohm@0
   843
(*Non-list versions*)
clasohm@0
   844
fun typ_tfrees T = add_typ_tfrees(T,[]);
clasohm@0
   845
fun typ_tvars T = add_typ_tvars(T,[]);
clasohm@0
   846
fun term_tfrees t = add_term_tfrees(t,[]);
clasohm@0
   847
fun term_tvars t = add_term_tvars(t,[]);
clasohm@0
   848
nipkow@949
   849
(*special code to enforce left-to-right collection of TVar-indexnames*)
nipkow@949
   850
nipkow@949
   851
fun add_typ_ixns(ixns,Type(_,Ts)) = foldl add_typ_ixns (ixns,Ts)
wenzelm@13000
   852
  | add_typ_ixns(ixns,TVar(ixn,_)) = if mem_ix (ixn, ixns) then ixns
wenzelm@9536
   853
                                     else ixns@[ixn]
nipkow@949
   854
  | add_typ_ixns(ixns,TFree(_)) = ixns;
nipkow@949
   855
nipkow@949
   856
fun add_term_tvar_ixns(Const(_,T),ixns) = add_typ_ixns(ixns,T)
nipkow@949
   857
  | add_term_tvar_ixns(Free(_,T),ixns) = add_typ_ixns(ixns,T)
nipkow@949
   858
  | add_term_tvar_ixns(Var(_,T),ixns) = add_typ_ixns(ixns,T)
nipkow@949
   859
  | add_term_tvar_ixns(Bound _,ixns) = ixns
nipkow@949
   860
  | add_term_tvar_ixns(Abs(_,T,t),ixns) =
nipkow@949
   861
      add_term_tvar_ixns(t,add_typ_ixns(ixns,T))
nipkow@949
   862
  | add_term_tvar_ixns(f$t,ixns) =
nipkow@949
   863
      add_term_tvar_ixns(t,add_term_tvar_ixns(f,ixns));
nipkow@949
   864
clasohm@0
   865
(** Frees and Vars **)
clasohm@0
   866
clasohm@0
   867
(*a partial ordering (not reflexive) for atomic terms*)
clasohm@0
   868
fun atless (Const (a,_), Const (b,_))  =  a<b
clasohm@0
   869
  | atless (Free (a,_), Free (b,_)) =  a<b
clasohm@0
   870
  | atless (Var(v,_), Var(w,_))  =  xless(v,w)
clasohm@0
   871
  | atless (Bound i, Bound j)  =   i<j
clasohm@0
   872
  | atless _  =  false;
clasohm@0
   873
clasohm@0
   874
(*insert atomic term into partially sorted list, suppressing duplicates (?)*)
clasohm@0
   875
fun insert_aterm (t,us) =
clasohm@0
   876
  let fun inserta [] = [t]
wenzelm@13000
   877
        | inserta (us as u::us') =
wenzelm@9536
   878
              if atless(t,u) then t::us
wenzelm@9536
   879
              else if t=u then us (*duplicate*)
wenzelm@9536
   880
              else u :: inserta(us')
clasohm@0
   881
  in  inserta us  end;
clasohm@0
   882
clasohm@0
   883
(*Accumulates the Vars in the term, suppressing duplicates*)
clasohm@0
   884
fun add_term_vars (t, vars: term list) = case t of
clasohm@0
   885
    Var   _ => insert_aterm(t,vars)
clasohm@0
   886
  | Abs (_,_,body) => add_term_vars(body,vars)
clasohm@0
   887
  | f$t =>  add_term_vars (f, add_term_vars(t, vars))
clasohm@0
   888
  | _ => vars;
clasohm@0
   889
clasohm@0
   890
fun term_vars t = add_term_vars(t,[]);
clasohm@0
   891
clasohm@0
   892
(*Accumulates the Frees in the term, suppressing duplicates*)
clasohm@0
   893
fun add_term_frees (t, frees: term list) = case t of
clasohm@0
   894
    Free   _ => insert_aterm(t,frees)
clasohm@0
   895
  | Abs (_,_,body) => add_term_frees(body,frees)
clasohm@0
   896
  | f$t =>  add_term_frees (f, add_term_frees(t, frees))
clasohm@0
   897
  | _ => frees;
clasohm@0
   898
clasohm@0
   899
fun term_frees t = add_term_frees(t,[]);
clasohm@0
   900
clasohm@0
   901
(*Given an abstraction over P, replaces the bound variable by a Free variable
clasohm@0
   902
  having a unique name. *)
clasohm@0
   903
fun variant_abs (a,T,P) =
clasohm@0
   904
  let val b = variant (add_term_names(P,[])) a
paulson@2192
   905
  in  (b,  subst_bound (Free(b,T), P))  end;
clasohm@0
   906
clasohm@0
   907
(* renames and reverses the strings in vars away from names *)
clasohm@0
   908
fun rename_aTs names vars : (string*typ)list =
clasohm@0
   909
  let fun rename_aT (vars,(a,T)) =
wenzelm@9536
   910
                (variant (map #1 vars @ names) a, T) :: vars
clasohm@0
   911
  in foldl rename_aT ([],vars) end;
clasohm@0
   912
clasohm@0
   913
fun rename_wrt_term t = rename_aTs (add_term_names(t,[]));
clasohm@1364
   914
paulson@1417
   915
wenzelm@4286
   916
(* left-ro-right traversal *)
wenzelm@4286
   917
wenzelm@4286
   918
(*foldl atoms of type*)
wenzelm@4286
   919
fun foldl_atyps f (x, Type (_, Ts)) = foldl (foldl_atyps f) (x, Ts)
wenzelm@4286
   920
  | foldl_atyps f x_atom = f x_atom;
wenzelm@4286
   921
wenzelm@4286
   922
(*foldl atoms of term*)
wenzelm@4286
   923
fun foldl_aterms f (x, t $ u) = foldl_aterms f (foldl_aterms f (x, t), u)
wenzelm@4286
   924
  | foldl_aterms f (x, Abs (_, _, t)) = foldl_aterms f (x, t)
wenzelm@4286
   925
  | foldl_aterms f x_atom = f x_atom;
wenzelm@4286
   926
wenzelm@6548
   927
fun foldl_map_aterms f (x, t $ u) =
wenzelm@6548
   928
      let val (x', t') = foldl_map_aterms f (x, t); val (x'', u') = foldl_map_aterms f (x', u);
wenzelm@6548
   929
      in (x'', t' $ u') end
wenzelm@6548
   930
  | foldl_map_aterms f (x, Abs (a, T, t)) =
wenzelm@6548
   931
      let val (x', t') = foldl_map_aterms f (x, t) in (x', Abs (a, T, t')) end
wenzelm@6548
   932
  | foldl_map_aterms f x_atom = f x_atom;
wenzelm@6548
   933
wenzelm@4286
   934
(*foldl types of term*)
wenzelm@8609
   935
fun foldl_term_types f (x, t as Const (_, T)) = f t (x, T)
wenzelm@8609
   936
  | foldl_term_types f (x, t as Free (_, T)) = f t (x, T)
wenzelm@8609
   937
  | foldl_term_types f (x, t as Var (_, T)) = f t (x, T)
wenzelm@8609
   938
  | foldl_term_types f (x, Bound _) = x
wenzelm@8609
   939
  | foldl_term_types f (x, t as Abs (_, T, b)) = foldl_term_types f (f t (x, T), b)
wenzelm@8609
   940
  | foldl_term_types f (x, t $ u) = foldl_term_types f (foldl_term_types f (x, t), u);
wenzelm@8609
   941
wenzelm@8609
   942
fun foldl_types f = foldl_term_types (fn _ => f);
wenzelm@4286
   943
wenzelm@12499
   944
(*collect variables*)
wenzelm@12499
   945
val add_tvarsT = foldl_atyps (fn (vs, TVar v) => v ins vs | (vs, _) => vs);
wenzelm@12499
   946
val add_tvars = foldl_types add_tvarsT;
wenzelm@12499
   947
val add_vars = foldl_aterms (fn (vs, Var v) => v ins vs | (vs, _) => vs);
wenzelm@12499
   948
val add_frees = foldl_aterms (fn (vs, Free v) => v ins vs | (vs, _) => vs);
wenzelm@12499
   949
wenzelm@15025
   950
(*collect variable names*)
wenzelm@15025
   951
val add_term_varnames = foldl_aterms (fn (xs, Var (x, _)) => ins_ix (x, xs) | (xs, _) => xs);
wenzelm@15025
   952
fun term_varnames t = add_term_varnames ([], t);
wenzelm@4286
   953
paulson@1417
   954
wenzelm@4444
   955
(** type and term orders **)
wenzelm@4444
   956
wenzelm@4444
   957
fun indexname_ord ((x, i), (y, j)) =
paulson@14472
   958
  (case Int.compare (i, j) of EQUAL => String.compare (x, y) | ord => ord);
wenzelm@4444
   959
paulson@14472
   960
val sort_ord = list_ord String.compare;
wenzelm@13000
   961
wenzelm@4444
   962
wenzelm@4444
   963
(* typ_ord *)
wenzelm@4444
   964
paulson@14472
   965
fun typ_ord (Type x, Type y) = prod_ord String.compare typs_ord (x, y)
wenzelm@4444
   966
  | typ_ord (Type _, _) = GREATER
wenzelm@4444
   967
  | typ_ord (TFree _, Type _) = LESS
paulson@14472
   968
  | typ_ord (TFree x, TFree y) = prod_ord String.compare sort_ord (x, y)
wenzelm@4444
   969
  | typ_ord (TFree _, TVar _) = GREATER
wenzelm@4444
   970
  | typ_ord (TVar _, Type _) = LESS
wenzelm@4444
   971
  | typ_ord (TVar _, TFree _) = LESS
wenzelm@13000
   972
  | typ_ord (TVar x, TVar y) = prod_ord indexname_ord sort_ord (x, y)
wenzelm@4444
   973
and typs_ord Ts_Us = list_ord typ_ord Ts_Us;
wenzelm@4444
   974
wenzelm@4444
   975
wenzelm@4444
   976
(* term_ord *)
wenzelm@4444
   977
wenzelm@4444
   978
(*a linear well-founded AC-compatible ordering for terms:
wenzelm@4444
   979
  s < t <=> 1. size(s) < size(t) or
wenzelm@4444
   980
            2. size(s) = size(t) and s=f(...) and t=g(...) and f<g or
wenzelm@4444
   981
            3. size(s) = size(t) and s=f(s1..sn) and t=f(t1..tn) and
wenzelm@4444
   982
               (s1..sn) < (t1..tn) (lexicographically)*)
wenzelm@4444
   983
wenzelm@4444
   984
fun dest_hd (Const (a, T)) = (((a, 0), T), 0)
wenzelm@4444
   985
  | dest_hd (Free (a, T)) = (((a, 0), T), 1)
wenzelm@4444
   986
  | dest_hd (Var v) = (v, 2)
wenzelm@4444
   987
  | dest_hd (Bound i) = ((("", i), dummyT), 3)
wenzelm@4444
   988
  | dest_hd (Abs (_, T, _)) = ((("", 0), T), 4);
wenzelm@4444
   989
wenzelm@4444
   990
fun term_ord (Abs (_, T, t), Abs(_, U, u)) =
wenzelm@4444
   991
      (case term_ord (t, u) of EQUAL => typ_ord (T, U) | ord => ord)
wenzelm@4444
   992
  | term_ord (t, u) =
paulson@14472
   993
      (case Int.compare (size_of_term t, size_of_term u) of
wenzelm@4444
   994
        EQUAL =>
wenzelm@4444
   995
          let val (f, ts) = strip_comb t and (g, us) = strip_comb u in
wenzelm@4444
   996
            (case hd_ord (f, g) of EQUAL => terms_ord (ts, us) | ord => ord)
wenzelm@4444
   997
          end
wenzelm@4444
   998
      | ord => ord)
wenzelm@4444
   999
and hd_ord (f, g) =
paulson@14472
  1000
  prod_ord (prod_ord indexname_ord typ_ord) Int.compare (dest_hd f, dest_hd g)
wenzelm@4444
  1001
and terms_ord (ts, us) = list_ord term_ord (ts, us);
wenzelm@4444
  1002
wenzelm@4444
  1003
fun termless tu = (term_ord tu = LESS);
wenzelm@4444
  1004
berghofe@8408
  1005
structure Vartab = TableFun(type key = indexname val ord = indexname_ord);
wenzelm@13000
  1006
structure Typtab = TableFun(type key = typ val ord = typ_ord);
berghofe@8408
  1007
structure Termtab = TableFun(type key = term val ord = term_ord);
berghofe@8408
  1008
berghofe@8408
  1009
(*Substitute for type Vars in a type, version using Vartab*)
berghofe@8408
  1010
fun typ_subst_TVars_Vartab iTs T = if Vartab.is_empty iTs then T else
berghofe@8408
  1011
  let fun subst(Type(a, Ts)) = Type(a, map subst Ts)
wenzelm@9536
  1012
        | subst(T as TFree _) = T
wenzelm@9536
  1013
        | subst(T as TVar(ixn, _)) =
skalberg@15531
  1014
            (case Vartab.lookup (iTs, ixn) of NONE => T | SOME(U) => U)
berghofe@8408
  1015
  in subst T end;
berghofe@8408
  1016
berghofe@8408
  1017
(*Substitute for type Vars in a term, version using Vartab*)
berghofe@8408
  1018
val subst_TVars_Vartab = map_term_types o typ_subst_TVars_Vartab;
wenzelm@4444
  1019
wenzelm@4444
  1020
wenzelm@13000
  1021
(*** Compression of terms and types by sharing common subtrees.
wenzelm@13000
  1022
     Saves 50-75% on storage requirements.  As it is a bit slow,
wenzelm@13000
  1023
     it should be called only for axioms, stored theorems, etc.
wenzelm@13000
  1024
     Recorded term and type fragments are never disposed. ***)
paulson@1417
  1025
paulson@1417
  1026
(** Sharing of types **)
paulson@1417
  1027
wenzelm@13000
  1028
val memo_types = ref (Typtab.empty: typ Typtab.table);
paulson@1417
  1029
paulson@1417
  1030
fun compress_type T =
wenzelm@13000
  1031
  (case Typtab.lookup (! memo_types, T) of
skalberg@15531
  1032
    SOME T' => T'
skalberg@15531
  1033
  | NONE =>
wenzelm@13000
  1034
      let val T' = (case T of Type (a, Ts) => Type (a, map compress_type Ts) | _ => T)
wenzelm@13000
  1035
      in memo_types := Typtab.update ((T', T'), ! memo_types); T' end);
wenzelm@13000
  1036
paulson@1417
  1037
paulson@1417
  1038
(** Sharing of atomic terms **)
paulson@1417
  1039
wenzelm@13000
  1040
val memo_terms = ref (Termtab.empty : term Termtab.table);
paulson@1417
  1041
paulson@1417
  1042
fun share_term (t $ u) = share_term t $ share_term u
wenzelm@13000
  1043
  | share_term (Abs (a, T, u)) = Abs (a, T, share_term u)
paulson@1417
  1044
  | share_term t =
wenzelm@13000
  1045
      (case Termtab.lookup (! memo_terms, t) of
skalberg@15531
  1046
        SOME t' => t'
skalberg@15531
  1047
      | NONE => (memo_terms := Termtab.update ((t, t), ! memo_terms); t));
paulson@1417
  1048
paulson@1417
  1049
val compress_term = share_term o map_term_types compress_type;
paulson@1417
  1050
wenzelm@4444
  1051
wenzelm@9536
  1052
(* dummy patterns *)
wenzelm@9536
  1053
wenzelm@9536
  1054
val dummy_patternN = "dummy_pattern";
wenzelm@9536
  1055
wenzelm@9536
  1056
fun is_dummy_pattern (Const ("dummy_pattern", _)) = true
wenzelm@9536
  1057
  | is_dummy_pattern _ = false;
wenzelm@9536
  1058
wenzelm@9536
  1059
fun no_dummy_patterns tm =
wenzelm@9536
  1060
  if not (foldl_aterms (fn (b, t) => b orelse is_dummy_pattern t) (false, tm)) then tm
wenzelm@9536
  1061
  else raise TERM ("Illegal occurrence of '_' dummy pattern", [tm]);
wenzelm@9536
  1062
wenzelm@11903
  1063
fun replace_dummy Ts (i, Const ("dummy_pattern", T)) =
wenzelm@11903
  1064
      (i + 1, list_comb (Var (("_dummy_", i), Ts ---> T), map Bound (0 upto length Ts - 1)))
wenzelm@11903
  1065
  | replace_dummy Ts (i, Abs (x, T, t)) =
wenzelm@11903
  1066
      let val (i', t') = replace_dummy (T :: Ts) (i, t)
wenzelm@11903
  1067
      in (i', Abs (x, T, t')) end
wenzelm@11903
  1068
  | replace_dummy Ts (i, t $ u) =
wenzelm@11903
  1069
      let val (i', t') = replace_dummy Ts (i, t); val (i'', u') = replace_dummy Ts (i', u)
wenzelm@11903
  1070
      in (i'', t' $ u') end
wenzelm@11903
  1071
  | replace_dummy _ (i, a) = (i, a);
wenzelm@11903
  1072
wenzelm@11903
  1073
val replace_dummy_patterns = replace_dummy [];
wenzelm@9536
  1074
wenzelm@10552
  1075
fun is_replaced_dummy_pattern ("_dummy_", _) = true
wenzelm@10552
  1076
  | is_replaced_dummy_pattern _ = false;
wenzelm@9536
  1077
wenzelm@13484
  1078
wenzelm@13484
  1079
(* adhoc freezing *)
wenzelm@13484
  1080
wenzelm@13484
  1081
fun adhoc_freeze_vars tm =
wenzelm@13484
  1082
  let
wenzelm@13484
  1083
    fun mk_inst (var as Var ((a, i), T)) =
wenzelm@13484
  1084
      let val x = a ^ Library.gensym "_" ^ string_of_int i
wenzelm@13484
  1085
      in ((var,  Free(x, T)), x) end;
wenzelm@13484
  1086
    val (insts, xs) = split_list (map mk_inst (term_vars tm));
wenzelm@13484
  1087
  in (subst_atomic insts tm, xs) end;
wenzelm@13484
  1088
wenzelm@13484
  1089
wenzelm@14786
  1090
(* string_of_vname *)
wenzelm@14786
  1091
berghofe@15472
  1092
val show_var_qmarks = ref true;
berghofe@15472
  1093
wenzelm@14786
  1094
fun string_of_vname (x, i) =
wenzelm@14786
  1095
  let
wenzelm@14786
  1096
    val si = string_of_int i;
wenzelm@14786
  1097
    val dot = if_none (try (Symbol.is_digit o last_elem o Symbol.explode) x) true;
berghofe@15472
  1098
    val qmark = if !show_var_qmarks then "?" else "";
wenzelm@14786
  1099
  in
berghofe@15472
  1100
    if dot then qmark ^ x ^ "." ^ si
berghofe@15472
  1101
    else if i = 0 then qmark ^ x
berghofe@15472
  1102
    else qmark ^ x ^ si
wenzelm@14786
  1103
  end;
wenzelm@14786
  1104
wenzelm@14786
  1105
fun string_of_vname' (x, ~1) = x
wenzelm@14786
  1106
  | string_of_vname' xi = string_of_vname xi;
wenzelm@14786
  1107
clasohm@1364
  1108
end;
clasohm@1364
  1109
wenzelm@4444
  1110
structure BasicTerm: BASIC_TERM = Term;
wenzelm@4444
  1111
open BasicTerm;