src/Pure/term.ML
author skalberg
Fri Mar 04 15:07:34 2005 +0100 (2005-03-04)
changeset 15574 b1d1b5bfc464
parent 15573 cf53c2dcf440
child 15598 4ab52355bb53
permissions -rw-r--r--
Removed practically all references to Library.foldr.
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(*  Title:      Pure/term.ML
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    ID:         $Id$
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    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
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    Copyright   Cambridge University 1992
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Simply typed lambda-calculus: types, terms, and basic operations.
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*)
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infix 9  $;
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infixr 5 -->;
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infixr --->;
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infix aconv;
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signature BASIC_TERM =
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sig
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  type indexname
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  type class
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  type sort
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  type arity
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  datatype typ =
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    Type  of string * typ list |
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    TFree of string * sort |
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    TVar  of indexname * sort
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  val --> : typ * typ -> typ
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  val ---> : typ list * typ -> typ
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  val is_TVar: typ -> bool
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  val is_funtype: typ -> bool
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  val domain_type: typ -> typ
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  val range_type: typ -> typ
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  val binder_types: typ -> typ list
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  val body_type: typ -> typ
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  val strip_type: typ -> typ list * typ
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  datatype term =
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    Const of string * typ |
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    Free of string * typ |
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    Var of indexname * typ |
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    Bound of int |
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    Abs of string * typ * term |
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    $ of term * term
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  structure Vartab : TABLE
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  structure Typtab : TABLE
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  structure Termtab : TABLE
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  exception TYPE of string * typ list * term list
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  exception TERM of string * term list
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  val is_Bound: term -> bool
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  val is_Const: term -> bool
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  val is_Free: term -> bool
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  val is_Var: term -> bool
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  val is_first_order: term -> bool
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  val dest_Type: typ -> string * typ list
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  val dest_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 ---> = Library.foldr (op -->);
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fun dest_Type (Type x) = x
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  | dest_Type T = raise TYPE ("dest_Type", [T], []);
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(** Discriminators **)
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fun is_Bound (Bound _) = true
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  | is_Bound _         = false;
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fun is_Const (Const _) = true
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  | is_Const _ = false;
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fun is_Free (Free _) = true
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  | is_Free _ = false;
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fun is_Var (Var _) = true
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  | is_Var _ = false;
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fun is_TVar (TVar _) = true
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  | is_TVar _ = false;
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(*Differs from proofterm/is_fun in its treatment of TVar*)
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fun is_funtype (Type("fun",[_,_])) = true
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  | is_funtype _ = false;
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(** Destructors **)
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fun dest_Const (Const x) =  x
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  | dest_Const t = raise TERM("dest_Const", [t]);
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fun dest_Free (Free x) =  x
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  | dest_Free t = raise TERM("dest_Free", [t]);
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fun dest_Var (Var x) =  x
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  | dest_Var t = raise TERM("dest_Var", [t]);
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fun domain_type (Type("fun", [T,_])) = T
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and range_type  (Type("fun", [_,T])) = T;
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(* maps  [T1,...,Tn]--->T  to the list  [T1,T2,...,Tn]*)
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fun binder_types (Type("fun",[S,T])) = S :: binder_types T
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  | binder_types _   =  [];
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(* maps  [T1,...,Tn]--->T  to T*)
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fun body_type (Type("fun",[S,T])) = body_type T
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  | body_type T   =  T;
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(* maps  [T1,...,Tn]--->T  to   ([T1,T2,...,Tn], T)  *)
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fun strip_type T : typ list * typ =
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  (binder_types T, body_type T);
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(*Compute the type of the term, checking that combinations are well-typed
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  Ts = [T0,T1,...] holds types of bound variables 0, 1, ...*)
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fun type_of1 (Ts, Const (_,T)) = T
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  | type_of1 (Ts, Free  (_,T)) = T
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  | type_of1 (Ts, Bound i) = (List.nth (Ts,i)
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        handle Subscript => raise TYPE("type_of: bound variable", [], [Bound i]))
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  | type_of1 (Ts, Var (_,T)) = T
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  | type_of1 (Ts, Abs (_,T,body)) = T --> type_of1(T::Ts, body)
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  | type_of1 (Ts, f$u) =
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      let val U = type_of1(Ts,u)
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          and T = type_of1(Ts,f)
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      in case T of
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            Type("fun",[T1,T2]) =>
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   327
              if T1=U then T2  else raise TYPE
wenzelm@9536
   328
                    ("type_of: type mismatch in application", [T1,U], [f$u])
wenzelm@13000
   329
          | _ => raise TYPE
wenzelm@9536
   330
                    ("type_of: function type is expected in application",
wenzelm@9536
   331
                     [T,U], [f$u])
clasohm@0
   332
      end;
clasohm@0
   333
clasohm@0
   334
fun type_of t : typ = type_of1 ([],t);
clasohm@0
   335
clasohm@0
   336
(*Determines the type of a term, with minimal checking*)
wenzelm@13000
   337
fun fastype_of1 (Ts, f$u) =
lcp@61
   338
    (case fastype_of1 (Ts,f) of
wenzelm@9536
   339
        Type("fun",[_,T]) => T
wenzelm@9536
   340
        | _ => raise TERM("fastype_of: expected function type", [f$u]))
lcp@61
   341
  | fastype_of1 (_, Const (_,T)) = T
lcp@61
   342
  | fastype_of1 (_, Free (_,T)) = T
skalberg@15570
   343
  | fastype_of1 (Ts, Bound i) = (List.nth(Ts,i)
skalberg@15570
   344
         handle Subscript => raise TERM("fastype_of: Bound", [Bound i]))
wenzelm@13000
   345
  | fastype_of1 (_, Var (_,T)) = T
lcp@61
   346
  | fastype_of1 (Ts, Abs (_,T,u)) = T --> fastype_of1 (T::Ts, u);
lcp@61
   347
lcp@61
   348
fun fastype_of t : typ = fastype_of1 ([],t);
clasohm@0
   349
clasohm@0
   350
skalberg@15570
   351
val list_abs = Library.foldr (fn ((x, T), t) => Abs (x, T, t));
wenzelm@10806
   352
clasohm@0
   353
(* maps  (x1,...,xn)t   to   t  *)
wenzelm@13000
   354
fun strip_abs_body (Abs(_,_,t))  =  strip_abs_body t
clasohm@0
   355
  | strip_abs_body u  =  u;
clasohm@0
   356
clasohm@0
   357
(* maps  (x1,...,xn)t   to   [x1, ..., xn]  *)
wenzelm@13000
   358
fun strip_abs_vars (Abs(a,T,t))  =  (a,T) :: strip_abs_vars t
clasohm@0
   359
  | strip_abs_vars u  =  [] : (string*typ) list;
clasohm@0
   360
clasohm@0
   361
clasohm@0
   362
fun strip_qnt_body qnt =
clasohm@0
   363
let fun strip(tm as Const(c,_)$Abs(_,_,t)) = if c=qnt then strip t else tm
clasohm@0
   364
      | strip t = t
clasohm@0
   365
in strip end;
clasohm@0
   366
clasohm@0
   367
fun strip_qnt_vars qnt =
clasohm@0
   368
let fun strip(Const(c,_)$Abs(a,T,t)) = if c=qnt then (a,T)::strip t else []
clasohm@0
   369
      | strip t  =  [] : (string*typ) list
clasohm@0
   370
in strip end;
clasohm@0
   371
clasohm@0
   372
clasohm@0
   373
(* maps   (f, [t1,...,tn])  to  f(t1,...,tn) *)
skalberg@15570
   374
val list_comb : term * term list -> term = Library.foldl (op $);
clasohm@0
   375
clasohm@0
   376
clasohm@0
   377
(* maps   f(t1,...,tn)  to  (f, [t1,...,tn]) ; naturally tail-recursive*)
wenzelm@13000
   378
fun strip_comb u : term * term list =
clasohm@0
   379
    let fun stripc (f$t, ts) = stripc (f, t::ts)
wenzelm@13000
   380
        |   stripc  x =  x
clasohm@0
   381
    in  stripc(u,[])  end;
clasohm@0
   382
clasohm@0
   383
clasohm@0
   384
(* maps   f(t1,...,tn)  to  f , which is never a combination *)
clasohm@0
   385
fun head_of (f$t) = head_of f
clasohm@0
   386
  | head_of u = u;
clasohm@0
   387
clasohm@0
   388
clasohm@0
   389
(*Number of atoms and abstractions in a term*)
clasohm@0
   390
fun size_of_term (Abs (_,_,body)) = 1 + size_of_term body
clasohm@0
   391
  | size_of_term (f$t) = size_of_term f  +  size_of_term t
clasohm@0
   392
  | size_of_term _ = 1;
clasohm@0
   393
nipkow@949
   394
fun map_type_tvar f (Type(a,Ts)) = Type(a, map (map_type_tvar f) Ts)
nipkow@949
   395
  | map_type_tvar f (T as TFree _) = T
nipkow@949
   396
  | map_type_tvar f (TVar x) = f x;
nipkow@949
   397
nipkow@949
   398
fun map_type_tfree f (Type(a,Ts)) = Type(a, map (map_type_tfree f) Ts)
nipkow@949
   399
  | map_type_tfree f (TFree x) = f x
nipkow@949
   400
  | map_type_tfree f (T as TVar _) = T;
nipkow@949
   401
clasohm@0
   402
(* apply a function to all types in a term *)
clasohm@0
   403
fun map_term_types f =
clasohm@0
   404
let fun map(Const(a,T)) = Const(a, f T)
clasohm@0
   405
      | map(Free(a,T)) = Free(a, f T)
clasohm@0
   406
      | map(Var(v,T)) = Var(v, f T)
clasohm@0
   407
      | map(t as Bound _)  = t
clasohm@0
   408
      | map(Abs(a,T,t)) = Abs(a, f T, map t)
clasohm@0
   409
      | map(f$t) = map f $ map t;
clasohm@0
   410
in map end;
clasohm@0
   411
clasohm@0
   412
(* iterate a function over all types in a term *)
clasohm@0
   413
fun it_term_types f =
clasohm@0
   414
let fun iter(Const(_,T), a) = f(T,a)
clasohm@0
   415
      | iter(Free(_,T), a) = f(T,a)
clasohm@0
   416
      | iter(Var(_,T), a) = f(T,a)
clasohm@0
   417
      | iter(Abs(_,T,t), a) = iter(t,f(T,a))
clasohm@0
   418
      | iter(f$u, a) = iter(f, iter(u, a))
clasohm@0
   419
      | iter(Bound _, a) = a
clasohm@0
   420
in iter end
clasohm@0
   421
clasohm@0
   422
clasohm@0
   423
(** Connectives of higher order logic **)
clasohm@0
   424
wenzelm@375
   425
fun itselfT ty = Type ("itself", [ty]);
wenzelm@14854
   426
val a_itselfT = itselfT (TFree ("'a", []));
wenzelm@375
   427
clasohm@0
   428
val propT : typ = Type("prop",[]);
clasohm@0
   429
clasohm@0
   430
val implies = Const("==>", propT-->propT-->propT);
clasohm@0
   431
clasohm@0
   432
fun all T = Const("all", (T-->propT)-->propT);
clasohm@0
   433
clasohm@0
   434
fun equals T = Const("==", T-->T-->propT);
clasohm@0
   435
clasohm@0
   436
(* maps  !!x1...xn. t   to   t  *)
wenzelm@13000
   437
fun strip_all_body (Const("all",_)$Abs(_,_,t))  =  strip_all_body t
clasohm@0
   438
  | strip_all_body t  =  t;
clasohm@0
   439
clasohm@0
   440
(* maps  !!x1...xn. t   to   [x1, ..., xn]  *)
clasohm@0
   441
fun strip_all_vars (Const("all",_)$Abs(a,T,t))  =
wenzelm@13000
   442
                (a,T) :: strip_all_vars t
clasohm@0
   443
  | strip_all_vars t  =  [] : (string*typ) list;
clasohm@0
   444
clasohm@0
   445
(*increments a term's non-local bound variables
clasohm@0
   446
  required when moving a term within abstractions
clasohm@0
   447
     inc is  increment for bound variables
clasohm@0
   448
     lev is  level at which a bound variable is considered 'loose'*)
wenzelm@13000
   449
fun incr_bv (inc, lev, u as Bound i) = if i>=lev then Bound(i+inc) else u
clasohm@0
   450
  | incr_bv (inc, lev, Abs(a,T,body)) =
wenzelm@9536
   451
        Abs(a, T, incr_bv(inc,lev+1,body))
wenzelm@13000
   452
  | incr_bv (inc, lev, f$t) =
clasohm@0
   453
      incr_bv(inc,lev,f) $ incr_bv(inc,lev,t)
clasohm@0
   454
  | incr_bv (inc, lev, u) = u;
clasohm@0
   455
clasohm@0
   456
fun incr_boundvars  0  t = t
clasohm@0
   457
  | incr_boundvars inc t = incr_bv(inc,0,t);
clasohm@0
   458
wenzelm@12981
   459
(*Scan a pair of terms; while they are similar,
wenzelm@12981
   460
  accumulate corresponding bound vars in "al"*)
wenzelm@12981
   461
fun match_bvs(Abs(x,_,s),Abs(y,_,t), al) =
wenzelm@12981
   462
      match_bvs(s, t, if x="" orelse y="" then al
wenzelm@12981
   463
                                          else (x,y)::al)
wenzelm@12981
   464
  | match_bvs(f$s, g$t, al) = match_bvs(f,g,match_bvs(s,t,al))
wenzelm@12981
   465
  | match_bvs(_,_,al) = al;
wenzelm@12981
   466
wenzelm@12981
   467
(* strip abstractions created by parameters *)
wenzelm@12981
   468
fun match_bvars((s,t),al) = match_bvs(strip_abs_body s, strip_abs_body t, al);
wenzelm@12981
   469
wenzelm@12981
   470
fun rename_abs pat obj t =
wenzelm@12981
   471
  let
wenzelm@12981
   472
    val ren = match_bvs (pat, obj, []);
wenzelm@12981
   473
    fun ren_abs (Abs (x, T, b)) =
skalberg@15570
   474
          Abs (getOpt (assoc_string (ren, x), x), T, ren_abs b)
wenzelm@12981
   475
      | ren_abs (f $ t) = ren_abs f $ ren_abs t
wenzelm@12981
   476
      | ren_abs t = t
skalberg@15531
   477
  in if null ren then NONE else SOME (ren_abs t) end;
clasohm@0
   478
clasohm@0
   479
(*Accumulate all 'loose' bound vars referring to level 'lev' or beyond.
clasohm@0
   480
   (Bound 0) is loose at level 0 *)
wenzelm@13000
   481
fun add_loose_bnos (Bound i, lev, js) =
wenzelm@9536
   482
        if i<lev then js  else  (i-lev) ins_int js
clasohm@0
   483
  | add_loose_bnos (Abs (_,_,t), lev, js) = add_loose_bnos (t, lev+1, js)
clasohm@0
   484
  | add_loose_bnos (f$t, lev, js) =
wenzelm@13000
   485
        add_loose_bnos (f, lev, add_loose_bnos (t, lev, js))
clasohm@0
   486
  | add_loose_bnos (_, _, js) = js;
clasohm@0
   487
clasohm@0
   488
fun loose_bnos t = add_loose_bnos (t, 0, []);
clasohm@0
   489
clasohm@0
   490
(* loose_bvar(t,k) iff t contains a 'loose' bound variable referring to
clasohm@0
   491
   level k or beyond. *)
clasohm@0
   492
fun loose_bvar(Bound i,k) = i >= k
clasohm@0
   493
  | loose_bvar(f$t, k) = loose_bvar(f,k) orelse loose_bvar(t,k)
clasohm@0
   494
  | loose_bvar(Abs(_,_,t),k) = loose_bvar(t,k+1)
clasohm@0
   495
  | loose_bvar _ = false;
clasohm@0
   496
nipkow@2792
   497
fun loose_bvar1(Bound i,k) = i = k
nipkow@2792
   498
  | loose_bvar1(f$t, k) = loose_bvar1(f,k) orelse loose_bvar1(t,k)
nipkow@2792
   499
  | loose_bvar1(Abs(_,_,t),k) = loose_bvar1(t,k+1)
nipkow@2792
   500
  | loose_bvar1 _ = false;
clasohm@0
   501
clasohm@0
   502
(*Substitute arguments for loose bound variables.
clasohm@0
   503
  Beta-reduction of arg(n-1)...arg0 into t replacing (Bound i) with (argi).
wenzelm@4626
   504
  Note that for ((%x y. c) a b), the bound vars in c are x=1 and y=0
wenzelm@9536
   505
        and the appropriate call is  subst_bounds([b,a], c) .
clasohm@0
   506
  Loose bound variables >=n are reduced by "n" to
clasohm@0
   507
     compensate for the disappearance of lambdas.
clasohm@0
   508
*)
wenzelm@13000
   509
fun subst_bounds (args: term list, t) : term =
clasohm@0
   510
  let val n = length args;
clasohm@0
   511
      fun subst (t as Bound i, lev) =
wenzelm@9536
   512
           (if i<lev then  t    (*var is locally bound*)
wenzelm@9536
   513
            else  incr_boundvars lev (List.nth(args, i-lev))
wenzelm@9536
   514
                    handle Subscript => Bound(i-n)  (*loose: change it*))
wenzelm@9536
   515
        | subst (Abs(a,T,body), lev) = Abs(a, T,  subst(body,lev+1))
wenzelm@9536
   516
        | subst (f$t, lev) =  subst(f,lev)  $  subst(t,lev)
wenzelm@9536
   517
        | subst (t,lev) = t
clasohm@0
   518
  in   case args of [] => t  | _ => subst (t,0)  end;
clasohm@0
   519
paulson@2192
   520
(*Special case: one argument*)
wenzelm@13000
   521
fun subst_bound (arg, t) : term =
paulson@2192
   522
  let fun subst (t as Bound i, lev) =
wenzelm@9536
   523
            if i<lev then  t    (*var is locally bound*)
wenzelm@9536
   524
            else  if i=lev then incr_boundvars lev arg
wenzelm@9536
   525
                           else Bound(i-1)  (*loose: change it*)
wenzelm@9536
   526
        | subst (Abs(a,T,body), lev) = Abs(a, T,  subst(body,lev+1))
wenzelm@9536
   527
        | subst (f$t, lev) =  subst(f,lev)  $  subst(t,lev)
wenzelm@9536
   528
        | subst (t,lev) = t
paulson@2192
   529
  in  subst (t,0)  end;
paulson@2192
   530
clasohm@0
   531
(*beta-reduce if possible, else form application*)
paulson@2192
   532
fun betapply (Abs(_,_,t), u) = subst_bound (u,t)
clasohm@0
   533
  | betapply (f,u) = f$u;
clasohm@0
   534
wenzelm@14786
   535
paulson@2192
   536
(** Equality, membership and insertion of indexnames (string*ints) **)
paulson@2192
   537
paulson@2192
   538
(*optimized equality test for indexnames.  Yields a huge gain under Poly/ML*)
wenzelm@2959
   539
fun eq_ix ((a, i):indexname, (a',i'):indexname) = (a=a') andalso i=i';
paulson@2192
   540
paulson@2192
   541
(*membership in a list, optimized version for indexnames*)
wenzelm@2959
   542
fun mem_ix (_, []) = false
paulson@2192
   543
  | mem_ix (x, y :: ys) = eq_ix(x,y) orelse mem_ix (x, ys);
paulson@2192
   544
paulson@2192
   545
(*insertion into list, optimized version for indexnames*)
paulson@2192
   546
fun ins_ix (x,xs) = if mem_ix (x, xs) then xs else x :: xs;
paulson@2192
   547
clasohm@0
   548
(*Tests whether 2 terms are alpha-convertible and have same type.
wenzelm@4626
   549
  Note that constants may have more than one type.*)
clasohm@0
   550
fun (Const(a,T)) aconv (Const(b,U)) = a=b  andalso  T=U
paulson@2752
   551
  | (Free(a,T))  aconv (Free(b,U))  = a=b  andalso  T=U
paulson@2752
   552
  | (Var(v,T))   aconv (Var(w,U))   = eq_ix(v,w)  andalso  T=U
paulson@2752
   553
  | (Bound i)    aconv (Bound j)    = i=j
clasohm@0
   554
  | (Abs(_,T,t)) aconv (Abs(_,U,u)) = t aconv u  andalso  T=U
paulson@2752
   555
  | (f$t)        aconv (g$u)        = (f aconv g) andalso (t aconv u)
clasohm@0
   556
  | _ aconv _  =  false;
clasohm@0
   557
paulson@2176
   558
(** Membership, insertion, union for terms **)
paulson@2176
   559
paulson@2176
   560
fun mem_term (_, []) = false
paulson@2176
   561
  | mem_term (t, t'::ts) = t aconv t' orelse mem_term(t,ts);
paulson@2176
   562
paulson@2182
   563
fun subset_term ([], ys) = true
paulson@2182
   564
  | subset_term (x :: xs, ys) = mem_term (x, ys) andalso subset_term(xs, ys);
paulson@2182
   565
paulson@2182
   566
fun eq_set_term (xs, ys) =
paulson@2182
   567
    xs = ys orelse (subset_term (xs, ys) andalso subset_term (ys, xs));
paulson@2182
   568
paulson@2176
   569
fun ins_term(t,ts) = if mem_term(t,ts) then ts else t :: ts;
paulson@2176
   570
paulson@2176
   571
fun union_term (xs, []) = xs
paulson@2176
   572
  | union_term ([], ys) = ys
paulson@2176
   573
  | union_term ((x :: xs), ys) = union_term (xs, ins_term (x, ys));
paulson@2176
   574
paulson@5585
   575
fun inter_term ([], ys) = []
paulson@5585
   576
  | inter_term (x::xs, ys) =
paulson@5585
   577
      if mem_term (x,ys) then x :: inter_term(xs,ys) else inter_term(xs,ys);
paulson@5585
   578
clasohm@0
   579
(*are two term lists alpha-convertible in corresponding elements?*)
clasohm@0
   580
fun aconvs ([],[]) = true
clasohm@0
   581
  | aconvs (t::ts, u::us) = t aconv u andalso aconvs(ts,us)
clasohm@0
   582
  | aconvs _ = false;
clasohm@0
   583
wenzelm@13000
   584
(*A fast unification filter: true unless the two terms cannot be unified.
clasohm@0
   585
  Terms must be NORMAL.  Treats all Vars as distinct. *)
clasohm@0
   586
fun could_unify (t,u) =
clasohm@0
   587
  let fun matchrands (f$t, g$u) = could_unify(t,u) andalso  matchrands(f,g)
wenzelm@9536
   588
        | matchrands _ = true
clasohm@0
   589
  in case (head_of t , head_of u) of
wenzelm@9536
   590
        (_, Var _) => true
clasohm@0
   591
      | (Var _, _) => true
clasohm@0
   592
      | (Const(a,_), Const(b,_)) =>  a=b andalso matchrands(t,u)
clasohm@0
   593
      | (Free(a,_), Free(b,_)) =>  a=b andalso matchrands(t,u)
clasohm@0
   594
      | (Bound i, Bound j) =>  i=j andalso matchrands(t,u)
clasohm@0
   595
      | (Abs _, _) =>  true   (*because of possible eta equality*)
clasohm@0
   596
      | (_, Abs _) =>  true
clasohm@0
   597
      | _ => false
clasohm@0
   598
  end;
clasohm@0
   599
clasohm@0
   600
(*Substitute new for free occurrences of old in a term*)
clasohm@0
   601
fun subst_free [] = (fn t=>t)
clasohm@0
   602
  | subst_free pairs =
wenzelm@13000
   603
      let fun substf u =
wenzelm@9536
   604
            case gen_assoc (op aconv) (pairs, u) of
skalberg@15531
   605
                SOME u' => u'
skalberg@15531
   606
              | NONE => (case u of Abs(a,T,t) => Abs(a, T, substf t)
wenzelm@9536
   607
                                 | t$u' => substf t $ substf u'
wenzelm@9536
   608
                                 | _ => u)
clasohm@0
   609
      in  substf  end;
clasohm@0
   610
clasohm@0
   611
(*a total, irreflexive ordering on index names*)
clasohm@0
   612
fun xless ((a,i), (b,j): indexname) = i<j  orelse  (i=j andalso a<b);
clasohm@0
   613
clasohm@0
   614
wenzelm@13000
   615
(*Abstraction of the term "body" over its occurrences of v,
clasohm@0
   616
    which must contain no loose bound variables.
clasohm@0
   617
  The resulting term is ready to become the body of an Abs.*)
clasohm@0
   618
fun abstract_over (v,body) =
clasohm@0
   619
  let fun abst (lev,u) = if (v aconv u) then (Bound lev) else
clasohm@0
   620
      (case u of
clasohm@0
   621
          Abs(a,T,t) => Abs(a, T, abst(lev+1, t))
wenzelm@9536
   622
        | f$rand => abst(lev,f) $ abst(lev,rand)
wenzelm@9536
   623
        | _ => u)
clasohm@0
   624
  in  abst(0,body)  end;
clasohm@0
   625
berghofe@13665
   626
fun lambda (v as Free (x, T)) t = Abs (x, T, abstract_over (v, t))
berghofe@13665
   627
  | lambda (v as Var ((x, _), T)) t = Abs (x, T, abstract_over (v, t))
berghofe@13665
   628
  | lambda v t = raise TERM ("lambda", [v, t]);
clasohm@0
   629
clasohm@0
   630
(*Form an abstraction over a free variable.*)
clasohm@0
   631
fun absfree (a,T,body) = Abs(a, T, abstract_over (Free(a,T), body));
clasohm@0
   632
clasohm@0
   633
(*Abstraction over a list of free variables*)
clasohm@0
   634
fun list_abs_free ([ ] ,     t) = t
wenzelm@13000
   635
  | list_abs_free ((a,T)::vars, t) =
clasohm@0
   636
      absfree(a, T, list_abs_free(vars,t));
clasohm@0
   637
clasohm@0
   638
(*Quantification over a list of free variables*)
clasohm@0
   639
fun list_all_free ([], t: term) = t
wenzelm@13000
   640
  | list_all_free ((a,T)::vars, t) =
clasohm@0
   641
        (all T) $ (absfree(a, T, list_all_free(vars,t)));
clasohm@0
   642
clasohm@0
   643
(*Quantification over a list of variables (already bound in body) *)
clasohm@0
   644
fun list_all ([], t) = t
wenzelm@13000
   645
  | list_all ((a,T)::vars, t) =
clasohm@0
   646
        (all T) $ (Abs(a, T, list_all(vars,t)));
clasohm@0
   647
wenzelm@13000
   648
(*Replace the ATOMIC term ti by ui;    instl = [(t1,u1), ..., (tn,un)].
clasohm@0
   649
  A simultaneous substitution:  [ (a,b), (b,a) ] swaps a and b.  *)
clasohm@0
   650
fun subst_atomic [] t = t : term
clasohm@0
   651
  | subst_atomic (instl: (term*term) list) t =
clasohm@0
   652
      let fun subst (Abs(a,T,body)) = Abs(a, T, subst body)
wenzelm@9536
   653
            | subst (f$t') = subst f $ subst t'
skalberg@15570
   654
            | subst t = getOpt (assoc(instl,t),t)
clasohm@0
   655
      in  subst t  end;
clasohm@0
   656
lcp@728
   657
(*Substitute for type Vars in a type*)
clasohm@0
   658
fun typ_subst_TVars iTs T = if null iTs then T else
clasohm@0
   659
  let fun subst(Type(a,Ts)) = Type(a, map subst Ts)
wenzelm@9536
   660
        | subst(T as TFree _) = T
skalberg@15570
   661
        | subst(T as TVar(ixn,_)) = getOpt (assoc(iTs,ixn),T)
clasohm@0
   662
  in subst T end;
clasohm@0
   663
lcp@728
   664
(*Substitute for type Vars in a term*)
clasohm@0
   665
val subst_TVars = map_term_types o typ_subst_TVars;
clasohm@0
   666
lcp@728
   667
(*Substitute for Vars in a term; see also envir/norm_term*)
clasohm@0
   668
fun subst_Vars itms t = if null itms then t else
skalberg@15570
   669
  let fun subst(v as Var(ixn,_)) = getOpt (assoc(itms,ixn),v)
clasohm@0
   670
        | subst(Abs(a,T,t)) = Abs(a,T,subst t)
clasohm@0
   671
        | subst(f$t) = subst f $ subst t
clasohm@0
   672
        | subst(t) = t
clasohm@0
   673
  in subst t end;
clasohm@0
   674
lcp@728
   675
(*Substitute for type/term Vars in a term; see also envir/norm_term*)
clasohm@0
   676
fun subst_vars(iTs,itms) = if null iTs then subst_Vars itms else
clasohm@0
   677
  let fun subst(Const(a,T)) = Const(a,typ_subst_TVars iTs T)
clasohm@0
   678
        | subst(Free(a,T)) = Free(a,typ_subst_TVars iTs T)
clasohm@0
   679
        | subst(v as Var(ixn,T)) = (case assoc(itms,ixn) of
skalberg@15531
   680
            NONE   => Var(ixn,typ_subst_TVars iTs T)
skalberg@15531
   681
          | SOME t => t)
clasohm@0
   682
        | subst(b as Bound _) = b
clasohm@0
   683
        | subst(Abs(a,T,t)) = Abs(a,typ_subst_TVars iTs T,subst t)
clasohm@0
   684
        | subst(f$t) = subst f $ subst t
clasohm@0
   685
  in subst end;
clasohm@0
   686
clasohm@0
   687
paulson@15573
   688
(** Identifying first-order terms **)
paulson@15573
   689
paulson@15573
   690
(*Argument Ts is a reverse list of binder types, needed if term t contains Bound vars*)
paulson@15573
   691
fun has_not_funtype Ts t = not (is_funtype (fastype_of1 (Ts,t)));
paulson@15573
   692
paulson@15573
   693
(*First order means in all terms of the form f(t1,...,tn) no argument has a function
paulson@15573
   694
  type.*)
paulson@15573
   695
fun first_order1 Ts (Abs (_,T,body)) = first_order1 (T::Ts) body
paulson@15573
   696
  | first_order1 Ts t =
paulson@15573
   697
      case strip_comb t of
paulson@15573
   698
	       (Var _, ts) => forall (first_order1 Ts andf has_not_funtype Ts) ts
paulson@15573
   699
	     | (Free _, ts) => forall (first_order1 Ts andf has_not_funtype Ts) ts
paulson@15573
   700
	     | (Const _, ts) => forall (first_order1 Ts andf has_not_funtype Ts) ts
paulson@15573
   701
	     | (Bound _, ts) => forall (first_order1 Ts andf has_not_funtype Ts) ts
paulson@15573
   702
	     | (Abs _, ts) => false (*not in beta-normal form*)
paulson@15573
   703
	     | _ => error "first_order: unexpected case";
paulson@15573
   704
paulson@15573
   705
val is_first_order = first_order1 [];
paulson@15573
   706
paulson@15573
   707
clasohm@0
   708
(*Computing the maximum index of a typ*)
paulson@2146
   709
fun maxidx_of_typ(Type(_,Ts)) = maxidx_of_typs Ts
clasohm@0
   710
  | maxidx_of_typ(TFree _) = ~1
paulson@2146
   711
  | maxidx_of_typ(TVar((_,i),_)) = i
paulson@2146
   712
and maxidx_of_typs [] = ~1
paulson@2146
   713
  | maxidx_of_typs (T::Ts) = Int.max(maxidx_of_typ T, maxidx_of_typs Ts);
clasohm@0
   714
clasohm@0
   715
clasohm@0
   716
(*Computing the maximum index of a term*)
clasohm@0
   717
fun maxidx_of_term (Const(_,T)) = maxidx_of_typ T
clasohm@0
   718
  | maxidx_of_term (Bound _) = ~1
clasohm@0
   719
  | maxidx_of_term (Free(_,T)) = maxidx_of_typ T
paulson@2146
   720
  | maxidx_of_term (Var ((_,i), T)) = Int.max(i, maxidx_of_typ T)
paulson@2146
   721
  | maxidx_of_term (Abs (_,T,u)) = Int.max(maxidx_of_term u, maxidx_of_typ T)
paulson@2146
   722
  | maxidx_of_term (f$t) = Int.max(maxidx_of_term f,  maxidx_of_term t);
clasohm@0
   723
skalberg@15570
   724
fun maxidx_of_terms ts = Library.foldl Int.max (~1, map maxidx_of_term ts);
berghofe@13665
   725
clasohm@0
   726
clasohm@0
   727
(* Increment the index of all Poly's in T by k *)
nipkow@949
   728
fun incr_tvar k = map_type_tvar (fn ((a,i),S) => TVar((a,i+k),S));
clasohm@0
   729
clasohm@0
   730
clasohm@0
   731
(**** Syntax-related declarations ****)
clasohm@0
   732
clasohm@0
   733
wenzelm@4626
   734
(*Dummy type for parsing and printing.  Will be replaced during type inference. *)
clasohm@0
   735
val dummyT = Type("dummy",[]);
clasohm@0
   736
wenzelm@14786
   737
fun no_dummyT typ =
wenzelm@14786
   738
  let
wenzelm@14786
   739
    fun check (T as Type ("dummy", _)) =
wenzelm@14786
   740
          raise TYPE ("Illegal occurrence of '_' dummy type", [T], [])
skalberg@15570
   741
      | check (Type (_, Ts)) = List.app check Ts
wenzelm@14786
   742
      | check _ = ();
wenzelm@14786
   743
  in check typ; typ end;
wenzelm@14786
   744
clasohm@0
   745
clasohm@0
   746
(*** Printing ***)
clasohm@0
   747
wenzelm@14676
   748
(*Makes a variant of a name distinct from the names in bs.
wenzelm@14676
   749
  First attaches the suffix and then increments this;
wenzelm@12306
   750
  preserves a suffix of underscores "_". *)
wenzelm@12306
   751
fun variant bs name =
wenzelm@12306
   752
  let
wenzelm@12306
   753
    val (c, u) = pairself implode (Library.take_suffix (equal "_") (Symbol.explode name));
wenzelm@12902
   754
    fun vary2 c = if ((c ^ u) mem_string bs) then vary2 (Symbol.bump_string c) else c;
wenzelm@14676
   755
    fun vary1 c = if ((c ^ u) mem_string bs) then vary2 (Symbol.bump_init c) else c;
wenzelm@12306
   756
  in vary1 (if c = "" then "u" else c) ^ u end;
clasohm@0
   757
clasohm@0
   758
(*Create variants of the list of names, with priority to the first ones*)
clasohm@0
   759
fun variantlist ([], used) = []
wenzelm@13000
   760
  | variantlist(b::bs, used) =
clasohm@0
   761
      let val b' = variant used b
clasohm@0
   762
      in  b' :: variantlist (bs, b'::used)  end;
clasohm@0
   763
wenzelm@14695
   764
(*Invent fresh names*)
wenzelm@14695
   765
fun invent_names _ _ 0 = []
wenzelm@14695
   766
  | invent_names used a n =
wenzelm@14695
   767
      let val b = Symbol.bump_string a in
wenzelm@14695
   768
        if a mem_string used then invent_names used b n
wenzelm@14695
   769
        else a :: invent_names used b (n - 1)
wenzelm@14695
   770
      end;
wenzelm@11353
   771
wenzelm@4017
   772
wenzelm@4017
   773
wenzelm@4017
   774
(** Consts etc. **)
wenzelm@4017
   775
skalberg@15574
   776
fun add_typ_classes (Type (_, Ts), cs) = foldr add_typ_classes cs Ts
wenzelm@4017
   777
  | add_typ_classes (TFree (_, S), cs) = S union cs
wenzelm@4017
   778
  | add_typ_classes (TVar (_, S), cs) = S union cs;
wenzelm@4017
   779
skalberg@15574
   780
fun add_typ_tycons (Type (c, Ts), cs) = foldr add_typ_tycons (c ins cs) Ts
wenzelm@4017
   781
  | add_typ_tycons (_, cs) = cs;
wenzelm@4017
   782
wenzelm@4017
   783
val add_term_classes = it_term_types add_typ_classes;
wenzelm@4017
   784
val add_term_tycons = it_term_types add_typ_tycons;
wenzelm@4017
   785
wenzelm@9319
   786
fun add_term_consts (Const (c, _), cs) = c ins_string cs
wenzelm@4017
   787
  | add_term_consts (t $ u, cs) = add_term_consts (t, add_term_consts (u, cs))
wenzelm@4017
   788
  | add_term_consts (Abs (_, _, t), cs) = add_term_consts (t, cs)
wenzelm@4017
   789
  | add_term_consts (_, cs) = cs;
wenzelm@4017
   790
nipkow@13646
   791
fun term_consts t = add_term_consts(t,[]);
nipkow@13646
   792
oheimb@4185
   793
fun exists_Const P t = let
wenzelm@9536
   794
        fun ex (Const c      ) = P c
wenzelm@9536
   795
        |   ex (t $ u        ) = ex t orelse ex u
wenzelm@9536
   796
        |   ex (Abs (_, _, t)) = ex t
wenzelm@9536
   797
        |   ex _               = false
oheimb@4185
   798
    in ex t end;
wenzelm@4017
   799
nipkow@4631
   800
fun exists_subterm P =
nipkow@4631
   801
  let fun ex t = P t orelse
nipkow@4631
   802
                 (case t of
nipkow@4631
   803
                    u $ v        => ex u orelse ex v
nipkow@4631
   804
                  | Abs(_, _, u) => ex u
nipkow@4631
   805
                  | _            => false)
nipkow@4631
   806
  in ex end;
nipkow@4631
   807
wenzelm@4017
   808
(*map classes, tycons*)
wenzelm@4017
   809
fun map_typ f g (Type (c, Ts)) = Type (g c, map (map_typ f g) Ts)
wenzelm@4017
   810
  | map_typ f _ (TFree (x, S)) = TFree (x, map f S)
wenzelm@4017
   811
  | map_typ f _ (TVar (xi, S)) = TVar (xi, map f S);
wenzelm@4017
   812
wenzelm@4017
   813
(*map classes, tycons, consts*)
wenzelm@4017
   814
fun map_term f g h (Const (c, T)) = Const (h c, map_typ f g T)
wenzelm@4017
   815
  | map_term f g _ (Free (x, T)) = Free (x, map_typ f g T)
wenzelm@4017
   816
  | map_term f g _ (Var (xi, T)) = Var (xi, map_typ f g T)
wenzelm@4017
   817
  | map_term _ _ _ (t as Bound _) = t
wenzelm@4017
   818
  | map_term f g h (Abs (x, T, t)) = Abs (x, map_typ f g T, map_term f g h t)
wenzelm@4017
   819
  | map_term f g h (t $ u) = map_term f g h t $ map_term f g h u;
wenzelm@4017
   820
wenzelm@4017
   821
wenzelm@4017
   822
clasohm@0
   823
(** TFrees and TVars **)
clasohm@0
   824
clasohm@0
   825
(*maps  (bs,v)  to   v'::bs    this reverses the identifiers bs*)
clasohm@0
   826
fun add_new_id (bs, c) : string list =  variant bs c  ::  bs;
clasohm@0
   827
wenzelm@12802
   828
(*Accumulates the names of Frees in the term, suppressing duplicates.*)
wenzelm@12802
   829
fun add_term_free_names (Free(a,_), bs) = a ins_string bs
wenzelm@12802
   830
  | add_term_free_names (f$u, bs) = add_term_free_names (f, add_term_free_names(u, bs))
wenzelm@12802
   831
  | add_term_free_names (Abs(_,_,t), bs) = add_term_free_names(t,bs)
wenzelm@12802
   832
  | add_term_free_names (_, bs) = bs;
wenzelm@12802
   833
clasohm@0
   834
(*Accumulates the names in the term, suppressing duplicates.
clasohm@0
   835
  Includes Frees and Consts.  For choosing unambiguous bound var names.*)
wenzelm@10666
   836
fun add_term_names (Const(a,_), bs) = NameSpace.base a ins_string bs
paulson@2176
   837
  | add_term_names (Free(a,_), bs) = a ins_string bs
clasohm@0
   838
  | add_term_names (f$u, bs) = add_term_names (f, add_term_names(u, bs))
clasohm@0
   839
  | add_term_names (Abs(_,_,t), bs) = add_term_names(t,bs)
clasohm@0
   840
  | add_term_names (_, bs) = bs;
clasohm@0
   841
clasohm@0
   842
(*Accumulates the TVars in a type, suppressing duplicates. *)
skalberg@15574
   843
fun add_typ_tvars(Type(_,Ts),vs) = foldr add_typ_tvars vs Ts
clasohm@0
   844
  | add_typ_tvars(TFree(_),vs) = vs
clasohm@0
   845
  | add_typ_tvars(TVar(v),vs) = v ins vs;
clasohm@0
   846
clasohm@0
   847
(*Accumulates the TFrees in a type, suppressing duplicates. *)
skalberg@15574
   848
fun add_typ_tfree_names(Type(_,Ts),fs) = foldr add_typ_tfree_names fs Ts
paulson@2176
   849
  | add_typ_tfree_names(TFree(f,_),fs) = f ins_string fs
clasohm@0
   850
  | add_typ_tfree_names(TVar(_),fs) = fs;
clasohm@0
   851
skalberg@15574
   852
fun add_typ_tfrees(Type(_,Ts),fs) = foldr add_typ_tfrees fs Ts
clasohm@0
   853
  | add_typ_tfrees(TFree(f),fs) = f ins fs
clasohm@0
   854
  | add_typ_tfrees(TVar(_),fs) = fs;
clasohm@0
   855
skalberg@15574
   856
fun add_typ_varnames(Type(_,Ts),nms) = foldr add_typ_varnames nms Ts
paulson@2176
   857
  | add_typ_varnames(TFree(nm,_),nms) = nm ins_string nms
paulson@2176
   858
  | add_typ_varnames(TVar((nm,_),_),nms) = nm ins_string nms;
nipkow@949
   859
clasohm@0
   860
(*Accumulates the TVars in a term, suppressing duplicates. *)
clasohm@0
   861
val add_term_tvars = it_term_types add_typ_tvars;
clasohm@0
   862
clasohm@0
   863
(*Accumulates the TFrees in a term, suppressing duplicates. *)
clasohm@0
   864
val add_term_tfrees = it_term_types add_typ_tfrees;
clasohm@0
   865
val add_term_tfree_names = it_term_types add_typ_tfree_names;
clasohm@0
   866
nipkow@949
   867
val add_term_tvarnames = it_term_types add_typ_varnames;
nipkow@949
   868
clasohm@0
   869
(*Non-list versions*)
clasohm@0
   870
fun typ_tfrees T = add_typ_tfrees(T,[]);
clasohm@0
   871
fun typ_tvars T = add_typ_tvars(T,[]);
clasohm@0
   872
fun term_tfrees t = add_term_tfrees(t,[]);
clasohm@0
   873
fun term_tvars t = add_term_tvars(t,[]);
clasohm@0
   874
nipkow@949
   875
(*special code to enforce left-to-right collection of TVar-indexnames*)
nipkow@949
   876
skalberg@15570
   877
fun add_typ_ixns(ixns,Type(_,Ts)) = Library.foldl add_typ_ixns (ixns,Ts)
wenzelm@13000
   878
  | add_typ_ixns(ixns,TVar(ixn,_)) = if mem_ix (ixn, ixns) then ixns
wenzelm@9536
   879
                                     else ixns@[ixn]
nipkow@949
   880
  | add_typ_ixns(ixns,TFree(_)) = ixns;
nipkow@949
   881
nipkow@949
   882
fun add_term_tvar_ixns(Const(_,T),ixns) = add_typ_ixns(ixns,T)
nipkow@949
   883
  | add_term_tvar_ixns(Free(_,T),ixns) = add_typ_ixns(ixns,T)
nipkow@949
   884
  | add_term_tvar_ixns(Var(_,T),ixns) = add_typ_ixns(ixns,T)
nipkow@949
   885
  | add_term_tvar_ixns(Bound _,ixns) = ixns
nipkow@949
   886
  | add_term_tvar_ixns(Abs(_,T,t),ixns) =
nipkow@949
   887
      add_term_tvar_ixns(t,add_typ_ixns(ixns,T))
nipkow@949
   888
  | add_term_tvar_ixns(f$t,ixns) =
nipkow@949
   889
      add_term_tvar_ixns(t,add_term_tvar_ixns(f,ixns));
nipkow@949
   890
clasohm@0
   891
(** Frees and Vars **)
clasohm@0
   892
clasohm@0
   893
(*a partial ordering (not reflexive) for atomic terms*)
clasohm@0
   894
fun atless (Const (a,_), Const (b,_))  =  a<b
clasohm@0
   895
  | atless (Free (a,_), Free (b,_)) =  a<b
clasohm@0
   896
  | atless (Var(v,_), Var(w,_))  =  xless(v,w)
clasohm@0
   897
  | atless (Bound i, Bound j)  =   i<j
clasohm@0
   898
  | atless _  =  false;
clasohm@0
   899
clasohm@0
   900
(*insert atomic term into partially sorted list, suppressing duplicates (?)*)
clasohm@0
   901
fun insert_aterm (t,us) =
clasohm@0
   902
  let fun inserta [] = [t]
wenzelm@13000
   903
        | inserta (us as u::us') =
wenzelm@9536
   904
              if atless(t,u) then t::us
wenzelm@9536
   905
              else if t=u then us (*duplicate*)
wenzelm@9536
   906
              else u :: inserta(us')
clasohm@0
   907
  in  inserta us  end;
clasohm@0
   908
clasohm@0
   909
(*Accumulates the Vars in the term, suppressing duplicates*)
clasohm@0
   910
fun add_term_vars (t, vars: term list) = case t of
clasohm@0
   911
    Var   _ => insert_aterm(t,vars)
clasohm@0
   912
  | Abs (_,_,body) => add_term_vars(body,vars)
clasohm@0
   913
  | f$t =>  add_term_vars (f, add_term_vars(t, vars))
clasohm@0
   914
  | _ => vars;
clasohm@0
   915
clasohm@0
   916
fun term_vars t = add_term_vars(t,[]);
clasohm@0
   917
clasohm@0
   918
(*Accumulates the Frees in the term, suppressing duplicates*)
clasohm@0
   919
fun add_term_frees (t, frees: term list) = case t of
clasohm@0
   920
    Free   _ => insert_aterm(t,frees)
clasohm@0
   921
  | Abs (_,_,body) => add_term_frees(body,frees)
clasohm@0
   922
  | f$t =>  add_term_frees (f, add_term_frees(t, frees))
clasohm@0
   923
  | _ => frees;
clasohm@0
   924
clasohm@0
   925
fun term_frees t = add_term_frees(t,[]);
clasohm@0
   926
clasohm@0
   927
(*Given an abstraction over P, replaces the bound variable by a Free variable
clasohm@0
   928
  having a unique name. *)
clasohm@0
   929
fun variant_abs (a,T,P) =
clasohm@0
   930
  let val b = variant (add_term_names(P,[])) a
paulson@2192
   931
  in  (b,  subst_bound (Free(b,T), P))  end;
clasohm@0
   932
clasohm@0
   933
(* renames and reverses the strings in vars away from names *)
clasohm@0
   934
fun rename_aTs names vars : (string*typ)list =
clasohm@0
   935
  let fun rename_aT (vars,(a,T)) =
wenzelm@9536
   936
                (variant (map #1 vars @ names) a, T) :: vars
skalberg@15570
   937
  in Library.foldl rename_aT ([],vars) end;
clasohm@0
   938
clasohm@0
   939
fun rename_wrt_term t = rename_aTs (add_term_names(t,[]));
clasohm@1364
   940
paulson@1417
   941
wenzelm@4286
   942
(* left-ro-right traversal *)
wenzelm@4286
   943
wenzelm@4286
   944
(*foldl atoms of type*)
skalberg@15570
   945
fun foldl_atyps f (x, Type (_, Ts)) = Library.foldl (foldl_atyps f) (x, Ts)
wenzelm@4286
   946
  | foldl_atyps f x_atom = f x_atom;
wenzelm@4286
   947
wenzelm@4286
   948
(*foldl atoms of term*)
wenzelm@4286
   949
fun foldl_aterms f (x, t $ u) = foldl_aterms f (foldl_aterms f (x, t), u)
wenzelm@4286
   950
  | foldl_aterms f (x, Abs (_, _, t)) = foldl_aterms f (x, t)
wenzelm@4286
   951
  | foldl_aterms f x_atom = f x_atom;
wenzelm@4286
   952
wenzelm@6548
   953
fun foldl_map_aterms f (x, t $ u) =
wenzelm@6548
   954
      let val (x', t') = foldl_map_aterms f (x, t); val (x'', u') = foldl_map_aterms f (x', u);
wenzelm@6548
   955
      in (x'', t' $ u') end
wenzelm@6548
   956
  | foldl_map_aterms f (x, Abs (a, T, t)) =
wenzelm@6548
   957
      let val (x', t') = foldl_map_aterms f (x, t) in (x', Abs (a, T, t')) end
wenzelm@6548
   958
  | foldl_map_aterms f x_atom = f x_atom;
wenzelm@6548
   959
wenzelm@4286
   960
(*foldl types of term*)
wenzelm@8609
   961
fun foldl_term_types f (x, t as Const (_, T)) = f t (x, T)
wenzelm@8609
   962
  | foldl_term_types f (x, t as Free (_, T)) = f t (x, T)
wenzelm@8609
   963
  | foldl_term_types f (x, t as Var (_, T)) = f t (x, T)
wenzelm@8609
   964
  | foldl_term_types f (x, Bound _) = x
wenzelm@8609
   965
  | foldl_term_types f (x, t as Abs (_, T, b)) = foldl_term_types f (f t (x, T), b)
wenzelm@8609
   966
  | foldl_term_types f (x, t $ u) = foldl_term_types f (foldl_term_types f (x, t), u);
wenzelm@8609
   967
wenzelm@8609
   968
fun foldl_types f = foldl_term_types (fn _ => f);
wenzelm@4286
   969
wenzelm@12499
   970
(*collect variables*)
wenzelm@12499
   971
val add_tvarsT = foldl_atyps (fn (vs, TVar v) => v ins vs | (vs, _) => vs);
wenzelm@12499
   972
val add_tvars = foldl_types add_tvarsT;
wenzelm@12499
   973
val add_vars = foldl_aterms (fn (vs, Var v) => v ins vs | (vs, _) => vs);
wenzelm@12499
   974
val add_frees = foldl_aterms (fn (vs, Free v) => v ins vs | (vs, _) => vs);
wenzelm@12499
   975
wenzelm@15025
   976
(*collect variable names*)
wenzelm@15025
   977
val add_term_varnames = foldl_aterms (fn (xs, Var (x, _)) => ins_ix (x, xs) | (xs, _) => xs);
wenzelm@15025
   978
fun term_varnames t = add_term_varnames ([], t);
wenzelm@4286
   979
paulson@1417
   980
wenzelm@4444
   981
(** type and term orders **)
wenzelm@4444
   982
wenzelm@4444
   983
fun indexname_ord ((x, i), (y, j)) =
paulson@14472
   984
  (case Int.compare (i, j) of EQUAL => String.compare (x, y) | ord => ord);
wenzelm@4444
   985
paulson@14472
   986
val sort_ord = list_ord String.compare;
wenzelm@13000
   987
wenzelm@4444
   988
wenzelm@4444
   989
(* typ_ord *)
wenzelm@4444
   990
paulson@14472
   991
fun typ_ord (Type x, Type y) = prod_ord String.compare typs_ord (x, y)
wenzelm@4444
   992
  | typ_ord (Type _, _) = GREATER
wenzelm@4444
   993
  | typ_ord (TFree _, Type _) = LESS
paulson@14472
   994
  | typ_ord (TFree x, TFree y) = prod_ord String.compare sort_ord (x, y)
wenzelm@4444
   995
  | typ_ord (TFree _, TVar _) = GREATER
wenzelm@4444
   996
  | typ_ord (TVar _, Type _) = LESS
wenzelm@4444
   997
  | typ_ord (TVar _, TFree _) = LESS
wenzelm@13000
   998
  | typ_ord (TVar x, TVar y) = prod_ord indexname_ord sort_ord (x, y)
wenzelm@4444
   999
and typs_ord Ts_Us = list_ord typ_ord Ts_Us;
wenzelm@4444
  1000
wenzelm@4444
  1001
wenzelm@4444
  1002
(* term_ord *)
wenzelm@4444
  1003
wenzelm@4444
  1004
(*a linear well-founded AC-compatible ordering for terms:
wenzelm@4444
  1005
  s < t <=> 1. size(s) < size(t) or
wenzelm@4444
  1006
            2. size(s) = size(t) and s=f(...) and t=g(...) and f<g or
wenzelm@4444
  1007
            3. size(s) = size(t) and s=f(s1..sn) and t=f(t1..tn) and
wenzelm@4444
  1008
               (s1..sn) < (t1..tn) (lexicographically)*)
wenzelm@4444
  1009
wenzelm@4444
  1010
fun dest_hd (Const (a, T)) = (((a, 0), T), 0)
wenzelm@4444
  1011
  | dest_hd (Free (a, T)) = (((a, 0), T), 1)
wenzelm@4444
  1012
  | dest_hd (Var v) = (v, 2)
wenzelm@4444
  1013
  | dest_hd (Bound i) = ((("", i), dummyT), 3)
wenzelm@4444
  1014
  | dest_hd (Abs (_, T, _)) = ((("", 0), T), 4);
wenzelm@4444
  1015
wenzelm@4444
  1016
fun term_ord (Abs (_, T, t), Abs(_, U, u)) =
wenzelm@4444
  1017
      (case term_ord (t, u) of EQUAL => typ_ord (T, U) | ord => ord)
wenzelm@4444
  1018
  | term_ord (t, u) =
paulson@14472
  1019
      (case Int.compare (size_of_term t, size_of_term u) of
wenzelm@4444
  1020
        EQUAL =>
wenzelm@4444
  1021
          let val (f, ts) = strip_comb t and (g, us) = strip_comb u in
wenzelm@4444
  1022
            (case hd_ord (f, g) of EQUAL => terms_ord (ts, us) | ord => ord)
wenzelm@4444
  1023
          end
wenzelm@4444
  1024
      | ord => ord)
wenzelm@4444
  1025
and hd_ord (f, g) =
paulson@14472
  1026
  prod_ord (prod_ord indexname_ord typ_ord) Int.compare (dest_hd f, dest_hd g)
wenzelm@4444
  1027
and terms_ord (ts, us) = list_ord term_ord (ts, us);
wenzelm@4444
  1028
wenzelm@4444
  1029
fun termless tu = (term_ord tu = LESS);
wenzelm@4444
  1030
berghofe@8408
  1031
structure Vartab = TableFun(type key = indexname val ord = indexname_ord);
wenzelm@13000
  1032
structure Typtab = TableFun(type key = typ val ord = typ_ord);
berghofe@8408
  1033
structure Termtab = TableFun(type key = term val ord = term_ord);
berghofe@8408
  1034
berghofe@8408
  1035
(*Substitute for type Vars in a type, version using Vartab*)
berghofe@8408
  1036
fun typ_subst_TVars_Vartab iTs T = if Vartab.is_empty iTs then T else
berghofe@8408
  1037
  let fun subst(Type(a, Ts)) = Type(a, map subst Ts)
wenzelm@9536
  1038
        | subst(T as TFree _) = T
wenzelm@9536
  1039
        | subst(T as TVar(ixn, _)) =
skalberg@15531
  1040
            (case Vartab.lookup (iTs, ixn) of NONE => T | SOME(U) => U)
berghofe@8408
  1041
  in subst T end;
berghofe@8408
  1042
berghofe@8408
  1043
(*Substitute for type Vars in a term, version using Vartab*)
berghofe@8408
  1044
val subst_TVars_Vartab = map_term_types o typ_subst_TVars_Vartab;
wenzelm@4444
  1045
wenzelm@4444
  1046
wenzelm@13000
  1047
(*** Compression of terms and types by sharing common subtrees.
wenzelm@13000
  1048
     Saves 50-75% on storage requirements.  As it is a bit slow,
wenzelm@13000
  1049
     it should be called only for axioms, stored theorems, etc.
wenzelm@13000
  1050
     Recorded term and type fragments are never disposed. ***)
paulson@1417
  1051
paulson@1417
  1052
(** Sharing of types **)
paulson@1417
  1053
wenzelm@13000
  1054
val memo_types = ref (Typtab.empty: typ Typtab.table);
paulson@1417
  1055
paulson@1417
  1056
fun compress_type T =
wenzelm@13000
  1057
  (case Typtab.lookup (! memo_types, T) of
skalberg@15531
  1058
    SOME T' => T'
skalberg@15531
  1059
  | NONE =>
wenzelm@13000
  1060
      let val T' = (case T of Type (a, Ts) => Type (a, map compress_type Ts) | _ => T)
wenzelm@13000
  1061
      in memo_types := Typtab.update ((T', T'), ! memo_types); T' end);
wenzelm@13000
  1062
paulson@1417
  1063
paulson@1417
  1064
(** Sharing of atomic terms **)
paulson@1417
  1065
wenzelm@13000
  1066
val memo_terms = ref (Termtab.empty : term Termtab.table);
paulson@1417
  1067
paulson@1417
  1068
fun share_term (t $ u) = share_term t $ share_term u
wenzelm@13000
  1069
  | share_term (Abs (a, T, u)) = Abs (a, T, share_term u)
paulson@1417
  1070
  | share_term t =
wenzelm@13000
  1071
      (case Termtab.lookup (! memo_terms, t) of
skalberg@15531
  1072
        SOME t' => t'
skalberg@15531
  1073
      | NONE => (memo_terms := Termtab.update ((t, t), ! memo_terms); t));
paulson@1417
  1074
paulson@1417
  1075
val compress_term = share_term o map_term_types compress_type;
paulson@1417
  1076
wenzelm@4444
  1077
wenzelm@9536
  1078
(* dummy patterns *)
wenzelm@9536
  1079
wenzelm@9536
  1080
val dummy_patternN = "dummy_pattern";
wenzelm@9536
  1081
wenzelm@9536
  1082
fun is_dummy_pattern (Const ("dummy_pattern", _)) = true
wenzelm@9536
  1083
  | is_dummy_pattern _ = false;
wenzelm@9536
  1084
wenzelm@9536
  1085
fun no_dummy_patterns tm =
wenzelm@9536
  1086
  if not (foldl_aterms (fn (b, t) => b orelse is_dummy_pattern t) (false, tm)) then tm
wenzelm@9536
  1087
  else raise TERM ("Illegal occurrence of '_' dummy pattern", [tm]);
wenzelm@9536
  1088
wenzelm@11903
  1089
fun replace_dummy Ts (i, Const ("dummy_pattern", T)) =
wenzelm@11903
  1090
      (i + 1, list_comb (Var (("_dummy_", i), Ts ---> T), map Bound (0 upto length Ts - 1)))
wenzelm@11903
  1091
  | replace_dummy Ts (i, Abs (x, T, t)) =
wenzelm@11903
  1092
      let val (i', t') = replace_dummy (T :: Ts) (i, t)
wenzelm@11903
  1093
      in (i', Abs (x, T, t')) end
wenzelm@11903
  1094
  | replace_dummy Ts (i, t $ u) =
wenzelm@11903
  1095
      let val (i', t') = replace_dummy Ts (i, t); val (i'', u') = replace_dummy Ts (i', u)
wenzelm@11903
  1096
      in (i'', t' $ u') end
wenzelm@11903
  1097
  | replace_dummy _ (i, a) = (i, a);
wenzelm@11903
  1098
wenzelm@11903
  1099
val replace_dummy_patterns = replace_dummy [];
wenzelm@9536
  1100
wenzelm@10552
  1101
fun is_replaced_dummy_pattern ("_dummy_", _) = true
wenzelm@10552
  1102
  | is_replaced_dummy_pattern _ = false;
wenzelm@9536
  1103
wenzelm@13484
  1104
wenzelm@13484
  1105
(* adhoc freezing *)
wenzelm@13484
  1106
wenzelm@13484
  1107
fun adhoc_freeze_vars tm =
wenzelm@13484
  1108
  let
wenzelm@13484
  1109
    fun mk_inst (var as Var ((a, i), T)) =
wenzelm@13484
  1110
      let val x = a ^ Library.gensym "_" ^ string_of_int i
wenzelm@13484
  1111
      in ((var,  Free(x, T)), x) end;
wenzelm@13484
  1112
    val (insts, xs) = split_list (map mk_inst (term_vars tm));
wenzelm@13484
  1113
  in (subst_atomic insts tm, xs) end;
wenzelm@13484
  1114
wenzelm@13484
  1115
wenzelm@14786
  1116
(* string_of_vname *)
wenzelm@14786
  1117
berghofe@15472
  1118
val show_var_qmarks = ref true;
berghofe@15472
  1119
wenzelm@14786
  1120
fun string_of_vname (x, i) =
wenzelm@14786
  1121
  let
wenzelm@14786
  1122
    val si = string_of_int i;
skalberg@15570
  1123
    val dot = getOpt (try (Symbol.is_digit o List.last o Symbol.explode) x, true);
berghofe@15472
  1124
    val qmark = if !show_var_qmarks then "?" else "";
wenzelm@14786
  1125
  in
berghofe@15472
  1126
    if dot then qmark ^ x ^ "." ^ si
berghofe@15472
  1127
    else if i = 0 then qmark ^ x
berghofe@15472
  1128
    else qmark ^ x ^ si
wenzelm@14786
  1129
  end;
wenzelm@14786
  1130
wenzelm@14786
  1131
fun string_of_vname' (x, ~1) = x
wenzelm@14786
  1132
  | string_of_vname' xi = string_of_vname xi;
wenzelm@14786
  1133
clasohm@1364
  1134
end;
clasohm@1364
  1135
wenzelm@4444
  1136
structure BasicTerm: BASIC_TERM = Term;
wenzelm@4444
  1137
open BasicTerm;