src/Pure/term.ML
author wenzelm
Tue Apr 03 19:24:18 2007 +0200 (2007-04-03)
changeset 22572 c6bbe56afbf7
parent 22031 70583c3f3fa5
child 22651 5ab11152daeb
permissions -rw-r--r--
signature: eqtype to accomodate Alice;
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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 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 -> 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 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 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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  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)
skalberg@15570
   327
        handle Subscript => raise TYPE("type_of: bound variable", [], [Bound i]))
clasohm@0
   328
  | type_of1 (Ts, Var (_,T)) = T
clasohm@0
   329
  | type_of1 (Ts, Abs (_,T,body)) = T --> type_of1(T::Ts, body)
wenzelm@13000
   330
  | type_of1 (Ts, f$u) =
clasohm@0
   331
      let val U = type_of1(Ts,u)
clasohm@0
   332
          and T = type_of1(Ts,f)
clasohm@0
   333
      in case T of
wenzelm@9536
   334
            Type("fun",[T1,T2]) =>
wenzelm@9536
   335
              if T1=U then T2  else raise TYPE
wenzelm@9536
   336
                    ("type_of: type mismatch in application", [T1,U], [f$u])
wenzelm@13000
   337
          | _ => raise TYPE
wenzelm@9536
   338
                    ("type_of: function type is expected in application",
wenzelm@9536
   339
                     [T,U], [f$u])
clasohm@0
   340
      end;
clasohm@0
   341
clasohm@0
   342
fun type_of t : typ = type_of1 ([],t);
clasohm@0
   343
clasohm@0
   344
(*Determines the type of a term, with minimal checking*)
wenzelm@13000
   345
fun fastype_of1 (Ts, f$u) =
lcp@61
   346
    (case fastype_of1 (Ts,f) of
wenzelm@9536
   347
        Type("fun",[_,T]) => T
wenzelm@9536
   348
        | _ => raise TERM("fastype_of: expected function type", [f$u]))
lcp@61
   349
  | fastype_of1 (_, Const (_,T)) = T
lcp@61
   350
  | fastype_of1 (_, Free (_,T)) = T
skalberg@15570
   351
  | fastype_of1 (Ts, Bound i) = (List.nth(Ts,i)
skalberg@15570
   352
         handle Subscript => raise TERM("fastype_of: Bound", [Bound i]))
wenzelm@13000
   353
  | fastype_of1 (_, Var (_,T)) = T
lcp@61
   354
  | fastype_of1 (Ts, Abs (_,T,u)) = T --> fastype_of1 (T::Ts, u);
lcp@61
   355
lcp@61
   356
fun fastype_of t : typ = fastype_of1 ([],t);
clasohm@0
   357
wenzelm@16678
   358
(*Determine the argument type of a function*)
wenzelm@16678
   359
fun argument_type_of tm =
wenzelm@16678
   360
  let
wenzelm@16678
   361
    fun argT i (Type ("fun", [T, U])) = if i = 0 then T else argT (i - 1) U
wenzelm@16678
   362
      | argT _ T = raise TYPE ("argument_type_of", [T], []);
wenzelm@16678
   363
wenzelm@16678
   364
    fun arg 0 _ (Abs (_, T, _)) = T
wenzelm@16678
   365
      | arg i Ts (Abs (_, T, t)) = arg (i - 1) (T :: Ts) t
wenzelm@16678
   366
      | arg i Ts (t $ _) = arg (i + 1) Ts t
wenzelm@16678
   367
      | arg i Ts a = argT i (fastype_of1 (Ts, a));
wenzelm@16678
   368
  in arg 0 [] tm end;
wenzelm@16678
   369
clasohm@0
   370
wenzelm@19473
   371
val list_abs = uncurry (fold_rev (fn (x, T) => fn t => Abs (x, T, t)));
wenzelm@10806
   372
haftmann@18927
   373
fun strip_abs (Abs (a, T, t)) =
haftmann@18927
   374
      let val (a', t') = strip_abs t
haftmann@18927
   375
      in ((a, T) :: a', t') end
haftmann@18927
   376
  | strip_abs t = ([], t);
haftmann@18927
   377
clasohm@0
   378
(* maps  (x1,...,xn)t   to   t  *)
wenzelm@13000
   379
fun strip_abs_body (Abs(_,_,t))  =  strip_abs_body t
clasohm@0
   380
  | strip_abs_body u  =  u;
clasohm@0
   381
clasohm@0
   382
(* maps  (x1,...,xn)t   to   [x1, ..., xn]  *)
wenzelm@13000
   383
fun strip_abs_vars (Abs(a,T,t))  =  (a,T) :: strip_abs_vars t
clasohm@0
   384
  | strip_abs_vars u  =  [] : (string*typ) list;
clasohm@0
   385
clasohm@0
   386
clasohm@0
   387
fun strip_qnt_body qnt =
clasohm@0
   388
let fun strip(tm as Const(c,_)$Abs(_,_,t)) = if c=qnt then strip t else tm
clasohm@0
   389
      | strip t = t
clasohm@0
   390
in strip end;
clasohm@0
   391
clasohm@0
   392
fun strip_qnt_vars qnt =
clasohm@0
   393
let fun strip(Const(c,_)$Abs(a,T,t)) = if c=qnt then (a,T)::strip t else []
clasohm@0
   394
      | strip t  =  [] : (string*typ) list
clasohm@0
   395
in strip end;
clasohm@0
   396
clasohm@0
   397
clasohm@0
   398
(* maps   (f, [t1,...,tn])  to  f(t1,...,tn) *)
skalberg@15570
   399
val list_comb : term * term list -> term = Library.foldl (op $);
clasohm@0
   400
clasohm@0
   401
clasohm@0
   402
(* maps   f(t1,...,tn)  to  (f, [t1,...,tn]) ; naturally tail-recursive*)
wenzelm@13000
   403
fun strip_comb u : term * term list =
clasohm@0
   404
    let fun stripc (f$t, ts) = stripc (f, t::ts)
wenzelm@13000
   405
        |   stripc  x =  x
clasohm@0
   406
    in  stripc(u,[])  end;
clasohm@0
   407
clasohm@0
   408
clasohm@0
   409
(* maps   f(t1,...,tn)  to  f , which is never a combination *)
clasohm@0
   410
fun head_of (f$t) = head_of f
clasohm@0
   411
  | head_of u = u;
clasohm@0
   412
wenzelm@21493
   413
fun head_name_of tm =
wenzelm@21493
   414
  (case head_of tm of
wenzelm@21493
   415
    t as Const (c, _) =>
wenzelm@21493
   416
      if NameSpace.is_qualified c then c
wenzelm@21493
   417
      else raise TERM ("Malformed constant name", [t])
wenzelm@21493
   418
  | t as Free (x, _) =>
wenzelm@21493
   419
      if not (NameSpace.is_qualified x) then x
wenzelm@21493
   420
      else raise TERM ("Malformed fixed variable name", [t])
wenzelm@21493
   421
  | t => raise TERM ("No fixed head of term", [t]));
clasohm@0
   422
wenzelm@16599
   423
(*number of atoms and abstractions in a term*)
wenzelm@16599
   424
fun size_of_term tm =
wenzelm@16599
   425
  let
wenzelm@16678
   426
    fun add_size (t $ u, n) = add_size (t, add_size (u, n))
wenzelm@16678
   427
      | add_size (Abs (_ ,_, t), n) = add_size (t, n + 1)
wenzelm@16678
   428
      | add_size (_, n) = n + 1;
wenzelm@16678
   429
  in add_size (tm, 0) end;
clasohm@0
   430
haftmann@18847
   431
fun map_atyps f (Type (a, Ts)) = Type (a, map (map_atyps f) Ts)
haftmann@18976
   432
  | map_atyps f T = f T;
haftmann@18847
   433
haftmann@18847
   434
fun map_aterms f (t $ u) = map_aterms f t $ map_aterms f u
haftmann@18847
   435
  | map_aterms f (Abs (a, T, t)) = Abs (a, T, map_aterms f t)
haftmann@18847
   436
  | map_aterms f t = f t;
haftmann@18847
   437
wenzelm@18981
   438
fun map_type_tvar f = map_atyps (fn TVar x => f x | T => T);
wenzelm@18981
   439
fun map_type_tfree f = map_atyps (fn TFree x => f x | T => T);
nipkow@949
   440
wenzelm@20548
   441
fun map_types f =
wenzelm@16678
   442
  let
wenzelm@16678
   443
    fun map_aux (Const (a, T)) = Const (a, f T)
wenzelm@16678
   444
      | map_aux (Free (a, T)) = Free (a, f T)
wenzelm@16678
   445
      | map_aux (Var (v, T)) = Var (v, f T)
wenzelm@16678
   446
      | map_aux (t as Bound _)  = t
wenzelm@16678
   447
      | map_aux (Abs (a, T, t)) = Abs (a, f T, map_aux t)
wenzelm@16678
   448
      | map_aux (t $ u) = map_aux t $ map_aux u;
wenzelm@16678
   449
  in map_aux end;
clasohm@0
   450
clasohm@0
   451
(* iterate a function over all types in a term *)
clasohm@0
   452
fun it_term_types f =
clasohm@0
   453
let fun iter(Const(_,T), a) = f(T,a)
clasohm@0
   454
      | iter(Free(_,T), a) = f(T,a)
clasohm@0
   455
      | iter(Var(_,T), a) = f(T,a)
clasohm@0
   456
      | iter(Abs(_,T,t), a) = iter(t,f(T,a))
clasohm@0
   457
      | iter(f$u, a) = iter(f, iter(u, a))
clasohm@0
   458
      | iter(Bound _, a) = a
clasohm@0
   459
in iter end
clasohm@0
   460
clasohm@0
   461
wenzelm@16943
   462
(* fold types and terms *)
wenzelm@16943
   463
wenzelm@16943
   464
(*fold atoms of type*)
wenzelm@16943
   465
fun fold_atyps f (Type (_, Ts)) = fold (fold_atyps f) Ts
wenzelm@16943
   466
  | fold_atyps f T = f T;
wenzelm@16943
   467
wenzelm@16943
   468
(*fold atoms of term*)
wenzelm@16943
   469
fun fold_aterms f (t $ u) = fold_aterms f t #> fold_aterms f u
wenzelm@16943
   470
  | fold_aterms f (Abs (_, _, t)) = fold_aterms f t
wenzelm@16943
   471
  | fold_aterms f a = f a;
wenzelm@16943
   472
wenzelm@16943
   473
(*fold types of term*)
wenzelm@16943
   474
fun fold_term_types f (t as Const (_, T)) = f t T
wenzelm@16943
   475
  | fold_term_types f (t as Free (_, T)) = f t T
wenzelm@16943
   476
  | fold_term_types f (t as Var (_, T)) = f t T
wenzelm@16943
   477
  | fold_term_types f (Bound _) = I
wenzelm@16943
   478
  | fold_term_types f (t as Abs (_, T, b)) = f t T #> fold_term_types f b
wenzelm@16943
   479
  | fold_term_types f (t $ u) = fold_term_types f t #> fold_term_types f u;
wenzelm@16943
   480
wenzelm@16943
   481
fun fold_types f = fold_term_types (K f);
wenzelm@16943
   482
wenzelm@16943
   483
(*collect variables*)
wenzelm@16943
   484
val add_tvarsT = fold_atyps (fn TVar v => insert (op =) v | _ => I);
wenzelm@16943
   485
val add_tvars = fold_types add_tvarsT;
wenzelm@16943
   486
val add_vars = fold_aterms (fn Var v => insert (op =) v | _ => I);
wenzelm@20199
   487
val add_varnames = fold_aterms (fn Var (xi, _) => insert (op =) xi | _ => I);
wenzelm@16943
   488
val add_tfreesT = fold_atyps (fn TFree v => insert (op =) v | _ => I);
wenzelm@16943
   489
val add_tfrees = fold_types add_tfreesT;
wenzelm@16943
   490
val add_frees = fold_aterms (fn Free v => insert (op =) v | _ => I);
wenzelm@16943
   491
wenzelm@21682
   492
(*extra type variables in a term, not covered by the type*)
wenzelm@21682
   493
fun hidden_polymorphism t T =
wenzelm@21682
   494
  let
wenzelm@21682
   495
    val tvarsT = add_tvarsT T [];
wenzelm@21682
   496
    val extra_tvars = fold_types (fold_atyps
wenzelm@21682
   497
      (fn TVar v => if member (op =) tvarsT v then I else insert (op =) v | _ => I)) t [];
wenzelm@21682
   498
  in extra_tvars end;
wenzelm@21682
   499
wenzelm@16943
   500
wenzelm@16678
   501
(** Comparing terms, types, sorts etc. **)
wenzelm@16537
   502
wenzelm@20511
   503
(* alpha equivalence -- tuned for equalities *)
wenzelm@20511
   504
wenzelm@20511
   505
fun tm1 aconv tm2 =
wenzelm@20511
   506
  pointer_eq (tm1, tm2) orelse
wenzelm@20511
   507
    (case (tm1, tm2) of
wenzelm@20511
   508
      (t1 $ u1, t2 $ u2) => t1 aconv t2 andalso u1 aconv u2
wenzelm@20511
   509
    | (Abs (_, T1, t1), Abs (_, T2, t2)) => t1 aconv t2 andalso T1 = T2
wenzelm@20511
   510
    | (a1, a2) => a1 = a2);
wenzelm@20511
   511
wenzelm@20511
   512
wenzelm@21797
   513
(* equivalence up to renaming of types variables *)
wenzelm@21797
   514
wenzelm@21797
   515
local
wenzelm@21797
   516
wenzelm@21797
   517
val invent_names = Name.invents Name.context "'a";
wenzelm@21797
   518
wenzelm@21797
   519
fun standard_types t =
wenzelm@21797
   520
  let
wenzelm@21797
   521
    val tfrees = add_tfrees t [];
wenzelm@21797
   522
    val tvars = add_tvars t [];
wenzelm@21797
   523
    val env1 = map2 (fn (a, S) => fn a' => (TFree (a, S), TFree (a', [])))
wenzelm@21797
   524
      tfrees (invent_names (length tfrees));
wenzelm@21797
   525
    val env2 = map2 (fn ((a, i), S) => fn a' => (TVar ((a, i), S), TVar ((a', 0), [])))
wenzelm@21797
   526
      tvars (invent_names (length tvars));
wenzelm@21797
   527
  in map_types (map_atyps (perhaps (AList.lookup (op =) (env1 @ env2)))) t end;
wenzelm@21797
   528
wenzelm@21797
   529
in
wenzelm@21797
   530
wenzelm@21797
   531
val equiv_types = op aconv o pairself standard_types;
wenzelm@21797
   532
wenzelm@21797
   533
end;
wenzelm@21797
   534
wenzelm@21797
   535
wenzelm@20511
   536
(* fast syntactic ordering -- tuned for inequalities *)
wenzelm@16678
   537
wenzelm@16678
   538
fun fast_indexname_ord ((x, i), (y, j)) =
wenzelm@16678
   539
  (case int_ord (i, j) of EQUAL => fast_string_ord (x, y) | ord => ord);
wenzelm@16537
   540
wenzelm@16599
   541
fun sort_ord SS =
wenzelm@16599
   542
  if pointer_eq SS then EQUAL
wenzelm@16990
   543
  else dict_ord fast_string_ord SS;
wenzelm@16678
   544
wenzelm@16678
   545
local
wenzelm@16537
   546
wenzelm@16678
   547
fun cons_nr (TVar _) = 0
wenzelm@16678
   548
  | cons_nr (TFree _) = 1
wenzelm@16678
   549
  | cons_nr (Type _) = 2;
wenzelm@16537
   550
wenzelm@16678
   551
in
wenzelm@16537
   552
wenzelm@16537
   553
fun typ_ord TU =
wenzelm@16537
   554
  if pointer_eq TU then EQUAL
wenzelm@16537
   555
  else
wenzelm@16537
   556
    (case TU of
wenzelm@16678
   557
      (Type (a, Ts), Type (b, Us)) =>
wenzelm@16990
   558
        (case fast_string_ord (a, b) of EQUAL => dict_ord typ_ord (Ts, Us) | ord => ord)
wenzelm@16678
   559
    | (TFree (a, S), TFree (b, S')) =>
wenzelm@16678
   560
        (case fast_string_ord (a, b) of EQUAL => sort_ord (S, S') | ord => ord)
wenzelm@16678
   561
    | (TVar (xi, S), TVar (yj, S')) =>
wenzelm@16678
   562
        (case fast_indexname_ord (xi, yj) of EQUAL => sort_ord (S, S') | ord => ord)
wenzelm@16678
   563
    | (T, U) => int_ord (cons_nr T, cons_nr U));
wenzelm@16678
   564
wenzelm@16678
   565
end;
wenzelm@16678
   566
wenzelm@16678
   567
local
wenzelm@16678
   568
wenzelm@16678
   569
fun cons_nr (Const _) = 0
wenzelm@16678
   570
  | cons_nr (Free _) = 1
wenzelm@16678
   571
  | cons_nr (Var _) = 2
wenzelm@16678
   572
  | cons_nr (Bound _) = 3
wenzelm@16678
   573
  | cons_nr (Abs _) = 4
wenzelm@16678
   574
  | cons_nr (_ $ _) = 5;
wenzelm@16678
   575
wenzelm@16678
   576
fun struct_ord (Abs (_, _, t), Abs (_, _, u)) = struct_ord (t, u)
wenzelm@16678
   577
  | struct_ord (t1 $ t2, u1 $ u2) =
wenzelm@16678
   578
      (case struct_ord (t1, u1) of EQUAL => struct_ord (t2, u2) | ord => ord)
wenzelm@16678
   579
  | struct_ord (t, u) = int_ord (cons_nr t, cons_nr u);
wenzelm@16678
   580
wenzelm@16678
   581
fun atoms_ord (Abs (_, _, t), Abs (_, _, u)) = atoms_ord (t, u)
wenzelm@16678
   582
  | atoms_ord (t1 $ t2, u1 $ u2) =
wenzelm@16678
   583
      (case atoms_ord (t1, u1) of EQUAL => atoms_ord (t2, u2) | ord => ord)
wenzelm@16678
   584
  | atoms_ord (Const (a, _), Const (b, _)) = fast_string_ord (a, b)
wenzelm@16678
   585
  | atoms_ord (Free (x, _), Free (y, _)) = fast_string_ord (x, y)
wenzelm@16678
   586
  | atoms_ord (Var (xi, _), Var (yj, _)) = fast_indexname_ord (xi, yj)
wenzelm@16678
   587
  | atoms_ord (Bound i, Bound j) = int_ord (i, j)
wenzelm@16678
   588
  | atoms_ord _ = sys_error "atoms_ord";
wenzelm@16678
   589
wenzelm@16678
   590
fun types_ord (Abs (_, T, t), Abs (_, U, u)) =
wenzelm@16678
   591
      (case typ_ord (T, U) of EQUAL => types_ord (t, u) | ord => ord)
wenzelm@16678
   592
  | types_ord (t1 $ t2, u1 $ u2) =
wenzelm@16678
   593
      (case types_ord (t1, u1) of EQUAL => types_ord (t2, u2) | ord => ord)
wenzelm@16678
   594
  | types_ord (Const (_, T), Const (_, U)) = typ_ord (T, U)
wenzelm@16678
   595
  | types_ord (Free (_, T), Free (_, U)) = typ_ord (T, U)
wenzelm@16678
   596
  | types_ord (Var (_, T), Var (_, U)) = typ_ord (T, U)
wenzelm@16678
   597
  | types_ord (Bound _, Bound _) = EQUAL
wenzelm@16678
   598
  | types_ord _ = sys_error "types_ord";
wenzelm@16678
   599
wenzelm@16678
   600
in
wenzelm@16678
   601
wenzelm@16678
   602
fun fast_term_ord tu =
wenzelm@16678
   603
  if pointer_eq tu then EQUAL
wenzelm@16678
   604
  else
wenzelm@16678
   605
    (case struct_ord tu of
wenzelm@16678
   606
      EQUAL => (case atoms_ord tu of EQUAL => types_ord tu | ord => ord)
wenzelm@16678
   607
    | ord => ord);
wenzelm@16678
   608
wenzelm@16678
   609
structure Vartab = TableFun(type key = indexname val ord = fast_indexname_ord);
wenzelm@16678
   610
structure Typtab = TableFun(type key = typ val ord = typ_ord);
wenzelm@16678
   611
structure Termtab = TableFun(type key = term val ord = fast_term_ord);
wenzelm@16678
   612
wenzelm@16678
   613
end;
wenzelm@16537
   614
wenzelm@16537
   615
wenzelm@16537
   616
(* term_ord *)
wenzelm@16537
   617
wenzelm@16537
   618
(*a linear well-founded AC-compatible ordering for terms:
wenzelm@16537
   619
  s < t <=> 1. size(s) < size(t) or
wenzelm@16537
   620
            2. size(s) = size(t) and s=f(...) and t=g(...) and f<g or
wenzelm@16537
   621
            3. size(s) = size(t) and s=f(s1..sn) and t=f(t1..tn) and
wenzelm@16537
   622
               (s1..sn) < (t1..tn) (lexicographically)*)
wenzelm@16678
   623
wenzelm@16678
   624
fun indexname_ord ((x, i), (y, j)) =
wenzelm@16678
   625
  (case int_ord (i, j) of EQUAL => string_ord (x, y) | ord => ord);
wenzelm@16678
   626
wenzelm@16667
   627
local
wenzelm@16667
   628
wenzelm@16667
   629
fun hd_depth (t $ _, n) = hd_depth (t, n + 1)
wenzelm@16667
   630
  | hd_depth p = p;
wenzelm@16537
   631
wenzelm@16537
   632
fun dest_hd (Const (a, T)) = (((a, 0), T), 0)
wenzelm@16537
   633
  | dest_hd (Free (a, T)) = (((a, 0), T), 1)
wenzelm@16537
   634
  | dest_hd (Var v) = (v, 2)
wenzelm@16537
   635
  | dest_hd (Bound i) = ((("", i), dummyT), 3)
wenzelm@16537
   636
  | dest_hd (Abs (_, T, _)) = ((("", 0), T), 4);
wenzelm@16537
   637
wenzelm@16667
   638
in
wenzelm@16667
   639
wenzelm@16537
   640
fun term_ord tu =
wenzelm@16537
   641
  if pointer_eq tu then EQUAL
wenzelm@16537
   642
  else
wenzelm@16537
   643
    (case tu of
wenzelm@16537
   644
      (Abs (_, T, t), Abs(_, U, u)) =>
wenzelm@16537
   645
        (case term_ord (t, u) of EQUAL => typ_ord (T, U) | ord => ord)
wenzelm@16667
   646
    | (t, u) =>
wenzelm@16537
   647
        (case int_ord (size_of_term t, size_of_term u) of
wenzelm@16537
   648
          EQUAL =>
wenzelm@16943
   649
            (case prod_ord hd_ord int_ord (hd_depth (t, 0), hd_depth (u, 0)) of
wenzelm@16943
   650
              EQUAL => args_ord (t, u) | ord => ord)
wenzelm@16537
   651
        | ord => ord))
wenzelm@16537
   652
and hd_ord (f, g) =
wenzelm@16537
   653
  prod_ord (prod_ord indexname_ord typ_ord) int_ord (dest_hd f, dest_hd g)
wenzelm@16667
   654
and args_ord (f $ t, g $ u) =
wenzelm@16667
   655
      (case args_ord (f, g) of EQUAL => term_ord (t, u) | ord => ord)
wenzelm@16667
   656
  | args_ord _ = EQUAL;
wenzelm@16537
   657
wenzelm@16537
   658
fun termless tu = (term_ord tu = LESS);
wenzelm@16537
   659
wenzelm@16667
   660
end;
wenzelm@16667
   661
wenzelm@16667
   662
wenzelm@16667
   663
(** Lexicographic path order on terms **)
wenzelm@16667
   664
wenzelm@16667
   665
(*
nipkow@16570
   666
  See Baader & Nipkow, Term rewriting, CUP 1998.
nipkow@16570
   667
  Without variables.  Const, Var, Bound, Free and Abs are treated all as
nipkow@16570
   668
  constants.
nipkow@16570
   669
ballarin@20129
   670
  f_ord maps terms to integers and serves two purposes:
nipkow@16570
   671
  - Predicate on constant symbols.  Those that are not recognised by f_ord
nipkow@16570
   672
    must be mapped to ~1.
nipkow@16570
   673
  - Order on the recognised symbols.  These must be mapped to distinct
nipkow@16570
   674
    integers >= 0.
ballarin@20129
   675
  The argument of f_ord is never an application.
wenzelm@16667
   676
*)
nipkow@16570
   677
nipkow@16570
   678
local
ballarin@20129
   679
ballarin@20129
   680
fun unrecognized (Const (a, T)) = ((1, ((a, 0), T)), 0)
ballarin@20129
   681
  | unrecognized (Free (a, T)) = ((1, ((a, 0), T)), 0)
ballarin@20129
   682
  | unrecognized (Var v) = ((1, v), 1)
ballarin@20129
   683
  | unrecognized (Bound i) = ((1, (("", i), dummyT)), 2)
ballarin@20129
   684
  | unrecognized (Abs (_, T, _)) = ((1, (("", 0), T)), 3);
ballarin@20129
   685
ballarin@20129
   686
fun dest_hd f_ord t =
ballarin@20129
   687
      let val ord = f_ord t in
ballarin@20129
   688
        if ord = ~1 then unrecognized t else ((0, (("", ord), fastype_of t)), 0)
nipkow@16570
   689
      end
nipkow@16570
   690
nipkow@16570
   691
fun term_lpo f_ord (s, t) =
nipkow@16570
   692
  let val (f, ss) = strip_comb s and (g, ts) = strip_comb t in
nipkow@16570
   693
    if forall (fn si => term_lpo f_ord (si, t) = LESS) ss
nipkow@16570
   694
    then case hd_ord f_ord (f, g) of
wenzelm@16667
   695
        GREATER =>
wenzelm@16667
   696
          if forall (fn ti => term_lpo f_ord (s, ti) = GREATER) ts
wenzelm@16667
   697
          then GREATER else LESS
nipkow@16570
   698
      | EQUAL =>
wenzelm@16667
   699
          if forall (fn ti => term_lpo f_ord (s, ti) = GREATER) ts
wenzelm@16667
   700
          then list_ord (term_lpo f_ord) (ss, ts)
wenzelm@16667
   701
          else LESS
nipkow@16570
   702
      | LESS => LESS
nipkow@16570
   703
    else GREATER
nipkow@16570
   704
  end
nipkow@16570
   705
and hd_ord f_ord (f, g) = case (f, g) of
nipkow@16570
   706
    (Abs (_, T, t), Abs (_, U, u)) =>
nipkow@16570
   707
      (case term_lpo f_ord (t, u) of EQUAL => typ_ord (T, U) | ord => ord)
nipkow@16570
   708
  | (_, _) => prod_ord (prod_ord int_ord
nipkow@16570
   709
                  (prod_ord indexname_ord typ_ord)) int_ord
nipkow@16570
   710
                (dest_hd f_ord f, dest_hd f_ord g)
nipkow@16570
   711
in
nipkow@16570
   712
val term_lpo = term_lpo
nipkow@16570
   713
end;
nipkow@16570
   714
wenzelm@16537
   715
clasohm@0
   716
(** Connectives of higher order logic **)
clasohm@0
   717
wenzelm@19394
   718
fun aT S = TFree ("'a", S);
wenzelm@19394
   719
wenzelm@375
   720
fun itselfT ty = Type ("itself", [ty]);
wenzelm@14854
   721
val a_itselfT = itselfT (TFree ("'a", []));
wenzelm@375
   722
clasohm@0
   723
val propT : typ = Type("prop",[]);
clasohm@0
   724
clasohm@0
   725
val implies = Const("==>", propT-->propT-->propT);
clasohm@0
   726
clasohm@0
   727
fun all T = Const("all", (T-->propT)-->propT);
clasohm@0
   728
clasohm@0
   729
fun equals T = Const("==", T-->T-->propT);
clasohm@0
   730
clasohm@0
   731
(* maps  !!x1...xn. t   to   t  *)
wenzelm@13000
   732
fun strip_all_body (Const("all",_)$Abs(_,_,t))  =  strip_all_body t
clasohm@0
   733
  | strip_all_body t  =  t;
clasohm@0
   734
clasohm@0
   735
(* maps  !!x1...xn. t   to   [x1, ..., xn]  *)
clasohm@0
   736
fun strip_all_vars (Const("all",_)$Abs(a,T,t))  =
wenzelm@13000
   737
                (a,T) :: strip_all_vars t
clasohm@0
   738
  | strip_all_vars t  =  [] : (string*typ) list;
clasohm@0
   739
clasohm@0
   740
(*increments a term's non-local bound variables
clasohm@0
   741
  required when moving a term within abstractions
clasohm@0
   742
     inc is  increment for bound variables
clasohm@0
   743
     lev is  level at which a bound variable is considered 'loose'*)
wenzelm@13000
   744
fun incr_bv (inc, lev, u as Bound i) = if i>=lev then Bound(i+inc) else u
clasohm@0
   745
  | incr_bv (inc, lev, Abs(a,T,body)) =
wenzelm@9536
   746
        Abs(a, T, incr_bv(inc,lev+1,body))
wenzelm@13000
   747
  | incr_bv (inc, lev, f$t) =
clasohm@0
   748
      incr_bv(inc,lev,f) $ incr_bv(inc,lev,t)
clasohm@0
   749
  | incr_bv (inc, lev, u) = u;
clasohm@0
   750
clasohm@0
   751
fun incr_boundvars  0  t = t
clasohm@0
   752
  | incr_boundvars inc t = incr_bv(inc,0,t);
clasohm@0
   753
wenzelm@12981
   754
(*Scan a pair of terms; while they are similar,
wenzelm@12981
   755
  accumulate corresponding bound vars in "al"*)
wenzelm@12981
   756
fun match_bvs(Abs(x,_,s),Abs(y,_,t), al) =
wenzelm@12981
   757
      match_bvs(s, t, if x="" orelse y="" then al
wenzelm@12981
   758
                                          else (x,y)::al)
wenzelm@12981
   759
  | match_bvs(f$s, g$t, al) = match_bvs(f,g,match_bvs(s,t,al))
wenzelm@12981
   760
  | match_bvs(_,_,al) = al;
wenzelm@12981
   761
wenzelm@12981
   762
(* strip abstractions created by parameters *)
wenzelm@12981
   763
fun match_bvars((s,t),al) = match_bvs(strip_abs_body s, strip_abs_body t, al);
wenzelm@12981
   764
haftmann@22031
   765
fun map_abs_vars f (t $ u) = map_abs_vars f t $ map_abs_vars f u
haftmann@22031
   766
  | map_abs_vars f (Abs (a, T, t)) = Abs (f a, T, map_abs_vars f t)
haftmann@22031
   767
  | map_abs_vars f t = t;
haftmann@22031
   768
wenzelm@12981
   769
fun rename_abs pat obj t =
wenzelm@12981
   770
  let
wenzelm@12981
   771
    val ren = match_bvs (pat, obj, []);
wenzelm@12981
   772
    fun ren_abs (Abs (x, T, b)) =
wenzelm@18942
   773
          Abs (the_default x (AList.lookup (op =) ren x), T, ren_abs b)
wenzelm@12981
   774
      | ren_abs (f $ t) = ren_abs f $ ren_abs t
wenzelm@12981
   775
      | ren_abs t = t
skalberg@15531
   776
  in if null ren then NONE else SOME (ren_abs t) end;
clasohm@0
   777
clasohm@0
   778
(*Accumulate all 'loose' bound vars referring to level 'lev' or beyond.
clasohm@0
   779
   (Bound 0) is loose at level 0 *)
wenzelm@13000
   780
fun add_loose_bnos (Bound i, lev, js) =
haftmann@20854
   781
        if i<lev then js else insert (op =) (i - lev) js
clasohm@0
   782
  | add_loose_bnos (Abs (_,_,t), lev, js) = add_loose_bnos (t, lev+1, js)
clasohm@0
   783
  | add_loose_bnos (f$t, lev, js) =
wenzelm@13000
   784
        add_loose_bnos (f, lev, add_loose_bnos (t, lev, js))
clasohm@0
   785
  | add_loose_bnos (_, _, js) = js;
clasohm@0
   786
clasohm@0
   787
fun loose_bnos t = add_loose_bnos (t, 0, []);
clasohm@0
   788
clasohm@0
   789
(* loose_bvar(t,k) iff t contains a 'loose' bound variable referring to
clasohm@0
   790
   level k or beyond. *)
clasohm@0
   791
fun loose_bvar(Bound i,k) = i >= k
clasohm@0
   792
  | loose_bvar(f$t, k) = loose_bvar(f,k) orelse loose_bvar(t,k)
clasohm@0
   793
  | loose_bvar(Abs(_,_,t),k) = loose_bvar(t,k+1)
clasohm@0
   794
  | loose_bvar _ = false;
clasohm@0
   795
nipkow@2792
   796
fun loose_bvar1(Bound i,k) = i = k
nipkow@2792
   797
  | loose_bvar1(f$t, k) = loose_bvar1(f,k) orelse loose_bvar1(t,k)
nipkow@2792
   798
  | loose_bvar1(Abs(_,_,t),k) = loose_bvar1(t,k+1)
nipkow@2792
   799
  | loose_bvar1 _ = false;
clasohm@0
   800
clasohm@0
   801
(*Substitute arguments for loose bound variables.
clasohm@0
   802
  Beta-reduction of arg(n-1)...arg0 into t replacing (Bound i) with (argi).
wenzelm@4626
   803
  Note that for ((%x y. c) a b), the bound vars in c are x=1 and y=0
wenzelm@9536
   804
        and the appropriate call is  subst_bounds([b,a], c) .
clasohm@0
   805
  Loose bound variables >=n are reduced by "n" to
clasohm@0
   806
     compensate for the disappearance of lambdas.
clasohm@0
   807
*)
wenzelm@13000
   808
fun subst_bounds (args: term list, t) : term =
wenzelm@19065
   809
  let
wenzelm@19065
   810
    exception SAME;
wenzelm@19065
   811
    val n = length args;
wenzelm@19065
   812
    fun subst (t as Bound i, lev) =
wenzelm@19065
   813
         (if i < lev then raise SAME   (*var is locally bound*)
wenzelm@19065
   814
          else incr_boundvars lev (List.nth (args, i - lev))
wenzelm@19065
   815
            handle Subscript => Bound (i - n))  (*loose: change it*)
wenzelm@19065
   816
      | subst (Abs (a, T, body), lev) = Abs (a, T, subst (body, lev + 1))
wenzelm@19065
   817
      | subst (f $ t, lev) =
wenzelm@19065
   818
          (subst (f, lev) $ (subst (t, lev) handle SAME => t) handle SAME => f $ subst (t, lev))
wenzelm@19065
   819
      | subst _ = raise SAME;
wenzelm@19065
   820
  in case args of [] => t | _ => (subst (t, 0) handle SAME => t) end;
clasohm@0
   821
paulson@2192
   822
(*Special case: one argument*)
wenzelm@13000
   823
fun subst_bound (arg, t) : term =
wenzelm@19065
   824
  let
wenzelm@19065
   825
    exception SAME;
wenzelm@19065
   826
    fun subst (Bound i, lev) =
wenzelm@19065
   827
          if i < lev then raise SAME   (*var is locally bound*)
wenzelm@19065
   828
          else if i = lev then incr_boundvars lev arg
wenzelm@19065
   829
          else Bound (i - 1)   (*loose: change it*)
wenzelm@19065
   830
      | subst (Abs (a, T, body), lev) = Abs (a, T, subst (body, lev + 1))
wenzelm@19065
   831
      | subst (f $ t, lev) =
wenzelm@19065
   832
          (subst (f, lev) $ (subst (t, lev) handle SAME => t) handle SAME => f $ subst (t, lev))
wenzelm@19065
   833
      | subst _ = raise SAME;
wenzelm@19065
   834
  in subst (t, 0) handle SAME => t end;
paulson@2192
   835
clasohm@0
   836
(*beta-reduce if possible, else form application*)
paulson@2192
   837
fun betapply (Abs(_,_,t), u) = subst_bound (u,t)
clasohm@0
   838
  | betapply (f,u) = f$u;
clasohm@0
   839
wenzelm@18183
   840
val betapplys = Library.foldl betapply;
wenzelm@18183
   841
wenzelm@14786
   842
haftmann@20109
   843
(*unfolding abstractions with substitution
haftmann@20109
   844
  of bound variables and implicit eta-expansion*)
haftmann@20109
   845
fun strip_abs_eta k t =
haftmann@20109
   846
  let
wenzelm@20122
   847
    val used = fold_aterms (fn Free (v, _) => Name.declare v | _ => I) t Name.context;
haftmann@20109
   848
    fun strip_abs t (0, used) = (([], t), (0, used))
haftmann@20109
   849
      | strip_abs (Abs (v, T, t)) (k, used) =
haftmann@20109
   850
          let
wenzelm@20122
   851
            val ([v'], used') = Name.variants [v] used;
haftmann@21013
   852
            val t' = subst_bound (Free (v', T), t);
wenzelm@20122
   853
            val ((vs, t''), (k', used'')) = strip_abs t' (k - 1, used');
wenzelm@20122
   854
          in (((v', T) :: vs, t''), (k', used'')) end
haftmann@20109
   855
      | strip_abs t (k, used) = (([], t), (k, used));
haftmann@20109
   856
    fun expand_eta [] t _ = ([], t)
haftmann@20109
   857
      | expand_eta (T::Ts) t used =
haftmann@20109
   858
          let
wenzelm@20122
   859
            val ([v], used') = Name.variants [""] used;
wenzelm@20122
   860
            val (vs, t') = expand_eta Ts (t $ Free (v, T)) used';
haftmann@20109
   861
          in ((v, T) :: vs, t') end;
haftmann@20109
   862
    val ((vs1, t'), (k', used')) = strip_abs t (k, used);
haftmann@20109
   863
    val Ts = (fst o chop k' o fst o strip_type o fastype_of) t';
haftmann@20109
   864
    val (vs2, t'') = expand_eta Ts t' used';
haftmann@20109
   865
  in (vs1 @ vs2, t'') end;
haftmann@20109
   866
haftmann@20109
   867
wenzelm@20199
   868
(* comparing variables *)
wenzelm@16882
   869
wenzelm@16724
   870
fun eq_ix ((x, i): indexname, (y, j)) = i = j andalso x = y;
paulson@2192
   871
wenzelm@16943
   872
fun eq_tvar ((xi, S: sort), (xi', S')) = eq_ix (xi, xi') andalso S = S';
wenzelm@16943
   873
fun eq_var ((xi, T: typ), (xi', T')) = eq_ix (xi, xi') andalso T = T';
wenzelm@16943
   874
wenzelm@16943
   875
val tvar_ord = prod_ord indexname_ord sort_ord;
wenzelm@16943
   876
val var_ord = prod_ord indexname_ord typ_ord;
wenzelm@16882
   877
wenzelm@16882
   878
wenzelm@13000
   879
(*A fast unification filter: true unless the two terms cannot be unified.
clasohm@0
   880
  Terms must be NORMAL.  Treats all Vars as distinct. *)
clasohm@0
   881
fun could_unify (t,u) =
clasohm@0
   882
  let fun matchrands (f$t, g$u) = could_unify(t,u) andalso  matchrands(f,g)
wenzelm@9536
   883
        | matchrands _ = true
clasohm@0
   884
  in case (head_of t , head_of u) of
wenzelm@9536
   885
        (_, Var _) => true
clasohm@0
   886
      | (Var _, _) => true
clasohm@0
   887
      | (Const(a,_), Const(b,_)) =>  a=b andalso matchrands(t,u)
clasohm@0
   888
      | (Free(a,_), Free(b,_)) =>  a=b andalso matchrands(t,u)
clasohm@0
   889
      | (Bound i, Bound j) =>  i=j andalso matchrands(t,u)
clasohm@0
   890
      | (Abs _, _) =>  true   (*because of possible eta equality*)
clasohm@0
   891
      | (_, Abs _) =>  true
clasohm@0
   892
      | _ => false
clasohm@0
   893
  end;
clasohm@0
   894
clasohm@0
   895
(*Substitute new for free occurrences of old in a term*)
clasohm@0
   896
fun subst_free [] = (fn t=>t)
clasohm@0
   897
  | subst_free pairs =
wenzelm@13000
   898
      let fun substf u =
haftmann@17314
   899
            case AList.lookup (op aconv) pairs u of
skalberg@15531
   900
                SOME u' => u'
skalberg@15531
   901
              | NONE => (case u of Abs(a,T,t) => Abs(a, T, substf t)
wenzelm@9536
   902
                                 | t$u' => substf t $ substf u'
wenzelm@9536
   903
                                 | _ => u)
clasohm@0
   904
      in  substf  end;
clasohm@0
   905
wenzelm@13000
   906
(*Abstraction of the term "body" over its occurrences of v,
clasohm@0
   907
    which must contain no loose bound variables.
clasohm@0
   908
  The resulting term is ready to become the body of an Abs.*)
wenzelm@16882
   909
fun abstract_over (v, body) =
wenzelm@16882
   910
  let
wenzelm@16990
   911
    exception SAME;
wenzelm@16990
   912
    fun abs lev tm =
wenzelm@16990
   913
      if v aconv tm then Bound lev
wenzelm@16882
   914
      else
wenzelm@16990
   915
        (case tm of
wenzelm@16990
   916
          Abs (a, T, t) => Abs (a, T, abs (lev + 1) t)
wenzelm@16990
   917
        | t $ u => (abs lev t $ (abs lev u handle SAME => u) handle SAME => t $ abs lev u)
wenzelm@16990
   918
        | _ => raise SAME);
wenzelm@16990
   919
  in abs 0 body handle SAME => body end;
clasohm@0
   920
wenzelm@21975
   921
fun lambda v t =
wenzelm@21975
   922
  let val x =
wenzelm@21975
   923
    (case v of
wenzelm@21975
   924
      Const (x, _) => NameSpace.base x
wenzelm@21975
   925
    | Free (x, _) => x
wenzelm@21975
   926
    | Var ((x, _), _) => x
wenzelm@21975
   927
    | _ => "uu")
wenzelm@21975
   928
  in Abs (x, fastype_of v, abstract_over (v, t)) end;
clasohm@0
   929
clasohm@0
   930
(*Form an abstraction over a free variable.*)
wenzelm@21975
   931
fun absfree (a,T,body) = Abs (a, T, abstract_over (Free (a, T), body));
wenzelm@21742
   932
fun absdummy (T, body) = Abs (Name.internal "x", T, body);
clasohm@0
   933
clasohm@0
   934
(*Abstraction over a list of free variables*)
clasohm@0
   935
fun list_abs_free ([ ] ,     t) = t
wenzelm@13000
   936
  | list_abs_free ((a,T)::vars, t) =
clasohm@0
   937
      absfree(a, T, list_abs_free(vars,t));
clasohm@0
   938
clasohm@0
   939
(*Quantification over a list of free variables*)
clasohm@0
   940
fun list_all_free ([], t: term) = t
wenzelm@13000
   941
  | list_all_free ((a,T)::vars, t) =
clasohm@0
   942
        (all T) $ (absfree(a, T, list_all_free(vars,t)));
clasohm@0
   943
clasohm@0
   944
(*Quantification over a list of variables (already bound in body) *)
clasohm@0
   945
fun list_all ([], t) = t
wenzelm@13000
   946
  | list_all ((a,T)::vars, t) =
clasohm@0
   947
        (all T) $ (Abs(a, T, list_all(vars,t)));
clasohm@0
   948
wenzelm@16678
   949
(*Replace the ATOMIC term ti by ui;    inst = [(t1,u1), ..., (tn,un)].
clasohm@0
   950
  A simultaneous substitution:  [ (a,b), (b,a) ] swaps a and b.  *)
wenzelm@16678
   951
fun subst_atomic [] tm = tm
wenzelm@16678
   952
  | subst_atomic inst tm =
wenzelm@16678
   953
      let
wenzelm@16678
   954
        fun subst (Abs (a, T, body)) = Abs (a, T, subst body)
wenzelm@16678
   955
          | subst (t $ u) = subst t $ subst u
wenzelm@18942
   956
          | subst t = the_default t (AList.lookup (op aconv) inst t);
wenzelm@16678
   957
      in subst tm end;
clasohm@0
   958
wenzelm@16678
   959
(*Replace the ATOMIC type Ti by Ui;    inst = [(T1,U1), ..., (Tn,Un)].*)
wenzelm@16678
   960
fun typ_subst_atomic [] ty = ty
wenzelm@16678
   961
  | typ_subst_atomic inst ty =
wenzelm@16678
   962
      let
wenzelm@16678
   963
        fun subst (Type (a, Ts)) = Type (a, map subst Ts)
wenzelm@18942
   964
          | subst T = the_default T (AList.lookup (op = : typ * typ -> bool) inst T);
wenzelm@16678
   965
      in subst ty end;
berghofe@15797
   966
wenzelm@16678
   967
fun subst_atomic_types [] tm = tm
wenzelm@20548
   968
  | subst_atomic_types inst tm = map_types (typ_subst_atomic inst) tm;
wenzelm@16678
   969
wenzelm@16678
   970
fun typ_subst_TVars [] ty = ty
wenzelm@16678
   971
  | typ_subst_TVars inst ty =
wenzelm@16678
   972
      let
wenzelm@16678
   973
        fun subst (Type (a, Ts)) = Type (a, map subst Ts)
wenzelm@18942
   974
          | subst (T as TVar (xi, _)) = the_default T (AList.lookup (op =) inst xi)
wenzelm@16678
   975
          | subst T = T;
wenzelm@16678
   976
      in subst ty end;
clasohm@0
   977
wenzelm@16678
   978
fun subst_TVars [] tm = tm
wenzelm@20548
   979
  | subst_TVars inst tm = map_types (typ_subst_TVars inst) tm;
clasohm@0
   980
wenzelm@16678
   981
fun subst_Vars [] tm = tm
wenzelm@16678
   982
  | subst_Vars inst tm =
wenzelm@16678
   983
      let
wenzelm@18942
   984
        fun subst (t as Var (xi, _)) = the_default t (AList.lookup (op =) inst xi)
wenzelm@16678
   985
          | subst (Abs (a, T, t)) = Abs (a, T, subst t)
wenzelm@16678
   986
          | subst (t $ u) = subst t $ subst u
wenzelm@16678
   987
          | subst t = t;
wenzelm@16678
   988
      in subst tm end;
clasohm@0
   989
wenzelm@16678
   990
fun subst_vars ([], []) tm = tm
wenzelm@16678
   991
  | subst_vars ([], inst) tm = subst_Vars inst tm
wenzelm@16678
   992
  | subst_vars (instT, inst) tm =
wenzelm@16678
   993
      let
wenzelm@16678
   994
        fun subst (Const (a, T)) = Const (a, typ_subst_TVars instT T)
wenzelm@16678
   995
          | subst (Free (a, T)) = Free (a, typ_subst_TVars instT T)
wenzelm@16678
   996
          | subst (t as Var (xi, T)) =
haftmann@17271
   997
              (case AList.lookup (op =) inst xi of
wenzelm@16678
   998
                NONE => Var (xi, typ_subst_TVars instT T)
wenzelm@16678
   999
              | SOME t => t)
wenzelm@16678
  1000
          | subst (t as Bound _) = t
wenzelm@16678
  1001
          | subst (Abs (a, T, t)) = Abs (a, typ_subst_TVars instT T, subst t)
wenzelm@16678
  1002
          | subst (t $ u) = subst t $ subst u;
wenzelm@16678
  1003
      in subst tm end;
clasohm@0
  1004
clasohm@0
  1005
paulson@15573
  1006
(** Identifying first-order terms **)
paulson@15573
  1007
wenzelm@20199
  1008
(*Differs from proofterm/is_fun in its treatment of TVar*)
wenzelm@20199
  1009
fun is_funtype (Type("fun",[_,_])) = true
wenzelm@20199
  1010
  | is_funtype _ = false;
wenzelm@20199
  1011
paulson@15573
  1012
(*Argument Ts is a reverse list of binder types, needed if term t contains Bound vars*)
paulson@15573
  1013
fun has_not_funtype Ts t = not (is_funtype (fastype_of1 (Ts,t)));
paulson@15573
  1014
wenzelm@16537
  1015
(*First order means in all terms of the form f(t1,...,tn) no argument has a
paulson@16589
  1016
  function type. The supplied quantifiers are excluded: their argument always
paulson@16589
  1017
  has a function type through a recursive call into its body.*)
wenzelm@16667
  1018
fun is_first_order quants =
paulson@16589
  1019
  let fun first_order1 Ts (Abs (_,T,body)) = first_order1 (T::Ts) body
wenzelm@16667
  1020
        | first_order1 Ts (Const(q,_) $ Abs(a,T,body)) =
wenzelm@20664
  1021
            member (op =) quants q  andalso   (*it is a known quantifier*)
paulson@16589
  1022
            not (is_funtype T)   andalso first_order1 (T::Ts) body
wenzelm@16667
  1023
        | first_order1 Ts t =
wenzelm@16667
  1024
            case strip_comb t of
wenzelm@16667
  1025
                 (Var _, ts) => forall (first_order1 Ts andf has_not_funtype Ts) ts
wenzelm@16667
  1026
               | (Free _, ts) => forall (first_order1 Ts andf has_not_funtype Ts) ts
wenzelm@16667
  1027
               | (Const _, ts) => forall (first_order1 Ts andf has_not_funtype Ts) ts
wenzelm@16667
  1028
               | (Bound _, ts) => forall (first_order1 Ts andf has_not_funtype Ts) ts
wenzelm@16667
  1029
               | (Abs _, ts) => false (*not in beta-normal form*)
wenzelm@16667
  1030
               | _ => error "first_order: unexpected case"
paulson@16589
  1031
    in  first_order1 []  end;
paulson@15573
  1032
wenzelm@16710
  1033
wenzelm@16990
  1034
(* maximum index of typs and terms *)
clasohm@0
  1035
wenzelm@16710
  1036
fun maxidx_typ (TVar ((_, j), _)) i = Int.max (i, j)
wenzelm@16710
  1037
  | maxidx_typ (Type (_, Ts)) i = maxidx_typs Ts i
wenzelm@16710
  1038
  | maxidx_typ (TFree _) i = i
wenzelm@16710
  1039
and maxidx_typs [] i = i
wenzelm@16710
  1040
  | maxidx_typs (T :: Ts) i = maxidx_typs Ts (maxidx_typ T i);
clasohm@0
  1041
wenzelm@16710
  1042
fun maxidx_term (Var ((_, j), T)) i = maxidx_typ T (Int.max (i, j))
wenzelm@16710
  1043
  | maxidx_term (Const (_, T)) i = maxidx_typ T i
wenzelm@16710
  1044
  | maxidx_term (Free (_, T)) i = maxidx_typ T i
wenzelm@16710
  1045
  | maxidx_term (Bound _) i = i
wenzelm@16710
  1046
  | maxidx_term (Abs (_, T, t)) i = maxidx_term t (maxidx_typ T i)
wenzelm@16710
  1047
  | maxidx_term (t $ u) i = maxidx_term u (maxidx_term t i);
clasohm@0
  1048
wenzelm@16710
  1049
fun maxidx_of_typ T = maxidx_typ T ~1;
wenzelm@16710
  1050
fun maxidx_of_typs Ts = maxidx_typs Ts ~1;
wenzelm@16710
  1051
fun maxidx_of_term t = maxidx_term t ~1;
berghofe@13665
  1052
clasohm@0
  1053
clasohm@0
  1054
clasohm@0
  1055
(**** Syntax-related declarations ****)
clasohm@0
  1056
wenzelm@19909
  1057
(* substructure *)
wenzelm@4017
  1058
wenzelm@19909
  1059
fun exists_subtype P =
wenzelm@19909
  1060
  let
wenzelm@19909
  1061
    fun ex ty = P ty orelse
wenzelm@19909
  1062
      (case ty of Type (_, Ts) => exists ex Ts | _ => false);
wenzelm@19909
  1063
  in ex end;
nipkow@13646
  1064
wenzelm@20531
  1065
fun exists_type P =
wenzelm@20531
  1066
  let
wenzelm@20531
  1067
    fun ex (Const (_, T)) = P T
wenzelm@20531
  1068
      | ex (Free (_, T)) = P T
wenzelm@20531
  1069
      | ex (Var (_, T)) = P T
wenzelm@20531
  1070
      | ex (Bound _) = false
wenzelm@20531
  1071
      | ex (Abs (_, T, t)) = P T orelse ex t
wenzelm@20531
  1072
      | ex (t $ u) = ex t orelse ex u;
wenzelm@20531
  1073
  in ex end;
wenzelm@20531
  1074
wenzelm@16943
  1075
fun exists_subterm P =
wenzelm@16943
  1076
  let
wenzelm@16943
  1077
    fun ex tm = P tm orelse
wenzelm@16943
  1078
      (case tm of
wenzelm@16943
  1079
        t $ u => ex t orelse ex u
wenzelm@16943
  1080
      | Abs (_, _, t) => ex t
wenzelm@16943
  1081
      | _ => false);
wenzelm@16943
  1082
  in ex end;
obua@16108
  1083
wenzelm@19909
  1084
wenzelm@19909
  1085
(** Consts etc. **)
wenzelm@19909
  1086
wenzelm@19909
  1087
fun add_term_consts (Const (c, _), cs) = insert (op =) c cs
wenzelm@19909
  1088
  | add_term_consts (t $ u, cs) = add_term_consts (t, add_term_consts (u, cs))
wenzelm@19909
  1089
  | add_term_consts (Abs (_, _, t), cs) = add_term_consts (t, cs)
wenzelm@19909
  1090
  | add_term_consts (_, cs) = cs;
wenzelm@19909
  1091
wenzelm@19909
  1092
fun term_consts t = add_term_consts(t,[]);
wenzelm@19909
  1093
wenzelm@16943
  1094
fun exists_Const P = exists_subterm (fn Const c => P c | _ => false);
nipkow@4631
  1095
wenzelm@4017
  1096
clasohm@0
  1097
(** TFrees and TVars **)
clasohm@0
  1098
wenzelm@12802
  1099
(*Accumulates the names of Frees in the term, suppressing duplicates.*)
haftmann@20854
  1100
fun add_term_free_names (Free(a,_), bs) = insert (op =) a bs
wenzelm@12802
  1101
  | add_term_free_names (f$u, bs) = add_term_free_names (f, add_term_free_names(u, bs))
wenzelm@12802
  1102
  | add_term_free_names (Abs(_,_,t), bs) = add_term_free_names(t,bs)
wenzelm@12802
  1103
  | add_term_free_names (_, bs) = bs;
wenzelm@12802
  1104
clasohm@0
  1105
(*Accumulates the names in the term, suppressing duplicates.
clasohm@0
  1106
  Includes Frees and Consts.  For choosing unambiguous bound var names.*)
haftmann@20854
  1107
fun add_term_names (Const(a,_), bs) = insert (op =) (NameSpace.base a) bs
haftmann@20854
  1108
  | add_term_names (Free(a,_), bs) = insert (op =) a bs
clasohm@0
  1109
  | add_term_names (f$u, bs) = add_term_names (f, add_term_names(u, bs))
clasohm@0
  1110
  | add_term_names (Abs(_,_,t), bs) = add_term_names(t,bs)
clasohm@0
  1111
  | add_term_names (_, bs) = bs;
clasohm@0
  1112
clasohm@0
  1113
(*Accumulates the TVars in a type, suppressing duplicates. *)
skalberg@15574
  1114
fun add_typ_tvars(Type(_,Ts),vs) = foldr add_typ_tvars vs Ts
clasohm@0
  1115
  | add_typ_tvars(TFree(_),vs) = vs
wenzelm@16294
  1116
  | add_typ_tvars(TVar(v),vs) = insert (op =) v vs;
clasohm@0
  1117
clasohm@0
  1118
(*Accumulates the TFrees in a type, suppressing duplicates. *)
skalberg@15574
  1119
fun add_typ_tfree_names(Type(_,Ts),fs) = foldr add_typ_tfree_names fs Ts
haftmann@20854
  1120
  | add_typ_tfree_names(TFree(f,_),fs) = insert (op =) f fs
clasohm@0
  1121
  | add_typ_tfree_names(TVar(_),fs) = fs;
clasohm@0
  1122
skalberg@15574
  1123
fun add_typ_tfrees(Type(_,Ts),fs) = foldr add_typ_tfrees fs Ts
wenzelm@16294
  1124
  | add_typ_tfrees(TFree(f),fs) = insert (op =) f fs
clasohm@0
  1125
  | add_typ_tfrees(TVar(_),fs) = fs;
clasohm@0
  1126
skalberg@15574
  1127
fun add_typ_varnames(Type(_,Ts),nms) = foldr add_typ_varnames nms Ts
haftmann@20854
  1128
  | add_typ_varnames(TFree(nm,_),nms) = insert (op =) nm nms
haftmann@20854
  1129
  | add_typ_varnames(TVar((nm,_),_),nms) = insert (op =) nm nms;
nipkow@949
  1130
clasohm@0
  1131
(*Accumulates the TVars in a term, suppressing duplicates. *)
clasohm@0
  1132
val add_term_tvars = it_term_types add_typ_tvars;
clasohm@0
  1133
clasohm@0
  1134
(*Accumulates the TFrees in a term, suppressing duplicates. *)
clasohm@0
  1135
val add_term_tfrees = it_term_types add_typ_tfrees;
clasohm@0
  1136
val add_term_tfree_names = it_term_types add_typ_tfree_names;
clasohm@0
  1137
clasohm@0
  1138
(*Non-list versions*)
clasohm@0
  1139
fun typ_tfrees T = add_typ_tfrees(T,[]);
clasohm@0
  1140
fun typ_tvars T = add_typ_tvars(T,[]);
clasohm@0
  1141
fun term_tfrees t = add_term_tfrees(t,[]);
clasohm@0
  1142
fun term_tvars t = add_term_tvars(t,[]);
clasohm@0
  1143
nipkow@949
  1144
(*special code to enforce left-to-right collection of TVar-indexnames*)
nipkow@949
  1145
skalberg@15570
  1146
fun add_typ_ixns(ixns,Type(_,Ts)) = Library.foldl add_typ_ixns (ixns,Ts)
wenzelm@20082
  1147
  | add_typ_ixns(ixns,TVar(ixn,_)) = if member (op =) ixns ixn then ixns
wenzelm@9536
  1148
                                     else ixns@[ixn]
nipkow@949
  1149
  | add_typ_ixns(ixns,TFree(_)) = ixns;
nipkow@949
  1150
nipkow@949
  1151
fun add_term_tvar_ixns(Const(_,T),ixns) = add_typ_ixns(ixns,T)
nipkow@949
  1152
  | add_term_tvar_ixns(Free(_,T),ixns) = add_typ_ixns(ixns,T)
nipkow@949
  1153
  | add_term_tvar_ixns(Var(_,T),ixns) = add_typ_ixns(ixns,T)
nipkow@949
  1154
  | add_term_tvar_ixns(Bound _,ixns) = ixns
nipkow@949
  1155
  | add_term_tvar_ixns(Abs(_,T,t),ixns) =
nipkow@949
  1156
      add_term_tvar_ixns(t,add_typ_ixns(ixns,T))
nipkow@949
  1157
  | add_term_tvar_ixns(f$t,ixns) =
nipkow@949
  1158
      add_term_tvar_ixns(t,add_term_tvar_ixns(f,ixns));
nipkow@949
  1159
wenzelm@16537
  1160
clasohm@0
  1161
(** Frees and Vars **)
clasohm@0
  1162
clasohm@0
  1163
(*Accumulates the Vars in the term, suppressing duplicates*)
clasohm@0
  1164
fun add_term_vars (t, vars: term list) = case t of
wenzelm@16990
  1165
    Var   _ => OrdList.insert term_ord t vars
clasohm@0
  1166
  | Abs (_,_,body) => add_term_vars(body,vars)
clasohm@0
  1167
  | f$t =>  add_term_vars (f, add_term_vars(t, vars))
clasohm@0
  1168
  | _ => vars;
clasohm@0
  1169
clasohm@0
  1170
fun term_vars t = add_term_vars(t,[]);
clasohm@0
  1171
clasohm@0
  1172
(*Accumulates the Frees in the term, suppressing duplicates*)
clasohm@0
  1173
fun add_term_frees (t, frees: term list) = case t of
wenzelm@16990
  1174
    Free   _ => OrdList.insert term_ord t frees
clasohm@0
  1175
  | Abs (_,_,body) => add_term_frees(body,frees)
clasohm@0
  1176
  | f$t =>  add_term_frees (f, add_term_frees(t, frees))
clasohm@0
  1177
  | _ => frees;
clasohm@0
  1178
clasohm@0
  1179
fun term_frees t = add_term_frees(t,[]);
clasohm@0
  1180
wenzelm@20199
  1181
wenzelm@20199
  1182
(* dest abstraction *)
clasohm@0
  1183
wenzelm@16678
  1184
fun dest_abs (x, T, body) =
wenzelm@16678
  1185
  let
wenzelm@16678
  1186
    fun name_clash (Free (y, _)) = (x = y)
wenzelm@16678
  1187
      | name_clash (t $ u) = name_clash t orelse name_clash u
wenzelm@16678
  1188
      | name_clash (Abs (_, _, t)) = name_clash t
wenzelm@16678
  1189
      | name_clash _ = false;
wenzelm@16678
  1190
  in
wenzelm@16678
  1191
    if name_clash body then
wenzelm@20082
  1192
      dest_abs (Name.variant [x] x, T, body)    (*potentially slow, but rarely happens*)
wenzelm@16678
  1193
    else (x, subst_bound (Free (x, T), body))
wenzelm@16678
  1194
  end;
wenzelm@16678
  1195
wenzelm@20160
  1196
wenzelm@20160
  1197
(* renaming variables *)
clasohm@0
  1198
wenzelm@20239
  1199
fun declare_term_names tm =
wenzelm@20239
  1200
  fold_aterms
wenzelm@20239
  1201
    (fn Const (a, _) => Name.declare (NameSpace.base a)
wenzelm@20239
  1202
      | Free (a, _) => Name.declare a
wenzelm@20239
  1203
      | _ => I) tm #>
wenzelm@20239
  1204
  fold_types (fold_atyps (fn TFree (a, _) => Name.declare a | _ => I)) tm;
wenzelm@20239
  1205
wenzelm@20160
  1206
fun variant_frees t frees =
wenzelm@20160
  1207
  fst (Name.variants (map fst frees) (declare_term_names t Name.context)) ~~ map snd frees;
wenzelm@20160
  1208
wenzelm@20160
  1209
fun rename_wrt_term t frees = rev (variant_frees t frees);  (*reversed result!*)
clasohm@1364
  1210
paulson@1417
  1211
wenzelm@9536
  1212
(* dummy patterns *)
wenzelm@9536
  1213
wenzelm@9536
  1214
val dummy_patternN = "dummy_pattern";
wenzelm@9536
  1215
wenzelm@18253
  1216
fun dummy_pattern T = Const (dummy_patternN, T);
wenzelm@18253
  1217
wenzelm@9536
  1218
fun is_dummy_pattern (Const ("dummy_pattern", _)) = true
wenzelm@9536
  1219
  | is_dummy_pattern _ = false;
wenzelm@9536
  1220
wenzelm@9536
  1221
fun no_dummy_patterns tm =
haftmann@16787
  1222
  if not (fold_aterms (fn t => fn b => b orelse is_dummy_pattern t) tm false) then tm
wenzelm@9536
  1223
  else raise TERM ("Illegal occurrence of '_' dummy pattern", [tm]);
wenzelm@9536
  1224
wenzelm@11903
  1225
fun replace_dummy Ts (i, Const ("dummy_pattern", T)) =
wenzelm@11903
  1226
      (i + 1, list_comb (Var (("_dummy_", i), Ts ---> T), map Bound (0 upto length Ts - 1)))
wenzelm@11903
  1227
  | replace_dummy Ts (i, Abs (x, T, t)) =
wenzelm@11903
  1228
      let val (i', t') = replace_dummy (T :: Ts) (i, t)
wenzelm@11903
  1229
      in (i', Abs (x, T, t')) end
wenzelm@11903
  1230
  | replace_dummy Ts (i, t $ u) =
wenzelm@11903
  1231
      let val (i', t') = replace_dummy Ts (i, t); val (i'', u') = replace_dummy Ts (i', u)
wenzelm@11903
  1232
      in (i'', t' $ u') end
wenzelm@11903
  1233
  | replace_dummy _ (i, a) = (i, a);
wenzelm@11903
  1234
wenzelm@11903
  1235
val replace_dummy_patterns = replace_dummy [];
wenzelm@9536
  1236
wenzelm@10552
  1237
fun is_replaced_dummy_pattern ("_dummy_", _) = true
wenzelm@10552
  1238
  | is_replaced_dummy_pattern _ = false;
wenzelm@9536
  1239
wenzelm@16035
  1240
fun show_dummy_patterns (Var (("_dummy_", _), T)) = Const ("dummy_pattern", T)
wenzelm@16035
  1241
  | show_dummy_patterns (t $ u) = show_dummy_patterns t $ show_dummy_patterns u
wenzelm@16035
  1242
  | show_dummy_patterns (Abs (x, T, t)) = Abs (x, T, show_dummy_patterns t)
wenzelm@16035
  1243
  | show_dummy_patterns a = a;
wenzelm@16035
  1244
wenzelm@13484
  1245
wenzelm@20100
  1246
(* display variables *)
wenzelm@20100
  1247
wenzelm@15986
  1248
val show_question_marks = ref true;
berghofe@15472
  1249
wenzelm@14786
  1250
fun string_of_vname (x, i) =
wenzelm@14786
  1251
  let
wenzelm@15986
  1252
    val question_mark = if ! show_question_marks then "?" else "";
wenzelm@15986
  1253
    val idx = string_of_int i;
wenzelm@15986
  1254
    val dot =
wenzelm@15986
  1255
      (case rev (Symbol.explode x) of
wenzelm@15986
  1256
        _ :: "\\<^isub>" :: _ => false
wenzelm@15986
  1257
      | _ :: "\\<^isup>" :: _ => false
wenzelm@15986
  1258
      | c :: _ => Symbol.is_digit c
wenzelm@15986
  1259
      | _ => true);
wenzelm@14786
  1260
  in
wenzelm@15986
  1261
    if dot then question_mark ^ x ^ "." ^ idx
wenzelm@15986
  1262
    else if i <> 0 then question_mark ^ x ^ idx
wenzelm@15986
  1263
    else question_mark ^ x
wenzelm@14786
  1264
  end;
wenzelm@14786
  1265
wenzelm@14786
  1266
fun string_of_vname' (x, ~1) = x
wenzelm@14786
  1267
  | string_of_vname' xi = string_of_vname xi;
wenzelm@14786
  1268
clasohm@1364
  1269
end;
clasohm@1364
  1270
wenzelm@4444
  1271
structure BasicTerm: BASIC_TERM = Term;
wenzelm@4444
  1272
open BasicTerm;