src/Pure/term.ML
author wenzelm
Thu Nov 23 20:33:29 2006 +0100 (2006-11-23)
changeset 21493 47050cdc1694
parent 21353 cfee13454195
child 21682 53c9a026fcb7
permissions -rw-r--r--
added head_name_of;
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(*  Title:      Pure/term.ML
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    ID:         $Id$
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    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
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    Copyright   Cambridge University 1992
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Simply typed lambda-calculus: types, terms, and basic operations.
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*)
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infix 9  $;
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infixr 5 -->;
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infixr --->;
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infix aconv;
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signature BASIC_TERM =
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sig
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  type indexname
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  type class
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  type sort
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  type arity
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  datatype typ =
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    Type  of string * typ list |
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    TFree of string * sort |
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    TVar  of indexname * sort
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  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_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 add_varnames: term -> indexname list -> indexname list
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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 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)
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        handle Subscript => raise TYPE("type_of: bound variable", [], [Bound i]))
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  | type_of1 (Ts, Var (_,T)) = T
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  | type_of1 (Ts, Abs (_,T,body)) = T --> type_of1(T::Ts, body)
wenzelm@13000
   327
  | type_of1 (Ts, f$u) =
clasohm@0
   328
      let val U = type_of1(Ts,u)
clasohm@0
   329
          and T = type_of1(Ts,f)
clasohm@0
   330
      in case T of
wenzelm@9536
   331
            Type("fun",[T1,T2]) =>
wenzelm@9536
   332
              if T1=U then T2  else raise TYPE
wenzelm@9536
   333
                    ("type_of: type mismatch in application", [T1,U], [f$u])
wenzelm@13000
   334
          | _ => raise TYPE
wenzelm@9536
   335
                    ("type_of: function type is expected in application",
wenzelm@9536
   336
                     [T,U], [f$u])
clasohm@0
   337
      end;
clasohm@0
   338
clasohm@0
   339
fun type_of t : typ = type_of1 ([],t);
clasohm@0
   340
clasohm@0
   341
(*Determines the type of a term, with minimal checking*)
wenzelm@13000
   342
fun fastype_of1 (Ts, f$u) =
lcp@61
   343
    (case fastype_of1 (Ts,f) of
wenzelm@9536
   344
        Type("fun",[_,T]) => T
wenzelm@9536
   345
        | _ => raise TERM("fastype_of: expected function type", [f$u]))
lcp@61
   346
  | fastype_of1 (_, Const (_,T)) = T
lcp@61
   347
  | fastype_of1 (_, Free (_,T)) = T
skalberg@15570
   348
  | fastype_of1 (Ts, Bound i) = (List.nth(Ts,i)
skalberg@15570
   349
         handle Subscript => raise TERM("fastype_of: Bound", [Bound i]))
wenzelm@13000
   350
  | fastype_of1 (_, Var (_,T)) = T
lcp@61
   351
  | fastype_of1 (Ts, Abs (_,T,u)) = T --> fastype_of1 (T::Ts, u);
lcp@61
   352
lcp@61
   353
fun fastype_of t : typ = fastype_of1 ([],t);
clasohm@0
   354
wenzelm@16678
   355
(*Determine the argument type of a function*)
wenzelm@16678
   356
fun argument_type_of tm =
wenzelm@16678
   357
  let
wenzelm@16678
   358
    fun argT i (Type ("fun", [T, U])) = if i = 0 then T else argT (i - 1) U
wenzelm@16678
   359
      | argT _ T = raise TYPE ("argument_type_of", [T], []);
wenzelm@16678
   360
wenzelm@16678
   361
    fun arg 0 _ (Abs (_, T, _)) = T
wenzelm@16678
   362
      | arg i Ts (Abs (_, T, t)) = arg (i - 1) (T :: Ts) t
wenzelm@16678
   363
      | arg i Ts (t $ _) = arg (i + 1) Ts t
wenzelm@16678
   364
      | arg i Ts a = argT i (fastype_of1 (Ts, a));
wenzelm@16678
   365
  in arg 0 [] tm end;
wenzelm@16678
   366
clasohm@0
   367
wenzelm@19473
   368
val list_abs = uncurry (fold_rev (fn (x, T) => fn t => Abs (x, T, t)));
wenzelm@10806
   369
haftmann@18927
   370
fun strip_abs (Abs (a, T, t)) =
haftmann@18927
   371
      let val (a', t') = strip_abs t
haftmann@18927
   372
      in ((a, T) :: a', t') end
haftmann@18927
   373
  | strip_abs t = ([], t);
haftmann@18927
   374
clasohm@0
   375
(* maps  (x1,...,xn)t   to   t  *)
wenzelm@13000
   376
fun strip_abs_body (Abs(_,_,t))  =  strip_abs_body t
clasohm@0
   377
  | strip_abs_body u  =  u;
clasohm@0
   378
clasohm@0
   379
(* maps  (x1,...,xn)t   to   [x1, ..., xn]  *)
wenzelm@13000
   380
fun strip_abs_vars (Abs(a,T,t))  =  (a,T) :: strip_abs_vars t
clasohm@0
   381
  | strip_abs_vars u  =  [] : (string*typ) list;
clasohm@0
   382
clasohm@0
   383
clasohm@0
   384
fun strip_qnt_body qnt =
clasohm@0
   385
let fun strip(tm as Const(c,_)$Abs(_,_,t)) = if c=qnt then strip t else tm
clasohm@0
   386
      | strip t = t
clasohm@0
   387
in strip end;
clasohm@0
   388
clasohm@0
   389
fun strip_qnt_vars qnt =
clasohm@0
   390
let fun strip(Const(c,_)$Abs(a,T,t)) = if c=qnt then (a,T)::strip t else []
clasohm@0
   391
      | strip t  =  [] : (string*typ) list
clasohm@0
   392
in strip end;
clasohm@0
   393
clasohm@0
   394
clasohm@0
   395
(* maps   (f, [t1,...,tn])  to  f(t1,...,tn) *)
skalberg@15570
   396
val list_comb : term * term list -> term = Library.foldl (op $);
clasohm@0
   397
clasohm@0
   398
clasohm@0
   399
(* maps   f(t1,...,tn)  to  (f, [t1,...,tn]) ; naturally tail-recursive*)
wenzelm@13000
   400
fun strip_comb u : term * term list =
clasohm@0
   401
    let fun stripc (f$t, ts) = stripc (f, t::ts)
wenzelm@13000
   402
        |   stripc  x =  x
clasohm@0
   403
    in  stripc(u,[])  end;
clasohm@0
   404
clasohm@0
   405
clasohm@0
   406
(* maps   f(t1,...,tn)  to  f , which is never a combination *)
clasohm@0
   407
fun head_of (f$t) = head_of f
clasohm@0
   408
  | head_of u = u;
clasohm@0
   409
wenzelm@21493
   410
fun head_name_of tm =
wenzelm@21493
   411
  (case head_of tm of
wenzelm@21493
   412
    t as Const (c, _) =>
wenzelm@21493
   413
      if NameSpace.is_qualified c then c
wenzelm@21493
   414
      else raise TERM ("Malformed constant name", [t])
wenzelm@21493
   415
  | t as Free (x, _) =>
wenzelm@21493
   416
      if not (NameSpace.is_qualified x) then x
wenzelm@21493
   417
      else raise TERM ("Malformed fixed variable name", [t])
wenzelm@21493
   418
  | t => raise TERM ("No fixed head of term", [t]));
clasohm@0
   419
wenzelm@16599
   420
(*number of atoms and abstractions in a term*)
wenzelm@16599
   421
fun size_of_term tm =
wenzelm@16599
   422
  let
wenzelm@16678
   423
    fun add_size (t $ u, n) = add_size (t, add_size (u, n))
wenzelm@16678
   424
      | add_size (Abs (_ ,_, t), n) = add_size (t, n + 1)
wenzelm@16678
   425
      | add_size (_, n) = n + 1;
wenzelm@16678
   426
  in add_size (tm, 0) end;
clasohm@0
   427
haftmann@18847
   428
fun map_atyps f (Type (a, Ts)) = Type (a, map (map_atyps f) Ts)
haftmann@18976
   429
  | map_atyps f T = f T;
haftmann@18847
   430
haftmann@18847
   431
fun map_aterms f (t $ u) = map_aterms f t $ map_aterms f u
haftmann@18847
   432
  | map_aterms f (Abs (a, T, t)) = Abs (a, T, map_aterms f t)
haftmann@18847
   433
  | map_aterms f t = f t;
haftmann@18847
   434
wenzelm@18981
   435
fun map_type_tvar f = map_atyps (fn TVar x => f x | T => T);
wenzelm@18981
   436
fun map_type_tfree f = map_atyps (fn TFree x => f x | T => T);
nipkow@949
   437
wenzelm@20548
   438
fun map_types f =
wenzelm@16678
   439
  let
wenzelm@16678
   440
    fun map_aux (Const (a, T)) = Const (a, f T)
wenzelm@16678
   441
      | map_aux (Free (a, T)) = Free (a, f T)
wenzelm@16678
   442
      | map_aux (Var (v, T)) = Var (v, f T)
wenzelm@16678
   443
      | map_aux (t as Bound _)  = t
wenzelm@16678
   444
      | map_aux (Abs (a, T, t)) = Abs (a, f T, map_aux t)
wenzelm@16678
   445
      | map_aux (t $ u) = map_aux t $ map_aux u;
wenzelm@16678
   446
  in map_aux end;
clasohm@0
   447
clasohm@0
   448
(* iterate a function over all types in a term *)
clasohm@0
   449
fun it_term_types f =
clasohm@0
   450
let fun iter(Const(_,T), a) = f(T,a)
clasohm@0
   451
      | iter(Free(_,T), a) = f(T,a)
clasohm@0
   452
      | iter(Var(_,T), a) = f(T,a)
clasohm@0
   453
      | iter(Abs(_,T,t), a) = iter(t,f(T,a))
clasohm@0
   454
      | iter(f$u, a) = iter(f, iter(u, a))
clasohm@0
   455
      | iter(Bound _, a) = a
clasohm@0
   456
in iter end
clasohm@0
   457
clasohm@0
   458
wenzelm@16943
   459
(* fold types and terms *)
wenzelm@16943
   460
wenzelm@16943
   461
(*fold atoms of type*)
wenzelm@16943
   462
fun fold_atyps f (Type (_, Ts)) = fold (fold_atyps f) Ts
wenzelm@16943
   463
  | fold_atyps f T = f T;
wenzelm@16943
   464
wenzelm@16943
   465
(*fold atoms of term*)
wenzelm@16943
   466
fun fold_aterms f (t $ u) = fold_aterms f t #> fold_aterms f u
wenzelm@16943
   467
  | fold_aterms f (Abs (_, _, t)) = fold_aterms f t
wenzelm@16943
   468
  | fold_aterms f a = f a;
wenzelm@16943
   469
wenzelm@16943
   470
(*fold types of term*)
wenzelm@16943
   471
fun fold_term_types f (t as Const (_, T)) = f t T
wenzelm@16943
   472
  | fold_term_types f (t as Free (_, T)) = f t T
wenzelm@16943
   473
  | fold_term_types f (t as Var (_, T)) = f t T
wenzelm@16943
   474
  | fold_term_types f (Bound _) = I
wenzelm@16943
   475
  | fold_term_types f (t as Abs (_, T, b)) = f t T #> fold_term_types f b
wenzelm@16943
   476
  | fold_term_types f (t $ u) = fold_term_types f t #> fold_term_types f u;
wenzelm@16943
   477
wenzelm@16943
   478
fun fold_types f = fold_term_types (K f);
wenzelm@16943
   479
wenzelm@16943
   480
(*collect variables*)
wenzelm@16943
   481
val add_tvarsT = fold_atyps (fn TVar v => insert (op =) v | _ => I);
wenzelm@16943
   482
val add_tvars = fold_types add_tvarsT;
wenzelm@16943
   483
val add_vars = fold_aterms (fn Var v => insert (op =) v | _ => I);
wenzelm@20199
   484
val add_varnames = fold_aterms (fn Var (xi, _) => insert (op =) xi | _ => I);
wenzelm@16943
   485
val add_tfreesT = fold_atyps (fn TFree v => insert (op =) v | _ => I);
wenzelm@16943
   486
val add_tfrees = fold_types add_tfreesT;
wenzelm@16943
   487
val add_frees = fold_aterms (fn Free v => insert (op =) v | _ => I);
wenzelm@16943
   488
wenzelm@16943
   489
wenzelm@16678
   490
(** Comparing terms, types, sorts etc. **)
wenzelm@16537
   491
wenzelm@20511
   492
(* alpha equivalence -- tuned for equalities *)
wenzelm@20511
   493
wenzelm@20511
   494
fun tm1 aconv tm2 =
wenzelm@20511
   495
  pointer_eq (tm1, tm2) orelse
wenzelm@20511
   496
    (case (tm1, tm2) of
wenzelm@20511
   497
      (t1 $ u1, t2 $ u2) => t1 aconv t2 andalso u1 aconv u2
wenzelm@20511
   498
    | (Abs (_, T1, t1), Abs (_, T2, t2)) => t1 aconv t2 andalso T1 = T2
wenzelm@20511
   499
    | (a1, a2) => a1 = a2);
wenzelm@20511
   500
wenzelm@20511
   501
wenzelm@20511
   502
(* fast syntactic ordering -- tuned for inequalities *)
wenzelm@16678
   503
wenzelm@16678
   504
fun fast_indexname_ord ((x, i), (y, j)) =
wenzelm@16678
   505
  (case int_ord (i, j) of EQUAL => fast_string_ord (x, y) | ord => ord);
wenzelm@16537
   506
wenzelm@16599
   507
fun sort_ord SS =
wenzelm@16599
   508
  if pointer_eq SS then EQUAL
wenzelm@16990
   509
  else dict_ord fast_string_ord SS;
wenzelm@16678
   510
wenzelm@16678
   511
local
wenzelm@16537
   512
wenzelm@16678
   513
fun cons_nr (TVar _) = 0
wenzelm@16678
   514
  | cons_nr (TFree _) = 1
wenzelm@16678
   515
  | cons_nr (Type _) = 2;
wenzelm@16537
   516
wenzelm@16678
   517
in
wenzelm@16537
   518
wenzelm@16537
   519
fun typ_ord TU =
wenzelm@16537
   520
  if pointer_eq TU then EQUAL
wenzelm@16537
   521
  else
wenzelm@16537
   522
    (case TU of
wenzelm@16678
   523
      (Type (a, Ts), Type (b, Us)) =>
wenzelm@16990
   524
        (case fast_string_ord (a, b) of EQUAL => dict_ord typ_ord (Ts, Us) | ord => ord)
wenzelm@16678
   525
    | (TFree (a, S), TFree (b, S')) =>
wenzelm@16678
   526
        (case fast_string_ord (a, b) of EQUAL => sort_ord (S, S') | ord => ord)
wenzelm@16678
   527
    | (TVar (xi, S), TVar (yj, S')) =>
wenzelm@16678
   528
        (case fast_indexname_ord (xi, yj) of EQUAL => sort_ord (S, S') | ord => ord)
wenzelm@16678
   529
    | (T, U) => int_ord (cons_nr T, cons_nr U));
wenzelm@16678
   530
wenzelm@16678
   531
end;
wenzelm@16678
   532
wenzelm@16678
   533
local
wenzelm@16678
   534
wenzelm@16678
   535
fun cons_nr (Const _) = 0
wenzelm@16678
   536
  | cons_nr (Free _) = 1
wenzelm@16678
   537
  | cons_nr (Var _) = 2
wenzelm@16678
   538
  | cons_nr (Bound _) = 3
wenzelm@16678
   539
  | cons_nr (Abs _) = 4
wenzelm@16678
   540
  | cons_nr (_ $ _) = 5;
wenzelm@16678
   541
wenzelm@16678
   542
fun struct_ord (Abs (_, _, t), Abs (_, _, u)) = struct_ord (t, u)
wenzelm@16678
   543
  | struct_ord (t1 $ t2, u1 $ u2) =
wenzelm@16678
   544
      (case struct_ord (t1, u1) of EQUAL => struct_ord (t2, u2) | ord => ord)
wenzelm@16678
   545
  | struct_ord (t, u) = int_ord (cons_nr t, cons_nr u);
wenzelm@16678
   546
wenzelm@16678
   547
fun atoms_ord (Abs (_, _, t), Abs (_, _, u)) = atoms_ord (t, u)
wenzelm@16678
   548
  | atoms_ord (t1 $ t2, u1 $ u2) =
wenzelm@16678
   549
      (case atoms_ord (t1, u1) of EQUAL => atoms_ord (t2, u2) | ord => ord)
wenzelm@16678
   550
  | atoms_ord (Const (a, _), Const (b, _)) = fast_string_ord (a, b)
wenzelm@16678
   551
  | atoms_ord (Free (x, _), Free (y, _)) = fast_string_ord (x, y)
wenzelm@16678
   552
  | atoms_ord (Var (xi, _), Var (yj, _)) = fast_indexname_ord (xi, yj)
wenzelm@16678
   553
  | atoms_ord (Bound i, Bound j) = int_ord (i, j)
wenzelm@16678
   554
  | atoms_ord _ = sys_error "atoms_ord";
wenzelm@16678
   555
wenzelm@16678
   556
fun types_ord (Abs (_, T, t), Abs (_, U, u)) =
wenzelm@16678
   557
      (case typ_ord (T, U) of EQUAL => types_ord (t, u) | ord => ord)
wenzelm@16678
   558
  | types_ord (t1 $ t2, u1 $ u2) =
wenzelm@16678
   559
      (case types_ord (t1, u1) of EQUAL => types_ord (t2, u2) | ord => ord)
wenzelm@16678
   560
  | types_ord (Const (_, T), Const (_, U)) = typ_ord (T, U)
wenzelm@16678
   561
  | types_ord (Free (_, T), Free (_, U)) = typ_ord (T, U)
wenzelm@16678
   562
  | types_ord (Var (_, T), Var (_, U)) = typ_ord (T, U)
wenzelm@16678
   563
  | types_ord (Bound _, Bound _) = EQUAL
wenzelm@16678
   564
  | types_ord _ = sys_error "types_ord";
wenzelm@16678
   565
wenzelm@16678
   566
in
wenzelm@16678
   567
wenzelm@16678
   568
fun fast_term_ord tu =
wenzelm@16678
   569
  if pointer_eq tu then EQUAL
wenzelm@16678
   570
  else
wenzelm@16678
   571
    (case struct_ord tu of
wenzelm@16678
   572
      EQUAL => (case atoms_ord tu of EQUAL => types_ord tu | ord => ord)
wenzelm@16678
   573
    | ord => ord);
wenzelm@16678
   574
wenzelm@16678
   575
structure Vartab = TableFun(type key = indexname val ord = fast_indexname_ord);
wenzelm@16678
   576
structure Typtab = TableFun(type key = typ val ord = typ_ord);
wenzelm@16678
   577
structure Termtab = TableFun(type key = term val ord = fast_term_ord);
wenzelm@16678
   578
wenzelm@16678
   579
end;
wenzelm@16537
   580
wenzelm@16537
   581
wenzelm@16537
   582
(* term_ord *)
wenzelm@16537
   583
wenzelm@16537
   584
(*a linear well-founded AC-compatible ordering for terms:
wenzelm@16537
   585
  s < t <=> 1. size(s) < size(t) or
wenzelm@16537
   586
            2. size(s) = size(t) and s=f(...) and t=g(...) and f<g or
wenzelm@16537
   587
            3. size(s) = size(t) and s=f(s1..sn) and t=f(t1..tn) and
wenzelm@16537
   588
               (s1..sn) < (t1..tn) (lexicographically)*)
wenzelm@16678
   589
wenzelm@16678
   590
fun indexname_ord ((x, i), (y, j)) =
wenzelm@16678
   591
  (case int_ord (i, j) of EQUAL => string_ord (x, y) | ord => ord);
wenzelm@16678
   592
wenzelm@16667
   593
local
wenzelm@16667
   594
wenzelm@16667
   595
fun hd_depth (t $ _, n) = hd_depth (t, n + 1)
wenzelm@16667
   596
  | hd_depth p = p;
wenzelm@16537
   597
wenzelm@16537
   598
fun dest_hd (Const (a, T)) = (((a, 0), T), 0)
wenzelm@16537
   599
  | dest_hd (Free (a, T)) = (((a, 0), T), 1)
wenzelm@16537
   600
  | dest_hd (Var v) = (v, 2)
wenzelm@16537
   601
  | dest_hd (Bound i) = ((("", i), dummyT), 3)
wenzelm@16537
   602
  | dest_hd (Abs (_, T, _)) = ((("", 0), T), 4);
wenzelm@16537
   603
wenzelm@16667
   604
in
wenzelm@16667
   605
wenzelm@16537
   606
fun term_ord tu =
wenzelm@16537
   607
  if pointer_eq tu then EQUAL
wenzelm@16537
   608
  else
wenzelm@16537
   609
    (case tu of
wenzelm@16537
   610
      (Abs (_, T, t), Abs(_, U, u)) =>
wenzelm@16537
   611
        (case term_ord (t, u) of EQUAL => typ_ord (T, U) | ord => ord)
wenzelm@16667
   612
    | (t, u) =>
wenzelm@16537
   613
        (case int_ord (size_of_term t, size_of_term u) of
wenzelm@16537
   614
          EQUAL =>
wenzelm@16943
   615
            (case prod_ord hd_ord int_ord (hd_depth (t, 0), hd_depth (u, 0)) of
wenzelm@16943
   616
              EQUAL => args_ord (t, u) | ord => ord)
wenzelm@16537
   617
        | ord => ord))
wenzelm@16537
   618
and hd_ord (f, g) =
wenzelm@16537
   619
  prod_ord (prod_ord indexname_ord typ_ord) int_ord (dest_hd f, dest_hd g)
wenzelm@16667
   620
and args_ord (f $ t, g $ u) =
wenzelm@16667
   621
      (case args_ord (f, g) of EQUAL => term_ord (t, u) | ord => ord)
wenzelm@16667
   622
  | args_ord _ = EQUAL;
wenzelm@16537
   623
wenzelm@16537
   624
fun termless tu = (term_ord tu = LESS);
wenzelm@16537
   625
wenzelm@16667
   626
end;
wenzelm@16667
   627
wenzelm@16667
   628
wenzelm@16667
   629
(** Lexicographic path order on terms **)
wenzelm@16667
   630
wenzelm@16667
   631
(*
nipkow@16570
   632
  See Baader & Nipkow, Term rewriting, CUP 1998.
nipkow@16570
   633
  Without variables.  Const, Var, Bound, Free and Abs are treated all as
nipkow@16570
   634
  constants.
nipkow@16570
   635
ballarin@20129
   636
  f_ord maps terms to integers and serves two purposes:
nipkow@16570
   637
  - Predicate on constant symbols.  Those that are not recognised by f_ord
nipkow@16570
   638
    must be mapped to ~1.
nipkow@16570
   639
  - Order on the recognised symbols.  These must be mapped to distinct
nipkow@16570
   640
    integers >= 0.
ballarin@20129
   641
  The argument of f_ord is never an application.
wenzelm@16667
   642
*)
nipkow@16570
   643
nipkow@16570
   644
local
ballarin@20129
   645
ballarin@20129
   646
fun unrecognized (Const (a, T)) = ((1, ((a, 0), T)), 0)
ballarin@20129
   647
  | unrecognized (Free (a, T)) = ((1, ((a, 0), T)), 0)
ballarin@20129
   648
  | unrecognized (Var v) = ((1, v), 1)
ballarin@20129
   649
  | unrecognized (Bound i) = ((1, (("", i), dummyT)), 2)
ballarin@20129
   650
  | unrecognized (Abs (_, T, _)) = ((1, (("", 0), T)), 3);
ballarin@20129
   651
ballarin@20129
   652
fun dest_hd f_ord t =
ballarin@20129
   653
      let val ord = f_ord t in
ballarin@20129
   654
        if ord = ~1 then unrecognized t else ((0, (("", ord), fastype_of t)), 0)
nipkow@16570
   655
      end
nipkow@16570
   656
nipkow@16570
   657
fun term_lpo f_ord (s, t) =
nipkow@16570
   658
  let val (f, ss) = strip_comb s and (g, ts) = strip_comb t in
nipkow@16570
   659
    if forall (fn si => term_lpo f_ord (si, t) = LESS) ss
nipkow@16570
   660
    then case hd_ord f_ord (f, g) of
wenzelm@16667
   661
        GREATER =>
wenzelm@16667
   662
          if forall (fn ti => term_lpo f_ord (s, ti) = GREATER) ts
wenzelm@16667
   663
          then GREATER else LESS
nipkow@16570
   664
      | EQUAL =>
wenzelm@16667
   665
          if forall (fn ti => term_lpo f_ord (s, ti) = GREATER) ts
wenzelm@16667
   666
          then list_ord (term_lpo f_ord) (ss, ts)
wenzelm@16667
   667
          else LESS
nipkow@16570
   668
      | LESS => LESS
nipkow@16570
   669
    else GREATER
nipkow@16570
   670
  end
nipkow@16570
   671
and hd_ord f_ord (f, g) = case (f, g) of
nipkow@16570
   672
    (Abs (_, T, t), Abs (_, U, u)) =>
nipkow@16570
   673
      (case term_lpo f_ord (t, u) of EQUAL => typ_ord (T, U) | ord => ord)
nipkow@16570
   674
  | (_, _) => prod_ord (prod_ord int_ord
nipkow@16570
   675
                  (prod_ord indexname_ord typ_ord)) int_ord
nipkow@16570
   676
                (dest_hd f_ord f, dest_hd f_ord g)
nipkow@16570
   677
in
nipkow@16570
   678
val term_lpo = term_lpo
nipkow@16570
   679
end;
nipkow@16570
   680
wenzelm@16537
   681
clasohm@0
   682
(** Connectives of higher order logic **)
clasohm@0
   683
wenzelm@19394
   684
fun aT S = TFree ("'a", S);
wenzelm@19394
   685
wenzelm@375
   686
fun itselfT ty = Type ("itself", [ty]);
wenzelm@14854
   687
val a_itselfT = itselfT (TFree ("'a", []));
wenzelm@375
   688
clasohm@0
   689
val propT : typ = Type("prop",[]);
clasohm@0
   690
clasohm@0
   691
val implies = Const("==>", propT-->propT-->propT);
clasohm@0
   692
clasohm@0
   693
fun all T = Const("all", (T-->propT)-->propT);
clasohm@0
   694
clasohm@0
   695
fun equals T = Const("==", T-->T-->propT);
clasohm@0
   696
clasohm@0
   697
(* maps  !!x1...xn. t   to   t  *)
wenzelm@13000
   698
fun strip_all_body (Const("all",_)$Abs(_,_,t))  =  strip_all_body t
clasohm@0
   699
  | strip_all_body t  =  t;
clasohm@0
   700
clasohm@0
   701
(* maps  !!x1...xn. t   to   [x1, ..., xn]  *)
clasohm@0
   702
fun strip_all_vars (Const("all",_)$Abs(a,T,t))  =
wenzelm@13000
   703
                (a,T) :: strip_all_vars t
clasohm@0
   704
  | strip_all_vars t  =  [] : (string*typ) list;
clasohm@0
   705
clasohm@0
   706
(*increments a term's non-local bound variables
clasohm@0
   707
  required when moving a term within abstractions
clasohm@0
   708
     inc is  increment for bound variables
clasohm@0
   709
     lev is  level at which a bound variable is considered 'loose'*)
wenzelm@13000
   710
fun incr_bv (inc, lev, u as Bound i) = if i>=lev then Bound(i+inc) else u
clasohm@0
   711
  | incr_bv (inc, lev, Abs(a,T,body)) =
wenzelm@9536
   712
        Abs(a, T, incr_bv(inc,lev+1,body))
wenzelm@13000
   713
  | incr_bv (inc, lev, f$t) =
clasohm@0
   714
      incr_bv(inc,lev,f) $ incr_bv(inc,lev,t)
clasohm@0
   715
  | incr_bv (inc, lev, u) = u;
clasohm@0
   716
clasohm@0
   717
fun incr_boundvars  0  t = t
clasohm@0
   718
  | incr_boundvars inc t = incr_bv(inc,0,t);
clasohm@0
   719
wenzelm@12981
   720
(*Scan a pair of terms; while they are similar,
wenzelm@12981
   721
  accumulate corresponding bound vars in "al"*)
wenzelm@12981
   722
fun match_bvs(Abs(x,_,s),Abs(y,_,t), al) =
wenzelm@12981
   723
      match_bvs(s, t, if x="" orelse y="" then al
wenzelm@12981
   724
                                          else (x,y)::al)
wenzelm@12981
   725
  | match_bvs(f$s, g$t, al) = match_bvs(f,g,match_bvs(s,t,al))
wenzelm@12981
   726
  | match_bvs(_,_,al) = al;
wenzelm@12981
   727
wenzelm@12981
   728
(* strip abstractions created by parameters *)
wenzelm@12981
   729
fun match_bvars((s,t),al) = match_bvs(strip_abs_body s, strip_abs_body t, al);
wenzelm@12981
   730
wenzelm@12981
   731
fun rename_abs pat obj t =
wenzelm@12981
   732
  let
wenzelm@12981
   733
    val ren = match_bvs (pat, obj, []);
wenzelm@12981
   734
    fun ren_abs (Abs (x, T, b)) =
wenzelm@18942
   735
          Abs (the_default x (AList.lookup (op =) ren x), T, ren_abs b)
wenzelm@12981
   736
      | ren_abs (f $ t) = ren_abs f $ ren_abs t
wenzelm@12981
   737
      | ren_abs t = t
skalberg@15531
   738
  in if null ren then NONE else SOME (ren_abs t) end;
clasohm@0
   739
clasohm@0
   740
(*Accumulate all 'loose' bound vars referring to level 'lev' or beyond.
clasohm@0
   741
   (Bound 0) is loose at level 0 *)
wenzelm@13000
   742
fun add_loose_bnos (Bound i, lev, js) =
haftmann@20854
   743
        if i<lev then js else insert (op =) (i - lev) js
clasohm@0
   744
  | add_loose_bnos (Abs (_,_,t), lev, js) = add_loose_bnos (t, lev+1, js)
clasohm@0
   745
  | add_loose_bnos (f$t, lev, js) =
wenzelm@13000
   746
        add_loose_bnos (f, lev, add_loose_bnos (t, lev, js))
clasohm@0
   747
  | add_loose_bnos (_, _, js) = js;
clasohm@0
   748
clasohm@0
   749
fun loose_bnos t = add_loose_bnos (t, 0, []);
clasohm@0
   750
clasohm@0
   751
(* loose_bvar(t,k) iff t contains a 'loose' bound variable referring to
clasohm@0
   752
   level k or beyond. *)
clasohm@0
   753
fun loose_bvar(Bound i,k) = i >= k
clasohm@0
   754
  | loose_bvar(f$t, k) = loose_bvar(f,k) orelse loose_bvar(t,k)
clasohm@0
   755
  | loose_bvar(Abs(_,_,t),k) = loose_bvar(t,k+1)
clasohm@0
   756
  | loose_bvar _ = false;
clasohm@0
   757
nipkow@2792
   758
fun loose_bvar1(Bound i,k) = i = k
nipkow@2792
   759
  | loose_bvar1(f$t, k) = loose_bvar1(f,k) orelse loose_bvar1(t,k)
nipkow@2792
   760
  | loose_bvar1(Abs(_,_,t),k) = loose_bvar1(t,k+1)
nipkow@2792
   761
  | loose_bvar1 _ = false;
clasohm@0
   762
clasohm@0
   763
(*Substitute arguments for loose bound variables.
clasohm@0
   764
  Beta-reduction of arg(n-1)...arg0 into t replacing (Bound i) with (argi).
wenzelm@4626
   765
  Note that for ((%x y. c) a b), the bound vars in c are x=1 and y=0
wenzelm@9536
   766
        and the appropriate call is  subst_bounds([b,a], c) .
clasohm@0
   767
  Loose bound variables >=n are reduced by "n" to
clasohm@0
   768
     compensate for the disappearance of lambdas.
clasohm@0
   769
*)
wenzelm@13000
   770
fun subst_bounds (args: term list, t) : term =
wenzelm@19065
   771
  let
wenzelm@19065
   772
    exception SAME;
wenzelm@19065
   773
    val n = length args;
wenzelm@19065
   774
    fun subst (t as Bound i, lev) =
wenzelm@19065
   775
         (if i < lev then raise SAME   (*var is locally bound*)
wenzelm@19065
   776
          else incr_boundvars lev (List.nth (args, i - lev))
wenzelm@19065
   777
            handle Subscript => Bound (i - n))  (*loose: change it*)
wenzelm@19065
   778
      | subst (Abs (a, T, body), lev) = Abs (a, T, subst (body, lev + 1))
wenzelm@19065
   779
      | subst (f $ t, lev) =
wenzelm@19065
   780
          (subst (f, lev) $ (subst (t, lev) handle SAME => t) handle SAME => f $ subst (t, lev))
wenzelm@19065
   781
      | subst _ = raise SAME;
wenzelm@19065
   782
  in case args of [] => t | _ => (subst (t, 0) handle SAME => t) end;
clasohm@0
   783
paulson@2192
   784
(*Special case: one argument*)
wenzelm@13000
   785
fun subst_bound (arg, t) : term =
wenzelm@19065
   786
  let
wenzelm@19065
   787
    exception SAME;
wenzelm@19065
   788
    fun subst (Bound i, lev) =
wenzelm@19065
   789
          if i < lev then raise SAME   (*var is locally bound*)
wenzelm@19065
   790
          else if i = lev then incr_boundvars lev arg
wenzelm@19065
   791
          else Bound (i - 1)   (*loose: change it*)
wenzelm@19065
   792
      | subst (Abs (a, T, body), lev) = Abs (a, T, subst (body, lev + 1))
wenzelm@19065
   793
      | subst (f $ t, lev) =
wenzelm@19065
   794
          (subst (f, lev) $ (subst (t, lev) handle SAME => t) handle SAME => f $ subst (t, lev))
wenzelm@19065
   795
      | subst _ = raise SAME;
wenzelm@19065
   796
  in subst (t, 0) handle SAME => t end;
paulson@2192
   797
clasohm@0
   798
(*beta-reduce if possible, else form application*)
paulson@2192
   799
fun betapply (Abs(_,_,t), u) = subst_bound (u,t)
clasohm@0
   800
  | betapply (f,u) = f$u;
clasohm@0
   801
wenzelm@18183
   802
val betapplys = Library.foldl betapply;
wenzelm@18183
   803
wenzelm@14786
   804
haftmann@20109
   805
(*unfolding abstractions with substitution
haftmann@20109
   806
  of bound variables and implicit eta-expansion*)
haftmann@20109
   807
fun strip_abs_eta k t =
haftmann@20109
   808
  let
wenzelm@20122
   809
    val used = fold_aterms (fn Free (v, _) => Name.declare v | _ => I) t Name.context;
haftmann@20109
   810
    fun strip_abs t (0, used) = (([], t), (0, used))
haftmann@20109
   811
      | strip_abs (Abs (v, T, t)) (k, used) =
haftmann@20109
   812
          let
wenzelm@20122
   813
            val ([v'], used') = Name.variants [v] used;
haftmann@21013
   814
            val t' = subst_bound (Free (v', T), t);
wenzelm@20122
   815
            val ((vs, t''), (k', used'')) = strip_abs t' (k - 1, used');
wenzelm@20122
   816
          in (((v', T) :: vs, t''), (k', used'')) end
haftmann@20109
   817
      | strip_abs t (k, used) = (([], t), (k, used));
haftmann@20109
   818
    fun expand_eta [] t _ = ([], t)
haftmann@20109
   819
      | expand_eta (T::Ts) t used =
haftmann@20109
   820
          let
wenzelm@20122
   821
            val ([v], used') = Name.variants [""] used;
wenzelm@20122
   822
            val (vs, t') = expand_eta Ts (t $ Free (v, T)) used';
haftmann@20109
   823
          in ((v, T) :: vs, t') end;
haftmann@20109
   824
    val ((vs1, t'), (k', used')) = strip_abs t (k, used);
haftmann@20109
   825
    val Ts = (fst o chop k' o fst o strip_type o fastype_of) t';
haftmann@20109
   826
    val (vs2, t'') = expand_eta Ts t' used';
haftmann@20109
   827
  in (vs1 @ vs2, t'') end;
haftmann@20109
   828
haftmann@20109
   829
wenzelm@20199
   830
(* comparing variables *)
wenzelm@16882
   831
wenzelm@16724
   832
fun eq_ix ((x, i): indexname, (y, j)) = i = j andalso x = y;
paulson@2192
   833
wenzelm@16943
   834
fun eq_tvar ((xi, S: sort), (xi', S')) = eq_ix (xi, xi') andalso S = S';
wenzelm@16943
   835
fun eq_var ((xi, T: typ), (xi', T')) = eq_ix (xi, xi') andalso T = T';
wenzelm@16943
   836
wenzelm@16943
   837
val tvar_ord = prod_ord indexname_ord sort_ord;
wenzelm@16943
   838
val var_ord = prod_ord indexname_ord typ_ord;
wenzelm@16882
   839
wenzelm@16882
   840
wenzelm@13000
   841
(*A fast unification filter: true unless the two terms cannot be unified.
clasohm@0
   842
  Terms must be NORMAL.  Treats all Vars as distinct. *)
clasohm@0
   843
fun could_unify (t,u) =
clasohm@0
   844
  let fun matchrands (f$t, g$u) = could_unify(t,u) andalso  matchrands(f,g)
wenzelm@9536
   845
        | matchrands _ = true
clasohm@0
   846
  in case (head_of t , head_of u) of
wenzelm@9536
   847
        (_, Var _) => true
clasohm@0
   848
      | (Var _, _) => true
clasohm@0
   849
      | (Const(a,_), Const(b,_)) =>  a=b andalso matchrands(t,u)
clasohm@0
   850
      | (Free(a,_), Free(b,_)) =>  a=b andalso matchrands(t,u)
clasohm@0
   851
      | (Bound i, Bound j) =>  i=j andalso matchrands(t,u)
clasohm@0
   852
      | (Abs _, _) =>  true   (*because of possible eta equality*)
clasohm@0
   853
      | (_, Abs _) =>  true
clasohm@0
   854
      | _ => false
clasohm@0
   855
  end;
clasohm@0
   856
clasohm@0
   857
(*Substitute new for free occurrences of old in a term*)
clasohm@0
   858
fun subst_free [] = (fn t=>t)
clasohm@0
   859
  | subst_free pairs =
wenzelm@13000
   860
      let fun substf u =
haftmann@17314
   861
            case AList.lookup (op aconv) pairs u of
skalberg@15531
   862
                SOME u' => u'
skalberg@15531
   863
              | NONE => (case u of Abs(a,T,t) => Abs(a, T, substf t)
wenzelm@9536
   864
                                 | t$u' => substf t $ substf u'
wenzelm@9536
   865
                                 | _ => u)
clasohm@0
   866
      in  substf  end;
clasohm@0
   867
wenzelm@13000
   868
(*Abstraction of the term "body" over its occurrences of v,
clasohm@0
   869
    which must contain no loose bound variables.
clasohm@0
   870
  The resulting term is ready to become the body of an Abs.*)
wenzelm@16882
   871
fun abstract_over (v, body) =
wenzelm@16882
   872
  let
wenzelm@16990
   873
    exception SAME;
wenzelm@16990
   874
    fun abs lev tm =
wenzelm@16990
   875
      if v aconv tm then Bound lev
wenzelm@16882
   876
      else
wenzelm@16990
   877
        (case tm of
wenzelm@16990
   878
          Abs (a, T, t) => Abs (a, T, abs (lev + 1) t)
wenzelm@16990
   879
        | t $ u => (abs lev t $ (abs lev u handle SAME => u) handle SAME => t $ abs lev u)
wenzelm@16990
   880
        | _ => raise SAME);
wenzelm@16990
   881
  in abs 0 body handle SAME => body end;
clasohm@0
   882
wenzelm@18975
   883
fun lambda (v as Const (x, T)) t = Abs (NameSpace.base x, T, abstract_over (v, t))
wenzelm@18942
   884
  | lambda (v as Free (x, T)) t = Abs (x, T, abstract_over (v, t))
berghofe@13665
   885
  | lambda (v as Var ((x, _), T)) t = Abs (x, T, abstract_over (v, t))
berghofe@13665
   886
  | lambda v t = raise TERM ("lambda", [v, t]);
clasohm@0
   887
clasohm@0
   888
(*Form an abstraction over a free variable.*)
clasohm@0
   889
fun absfree (a,T,body) = Abs(a, T, abstract_over (Free(a,T), body));
wenzelm@17786
   890
fun absdummy (T, body) = Abs ("uu", T, body);
clasohm@0
   891
clasohm@0
   892
(*Abstraction over a list of free variables*)
clasohm@0
   893
fun list_abs_free ([ ] ,     t) = t
wenzelm@13000
   894
  | list_abs_free ((a,T)::vars, t) =
clasohm@0
   895
      absfree(a, T, list_abs_free(vars,t));
clasohm@0
   896
clasohm@0
   897
(*Quantification over a list of free variables*)
clasohm@0
   898
fun list_all_free ([], t: term) = t
wenzelm@13000
   899
  | list_all_free ((a,T)::vars, t) =
clasohm@0
   900
        (all T) $ (absfree(a, T, list_all_free(vars,t)));
clasohm@0
   901
clasohm@0
   902
(*Quantification over a list of variables (already bound in body) *)
clasohm@0
   903
fun list_all ([], t) = t
wenzelm@13000
   904
  | list_all ((a,T)::vars, t) =
clasohm@0
   905
        (all T) $ (Abs(a, T, list_all(vars,t)));
clasohm@0
   906
wenzelm@16678
   907
(*Replace the ATOMIC term ti by ui;    inst = [(t1,u1), ..., (tn,un)].
clasohm@0
   908
  A simultaneous substitution:  [ (a,b), (b,a) ] swaps a and b.  *)
wenzelm@16678
   909
fun subst_atomic [] tm = tm
wenzelm@16678
   910
  | subst_atomic inst tm =
wenzelm@16678
   911
      let
wenzelm@16678
   912
        fun subst (Abs (a, T, body)) = Abs (a, T, subst body)
wenzelm@16678
   913
          | subst (t $ u) = subst t $ subst u
wenzelm@18942
   914
          | subst t = the_default t (AList.lookup (op aconv) inst t);
wenzelm@16678
   915
      in subst tm end;
clasohm@0
   916
wenzelm@16678
   917
(*Replace the ATOMIC type Ti by Ui;    inst = [(T1,U1), ..., (Tn,Un)].*)
wenzelm@16678
   918
fun typ_subst_atomic [] ty = ty
wenzelm@16678
   919
  | typ_subst_atomic inst ty =
wenzelm@16678
   920
      let
wenzelm@16678
   921
        fun subst (Type (a, Ts)) = Type (a, map subst Ts)
wenzelm@18942
   922
          | subst T = the_default T (AList.lookup (op = : typ * typ -> bool) inst T);
wenzelm@16678
   923
      in subst ty end;
berghofe@15797
   924
wenzelm@16678
   925
fun subst_atomic_types [] tm = tm
wenzelm@20548
   926
  | subst_atomic_types inst tm = map_types (typ_subst_atomic inst) tm;
wenzelm@16678
   927
wenzelm@16678
   928
fun typ_subst_TVars [] ty = ty
wenzelm@16678
   929
  | typ_subst_TVars inst ty =
wenzelm@16678
   930
      let
wenzelm@16678
   931
        fun subst (Type (a, Ts)) = Type (a, map subst Ts)
wenzelm@18942
   932
          | subst (T as TVar (xi, _)) = the_default T (AList.lookup (op =) inst xi)
wenzelm@16678
   933
          | subst T = T;
wenzelm@16678
   934
      in subst ty end;
clasohm@0
   935
wenzelm@16678
   936
fun subst_TVars [] tm = tm
wenzelm@20548
   937
  | subst_TVars inst tm = map_types (typ_subst_TVars inst) tm;
clasohm@0
   938
wenzelm@16678
   939
fun subst_Vars [] tm = tm
wenzelm@16678
   940
  | subst_Vars inst tm =
wenzelm@16678
   941
      let
wenzelm@18942
   942
        fun subst (t as Var (xi, _)) = the_default t (AList.lookup (op =) inst xi)
wenzelm@16678
   943
          | subst (Abs (a, T, t)) = Abs (a, T, subst t)
wenzelm@16678
   944
          | subst (t $ u) = subst t $ subst u
wenzelm@16678
   945
          | subst t = t;
wenzelm@16678
   946
      in subst tm end;
clasohm@0
   947
wenzelm@16678
   948
fun subst_vars ([], []) tm = tm
wenzelm@16678
   949
  | subst_vars ([], inst) tm = subst_Vars inst tm
wenzelm@16678
   950
  | subst_vars (instT, inst) tm =
wenzelm@16678
   951
      let
wenzelm@16678
   952
        fun subst (Const (a, T)) = Const (a, typ_subst_TVars instT T)
wenzelm@16678
   953
          | subst (Free (a, T)) = Free (a, typ_subst_TVars instT T)
wenzelm@16678
   954
          | subst (t as Var (xi, T)) =
haftmann@17271
   955
              (case AList.lookup (op =) inst xi of
wenzelm@16678
   956
                NONE => Var (xi, typ_subst_TVars instT T)
wenzelm@16678
   957
              | SOME t => t)
wenzelm@16678
   958
          | subst (t as Bound _) = t
wenzelm@16678
   959
          | subst (Abs (a, T, t)) = Abs (a, typ_subst_TVars instT T, subst t)
wenzelm@16678
   960
          | subst (t $ u) = subst t $ subst u;
wenzelm@16678
   961
      in subst tm end;
clasohm@0
   962
clasohm@0
   963
paulson@15573
   964
(** Identifying first-order terms **)
paulson@15573
   965
wenzelm@20199
   966
(*Differs from proofterm/is_fun in its treatment of TVar*)
wenzelm@20199
   967
fun is_funtype (Type("fun",[_,_])) = true
wenzelm@20199
   968
  | is_funtype _ = false;
wenzelm@20199
   969
paulson@15573
   970
(*Argument Ts is a reverse list of binder types, needed if term t contains Bound vars*)
paulson@15573
   971
fun has_not_funtype Ts t = not (is_funtype (fastype_of1 (Ts,t)));
paulson@15573
   972
wenzelm@16537
   973
(*First order means in all terms of the form f(t1,...,tn) no argument has a
paulson@16589
   974
  function type. The supplied quantifiers are excluded: their argument always
paulson@16589
   975
  has a function type through a recursive call into its body.*)
wenzelm@16667
   976
fun is_first_order quants =
paulson@16589
   977
  let fun first_order1 Ts (Abs (_,T,body)) = first_order1 (T::Ts) body
wenzelm@16667
   978
        | first_order1 Ts (Const(q,_) $ Abs(a,T,body)) =
wenzelm@20664
   979
            member (op =) quants q  andalso   (*it is a known quantifier*)
paulson@16589
   980
            not (is_funtype T)   andalso first_order1 (T::Ts) body
wenzelm@16667
   981
        | first_order1 Ts t =
wenzelm@16667
   982
            case strip_comb t of
wenzelm@16667
   983
                 (Var _, ts) => forall (first_order1 Ts andf has_not_funtype Ts) ts
wenzelm@16667
   984
               | (Free _, ts) => forall (first_order1 Ts andf has_not_funtype Ts) ts
wenzelm@16667
   985
               | (Const _, ts) => forall (first_order1 Ts andf has_not_funtype Ts) ts
wenzelm@16667
   986
               | (Bound _, ts) => forall (first_order1 Ts andf has_not_funtype Ts) ts
wenzelm@16667
   987
               | (Abs _, ts) => false (*not in beta-normal form*)
wenzelm@16667
   988
               | _ => error "first_order: unexpected case"
paulson@16589
   989
    in  first_order1 []  end;
paulson@15573
   990
wenzelm@16710
   991
wenzelm@16990
   992
(* maximum index of typs and terms *)
clasohm@0
   993
wenzelm@16710
   994
fun maxidx_typ (TVar ((_, j), _)) i = Int.max (i, j)
wenzelm@16710
   995
  | maxidx_typ (Type (_, Ts)) i = maxidx_typs Ts i
wenzelm@16710
   996
  | maxidx_typ (TFree _) i = i
wenzelm@16710
   997
and maxidx_typs [] i = i
wenzelm@16710
   998
  | maxidx_typs (T :: Ts) i = maxidx_typs Ts (maxidx_typ T i);
clasohm@0
   999
wenzelm@16710
  1000
fun maxidx_term (Var ((_, j), T)) i = maxidx_typ T (Int.max (i, j))
wenzelm@16710
  1001
  | maxidx_term (Const (_, T)) i = maxidx_typ T i
wenzelm@16710
  1002
  | maxidx_term (Free (_, T)) i = maxidx_typ T i
wenzelm@16710
  1003
  | maxidx_term (Bound _) i = i
wenzelm@16710
  1004
  | maxidx_term (Abs (_, T, t)) i = maxidx_term t (maxidx_typ T i)
wenzelm@16710
  1005
  | maxidx_term (t $ u) i = maxidx_term u (maxidx_term t i);
clasohm@0
  1006
wenzelm@16710
  1007
fun maxidx_of_typ T = maxidx_typ T ~1;
wenzelm@16710
  1008
fun maxidx_of_typs Ts = maxidx_typs Ts ~1;
wenzelm@16710
  1009
fun maxidx_of_term t = maxidx_term t ~1;
berghofe@13665
  1010
clasohm@0
  1011
clasohm@0
  1012
clasohm@0
  1013
(**** Syntax-related declarations ****)
clasohm@0
  1014
wenzelm@19909
  1015
(* substructure *)
wenzelm@4017
  1016
wenzelm@19909
  1017
fun exists_subtype P =
wenzelm@19909
  1018
  let
wenzelm@19909
  1019
    fun ex ty = P ty orelse
wenzelm@19909
  1020
      (case ty of Type (_, Ts) => exists ex Ts | _ => false);
wenzelm@19909
  1021
  in ex end;
nipkow@13646
  1022
wenzelm@20531
  1023
fun exists_type P =
wenzelm@20531
  1024
  let
wenzelm@20531
  1025
    fun ex (Const (_, T)) = P T
wenzelm@20531
  1026
      | ex (Free (_, T)) = P T
wenzelm@20531
  1027
      | ex (Var (_, T)) = P T
wenzelm@20531
  1028
      | ex (Bound _) = false
wenzelm@20531
  1029
      | ex (Abs (_, T, t)) = P T orelse ex t
wenzelm@20531
  1030
      | ex (t $ u) = ex t orelse ex u;
wenzelm@20531
  1031
  in ex end;
wenzelm@20531
  1032
wenzelm@16943
  1033
fun exists_subterm P =
wenzelm@16943
  1034
  let
wenzelm@16943
  1035
    fun ex tm = P tm orelse
wenzelm@16943
  1036
      (case tm of
wenzelm@16943
  1037
        t $ u => ex t orelse ex u
wenzelm@16943
  1038
      | Abs (_, _, t) => ex t
wenzelm@16943
  1039
      | _ => false);
wenzelm@16943
  1040
  in ex end;
obua@16108
  1041
wenzelm@19909
  1042
wenzelm@19909
  1043
(** Consts etc. **)
wenzelm@19909
  1044
wenzelm@19909
  1045
fun add_term_consts (Const (c, _), cs) = insert (op =) c cs
wenzelm@19909
  1046
  | add_term_consts (t $ u, cs) = add_term_consts (t, add_term_consts (u, cs))
wenzelm@19909
  1047
  | add_term_consts (Abs (_, _, t), cs) = add_term_consts (t, cs)
wenzelm@19909
  1048
  | add_term_consts (_, cs) = cs;
wenzelm@19909
  1049
wenzelm@19909
  1050
fun term_consts t = add_term_consts(t,[]);
wenzelm@19909
  1051
wenzelm@16943
  1052
fun exists_Const P = exists_subterm (fn Const c => P c | _ => false);
nipkow@4631
  1053
wenzelm@4017
  1054
clasohm@0
  1055
(** TFrees and TVars **)
clasohm@0
  1056
wenzelm@12802
  1057
(*Accumulates the names of Frees in the term, suppressing duplicates.*)
haftmann@20854
  1058
fun add_term_free_names (Free(a,_), bs) = insert (op =) a bs
wenzelm@12802
  1059
  | add_term_free_names (f$u, bs) = add_term_free_names (f, add_term_free_names(u, bs))
wenzelm@12802
  1060
  | add_term_free_names (Abs(_,_,t), bs) = add_term_free_names(t,bs)
wenzelm@12802
  1061
  | add_term_free_names (_, bs) = bs;
wenzelm@12802
  1062
clasohm@0
  1063
(*Accumulates the names in the term, suppressing duplicates.
clasohm@0
  1064
  Includes Frees and Consts.  For choosing unambiguous bound var names.*)
haftmann@20854
  1065
fun add_term_names (Const(a,_), bs) = insert (op =) (NameSpace.base a) bs
haftmann@20854
  1066
  | add_term_names (Free(a,_), bs) = insert (op =) a bs
clasohm@0
  1067
  | add_term_names (f$u, bs) = add_term_names (f, add_term_names(u, bs))
clasohm@0
  1068
  | add_term_names (Abs(_,_,t), bs) = add_term_names(t,bs)
clasohm@0
  1069
  | add_term_names (_, bs) = bs;
clasohm@0
  1070
clasohm@0
  1071
(*Accumulates the TVars in a type, suppressing duplicates. *)
skalberg@15574
  1072
fun add_typ_tvars(Type(_,Ts),vs) = foldr add_typ_tvars vs Ts
clasohm@0
  1073
  | add_typ_tvars(TFree(_),vs) = vs
wenzelm@16294
  1074
  | add_typ_tvars(TVar(v),vs) = insert (op =) v vs;
clasohm@0
  1075
clasohm@0
  1076
(*Accumulates the TFrees in a type, suppressing duplicates. *)
skalberg@15574
  1077
fun add_typ_tfree_names(Type(_,Ts),fs) = foldr add_typ_tfree_names fs Ts
haftmann@20854
  1078
  | add_typ_tfree_names(TFree(f,_),fs) = insert (op =) f fs
clasohm@0
  1079
  | add_typ_tfree_names(TVar(_),fs) = fs;
clasohm@0
  1080
skalberg@15574
  1081
fun add_typ_tfrees(Type(_,Ts),fs) = foldr add_typ_tfrees fs Ts
wenzelm@16294
  1082
  | add_typ_tfrees(TFree(f),fs) = insert (op =) f fs
clasohm@0
  1083
  | add_typ_tfrees(TVar(_),fs) = fs;
clasohm@0
  1084
skalberg@15574
  1085
fun add_typ_varnames(Type(_,Ts),nms) = foldr add_typ_varnames nms Ts
haftmann@20854
  1086
  | add_typ_varnames(TFree(nm,_),nms) = insert (op =) nm nms
haftmann@20854
  1087
  | add_typ_varnames(TVar((nm,_),_),nms) = insert (op =) nm nms;
nipkow@949
  1088
clasohm@0
  1089
(*Accumulates the TVars in a term, suppressing duplicates. *)
clasohm@0
  1090
val add_term_tvars = it_term_types add_typ_tvars;
clasohm@0
  1091
clasohm@0
  1092
(*Accumulates the TFrees in a term, suppressing duplicates. *)
clasohm@0
  1093
val add_term_tfrees = it_term_types add_typ_tfrees;
clasohm@0
  1094
val add_term_tfree_names = it_term_types add_typ_tfree_names;
clasohm@0
  1095
clasohm@0
  1096
(*Non-list versions*)
clasohm@0
  1097
fun typ_tfrees T = add_typ_tfrees(T,[]);
clasohm@0
  1098
fun typ_tvars T = add_typ_tvars(T,[]);
clasohm@0
  1099
fun term_tfrees t = add_term_tfrees(t,[]);
clasohm@0
  1100
fun term_tvars t = add_term_tvars(t,[]);
clasohm@0
  1101
nipkow@949
  1102
(*special code to enforce left-to-right collection of TVar-indexnames*)
nipkow@949
  1103
skalberg@15570
  1104
fun add_typ_ixns(ixns,Type(_,Ts)) = Library.foldl add_typ_ixns (ixns,Ts)
wenzelm@20082
  1105
  | add_typ_ixns(ixns,TVar(ixn,_)) = if member (op =) ixns ixn then ixns
wenzelm@9536
  1106
                                     else ixns@[ixn]
nipkow@949
  1107
  | add_typ_ixns(ixns,TFree(_)) = ixns;
nipkow@949
  1108
nipkow@949
  1109
fun add_term_tvar_ixns(Const(_,T),ixns) = add_typ_ixns(ixns,T)
nipkow@949
  1110
  | add_term_tvar_ixns(Free(_,T),ixns) = add_typ_ixns(ixns,T)
nipkow@949
  1111
  | add_term_tvar_ixns(Var(_,T),ixns) = add_typ_ixns(ixns,T)
nipkow@949
  1112
  | add_term_tvar_ixns(Bound _,ixns) = ixns
nipkow@949
  1113
  | add_term_tvar_ixns(Abs(_,T,t),ixns) =
nipkow@949
  1114
      add_term_tvar_ixns(t,add_typ_ixns(ixns,T))
nipkow@949
  1115
  | add_term_tvar_ixns(f$t,ixns) =
nipkow@949
  1116
      add_term_tvar_ixns(t,add_term_tvar_ixns(f,ixns));
nipkow@949
  1117
wenzelm@16537
  1118
clasohm@0
  1119
(** Frees and Vars **)
clasohm@0
  1120
clasohm@0
  1121
(*Accumulates the Vars in the term, suppressing duplicates*)
clasohm@0
  1122
fun add_term_vars (t, vars: term list) = case t of
wenzelm@16990
  1123
    Var   _ => OrdList.insert term_ord t vars
clasohm@0
  1124
  | Abs (_,_,body) => add_term_vars(body,vars)
clasohm@0
  1125
  | f$t =>  add_term_vars (f, add_term_vars(t, vars))
clasohm@0
  1126
  | _ => vars;
clasohm@0
  1127
clasohm@0
  1128
fun term_vars t = add_term_vars(t,[]);
clasohm@0
  1129
clasohm@0
  1130
(*Accumulates the Frees in the term, suppressing duplicates*)
clasohm@0
  1131
fun add_term_frees (t, frees: term list) = case t of
wenzelm@16990
  1132
    Free   _ => OrdList.insert term_ord t frees
clasohm@0
  1133
  | Abs (_,_,body) => add_term_frees(body,frees)
clasohm@0
  1134
  | f$t =>  add_term_frees (f, add_term_frees(t, frees))
clasohm@0
  1135
  | _ => frees;
clasohm@0
  1136
clasohm@0
  1137
fun term_frees t = add_term_frees(t,[]);
clasohm@0
  1138
wenzelm@20199
  1139
wenzelm@20199
  1140
(* dest abstraction *)
clasohm@0
  1141
wenzelm@16678
  1142
fun dest_abs (x, T, body) =
wenzelm@16678
  1143
  let
wenzelm@16678
  1144
    fun name_clash (Free (y, _)) = (x = y)
wenzelm@16678
  1145
      | name_clash (t $ u) = name_clash t orelse name_clash u
wenzelm@16678
  1146
      | name_clash (Abs (_, _, t)) = name_clash t
wenzelm@16678
  1147
      | name_clash _ = false;
wenzelm@16678
  1148
  in
wenzelm@16678
  1149
    if name_clash body then
wenzelm@20082
  1150
      dest_abs (Name.variant [x] x, T, body)    (*potentially slow, but rarely happens*)
wenzelm@16678
  1151
    else (x, subst_bound (Free (x, T), body))
wenzelm@16678
  1152
  end;
wenzelm@16678
  1153
wenzelm@20160
  1154
wenzelm@20160
  1155
(* renaming variables *)
clasohm@0
  1156
wenzelm@20239
  1157
fun declare_term_names tm =
wenzelm@20239
  1158
  fold_aterms
wenzelm@20239
  1159
    (fn Const (a, _) => Name.declare (NameSpace.base a)
wenzelm@20239
  1160
      | Free (a, _) => Name.declare a
wenzelm@20239
  1161
      | _ => I) tm #>
wenzelm@20239
  1162
  fold_types (fold_atyps (fn TFree (a, _) => Name.declare a | _ => I)) tm;
wenzelm@20239
  1163
wenzelm@20160
  1164
fun variant_frees t frees =
wenzelm@20160
  1165
  fst (Name.variants (map fst frees) (declare_term_names t Name.context)) ~~ map snd frees;
wenzelm@20160
  1166
wenzelm@20160
  1167
fun rename_wrt_term t frees = rev (variant_frees t frees);  (*reversed result!*)
clasohm@1364
  1168
paulson@1417
  1169
wenzelm@9536
  1170
(* dummy patterns *)
wenzelm@9536
  1171
wenzelm@9536
  1172
val dummy_patternN = "dummy_pattern";
wenzelm@9536
  1173
wenzelm@18253
  1174
fun dummy_pattern T = Const (dummy_patternN, T);
wenzelm@18253
  1175
wenzelm@9536
  1176
fun is_dummy_pattern (Const ("dummy_pattern", _)) = true
wenzelm@9536
  1177
  | is_dummy_pattern _ = false;
wenzelm@9536
  1178
wenzelm@9536
  1179
fun no_dummy_patterns tm =
haftmann@16787
  1180
  if not (fold_aterms (fn t => fn b => b orelse is_dummy_pattern t) tm false) then tm
wenzelm@9536
  1181
  else raise TERM ("Illegal occurrence of '_' dummy pattern", [tm]);
wenzelm@9536
  1182
wenzelm@11903
  1183
fun replace_dummy Ts (i, Const ("dummy_pattern", T)) =
wenzelm@11903
  1184
      (i + 1, list_comb (Var (("_dummy_", i), Ts ---> T), map Bound (0 upto length Ts - 1)))
wenzelm@11903
  1185
  | replace_dummy Ts (i, Abs (x, T, t)) =
wenzelm@11903
  1186
      let val (i', t') = replace_dummy (T :: Ts) (i, t)
wenzelm@11903
  1187
      in (i', Abs (x, T, t')) end
wenzelm@11903
  1188
  | replace_dummy Ts (i, t $ u) =
wenzelm@11903
  1189
      let val (i', t') = replace_dummy Ts (i, t); val (i'', u') = replace_dummy Ts (i', u)
wenzelm@11903
  1190
      in (i'', t' $ u') end
wenzelm@11903
  1191
  | replace_dummy _ (i, a) = (i, a);
wenzelm@11903
  1192
wenzelm@11903
  1193
val replace_dummy_patterns = replace_dummy [];
wenzelm@9536
  1194
wenzelm@10552
  1195
fun is_replaced_dummy_pattern ("_dummy_", _) = true
wenzelm@10552
  1196
  | is_replaced_dummy_pattern _ = false;
wenzelm@9536
  1197
wenzelm@16035
  1198
fun show_dummy_patterns (Var (("_dummy_", _), T)) = Const ("dummy_pattern", T)
wenzelm@16035
  1199
  | show_dummy_patterns (t $ u) = show_dummy_patterns t $ show_dummy_patterns u
wenzelm@16035
  1200
  | show_dummy_patterns (Abs (x, T, t)) = Abs (x, T, show_dummy_patterns t)
wenzelm@16035
  1201
  | show_dummy_patterns a = a;
wenzelm@16035
  1202
wenzelm@13484
  1203
wenzelm@20100
  1204
(* display variables *)
wenzelm@20100
  1205
wenzelm@15986
  1206
val show_question_marks = ref true;
berghofe@15472
  1207
wenzelm@14786
  1208
fun string_of_vname (x, i) =
wenzelm@14786
  1209
  let
wenzelm@15986
  1210
    val question_mark = if ! show_question_marks then "?" else "";
wenzelm@15986
  1211
    val idx = string_of_int i;
wenzelm@15986
  1212
    val dot =
wenzelm@15986
  1213
      (case rev (Symbol.explode x) of
wenzelm@15986
  1214
        _ :: "\\<^isub>" :: _ => false
wenzelm@15986
  1215
      | _ :: "\\<^isup>" :: _ => false
wenzelm@15986
  1216
      | c :: _ => Symbol.is_digit c
wenzelm@15986
  1217
      | _ => true);
wenzelm@14786
  1218
  in
wenzelm@15986
  1219
    if dot then question_mark ^ x ^ "." ^ idx
wenzelm@15986
  1220
    else if i <> 0 then question_mark ^ x ^ idx
wenzelm@15986
  1221
    else question_mark ^ x
wenzelm@14786
  1222
  end;
wenzelm@14786
  1223
wenzelm@14786
  1224
fun string_of_vname' (x, ~1) = x
wenzelm@14786
  1225
  | string_of_vname' xi = string_of_vname xi;
wenzelm@14786
  1226
clasohm@1364
  1227
end;
clasohm@1364
  1228
wenzelm@4444
  1229
structure BasicTerm: BASIC_TERM = Term;
wenzelm@4444
  1230
open BasicTerm;