src/Pure/term.ML
author wenzelm
Fri Sep 21 22:51:12 2007 +0200 (2007-09-21)
changeset 24671 35075a1e9599
parent 24483 0b1a8fd26da9
child 24733 59e0b49688fb
permissions -rw-r--r--
added has_abs (from envir.ML);
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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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  eqtype indexname
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  eqtype class
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  eqtype sort
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  eqtype arity
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  datatype typ =
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    Type  of string * typ list |
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    TFree of string * sort |
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    TVar  of indexname * sort
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  datatype term =
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    Const of string * typ |
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    Free of string * typ |
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    Var of indexname * typ |
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    Bound of int |
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    Abs of string * typ * term |
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    $ of term * term
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  exception TYPE of string * typ list * term list
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  exception TERM of string * term list
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  val dummyS: sort
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  val dummyT: typ
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  val no_dummyT: typ -> typ
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  val --> : typ * typ -> typ
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  val ---> : typ list * typ -> typ
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  val dest_Type: typ -> string * typ list
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  val dest_TVar: typ -> indexname * sort
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  val dest_TFree: typ -> string * sort
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  val is_Bound: term -> bool
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  val is_Const: term -> bool
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  val is_Free: term -> bool
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  val is_Var: term -> bool
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  val is_TVar: typ -> bool
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  val dest_Const: term -> string * typ
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  val dest_Free: term -> string * typ
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  val dest_Var: term -> indexname * typ
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  val domain_type: typ -> typ
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  val range_type: typ -> typ
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  val binder_types: typ -> typ list
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  val body_type: typ -> typ
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  val strip_type: typ -> typ list * typ
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  val type_of1: typ list * term -> typ
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  val type_of: term -> typ
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  val fastype_of1: typ list * term -> typ
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  val fastype_of: term -> typ
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  val list_abs: (string * typ) list * term -> term
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  val strip_abs: term -> (string * typ) list * term
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  val strip_abs_body: term -> term
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  val strip_abs_vars: term -> (string * typ) list
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  val strip_qnt_body: string -> term -> term
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  val strip_qnt_vars: string -> term -> (string * typ) list
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  val list_comb: term * term list -> term
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  val strip_comb: term -> term * term list
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  val head_of: term -> term
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  val size_of_term: term -> int
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  val map_atyps: (typ -> typ) -> typ -> typ
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  val map_aterms: (term -> term) -> term -> term
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  val map_type_tvar: (indexname * sort -> typ) -> typ -> typ
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  val map_type_tfree: (string * sort -> typ) -> typ -> typ
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  val map_types: (typ -> typ) -> term -> term
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  val fold_atyps: (typ -> 'a -> 'a) -> typ -> 'a -> 'a
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  val fold_aterms: (term -> 'a -> 'a) -> term -> 'a -> 'a
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  val fold_term_types: (term -> typ -> 'a -> 'a) -> term -> 'a -> 'a
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  val fold_types: (typ -> 'a -> 'a) -> term -> 'a -> 'a
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  val burrow_types: (typ list -> typ list) -> term list -> term list
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  val it_term_types: (typ * 'a -> 'a) -> term * 'a -> 'a
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  val add_term_names: term * string list -> string list
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  val aconv: term * term -> bool
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  structure Vartab: TABLE
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  structure Typtab: TABLE
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  structure Termtab: TABLE
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  val propT: typ
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  val implies: term
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  val all: typ -> term
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  val equals: typ -> term
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  val strip_all_body: term -> term
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  val strip_all_vars: term -> (string * typ) list
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  val incr_bv: int * int * term -> term
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  val incr_boundvars: int -> term -> term
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  val add_loose_bnos: term * int * int list -> int list
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  val loose_bnos: term -> int list
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  val loose_bvar: term * int -> bool
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  val loose_bvar1: term * int -> bool
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  val subst_bounds: term list * term -> term
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  val subst_bound: term * term -> term
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  val betapply: term * term -> term
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  val betapplys: term * term list -> term
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  val eq_ix: indexname * indexname -> bool
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  val could_unify: term * term -> bool
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  val subst_free: (term * term) list -> term -> term
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  val abstract_over: term * term -> term
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  val lambda: term -> term -> term
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  val absfree: string * typ * term -> term
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  val absdummy: typ * term -> term
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  val list_abs_free: (string * typ) list * term -> term
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  val list_all_free: (string * typ) list * term -> term
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  val list_all: (string * typ) list * term -> term
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  val subst_atomic: (term * term) list -> term -> term
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  val typ_subst_atomic: (typ * typ) list -> typ -> typ
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  val subst_atomic_types: (typ * typ) list -> term -> term
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  val typ_subst_TVars: (indexname * typ) list -> typ -> typ
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  val subst_TVars: (indexname * typ) list -> term -> term
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  val subst_Vars: (indexname * term) list -> term -> term
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  val subst_vars: (indexname * typ) list * (indexname * term) list -> term -> term
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  val is_first_order: string list -> term -> bool
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  val maxidx_of_typ: typ -> int
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  val maxidx_of_typs: typ list -> int
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  val maxidx_of_term: term -> int
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  val add_term_consts: term * string list -> string list
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  val term_consts: term -> string list
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  val exists_subtype: (typ -> bool) -> typ -> bool
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  val exists_type: (typ -> bool) -> term -> bool
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  val exists_subterm: (term -> bool) -> term -> bool
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  val exists_Const: (string * typ -> bool) -> term -> bool
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  val add_term_free_names: term * string list -> string list
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  val add_typ_tvars: typ * (indexname * sort) list -> (indexname * sort) list
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  val add_typ_tfree_names: typ * string list -> string list
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  val add_typ_tfrees: typ * (string * sort) list -> (string * sort) list
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  val add_typ_varnames: typ * string list -> string list
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  val add_term_tvars: term * (indexname * sort) list -> (indexname * sort) list
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  val add_term_tfrees: term * (string * sort) list -> (string * sort) list
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  val add_term_tfree_names: term * string list -> string list
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  val typ_tfrees: typ -> (string * sort) list
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  val typ_tvars: typ -> (indexname * sort) list
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  val term_tfrees: term -> (string * sort) list
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  val term_tvars: term -> (indexname * sort) list
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  val add_typ_ixns: indexname list * typ -> indexname list
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  val add_term_tvar_ixns: term * indexname list -> indexname list
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  val add_term_vars: term * term list -> term list
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  val term_vars: term -> term list
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  val add_term_frees: term * term list -> term list
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  val term_frees: term -> term list
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  val rename_wrt_term: term -> (string * 'a) list -> (string * 'a) list
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  val show_question_marks: bool ref
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end;
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signature TERM =
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sig
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  include BASIC_TERM
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  val aT: sort -> typ
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  val itselfT: typ -> typ
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  val a_itselfT: typ
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  val argument_type_of: term -> int -> typ
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  val head_name_of: term -> string
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  val add_tvarsT: typ -> (indexname * sort) list -> (indexname * sort) list
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  val add_tvars: term -> (indexname * sort) list -> (indexname * sort) list
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  val add_vars: term -> (indexname * typ) list -> (indexname * typ) list
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  val add_varnames: term -> indexname list -> indexname list
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  val add_tfreesT: typ -> (string * sort) list -> (string * sort) list
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  val add_tfrees: term -> (string * sort) list -> (string * sort) list
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  val add_frees: term -> (string * typ) list -> (string * typ) list
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  val hidden_polymorphism: term -> typ -> (indexname * sort) list
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  val equiv_types: term * term -> bool
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  val strip_abs_eta: int -> term -> (string * typ) list * term
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  val fast_indexname_ord: indexname * indexname -> order
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  val indexname_ord: indexname * indexname -> order
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  val sort_ord: sort * sort -> order
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  val typ_ord: typ * typ -> order
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  val fast_term_ord: term * term -> order
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  val term_ord: term * term -> order
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  val hd_ord: term * term -> order
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  val termless: term * term -> bool
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  val term_lpo: (term -> int) -> term * term -> order
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  val match_bvars: (term * term) * (string * string) list -> (string * string) list
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  val map_abs_vars: (string -> string) -> term -> term
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  val rename_abs: term -> term -> term -> term option
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  val eq_tvar: (indexname * sort) * (indexname * sort) -> bool
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  val eq_var: (indexname * typ) * (indexname * typ) -> bool
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  val tvar_ord: (indexname * sort) * (indexname * sort) -> order
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  val var_ord: (indexname * typ) * (indexname * typ) -> order
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  val maxidx_typ: typ -> int -> int
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  val maxidx_typs: typ list -> int -> int
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  val maxidx_term: term -> int -> int
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  val has_abs: term -> bool
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  val dest_abs: string * typ * term -> string * term
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  val declare_term_names: term -> Name.context -> Name.context
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  val variant_frees: term -> (string * 'a) list -> (string * 'a) list
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  val dummy_patternN: string
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  val dummy_pattern: typ -> term
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  val is_dummy_pattern: term -> bool
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  val no_dummy_patterns: term -> term
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  val replace_dummy_patterns: int * term -> int * term
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  val is_replaced_dummy_pattern: indexname -> bool
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  val show_dummy_patterns: term -> term
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  val string_of_vname: indexname -> string
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  val string_of_vname': indexname -> string
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end;
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structure Term: TERM =
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struct
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(*Indexnames can be quickly renamed by adding an offset to the integer part,
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  for resolution.*)
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type indexname = string * int;
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(* Types are classified by sorts. *)
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type class = string;
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type sort  = class list;
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type arity = string * sort list * sort;
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(* The sorts attached to TFrees and TVars specify the sort of that variable *)
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datatype typ = Type  of string * typ list
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             | TFree of string * sort
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             | TVar  of indexname * sort;
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(*Terms.  Bound variables are indicated by depth number.
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  Free variables, (scheme) variables and constants have names.
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  An term is "closed" if every bound variable of level "lev"
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  is enclosed by at least "lev" abstractions.
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  It is possible to create meaningless terms containing loose bound vars
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  or type mismatches.  But such terms are not allowed in rules. *)
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datatype term =
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    Const of string * typ
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  | Free  of string * typ
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  | Var   of indexname * typ
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  | Bound of int
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  | Abs   of string*typ*term
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  | op $  of term*term;
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(*Errors involving type mismatches*)
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exception TYPE of string * typ list * term list;
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(*Errors errors involving terms*)
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exception TERM of string * term list;
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(*Note variable naming conventions!
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    a,b,c: string
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    f,g,h: functions (including terms of function type)
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    i,j,m,n: int
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    t,u: term
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    v,w: indexnames
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    x,y: any
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    A,B,C: term (denoting formulae)
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    T,U: typ
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*)
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(** Types **)
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(*dummies for type-inference etc.*)
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val dummyS = [""];
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val dummyT = Type ("dummy", []);
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fun no_dummyT typ =
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  let
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    fun check (T as Type ("dummy", _)) =
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          raise TYPE ("Illegal occurrence of '_' dummy type", [T], [])
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      | check (Type (_, Ts)) = List.app check Ts
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      | check _ = ();
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  in check typ; typ end;
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fun S --> T = Type("fun",[S,T]);
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(*handy for multiple args: [T1,...,Tn]--->T  gives  T1-->(T2--> ... -->T)*)
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val op ---> = Library.foldr (op -->);
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fun dest_Type (Type x) = x
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  | dest_Type T = raise TYPE ("dest_Type", [T], []);
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fun dest_TVar (TVar x) = x
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  | dest_TVar T = raise TYPE ("dest_TVar", [T], []);
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fun dest_TFree (TFree x) = x
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  | dest_TFree T = raise TYPE ("dest_TFree", [T], []);
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(** Discriminators **)
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fun is_Bound (Bound _) = true
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  | is_Bound _         = false;
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fun is_Const (Const _) = true
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  | is_Const _ = false;
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fun is_Free (Free _) = true
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  | is_Free _ = false;
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fun is_Var (Var _) = true
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  | is_Var _ = false;
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fun is_TVar (TVar _) = true
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  | is_TVar _ = false;
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(** 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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   326
  Ts = [T0,T1,...] holds types of bound variables 0, 1, ...*)
clasohm@0
   327
fun type_of1 (Ts, Const (_,T)) = T
clasohm@0
   328
  | type_of1 (Ts, Free  (_,T)) = T
skalberg@15570
   329
  | type_of1 (Ts, Bound i) = (List.nth (Ts,i)
skalberg@15570
   330
        handle Subscript => raise TYPE("type_of: bound variable", [], [Bound i]))
clasohm@0
   331
  | type_of1 (Ts, Var (_,T)) = T
clasohm@0
   332
  | type_of1 (Ts, Abs (_,T,body)) = T --> type_of1(T::Ts, body)
wenzelm@13000
   333
  | type_of1 (Ts, f$u) =
clasohm@0
   334
      let val U = type_of1(Ts,u)
clasohm@0
   335
          and T = type_of1(Ts,f)
clasohm@0
   336
      in case T of
wenzelm@9536
   337
            Type("fun",[T1,T2]) =>
wenzelm@9536
   338
              if T1=U then T2  else raise TYPE
wenzelm@9536
   339
                    ("type_of: type mismatch in application", [T1,U], [f$u])
wenzelm@13000
   340
          | _ => raise TYPE
wenzelm@9536
   341
                    ("type_of: function type is expected in application",
wenzelm@9536
   342
                     [T,U], [f$u])
clasohm@0
   343
      end;
clasohm@0
   344
clasohm@0
   345
fun type_of t : typ = type_of1 ([],t);
clasohm@0
   346
clasohm@0
   347
(*Determines the type of a term, with minimal checking*)
wenzelm@13000
   348
fun fastype_of1 (Ts, f$u) =
lcp@61
   349
    (case fastype_of1 (Ts,f) of
wenzelm@9536
   350
        Type("fun",[_,T]) => T
wenzelm@9536
   351
        | _ => raise TERM("fastype_of: expected function type", [f$u]))
lcp@61
   352
  | fastype_of1 (_, Const (_,T)) = T
lcp@61
   353
  | fastype_of1 (_, Free (_,T)) = T
skalberg@15570
   354
  | fastype_of1 (Ts, Bound i) = (List.nth(Ts,i)
skalberg@15570
   355
         handle Subscript => raise TERM("fastype_of: Bound", [Bound i]))
wenzelm@13000
   356
  | fastype_of1 (_, Var (_,T)) = T
lcp@61
   357
  | fastype_of1 (Ts, Abs (_,T,u)) = T --> fastype_of1 (T::Ts, u);
lcp@61
   358
lcp@61
   359
fun fastype_of t : typ = fastype_of1 ([],t);
clasohm@0
   360
wenzelm@16678
   361
(*Determine the argument type of a function*)
wenzelm@22908
   362
fun argument_type_of tm k =
wenzelm@16678
   363
  let
wenzelm@16678
   364
    fun argT i (Type ("fun", [T, U])) = if i = 0 then T else argT (i - 1) U
wenzelm@16678
   365
      | argT _ T = raise TYPE ("argument_type_of", [T], []);
wenzelm@16678
   366
wenzelm@16678
   367
    fun arg 0 _ (Abs (_, T, _)) = T
wenzelm@16678
   368
      | arg i Ts (Abs (_, T, t)) = arg (i - 1) (T :: Ts) t
wenzelm@16678
   369
      | arg i Ts (t $ _) = arg (i + 1) Ts t
wenzelm@16678
   370
      | arg i Ts a = argT i (fastype_of1 (Ts, a));
wenzelm@22908
   371
  in arg k [] tm end;
wenzelm@16678
   372
clasohm@0
   373
wenzelm@19473
   374
val list_abs = uncurry (fold_rev (fn (x, T) => fn t => Abs (x, T, t)));
wenzelm@10806
   375
haftmann@18927
   376
fun strip_abs (Abs (a, T, t)) =
haftmann@18927
   377
      let val (a', t') = strip_abs t
haftmann@18927
   378
      in ((a, T) :: a', t') end
haftmann@18927
   379
  | strip_abs t = ([], t);
haftmann@18927
   380
clasohm@0
   381
(* maps  (x1,...,xn)t   to   t  *)
wenzelm@13000
   382
fun strip_abs_body (Abs(_,_,t))  =  strip_abs_body t
clasohm@0
   383
  | strip_abs_body u  =  u;
clasohm@0
   384
clasohm@0
   385
(* maps  (x1,...,xn)t   to   [x1, ..., xn]  *)
wenzelm@13000
   386
fun strip_abs_vars (Abs(a,T,t))  =  (a,T) :: strip_abs_vars t
clasohm@0
   387
  | strip_abs_vars u  =  [] : (string*typ) list;
clasohm@0
   388
clasohm@0
   389
clasohm@0
   390
fun strip_qnt_body qnt =
clasohm@0
   391
let fun strip(tm as Const(c,_)$Abs(_,_,t)) = if c=qnt then strip t else tm
clasohm@0
   392
      | strip t = t
clasohm@0
   393
in strip end;
clasohm@0
   394
clasohm@0
   395
fun strip_qnt_vars qnt =
clasohm@0
   396
let fun strip(Const(c,_)$Abs(a,T,t)) = if c=qnt then (a,T)::strip t else []
clasohm@0
   397
      | strip t  =  [] : (string*typ) list
clasohm@0
   398
in strip end;
clasohm@0
   399
clasohm@0
   400
clasohm@0
   401
(* maps   (f, [t1,...,tn])  to  f(t1,...,tn) *)
skalberg@15570
   402
val list_comb : term * term list -> term = Library.foldl (op $);
clasohm@0
   403
clasohm@0
   404
clasohm@0
   405
(* maps   f(t1,...,tn)  to  (f, [t1,...,tn]) ; naturally tail-recursive*)
wenzelm@13000
   406
fun strip_comb u : term * term list =
clasohm@0
   407
    let fun stripc (f$t, ts) = stripc (f, t::ts)
wenzelm@13000
   408
        |   stripc  x =  x
clasohm@0
   409
    in  stripc(u,[])  end;
clasohm@0
   410
clasohm@0
   411
clasohm@0
   412
(* maps   f(t1,...,tn)  to  f , which is never a combination *)
clasohm@0
   413
fun head_of (f$t) = head_of f
clasohm@0
   414
  | head_of u = u;
clasohm@0
   415
wenzelm@21493
   416
fun head_name_of tm =
wenzelm@21493
   417
  (case head_of tm of
wenzelm@21493
   418
    t as Const (c, _) =>
wenzelm@21493
   419
      if NameSpace.is_qualified c then c
wenzelm@21493
   420
      else raise TERM ("Malformed constant name", [t])
wenzelm@21493
   421
  | t as Free (x, _) =>
wenzelm@21493
   422
      if not (NameSpace.is_qualified x) then x
wenzelm@21493
   423
      else raise TERM ("Malformed fixed variable name", [t])
wenzelm@21493
   424
  | t => raise TERM ("No fixed head of term", [t]));
clasohm@0
   425
wenzelm@16599
   426
(*number of atoms and abstractions in a term*)
wenzelm@16599
   427
fun size_of_term tm =
wenzelm@16599
   428
  let
wenzelm@16678
   429
    fun add_size (t $ u, n) = add_size (t, add_size (u, n))
wenzelm@16678
   430
      | add_size (Abs (_ ,_, t), n) = add_size (t, n + 1)
wenzelm@16678
   431
      | add_size (_, n) = n + 1;
wenzelm@16678
   432
  in add_size (tm, 0) end;
clasohm@0
   433
haftmann@18847
   434
fun map_atyps f (Type (a, Ts)) = Type (a, map (map_atyps f) Ts)
haftmann@18976
   435
  | map_atyps f T = f T;
haftmann@18847
   436
haftmann@18847
   437
fun map_aterms f (t $ u) = map_aterms f t $ map_aterms f u
haftmann@18847
   438
  | map_aterms f (Abs (a, T, t)) = Abs (a, T, map_aterms f t)
haftmann@18847
   439
  | map_aterms f t = f t;
haftmann@18847
   440
wenzelm@18981
   441
fun map_type_tvar f = map_atyps (fn TVar x => f x | T => T);
wenzelm@18981
   442
fun map_type_tfree f = map_atyps (fn TFree x => f x | T => T);
nipkow@949
   443
wenzelm@20548
   444
fun map_types f =
wenzelm@16678
   445
  let
wenzelm@16678
   446
    fun map_aux (Const (a, T)) = Const (a, f T)
wenzelm@16678
   447
      | map_aux (Free (a, T)) = Free (a, f T)
wenzelm@16678
   448
      | map_aux (Var (v, T)) = Var (v, f T)
wenzelm@16678
   449
      | map_aux (t as Bound _)  = t
wenzelm@16678
   450
      | map_aux (Abs (a, T, t)) = Abs (a, f T, map_aux t)
wenzelm@16678
   451
      | map_aux (t $ u) = map_aux t $ map_aux u;
wenzelm@16678
   452
  in map_aux end;
clasohm@0
   453
clasohm@0
   454
(* iterate a function over all types in a term *)
clasohm@0
   455
fun it_term_types f =
clasohm@0
   456
let fun iter(Const(_,T), a) = f(T,a)
clasohm@0
   457
      | iter(Free(_,T), a) = f(T,a)
clasohm@0
   458
      | iter(Var(_,T), a) = f(T,a)
clasohm@0
   459
      | iter(Abs(_,T,t), a) = iter(t,f(T,a))
clasohm@0
   460
      | iter(f$u, a) = iter(f, iter(u, a))
clasohm@0
   461
      | iter(Bound _, a) = a
clasohm@0
   462
in iter end
clasohm@0
   463
clasohm@0
   464
wenzelm@16943
   465
(* fold types and terms *)
wenzelm@16943
   466
wenzelm@16943
   467
(*fold atoms of type*)
wenzelm@16943
   468
fun fold_atyps f (Type (_, Ts)) = fold (fold_atyps f) Ts
wenzelm@16943
   469
  | fold_atyps f T = f T;
wenzelm@16943
   470
wenzelm@16943
   471
(*fold atoms of term*)
wenzelm@16943
   472
fun fold_aterms f (t $ u) = fold_aterms f t #> fold_aterms f u
wenzelm@16943
   473
  | fold_aterms f (Abs (_, _, t)) = fold_aterms f t
wenzelm@16943
   474
  | fold_aterms f a = f a;
wenzelm@16943
   475
wenzelm@16943
   476
(*fold types of term*)
wenzelm@16943
   477
fun fold_term_types f (t as Const (_, T)) = f t T
wenzelm@16943
   478
  | fold_term_types f (t as Free (_, T)) = f t T
wenzelm@16943
   479
  | fold_term_types f (t as Var (_, T)) = f t T
wenzelm@16943
   480
  | fold_term_types f (Bound _) = I
wenzelm@16943
   481
  | fold_term_types f (t as Abs (_, T, b)) = f t T #> fold_term_types f b
wenzelm@16943
   482
  | fold_term_types f (t $ u) = fold_term_types f t #> fold_term_types f u;
wenzelm@16943
   483
wenzelm@16943
   484
fun fold_types f = fold_term_types (K f);
wenzelm@16943
   485
wenzelm@24483
   486
fun replace_types (Const (c, _)) (T :: Ts) = (Const (c, T), Ts)
wenzelm@24483
   487
  | replace_types (Free (x, _)) (T :: Ts) = (Free (x, T), Ts)
wenzelm@24483
   488
  | replace_types (Var (xi, _)) (T :: Ts) = (Var (xi, T), Ts)
wenzelm@24483
   489
  | replace_types (Bound i) Ts = (Bound i, Ts)
wenzelm@24483
   490
  | replace_types (Abs (x, _, b)) (T :: Ts) =
wenzelm@24483
   491
      let val (b', Ts') = replace_types b Ts
wenzelm@24483
   492
      in (Abs (x, T, b'), Ts') end
wenzelm@24483
   493
  | replace_types (t $ u) Ts =
wenzelm@24483
   494
      let
wenzelm@24483
   495
        val (t', Ts') = replace_types t Ts;
wenzelm@24483
   496
        val (u', Ts'') = replace_types u Ts';
wenzelm@24483
   497
      in (t' $ u', Ts'') end;
wenzelm@24483
   498
wenzelm@24483
   499
fun burrow_types f ts =
wenzelm@24483
   500
  let
wenzelm@24483
   501
    val Ts = rev (fold (fold_types cons) ts []);
wenzelm@24483
   502
    val Ts' = f Ts;
wenzelm@24483
   503
    val (ts', []) = fold_map replace_types ts Ts';
wenzelm@24483
   504
  in ts' end;
wenzelm@24483
   505
wenzelm@16943
   506
(*collect variables*)
wenzelm@16943
   507
val add_tvarsT = fold_atyps (fn TVar v => insert (op =) v | _ => I);
wenzelm@16943
   508
val add_tvars = fold_types add_tvarsT;
wenzelm@16943
   509
val add_vars = fold_aterms (fn Var v => insert (op =) v | _ => I);
wenzelm@20199
   510
val add_varnames = fold_aterms (fn Var (xi, _) => insert (op =) xi | _ => I);
wenzelm@16943
   511
val add_tfreesT = fold_atyps (fn TFree v => insert (op =) v | _ => I);
wenzelm@16943
   512
val add_tfrees = fold_types add_tfreesT;
wenzelm@16943
   513
val add_frees = fold_aterms (fn Free v => insert (op =) v | _ => I);
wenzelm@16943
   514
wenzelm@21682
   515
(*extra type variables in a term, not covered by the type*)
wenzelm@21682
   516
fun hidden_polymorphism t T =
wenzelm@21682
   517
  let
wenzelm@21682
   518
    val tvarsT = add_tvarsT T [];
wenzelm@21682
   519
    val extra_tvars = fold_types (fold_atyps
wenzelm@21682
   520
      (fn TVar v => if member (op =) tvarsT v then I else insert (op =) v | _ => I)) t [];
wenzelm@21682
   521
  in extra_tvars end;
wenzelm@21682
   522
wenzelm@16943
   523
wenzelm@16678
   524
(** Comparing terms, types, sorts etc. **)
wenzelm@16537
   525
wenzelm@20511
   526
(* alpha equivalence -- tuned for equalities *)
wenzelm@20511
   527
wenzelm@20511
   528
fun tm1 aconv tm2 =
wenzelm@20511
   529
  pointer_eq (tm1, tm2) orelse
wenzelm@20511
   530
    (case (tm1, tm2) of
wenzelm@20511
   531
      (t1 $ u1, t2 $ u2) => t1 aconv t2 andalso u1 aconv u2
wenzelm@20511
   532
    | (Abs (_, T1, t1), Abs (_, T2, t2)) => t1 aconv t2 andalso T1 = T2
wenzelm@20511
   533
    | (a1, a2) => a1 = a2);
wenzelm@20511
   534
wenzelm@20511
   535
wenzelm@21797
   536
(* equivalence up to renaming of types variables *)
wenzelm@21797
   537
wenzelm@21797
   538
local
wenzelm@21797
   539
wenzelm@21797
   540
val invent_names = Name.invents Name.context "'a";
wenzelm@21797
   541
wenzelm@21797
   542
fun standard_types t =
wenzelm@21797
   543
  let
wenzelm@21797
   544
    val tfrees = add_tfrees t [];
wenzelm@21797
   545
    val tvars = add_tvars t [];
wenzelm@21797
   546
    val env1 = map2 (fn (a, S) => fn a' => (TFree (a, S), TFree (a', [])))
wenzelm@21797
   547
      tfrees (invent_names (length tfrees));
wenzelm@21797
   548
    val env2 = map2 (fn ((a, i), S) => fn a' => (TVar ((a, i), S), TVar ((a', 0), [])))
wenzelm@21797
   549
      tvars (invent_names (length tvars));
wenzelm@21797
   550
  in map_types (map_atyps (perhaps (AList.lookup (op =) (env1 @ env2)))) t end;
wenzelm@21797
   551
wenzelm@21797
   552
in
wenzelm@21797
   553
wenzelm@21797
   554
val equiv_types = op aconv o pairself standard_types;
wenzelm@21797
   555
wenzelm@21797
   556
end;
wenzelm@21797
   557
wenzelm@21797
   558
wenzelm@20511
   559
(* fast syntactic ordering -- tuned for inequalities *)
wenzelm@16678
   560
wenzelm@16678
   561
fun fast_indexname_ord ((x, i), (y, j)) =
wenzelm@16678
   562
  (case int_ord (i, j) of EQUAL => fast_string_ord (x, y) | ord => ord);
wenzelm@16537
   563
wenzelm@16599
   564
fun sort_ord SS =
wenzelm@16599
   565
  if pointer_eq SS then EQUAL
wenzelm@16990
   566
  else dict_ord fast_string_ord SS;
wenzelm@16678
   567
wenzelm@16678
   568
local
wenzelm@16537
   569
wenzelm@16678
   570
fun cons_nr (TVar _) = 0
wenzelm@16678
   571
  | cons_nr (TFree _) = 1
wenzelm@16678
   572
  | cons_nr (Type _) = 2;
wenzelm@16537
   573
wenzelm@16678
   574
in
wenzelm@16537
   575
wenzelm@16537
   576
fun typ_ord TU =
wenzelm@16537
   577
  if pointer_eq TU then EQUAL
wenzelm@16537
   578
  else
wenzelm@16537
   579
    (case TU of
wenzelm@16678
   580
      (Type (a, Ts), Type (b, Us)) =>
wenzelm@16990
   581
        (case fast_string_ord (a, b) of EQUAL => dict_ord typ_ord (Ts, Us) | ord => ord)
wenzelm@16678
   582
    | (TFree (a, S), TFree (b, S')) =>
wenzelm@16678
   583
        (case fast_string_ord (a, b) of EQUAL => sort_ord (S, S') | ord => ord)
wenzelm@16678
   584
    | (TVar (xi, S), TVar (yj, S')) =>
wenzelm@16678
   585
        (case fast_indexname_ord (xi, yj) of EQUAL => sort_ord (S, S') | ord => ord)
wenzelm@16678
   586
    | (T, U) => int_ord (cons_nr T, cons_nr U));
wenzelm@16678
   587
wenzelm@16678
   588
end;
wenzelm@16678
   589
wenzelm@16678
   590
local
wenzelm@16678
   591
wenzelm@16678
   592
fun cons_nr (Const _) = 0
wenzelm@16678
   593
  | cons_nr (Free _) = 1
wenzelm@16678
   594
  | cons_nr (Var _) = 2
wenzelm@16678
   595
  | cons_nr (Bound _) = 3
wenzelm@16678
   596
  | cons_nr (Abs _) = 4
wenzelm@16678
   597
  | cons_nr (_ $ _) = 5;
wenzelm@16678
   598
wenzelm@16678
   599
fun struct_ord (Abs (_, _, t), Abs (_, _, u)) = struct_ord (t, u)
wenzelm@16678
   600
  | struct_ord (t1 $ t2, u1 $ u2) =
wenzelm@16678
   601
      (case struct_ord (t1, u1) of EQUAL => struct_ord (t2, u2) | ord => ord)
wenzelm@16678
   602
  | struct_ord (t, u) = int_ord (cons_nr t, cons_nr u);
wenzelm@16678
   603
wenzelm@16678
   604
fun atoms_ord (Abs (_, _, t), Abs (_, _, u)) = atoms_ord (t, u)
wenzelm@16678
   605
  | atoms_ord (t1 $ t2, u1 $ u2) =
wenzelm@16678
   606
      (case atoms_ord (t1, u1) of EQUAL => atoms_ord (t2, u2) | ord => ord)
wenzelm@16678
   607
  | atoms_ord (Const (a, _), Const (b, _)) = fast_string_ord (a, b)
wenzelm@16678
   608
  | atoms_ord (Free (x, _), Free (y, _)) = fast_string_ord (x, y)
wenzelm@16678
   609
  | atoms_ord (Var (xi, _), Var (yj, _)) = fast_indexname_ord (xi, yj)
wenzelm@16678
   610
  | atoms_ord (Bound i, Bound j) = int_ord (i, j)
wenzelm@16678
   611
  | atoms_ord _ = sys_error "atoms_ord";
wenzelm@16678
   612
wenzelm@16678
   613
fun types_ord (Abs (_, T, t), Abs (_, U, u)) =
wenzelm@16678
   614
      (case typ_ord (T, U) of EQUAL => types_ord (t, u) | ord => ord)
wenzelm@16678
   615
  | types_ord (t1 $ t2, u1 $ u2) =
wenzelm@16678
   616
      (case types_ord (t1, u1) of EQUAL => types_ord (t2, u2) | ord => ord)
wenzelm@16678
   617
  | types_ord (Const (_, T), Const (_, U)) = typ_ord (T, U)
wenzelm@16678
   618
  | types_ord (Free (_, T), Free (_, U)) = typ_ord (T, U)
wenzelm@16678
   619
  | types_ord (Var (_, T), Var (_, U)) = typ_ord (T, U)
wenzelm@16678
   620
  | types_ord (Bound _, Bound _) = EQUAL
wenzelm@16678
   621
  | types_ord _ = sys_error "types_ord";
wenzelm@16678
   622
wenzelm@16678
   623
in
wenzelm@16678
   624
wenzelm@16678
   625
fun fast_term_ord tu =
wenzelm@16678
   626
  if pointer_eq tu then EQUAL
wenzelm@16678
   627
  else
wenzelm@16678
   628
    (case struct_ord tu of
wenzelm@16678
   629
      EQUAL => (case atoms_ord tu of EQUAL => types_ord tu | ord => ord)
wenzelm@16678
   630
    | ord => ord);
wenzelm@16678
   631
wenzelm@16678
   632
structure Vartab = TableFun(type key = indexname val ord = fast_indexname_ord);
wenzelm@16678
   633
structure Typtab = TableFun(type key = typ val ord = typ_ord);
wenzelm@16678
   634
structure Termtab = TableFun(type key = term val ord = fast_term_ord);
wenzelm@16678
   635
wenzelm@16678
   636
end;
wenzelm@16537
   637
wenzelm@16537
   638
wenzelm@16537
   639
(* term_ord *)
wenzelm@16537
   640
wenzelm@16537
   641
(*a linear well-founded AC-compatible ordering for terms:
wenzelm@16537
   642
  s < t <=> 1. size(s) < size(t) or
wenzelm@16537
   643
            2. size(s) = size(t) and s=f(...) and t=g(...) and f<g or
wenzelm@16537
   644
            3. size(s) = size(t) and s=f(s1..sn) and t=f(t1..tn) and
wenzelm@16537
   645
               (s1..sn) < (t1..tn) (lexicographically)*)
wenzelm@16678
   646
wenzelm@16678
   647
fun indexname_ord ((x, i), (y, j)) =
wenzelm@16678
   648
  (case int_ord (i, j) of EQUAL => string_ord (x, y) | ord => ord);
wenzelm@16678
   649
wenzelm@16667
   650
local
wenzelm@16667
   651
wenzelm@16667
   652
fun hd_depth (t $ _, n) = hd_depth (t, n + 1)
wenzelm@16667
   653
  | hd_depth p = p;
wenzelm@16537
   654
wenzelm@16537
   655
fun dest_hd (Const (a, T)) = (((a, 0), T), 0)
wenzelm@16537
   656
  | dest_hd (Free (a, T)) = (((a, 0), T), 1)
wenzelm@16537
   657
  | dest_hd (Var v) = (v, 2)
wenzelm@16537
   658
  | dest_hd (Bound i) = ((("", i), dummyT), 3)
wenzelm@16537
   659
  | dest_hd (Abs (_, T, _)) = ((("", 0), T), 4);
wenzelm@16537
   660
wenzelm@16667
   661
in
wenzelm@16667
   662
wenzelm@16537
   663
fun term_ord tu =
wenzelm@16537
   664
  if pointer_eq tu then EQUAL
wenzelm@16537
   665
  else
wenzelm@16537
   666
    (case tu of
wenzelm@16537
   667
      (Abs (_, T, t), Abs(_, U, u)) =>
wenzelm@16537
   668
        (case term_ord (t, u) of EQUAL => typ_ord (T, U) | ord => ord)
wenzelm@16667
   669
    | (t, u) =>
wenzelm@16537
   670
        (case int_ord (size_of_term t, size_of_term u) of
wenzelm@16537
   671
          EQUAL =>
wenzelm@16943
   672
            (case prod_ord hd_ord int_ord (hd_depth (t, 0), hd_depth (u, 0)) of
wenzelm@16943
   673
              EQUAL => args_ord (t, u) | ord => ord)
wenzelm@16537
   674
        | ord => ord))
wenzelm@16537
   675
and hd_ord (f, g) =
wenzelm@16537
   676
  prod_ord (prod_ord indexname_ord typ_ord) int_ord (dest_hd f, dest_hd g)
wenzelm@16667
   677
and args_ord (f $ t, g $ u) =
wenzelm@16667
   678
      (case args_ord (f, g) of EQUAL => term_ord (t, u) | ord => ord)
wenzelm@16667
   679
  | args_ord _ = EQUAL;
wenzelm@16537
   680
wenzelm@16537
   681
fun termless tu = (term_ord tu = LESS);
wenzelm@16537
   682
wenzelm@16667
   683
end;
wenzelm@16667
   684
wenzelm@16667
   685
wenzelm@16667
   686
(** Lexicographic path order on terms **)
wenzelm@16667
   687
wenzelm@16667
   688
(*
nipkow@16570
   689
  See Baader & Nipkow, Term rewriting, CUP 1998.
nipkow@16570
   690
  Without variables.  Const, Var, Bound, Free and Abs are treated all as
nipkow@16570
   691
  constants.
nipkow@16570
   692
ballarin@20129
   693
  f_ord maps terms to integers and serves two purposes:
nipkow@16570
   694
  - Predicate on constant symbols.  Those that are not recognised by f_ord
nipkow@16570
   695
    must be mapped to ~1.
nipkow@16570
   696
  - Order on the recognised symbols.  These must be mapped to distinct
nipkow@16570
   697
    integers >= 0.
ballarin@20129
   698
  The argument of f_ord is never an application.
wenzelm@16667
   699
*)
nipkow@16570
   700
nipkow@16570
   701
local
ballarin@20129
   702
ballarin@20129
   703
fun unrecognized (Const (a, T)) = ((1, ((a, 0), T)), 0)
ballarin@20129
   704
  | unrecognized (Free (a, T)) = ((1, ((a, 0), T)), 0)
ballarin@20129
   705
  | unrecognized (Var v) = ((1, v), 1)
ballarin@20129
   706
  | unrecognized (Bound i) = ((1, (("", i), dummyT)), 2)
ballarin@20129
   707
  | unrecognized (Abs (_, T, _)) = ((1, (("", 0), T)), 3);
ballarin@20129
   708
ballarin@20129
   709
fun dest_hd f_ord t =
ballarin@20129
   710
      let val ord = f_ord t in
ballarin@20129
   711
        if ord = ~1 then unrecognized t else ((0, (("", ord), fastype_of t)), 0)
nipkow@16570
   712
      end
nipkow@16570
   713
nipkow@16570
   714
fun term_lpo f_ord (s, t) =
nipkow@16570
   715
  let val (f, ss) = strip_comb s and (g, ts) = strip_comb t in
nipkow@16570
   716
    if forall (fn si => term_lpo f_ord (si, t) = LESS) ss
nipkow@16570
   717
    then case hd_ord f_ord (f, g) of
wenzelm@16667
   718
        GREATER =>
wenzelm@16667
   719
          if forall (fn ti => term_lpo f_ord (s, ti) = GREATER) ts
wenzelm@16667
   720
          then GREATER else LESS
nipkow@16570
   721
      | EQUAL =>
wenzelm@16667
   722
          if forall (fn ti => term_lpo f_ord (s, ti) = GREATER) ts
wenzelm@16667
   723
          then list_ord (term_lpo f_ord) (ss, ts)
wenzelm@16667
   724
          else LESS
nipkow@16570
   725
      | LESS => LESS
nipkow@16570
   726
    else GREATER
nipkow@16570
   727
  end
nipkow@16570
   728
and hd_ord f_ord (f, g) = case (f, g) of
nipkow@16570
   729
    (Abs (_, T, t), Abs (_, U, u)) =>
nipkow@16570
   730
      (case term_lpo f_ord (t, u) of EQUAL => typ_ord (T, U) | ord => ord)
nipkow@16570
   731
  | (_, _) => prod_ord (prod_ord int_ord
nipkow@16570
   732
                  (prod_ord indexname_ord typ_ord)) int_ord
nipkow@16570
   733
                (dest_hd f_ord f, dest_hd f_ord g)
nipkow@16570
   734
in
nipkow@16570
   735
val term_lpo = term_lpo
nipkow@16570
   736
end;
nipkow@16570
   737
wenzelm@16537
   738
clasohm@0
   739
(** Connectives of higher order logic **)
clasohm@0
   740
wenzelm@19394
   741
fun aT S = TFree ("'a", S);
wenzelm@19394
   742
wenzelm@375
   743
fun itselfT ty = Type ("itself", [ty]);
wenzelm@14854
   744
val a_itselfT = itselfT (TFree ("'a", []));
wenzelm@375
   745
clasohm@0
   746
val propT : typ = Type("prop",[]);
clasohm@0
   747
clasohm@0
   748
val implies = Const("==>", propT-->propT-->propT);
clasohm@0
   749
clasohm@0
   750
fun all T = Const("all", (T-->propT)-->propT);
clasohm@0
   751
clasohm@0
   752
fun equals T = Const("==", T-->T-->propT);
clasohm@0
   753
clasohm@0
   754
(* maps  !!x1...xn. t   to   t  *)
wenzelm@13000
   755
fun strip_all_body (Const("all",_)$Abs(_,_,t))  =  strip_all_body t
clasohm@0
   756
  | strip_all_body t  =  t;
clasohm@0
   757
clasohm@0
   758
(* maps  !!x1...xn. t   to   [x1, ..., xn]  *)
clasohm@0
   759
fun strip_all_vars (Const("all",_)$Abs(a,T,t))  =
wenzelm@13000
   760
                (a,T) :: strip_all_vars t
clasohm@0
   761
  | strip_all_vars t  =  [] : (string*typ) list;
clasohm@0
   762
clasohm@0
   763
(*increments a term's non-local bound variables
clasohm@0
   764
  required when moving a term within abstractions
clasohm@0
   765
     inc is  increment for bound variables
clasohm@0
   766
     lev is  level at which a bound variable is considered 'loose'*)
wenzelm@13000
   767
fun incr_bv (inc, lev, u as Bound i) = if i>=lev then Bound(i+inc) else u
clasohm@0
   768
  | incr_bv (inc, lev, Abs(a,T,body)) =
wenzelm@9536
   769
        Abs(a, T, incr_bv(inc,lev+1,body))
wenzelm@13000
   770
  | incr_bv (inc, lev, f$t) =
clasohm@0
   771
      incr_bv(inc,lev,f) $ incr_bv(inc,lev,t)
clasohm@0
   772
  | incr_bv (inc, lev, u) = u;
clasohm@0
   773
clasohm@0
   774
fun incr_boundvars  0  t = t
clasohm@0
   775
  | incr_boundvars inc t = incr_bv(inc,0,t);
clasohm@0
   776
wenzelm@12981
   777
(*Scan a pair of terms; while they are similar,
wenzelm@12981
   778
  accumulate corresponding bound vars in "al"*)
wenzelm@12981
   779
fun match_bvs(Abs(x,_,s),Abs(y,_,t), al) =
wenzelm@12981
   780
      match_bvs(s, t, if x="" orelse y="" then al
wenzelm@12981
   781
                                          else (x,y)::al)
wenzelm@12981
   782
  | match_bvs(f$s, g$t, al) = match_bvs(f,g,match_bvs(s,t,al))
wenzelm@12981
   783
  | match_bvs(_,_,al) = al;
wenzelm@12981
   784
wenzelm@12981
   785
(* strip abstractions created by parameters *)
wenzelm@12981
   786
fun match_bvars((s,t),al) = match_bvs(strip_abs_body s, strip_abs_body t, al);
wenzelm@12981
   787
haftmann@22031
   788
fun map_abs_vars f (t $ u) = map_abs_vars f t $ map_abs_vars f u
haftmann@22031
   789
  | map_abs_vars f (Abs (a, T, t)) = Abs (f a, T, map_abs_vars f t)
haftmann@22031
   790
  | map_abs_vars f t = t;
haftmann@22031
   791
wenzelm@12981
   792
fun rename_abs pat obj t =
wenzelm@12981
   793
  let
wenzelm@12981
   794
    val ren = match_bvs (pat, obj, []);
wenzelm@12981
   795
    fun ren_abs (Abs (x, T, b)) =
wenzelm@18942
   796
          Abs (the_default x (AList.lookup (op =) ren x), T, ren_abs b)
wenzelm@12981
   797
      | ren_abs (f $ t) = ren_abs f $ ren_abs t
wenzelm@12981
   798
      | ren_abs t = t
skalberg@15531
   799
  in if null ren then NONE else SOME (ren_abs t) end;
clasohm@0
   800
clasohm@0
   801
(*Accumulate all 'loose' bound vars referring to level 'lev' or beyond.
clasohm@0
   802
   (Bound 0) is loose at level 0 *)
wenzelm@13000
   803
fun add_loose_bnos (Bound i, lev, js) =
haftmann@20854
   804
        if i<lev then js else insert (op =) (i - lev) js
clasohm@0
   805
  | add_loose_bnos (Abs (_,_,t), lev, js) = add_loose_bnos (t, lev+1, js)
clasohm@0
   806
  | add_loose_bnos (f$t, lev, js) =
wenzelm@13000
   807
        add_loose_bnos (f, lev, add_loose_bnos (t, lev, js))
clasohm@0
   808
  | add_loose_bnos (_, _, js) = js;
clasohm@0
   809
clasohm@0
   810
fun loose_bnos t = add_loose_bnos (t, 0, []);
clasohm@0
   811
clasohm@0
   812
(* loose_bvar(t,k) iff t contains a 'loose' bound variable referring to
clasohm@0
   813
   level k or beyond. *)
clasohm@0
   814
fun loose_bvar(Bound i,k) = i >= k
clasohm@0
   815
  | loose_bvar(f$t, k) = loose_bvar(f,k) orelse loose_bvar(t,k)
clasohm@0
   816
  | loose_bvar(Abs(_,_,t),k) = loose_bvar(t,k+1)
clasohm@0
   817
  | loose_bvar _ = false;
clasohm@0
   818
nipkow@2792
   819
fun loose_bvar1(Bound i,k) = i = k
nipkow@2792
   820
  | loose_bvar1(f$t, k) = loose_bvar1(f,k) orelse loose_bvar1(t,k)
nipkow@2792
   821
  | loose_bvar1(Abs(_,_,t),k) = loose_bvar1(t,k+1)
nipkow@2792
   822
  | loose_bvar1 _ = false;
clasohm@0
   823
clasohm@0
   824
(*Substitute arguments for loose bound variables.
clasohm@0
   825
  Beta-reduction of arg(n-1)...arg0 into t replacing (Bound i) with (argi).
wenzelm@4626
   826
  Note that for ((%x y. c) a b), the bound vars in c are x=1 and y=0
wenzelm@9536
   827
        and the appropriate call is  subst_bounds([b,a], c) .
clasohm@0
   828
  Loose bound variables >=n are reduced by "n" to
clasohm@0
   829
     compensate for the disappearance of lambdas.
clasohm@0
   830
*)
wenzelm@13000
   831
fun subst_bounds (args: term list, t) : term =
wenzelm@19065
   832
  let
wenzelm@19065
   833
    exception SAME;
wenzelm@19065
   834
    val n = length args;
wenzelm@19065
   835
    fun subst (t as Bound i, lev) =
wenzelm@19065
   836
         (if i < lev then raise SAME   (*var is locally bound*)
wenzelm@19065
   837
          else incr_boundvars lev (List.nth (args, i - lev))
wenzelm@19065
   838
            handle Subscript => Bound (i - n))  (*loose: change it*)
wenzelm@19065
   839
      | subst (Abs (a, T, body), lev) = Abs (a, T, subst (body, lev + 1))
wenzelm@19065
   840
      | subst (f $ t, lev) =
wenzelm@19065
   841
          (subst (f, lev) $ (subst (t, lev) handle SAME => t) handle SAME => f $ subst (t, lev))
wenzelm@19065
   842
      | subst _ = raise SAME;
wenzelm@19065
   843
  in case args of [] => t | _ => (subst (t, 0) handle SAME => t) end;
clasohm@0
   844
paulson@2192
   845
(*Special case: one argument*)
wenzelm@13000
   846
fun subst_bound (arg, t) : term =
wenzelm@19065
   847
  let
wenzelm@19065
   848
    exception SAME;
wenzelm@19065
   849
    fun subst (Bound i, lev) =
wenzelm@19065
   850
          if i < lev then raise SAME   (*var is locally bound*)
wenzelm@19065
   851
          else if i = lev then incr_boundvars lev arg
wenzelm@19065
   852
          else Bound (i - 1)   (*loose: change it*)
wenzelm@19065
   853
      | subst (Abs (a, T, body), lev) = Abs (a, T, subst (body, lev + 1))
wenzelm@19065
   854
      | subst (f $ t, lev) =
wenzelm@19065
   855
          (subst (f, lev) $ (subst (t, lev) handle SAME => t) handle SAME => f $ subst (t, lev))
wenzelm@19065
   856
      | subst _ = raise SAME;
wenzelm@19065
   857
  in subst (t, 0) handle SAME => t end;
paulson@2192
   858
clasohm@0
   859
(*beta-reduce if possible, else form application*)
paulson@2192
   860
fun betapply (Abs(_,_,t), u) = subst_bound (u,t)
clasohm@0
   861
  | betapply (f,u) = f$u;
clasohm@0
   862
wenzelm@18183
   863
val betapplys = Library.foldl betapply;
wenzelm@18183
   864
wenzelm@14786
   865
haftmann@20109
   866
(*unfolding abstractions with substitution
haftmann@20109
   867
  of bound variables and implicit eta-expansion*)
haftmann@20109
   868
fun strip_abs_eta k t =
haftmann@20109
   869
  let
wenzelm@20122
   870
    val used = fold_aterms (fn Free (v, _) => Name.declare v | _ => I) t Name.context;
haftmann@20109
   871
    fun strip_abs t (0, used) = (([], t), (0, used))
haftmann@20109
   872
      | strip_abs (Abs (v, T, t)) (k, used) =
haftmann@20109
   873
          let
wenzelm@20122
   874
            val ([v'], used') = Name.variants [v] used;
haftmann@21013
   875
            val t' = subst_bound (Free (v', T), t);
wenzelm@20122
   876
            val ((vs, t''), (k', used'')) = strip_abs t' (k - 1, used');
wenzelm@20122
   877
          in (((v', T) :: vs, t''), (k', used'')) end
haftmann@20109
   878
      | strip_abs t (k, used) = (([], t), (k, used));
haftmann@20109
   879
    fun expand_eta [] t _ = ([], t)
haftmann@20109
   880
      | expand_eta (T::Ts) t used =
haftmann@20109
   881
          let
wenzelm@20122
   882
            val ([v], used') = Name.variants [""] used;
wenzelm@20122
   883
            val (vs, t') = expand_eta Ts (t $ Free (v, T)) used';
haftmann@20109
   884
          in ((v, T) :: vs, t') end;
haftmann@20109
   885
    val ((vs1, t'), (k', used')) = strip_abs t (k, used);
haftmann@20109
   886
    val Ts = (fst o chop k' o fst o strip_type o fastype_of) t';
haftmann@20109
   887
    val (vs2, t'') = expand_eta Ts t' used';
haftmann@20109
   888
  in (vs1 @ vs2, t'') end;
haftmann@20109
   889
haftmann@20109
   890
wenzelm@20199
   891
(* comparing variables *)
wenzelm@16882
   892
wenzelm@16724
   893
fun eq_ix ((x, i): indexname, (y, j)) = i = j andalso x = y;
paulson@2192
   894
wenzelm@16943
   895
fun eq_tvar ((xi, S: sort), (xi', S')) = eq_ix (xi, xi') andalso S = S';
wenzelm@16943
   896
fun eq_var ((xi, T: typ), (xi', T')) = eq_ix (xi, xi') andalso T = T';
wenzelm@16943
   897
wenzelm@16943
   898
val tvar_ord = prod_ord indexname_ord sort_ord;
wenzelm@16943
   899
val var_ord = prod_ord indexname_ord typ_ord;
wenzelm@16882
   900
wenzelm@16882
   901
wenzelm@13000
   902
(*A fast unification filter: true unless the two terms cannot be unified.
clasohm@0
   903
  Terms must be NORMAL.  Treats all Vars as distinct. *)
clasohm@0
   904
fun could_unify (t,u) =
clasohm@0
   905
  let fun matchrands (f$t, g$u) = could_unify(t,u) andalso  matchrands(f,g)
wenzelm@9536
   906
        | matchrands _ = true
clasohm@0
   907
  in case (head_of t , head_of u) of
wenzelm@9536
   908
        (_, Var _) => true
clasohm@0
   909
      | (Var _, _) => true
clasohm@0
   910
      | (Const(a,_), Const(b,_)) =>  a=b andalso matchrands(t,u)
clasohm@0
   911
      | (Free(a,_), Free(b,_)) =>  a=b andalso matchrands(t,u)
clasohm@0
   912
      | (Bound i, Bound j) =>  i=j andalso matchrands(t,u)
clasohm@0
   913
      | (Abs _, _) =>  true   (*because of possible eta equality*)
clasohm@0
   914
      | (_, Abs _) =>  true
clasohm@0
   915
      | _ => false
clasohm@0
   916
  end;
clasohm@0
   917
clasohm@0
   918
(*Substitute new for free occurrences of old in a term*)
clasohm@0
   919
fun subst_free [] = (fn t=>t)
clasohm@0
   920
  | subst_free pairs =
wenzelm@13000
   921
      let fun substf u =
haftmann@17314
   922
            case AList.lookup (op aconv) pairs u of
skalberg@15531
   923
                SOME u' => u'
skalberg@15531
   924
              | NONE => (case u of Abs(a,T,t) => Abs(a, T, substf t)
wenzelm@9536
   925
                                 | t$u' => substf t $ substf u'
wenzelm@9536
   926
                                 | _ => u)
clasohm@0
   927
      in  substf  end;
clasohm@0
   928
wenzelm@13000
   929
(*Abstraction of the term "body" over its occurrences of v,
clasohm@0
   930
    which must contain no loose bound variables.
clasohm@0
   931
  The resulting term is ready to become the body of an Abs.*)
wenzelm@16882
   932
fun abstract_over (v, body) =
wenzelm@16882
   933
  let
wenzelm@16990
   934
    exception SAME;
wenzelm@16990
   935
    fun abs lev tm =
wenzelm@16990
   936
      if v aconv tm then Bound lev
wenzelm@16882
   937
      else
wenzelm@16990
   938
        (case tm of
wenzelm@16990
   939
          Abs (a, T, t) => Abs (a, T, abs (lev + 1) t)
wenzelm@16990
   940
        | t $ u => (abs lev t $ (abs lev u handle SAME => u) handle SAME => t $ abs lev u)
wenzelm@16990
   941
        | _ => raise SAME);
wenzelm@16990
   942
  in abs 0 body handle SAME => body end;
clasohm@0
   943
wenzelm@21975
   944
fun lambda v t =
wenzelm@21975
   945
  let val x =
wenzelm@21975
   946
    (case v of
wenzelm@21975
   947
      Const (x, _) => NameSpace.base x
wenzelm@21975
   948
    | Free (x, _) => x
wenzelm@21975
   949
    | Var ((x, _), _) => x
wenzelm@21975
   950
    | _ => "uu")
wenzelm@21975
   951
  in Abs (x, fastype_of v, abstract_over (v, t)) end;
clasohm@0
   952
clasohm@0
   953
(*Form an abstraction over a free variable.*)
wenzelm@21975
   954
fun absfree (a,T,body) = Abs (a, T, abstract_over (Free (a, T), body));
wenzelm@22651
   955
fun absdummy (T, body) = Abs (Name.internal "uu", T, body);
clasohm@0
   956
clasohm@0
   957
(*Abstraction over a list of free variables*)
clasohm@0
   958
fun list_abs_free ([ ] ,     t) = t
wenzelm@13000
   959
  | list_abs_free ((a,T)::vars, t) =
clasohm@0
   960
      absfree(a, T, list_abs_free(vars,t));
clasohm@0
   961
clasohm@0
   962
(*Quantification over a list of free variables*)
clasohm@0
   963
fun list_all_free ([], t: term) = t
wenzelm@13000
   964
  | list_all_free ((a,T)::vars, t) =
clasohm@0
   965
        (all T) $ (absfree(a, T, list_all_free(vars,t)));
clasohm@0
   966
clasohm@0
   967
(*Quantification over a list of variables (already bound in body) *)
clasohm@0
   968
fun list_all ([], t) = t
wenzelm@13000
   969
  | list_all ((a,T)::vars, t) =
clasohm@0
   970
        (all T) $ (Abs(a, T, list_all(vars,t)));
clasohm@0
   971
wenzelm@16678
   972
(*Replace the ATOMIC term ti by ui;    inst = [(t1,u1), ..., (tn,un)].
clasohm@0
   973
  A simultaneous substitution:  [ (a,b), (b,a) ] swaps a and b.  *)
wenzelm@16678
   974
fun subst_atomic [] tm = tm
wenzelm@16678
   975
  | subst_atomic inst tm =
wenzelm@16678
   976
      let
wenzelm@16678
   977
        fun subst (Abs (a, T, body)) = Abs (a, T, subst body)
wenzelm@16678
   978
          | subst (t $ u) = subst t $ subst u
wenzelm@18942
   979
          | subst t = the_default t (AList.lookup (op aconv) inst t);
wenzelm@16678
   980
      in subst tm end;
clasohm@0
   981
wenzelm@16678
   982
(*Replace the ATOMIC type Ti by Ui;    inst = [(T1,U1), ..., (Tn,Un)].*)
wenzelm@16678
   983
fun typ_subst_atomic [] ty = ty
wenzelm@16678
   984
  | typ_subst_atomic inst ty =
wenzelm@16678
   985
      let
wenzelm@16678
   986
        fun subst (Type (a, Ts)) = Type (a, map subst Ts)
wenzelm@18942
   987
          | subst T = the_default T (AList.lookup (op = : typ * typ -> bool) inst T);
wenzelm@16678
   988
      in subst ty end;
berghofe@15797
   989
wenzelm@16678
   990
fun subst_atomic_types [] tm = tm
wenzelm@20548
   991
  | subst_atomic_types inst tm = map_types (typ_subst_atomic inst) tm;
wenzelm@16678
   992
wenzelm@16678
   993
fun typ_subst_TVars [] ty = ty
wenzelm@16678
   994
  | typ_subst_TVars inst ty =
wenzelm@16678
   995
      let
wenzelm@16678
   996
        fun subst (Type (a, Ts)) = Type (a, map subst Ts)
wenzelm@18942
   997
          | subst (T as TVar (xi, _)) = the_default T (AList.lookup (op =) inst xi)
wenzelm@16678
   998
          | subst T = T;
wenzelm@16678
   999
      in subst ty end;
clasohm@0
  1000
wenzelm@16678
  1001
fun subst_TVars [] tm = tm
wenzelm@20548
  1002
  | subst_TVars inst tm = map_types (typ_subst_TVars inst) tm;
clasohm@0
  1003
wenzelm@16678
  1004
fun subst_Vars [] tm = tm
wenzelm@16678
  1005
  | subst_Vars inst tm =
wenzelm@16678
  1006
      let
wenzelm@18942
  1007
        fun subst (t as Var (xi, _)) = the_default t (AList.lookup (op =) inst xi)
wenzelm@16678
  1008
          | subst (Abs (a, T, t)) = Abs (a, T, subst t)
wenzelm@16678
  1009
          | subst (t $ u) = subst t $ subst u
wenzelm@16678
  1010
          | subst t = t;
wenzelm@16678
  1011
      in subst tm end;
clasohm@0
  1012
wenzelm@16678
  1013
fun subst_vars ([], []) tm = tm
wenzelm@16678
  1014
  | subst_vars ([], inst) tm = subst_Vars inst tm
wenzelm@16678
  1015
  | subst_vars (instT, inst) tm =
wenzelm@16678
  1016
      let
wenzelm@16678
  1017
        fun subst (Const (a, T)) = Const (a, typ_subst_TVars instT T)
wenzelm@16678
  1018
          | subst (Free (a, T)) = Free (a, typ_subst_TVars instT T)
wenzelm@16678
  1019
          | subst (t as Var (xi, T)) =
haftmann@17271
  1020
              (case AList.lookup (op =) inst xi of
wenzelm@16678
  1021
                NONE => Var (xi, typ_subst_TVars instT T)
wenzelm@16678
  1022
              | SOME t => t)
wenzelm@16678
  1023
          | subst (t as Bound _) = t
wenzelm@16678
  1024
          | subst (Abs (a, T, t)) = Abs (a, typ_subst_TVars instT T, subst t)
wenzelm@16678
  1025
          | subst (t $ u) = subst t $ subst u;
wenzelm@16678
  1026
      in subst tm end;
clasohm@0
  1027
clasohm@0
  1028
paulson@15573
  1029
(** Identifying first-order terms **)
paulson@15573
  1030
wenzelm@20199
  1031
(*Differs from proofterm/is_fun in its treatment of TVar*)
wenzelm@20199
  1032
fun is_funtype (Type("fun",[_,_])) = true
wenzelm@20199
  1033
  | is_funtype _ = false;
wenzelm@20199
  1034
paulson@15573
  1035
(*Argument Ts is a reverse list of binder types, needed if term t contains Bound vars*)
paulson@15573
  1036
fun has_not_funtype Ts t = not (is_funtype (fastype_of1 (Ts,t)));
paulson@15573
  1037
wenzelm@16537
  1038
(*First order means in all terms of the form f(t1,...,tn) no argument has a
paulson@16589
  1039
  function type. The supplied quantifiers are excluded: their argument always
paulson@16589
  1040
  has a function type through a recursive call into its body.*)
wenzelm@16667
  1041
fun is_first_order quants =
paulson@16589
  1042
  let fun first_order1 Ts (Abs (_,T,body)) = first_order1 (T::Ts) body
wenzelm@16667
  1043
        | first_order1 Ts (Const(q,_) $ Abs(a,T,body)) =
wenzelm@20664
  1044
            member (op =) quants q  andalso   (*it is a known quantifier*)
paulson@16589
  1045
            not (is_funtype T)   andalso first_order1 (T::Ts) body
wenzelm@16667
  1046
        | first_order1 Ts t =
wenzelm@16667
  1047
            case strip_comb t of
wenzelm@16667
  1048
                 (Var _, ts) => forall (first_order1 Ts andf has_not_funtype Ts) ts
wenzelm@16667
  1049
               | (Free _, ts) => forall (first_order1 Ts andf has_not_funtype Ts) ts
wenzelm@16667
  1050
               | (Const _, ts) => forall (first_order1 Ts andf has_not_funtype Ts) ts
wenzelm@16667
  1051
               | (Bound _, ts) => forall (first_order1 Ts andf has_not_funtype Ts) ts
wenzelm@16667
  1052
               | (Abs _, ts) => false (*not in beta-normal form*)
wenzelm@16667
  1053
               | _ => error "first_order: unexpected case"
paulson@16589
  1054
    in  first_order1 []  end;
paulson@15573
  1055
wenzelm@16710
  1056
wenzelm@16990
  1057
(* maximum index of typs and terms *)
clasohm@0
  1058
wenzelm@16710
  1059
fun maxidx_typ (TVar ((_, j), _)) i = Int.max (i, j)
wenzelm@16710
  1060
  | maxidx_typ (Type (_, Ts)) i = maxidx_typs Ts i
wenzelm@16710
  1061
  | maxidx_typ (TFree _) i = i
wenzelm@16710
  1062
and maxidx_typs [] i = i
wenzelm@16710
  1063
  | maxidx_typs (T :: Ts) i = maxidx_typs Ts (maxidx_typ T i);
clasohm@0
  1064
wenzelm@16710
  1065
fun maxidx_term (Var ((_, j), T)) i = maxidx_typ T (Int.max (i, j))
wenzelm@16710
  1066
  | maxidx_term (Const (_, T)) i = maxidx_typ T i
wenzelm@16710
  1067
  | maxidx_term (Free (_, T)) i = maxidx_typ T i
wenzelm@16710
  1068
  | maxidx_term (Bound _) i = i
wenzelm@16710
  1069
  | maxidx_term (Abs (_, T, t)) i = maxidx_term t (maxidx_typ T i)
wenzelm@16710
  1070
  | maxidx_term (t $ u) i = maxidx_term u (maxidx_term t i);
clasohm@0
  1071
wenzelm@16710
  1072
fun maxidx_of_typ T = maxidx_typ T ~1;
wenzelm@16710
  1073
fun maxidx_of_typs Ts = maxidx_typs Ts ~1;
wenzelm@16710
  1074
fun maxidx_of_term t = maxidx_term t ~1;
berghofe@13665
  1075
clasohm@0
  1076
clasohm@0
  1077
clasohm@0
  1078
(**** Syntax-related declarations ****)
clasohm@0
  1079
wenzelm@19909
  1080
(* substructure *)
wenzelm@4017
  1081
wenzelm@19909
  1082
fun exists_subtype P =
wenzelm@19909
  1083
  let
wenzelm@19909
  1084
    fun ex ty = P ty orelse
wenzelm@19909
  1085
      (case ty of Type (_, Ts) => exists ex Ts | _ => false);
wenzelm@19909
  1086
  in ex end;
nipkow@13646
  1087
wenzelm@20531
  1088
fun exists_type P =
wenzelm@20531
  1089
  let
wenzelm@20531
  1090
    fun ex (Const (_, T)) = P T
wenzelm@20531
  1091
      | ex (Free (_, T)) = P T
wenzelm@20531
  1092
      | ex (Var (_, T)) = P T
wenzelm@20531
  1093
      | ex (Bound _) = false
wenzelm@20531
  1094
      | ex (Abs (_, T, t)) = P T orelse ex t
wenzelm@20531
  1095
      | ex (t $ u) = ex t orelse ex u;
wenzelm@20531
  1096
  in ex end;
wenzelm@20531
  1097
wenzelm@16943
  1098
fun exists_subterm P =
wenzelm@16943
  1099
  let
wenzelm@16943
  1100
    fun ex tm = P tm orelse
wenzelm@16943
  1101
      (case tm of
wenzelm@16943
  1102
        t $ u => ex t orelse ex u
wenzelm@16943
  1103
      | Abs (_, _, t) => ex t
wenzelm@16943
  1104
      | _ => false);
wenzelm@16943
  1105
  in ex end;
obua@16108
  1106
wenzelm@24671
  1107
fun has_abs (Abs _) = true
wenzelm@24671
  1108
  | has_abs (t $ u) = has_abs t orelse has_abs u
wenzelm@24671
  1109
  | has_abs _ = false;
wenzelm@24671
  1110
wenzelm@24671
  1111
wenzelm@19909
  1112
wenzelm@19909
  1113
(** Consts etc. **)
wenzelm@19909
  1114
wenzelm@19909
  1115
fun add_term_consts (Const (c, _), cs) = insert (op =) c cs
wenzelm@19909
  1116
  | add_term_consts (t $ u, cs) = add_term_consts (t, add_term_consts (u, cs))
wenzelm@19909
  1117
  | add_term_consts (Abs (_, _, t), cs) = add_term_consts (t, cs)
wenzelm@19909
  1118
  | add_term_consts (_, cs) = cs;
wenzelm@19909
  1119
wenzelm@19909
  1120
fun term_consts t = add_term_consts(t,[]);
wenzelm@19909
  1121
wenzelm@16943
  1122
fun exists_Const P = exists_subterm (fn Const c => P c | _ => false);
nipkow@4631
  1123
wenzelm@4017
  1124
clasohm@0
  1125
(** TFrees and TVars **)
clasohm@0
  1126
wenzelm@12802
  1127
(*Accumulates the names of Frees in the term, suppressing duplicates.*)
haftmann@20854
  1128
fun add_term_free_names (Free(a,_), bs) = insert (op =) a bs
wenzelm@12802
  1129
  | add_term_free_names (f$u, bs) = add_term_free_names (f, add_term_free_names(u, bs))
wenzelm@12802
  1130
  | add_term_free_names (Abs(_,_,t), bs) = add_term_free_names(t,bs)
wenzelm@12802
  1131
  | add_term_free_names (_, bs) = bs;
wenzelm@12802
  1132
clasohm@0
  1133
(*Accumulates the names in the term, suppressing duplicates.
clasohm@0
  1134
  Includes Frees and Consts.  For choosing unambiguous bound var names.*)
haftmann@20854
  1135
fun add_term_names (Const(a,_), bs) = insert (op =) (NameSpace.base a) bs
haftmann@20854
  1136
  | add_term_names (Free(a,_), bs) = insert (op =) a bs
clasohm@0
  1137
  | add_term_names (f$u, bs) = add_term_names (f, add_term_names(u, bs))
clasohm@0
  1138
  | add_term_names (Abs(_,_,t), bs) = add_term_names(t,bs)
clasohm@0
  1139
  | add_term_names (_, bs) = bs;
clasohm@0
  1140
clasohm@0
  1141
(*Accumulates the TVars in a type, suppressing duplicates. *)
wenzelm@23178
  1142
fun add_typ_tvars(Type(_,Ts),vs) = List.foldr add_typ_tvars vs Ts
clasohm@0
  1143
  | add_typ_tvars(TFree(_),vs) = vs
wenzelm@16294
  1144
  | add_typ_tvars(TVar(v),vs) = insert (op =) v vs;
clasohm@0
  1145
clasohm@0
  1146
(*Accumulates the TFrees in a type, suppressing duplicates. *)
wenzelm@23178
  1147
fun add_typ_tfree_names(Type(_,Ts),fs) = List.foldr add_typ_tfree_names fs Ts
haftmann@20854
  1148
  | add_typ_tfree_names(TFree(f,_),fs) = insert (op =) f fs
clasohm@0
  1149
  | add_typ_tfree_names(TVar(_),fs) = fs;
clasohm@0
  1150
wenzelm@23178
  1151
fun add_typ_tfrees(Type(_,Ts),fs) = List.foldr add_typ_tfrees fs Ts
wenzelm@16294
  1152
  | add_typ_tfrees(TFree(f),fs) = insert (op =) f fs
clasohm@0
  1153
  | add_typ_tfrees(TVar(_),fs) = fs;
clasohm@0
  1154
wenzelm@23178
  1155
fun add_typ_varnames(Type(_,Ts),nms) = List.foldr add_typ_varnames nms Ts
haftmann@20854
  1156
  | add_typ_varnames(TFree(nm,_),nms) = insert (op =) nm nms
haftmann@20854
  1157
  | add_typ_varnames(TVar((nm,_),_),nms) = insert (op =) nm nms;
nipkow@949
  1158
clasohm@0
  1159
(*Accumulates the TVars in a term, suppressing duplicates. *)
clasohm@0
  1160
val add_term_tvars = it_term_types add_typ_tvars;
clasohm@0
  1161
clasohm@0
  1162
(*Accumulates the TFrees in a term, suppressing duplicates. *)
clasohm@0
  1163
val add_term_tfrees = it_term_types add_typ_tfrees;
clasohm@0
  1164
val add_term_tfree_names = it_term_types add_typ_tfree_names;
clasohm@0
  1165
clasohm@0
  1166
(*Non-list versions*)
clasohm@0
  1167
fun typ_tfrees T = add_typ_tfrees(T,[]);
clasohm@0
  1168
fun typ_tvars T = add_typ_tvars(T,[]);
clasohm@0
  1169
fun term_tfrees t = add_term_tfrees(t,[]);
clasohm@0
  1170
fun term_tvars t = add_term_tvars(t,[]);
clasohm@0
  1171
nipkow@949
  1172
(*special code to enforce left-to-right collection of TVar-indexnames*)
nipkow@949
  1173
skalberg@15570
  1174
fun add_typ_ixns(ixns,Type(_,Ts)) = Library.foldl add_typ_ixns (ixns,Ts)
wenzelm@20082
  1175
  | add_typ_ixns(ixns,TVar(ixn,_)) = if member (op =) ixns ixn then ixns
wenzelm@9536
  1176
                                     else ixns@[ixn]
nipkow@949
  1177
  | add_typ_ixns(ixns,TFree(_)) = ixns;
nipkow@949
  1178
nipkow@949
  1179
fun add_term_tvar_ixns(Const(_,T),ixns) = add_typ_ixns(ixns,T)
nipkow@949
  1180
  | add_term_tvar_ixns(Free(_,T),ixns) = add_typ_ixns(ixns,T)
nipkow@949
  1181
  | add_term_tvar_ixns(Var(_,T),ixns) = add_typ_ixns(ixns,T)
nipkow@949
  1182
  | add_term_tvar_ixns(Bound _,ixns) = ixns
nipkow@949
  1183
  | add_term_tvar_ixns(Abs(_,T,t),ixns) =
nipkow@949
  1184
      add_term_tvar_ixns(t,add_typ_ixns(ixns,T))
nipkow@949
  1185
  | add_term_tvar_ixns(f$t,ixns) =
nipkow@949
  1186
      add_term_tvar_ixns(t,add_term_tvar_ixns(f,ixns));
nipkow@949
  1187
wenzelm@16537
  1188
clasohm@0
  1189
(** Frees and Vars **)
clasohm@0
  1190
clasohm@0
  1191
(*Accumulates the Vars in the term, suppressing duplicates*)
clasohm@0
  1192
fun add_term_vars (t, vars: term list) = case t of
wenzelm@16990
  1193
    Var   _ => OrdList.insert term_ord t vars
clasohm@0
  1194
  | Abs (_,_,body) => add_term_vars(body,vars)
clasohm@0
  1195
  | f$t =>  add_term_vars (f, add_term_vars(t, vars))
clasohm@0
  1196
  | _ => vars;
clasohm@0
  1197
clasohm@0
  1198
fun term_vars t = add_term_vars(t,[]);
clasohm@0
  1199
clasohm@0
  1200
(*Accumulates the Frees in the term, suppressing duplicates*)
clasohm@0
  1201
fun add_term_frees (t, frees: term list) = case t of
wenzelm@16990
  1202
    Free   _ => OrdList.insert term_ord t frees
clasohm@0
  1203
  | Abs (_,_,body) => add_term_frees(body,frees)
clasohm@0
  1204
  | f$t =>  add_term_frees (f, add_term_frees(t, frees))
clasohm@0
  1205
  | _ => frees;
clasohm@0
  1206
clasohm@0
  1207
fun term_frees t = add_term_frees(t,[]);
clasohm@0
  1208
wenzelm@20199
  1209
wenzelm@20199
  1210
(* dest abstraction *)
clasohm@0
  1211
wenzelm@16678
  1212
fun dest_abs (x, T, body) =
wenzelm@16678
  1213
  let
wenzelm@16678
  1214
    fun name_clash (Free (y, _)) = (x = y)
wenzelm@16678
  1215
      | name_clash (t $ u) = name_clash t orelse name_clash u
wenzelm@16678
  1216
      | name_clash (Abs (_, _, t)) = name_clash t
wenzelm@16678
  1217
      | name_clash _ = false;
wenzelm@16678
  1218
  in
wenzelm@16678
  1219
    if name_clash body then
wenzelm@20082
  1220
      dest_abs (Name.variant [x] x, T, body)    (*potentially slow, but rarely happens*)
wenzelm@16678
  1221
    else (x, subst_bound (Free (x, T), body))
wenzelm@16678
  1222
  end;
wenzelm@16678
  1223
wenzelm@20160
  1224
wenzelm@20160
  1225
(* renaming variables *)
clasohm@0
  1226
wenzelm@20239
  1227
fun declare_term_names tm =
wenzelm@20239
  1228
  fold_aterms
wenzelm@20239
  1229
    (fn Const (a, _) => Name.declare (NameSpace.base a)
wenzelm@20239
  1230
      | Free (a, _) => Name.declare a
wenzelm@20239
  1231
      | _ => I) tm #>
wenzelm@20239
  1232
  fold_types (fold_atyps (fn TFree (a, _) => Name.declare a | _ => I)) tm;
wenzelm@20239
  1233
wenzelm@20160
  1234
fun variant_frees t frees =
wenzelm@20160
  1235
  fst (Name.variants (map fst frees) (declare_term_names t Name.context)) ~~ map snd frees;
wenzelm@20160
  1236
wenzelm@20160
  1237
fun rename_wrt_term t frees = rev (variant_frees t frees);  (*reversed result!*)
clasohm@1364
  1238
paulson@1417
  1239
wenzelm@9536
  1240
(* dummy patterns *)
wenzelm@9536
  1241
wenzelm@9536
  1242
val dummy_patternN = "dummy_pattern";
wenzelm@9536
  1243
wenzelm@18253
  1244
fun dummy_pattern T = Const (dummy_patternN, T);
wenzelm@18253
  1245
wenzelm@9536
  1246
fun is_dummy_pattern (Const ("dummy_pattern", _)) = true
wenzelm@9536
  1247
  | is_dummy_pattern _ = false;
wenzelm@9536
  1248
wenzelm@9536
  1249
fun no_dummy_patterns tm =
haftmann@16787
  1250
  if not (fold_aterms (fn t => fn b => b orelse is_dummy_pattern t) tm false) then tm
wenzelm@9536
  1251
  else raise TERM ("Illegal occurrence of '_' dummy pattern", [tm]);
wenzelm@9536
  1252
wenzelm@11903
  1253
fun replace_dummy Ts (i, Const ("dummy_pattern", T)) =
wenzelm@11903
  1254
      (i + 1, list_comb (Var (("_dummy_", i), Ts ---> T), map Bound (0 upto length Ts - 1)))
wenzelm@11903
  1255
  | replace_dummy Ts (i, Abs (x, T, t)) =
wenzelm@11903
  1256
      let val (i', t') = replace_dummy (T :: Ts) (i, t)
wenzelm@11903
  1257
      in (i', Abs (x, T, t')) end
wenzelm@11903
  1258
  | replace_dummy Ts (i, t $ u) =
wenzelm@11903
  1259
      let val (i', t') = replace_dummy Ts (i, t); val (i'', u') = replace_dummy Ts (i', u)
wenzelm@11903
  1260
      in (i'', t' $ u') end
wenzelm@11903
  1261
  | replace_dummy _ (i, a) = (i, a);
wenzelm@11903
  1262
wenzelm@11903
  1263
val replace_dummy_patterns = replace_dummy [];
wenzelm@9536
  1264
wenzelm@10552
  1265
fun is_replaced_dummy_pattern ("_dummy_", _) = true
wenzelm@10552
  1266
  | is_replaced_dummy_pattern _ = false;
wenzelm@9536
  1267
wenzelm@16035
  1268
fun show_dummy_patterns (Var (("_dummy_", _), T)) = Const ("dummy_pattern", T)
wenzelm@16035
  1269
  | show_dummy_patterns (t $ u) = show_dummy_patterns t $ show_dummy_patterns u
wenzelm@16035
  1270
  | show_dummy_patterns (Abs (x, T, t)) = Abs (x, T, show_dummy_patterns t)
wenzelm@16035
  1271
  | show_dummy_patterns a = a;
wenzelm@16035
  1272
wenzelm@13484
  1273
wenzelm@20100
  1274
(* display variables *)
wenzelm@20100
  1275
wenzelm@15986
  1276
val show_question_marks = ref true;
berghofe@15472
  1277
wenzelm@14786
  1278
fun string_of_vname (x, i) =
wenzelm@14786
  1279
  let
wenzelm@15986
  1280
    val question_mark = if ! show_question_marks then "?" else "";
wenzelm@15986
  1281
    val idx = string_of_int i;
wenzelm@15986
  1282
    val dot =
wenzelm@15986
  1283
      (case rev (Symbol.explode x) of
wenzelm@15986
  1284
        _ :: "\\<^isub>" :: _ => false
wenzelm@15986
  1285
      | _ :: "\\<^isup>" :: _ => false
wenzelm@15986
  1286
      | c :: _ => Symbol.is_digit c
wenzelm@15986
  1287
      | _ => true);
wenzelm@14786
  1288
  in
wenzelm@15986
  1289
    if dot then question_mark ^ x ^ "." ^ idx
wenzelm@15986
  1290
    else if i <> 0 then question_mark ^ x ^ idx
wenzelm@15986
  1291
    else question_mark ^ x
wenzelm@14786
  1292
  end;
wenzelm@14786
  1293
wenzelm@14786
  1294
fun string_of_vname' (x, ~1) = x
wenzelm@14786
  1295
  | string_of_vname' xi = string_of_vname xi;
wenzelm@14786
  1296
clasohm@1364
  1297
end;
clasohm@1364
  1298
wenzelm@4444
  1299
structure BasicTerm: BASIC_TERM = Term;
wenzelm@4444
  1300
open BasicTerm;