src/Pure/term.ML
author wenzelm
Wed Apr 26 22:38:05 2006 +0200 (2006-04-26)
changeset 19473 d87a8838afa4
parent 19455 d828bfab05af
child 19647 043921b0e587
permissions -rw-r--r--
tuned;
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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 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 is_funtype: 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_term_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 add_term_varnames: term -> indexname list -> indexname list
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  val term_varnames: term -> indexname list
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  val find_free: term -> string -> term option
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  val aconv: term * term -> bool
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  val aconvs: term list * term list -> 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 ins_ix: indexname * indexname list -> indexname list
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  val mem_ix: indexname * indexname list -> bool
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  val mem_term: term * term list -> bool
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  val ins_term: term * term list -> term list
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  val could_unify: term * term -> bool
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  val subst_free: (term * term) list -> term -> term
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  val xless: (string * int) * indexname -> bool
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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 variant: string list -> string -> string
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  val variantlist: string list * string list -> string list
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    (*note reversed order of args wrt. variant!*)
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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_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 add_term_tvarnames: 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 variant_abs: string * typ * term -> string * term
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  val rename_wrt_term: term -> (string * typ) list -> (string * typ) list
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  val 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 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 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: (string -> 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 instantiate: ((indexname * sort) * typ) list * ((indexname * typ) * term) list
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    -> term -> term
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  val instantiateT: ((indexname * sort) * typ) list -> typ -> typ
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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 variant_name: (string -> bool) -> string -> string
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  val invent_names: string list -> string -> int -> string list
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  val dest_abs: string * typ * term -> string * term
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  val bound: int -> string
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  val is_bound: string -> bool
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  val zero_var_indexesT: typ -> typ
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  val zero_var_indexes: term -> term
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  val zero_var_indexes_inst: term ->
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    ((indexname * sort) * typ) list * ((indexname * typ) * term) 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 adhoc_freeze_vars: term -> term * string list
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  val string_of_vname: indexname -> string
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  val string_of_vname': indexname -> string
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  val str_of_sort: sort -> string
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  val str_of_typ: typ -> string
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  val str_of_term: term -> 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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(*dummy type for parsing and printing etc.*)
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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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(*Differs from proofterm/is_fun in its treatment of TVar*)
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fun is_funtype (Type("fun",[_,_])) = true
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  | is_funtype _ = false;
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(** Destructors **)
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fun dest_Const (Const x) =  x
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  | dest_Const t = raise TERM("dest_Const", [t]);
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fun dest_Free (Free x) =  x
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  | dest_Free t = raise TERM("dest_Free", [t]);
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fun dest_Var (Var x) =  x
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  | dest_Var t = raise TERM("dest_Var", [t]);
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clasohm@0
   327
paulson@4464
   328
fun domain_type (Type("fun", [T,_])) = T
paulson@4464
   329
and range_type  (Type("fun", [_,T])) = T;
paulson@4064
   330
clasohm@0
   331
(* maps  [T1,...,Tn]--->T  to the list  [T1,T2,...,Tn]*)
clasohm@0
   332
fun binder_types (Type("fun",[S,T])) = S :: binder_types T
clasohm@0
   333
  | binder_types _   =  [];
clasohm@0
   334
clasohm@0
   335
(* maps  [T1,...,Tn]--->T  to T*)
clasohm@0
   336
fun body_type (Type("fun",[S,T])) = body_type T
clasohm@0
   337
  | body_type T   =  T;
clasohm@0
   338
clasohm@0
   339
(* maps  [T1,...,Tn]--->T  to   ([T1,T2,...,Tn], T)  *)
clasohm@0
   340
fun strip_type T : typ list * typ =
clasohm@0
   341
  (binder_types T, body_type T);
clasohm@0
   342
clasohm@0
   343
clasohm@0
   344
(*Compute the type of the term, checking that combinations are well-typed
clasohm@0
   345
  Ts = [T0,T1,...] holds types of bound variables 0, 1, ...*)
clasohm@0
   346
fun type_of1 (Ts, Const (_,T)) = T
clasohm@0
   347
  | type_of1 (Ts, Free  (_,T)) = T
skalberg@15570
   348
  | type_of1 (Ts, Bound i) = (List.nth (Ts,i)
skalberg@15570
   349
        handle Subscript => raise TYPE("type_of: bound variable", [], [Bound i]))
clasohm@0
   350
  | type_of1 (Ts, Var (_,T)) = T
clasohm@0
   351
  | type_of1 (Ts, Abs (_,T,body)) = T --> type_of1(T::Ts, body)
wenzelm@13000
   352
  | type_of1 (Ts, f$u) =
clasohm@0
   353
      let val U = type_of1(Ts,u)
clasohm@0
   354
          and T = type_of1(Ts,f)
clasohm@0
   355
      in case T of
wenzelm@9536
   356
            Type("fun",[T1,T2]) =>
wenzelm@9536
   357
              if T1=U then T2  else raise TYPE
wenzelm@9536
   358
                    ("type_of: type mismatch in application", [T1,U], [f$u])
wenzelm@13000
   359
          | _ => raise TYPE
wenzelm@9536
   360
                    ("type_of: function type is expected in application",
wenzelm@9536
   361
                     [T,U], [f$u])
clasohm@0
   362
      end;
clasohm@0
   363
clasohm@0
   364
fun type_of t : typ = type_of1 ([],t);
clasohm@0
   365
clasohm@0
   366
(*Determines the type of a term, with minimal checking*)
wenzelm@13000
   367
fun fastype_of1 (Ts, f$u) =
lcp@61
   368
    (case fastype_of1 (Ts,f) of
wenzelm@9536
   369
        Type("fun",[_,T]) => T
wenzelm@9536
   370
        | _ => raise TERM("fastype_of: expected function type", [f$u]))
lcp@61
   371
  | fastype_of1 (_, Const (_,T)) = T
lcp@61
   372
  | fastype_of1 (_, Free (_,T)) = T
skalberg@15570
   373
  | fastype_of1 (Ts, Bound i) = (List.nth(Ts,i)
skalberg@15570
   374
         handle Subscript => raise TERM("fastype_of: Bound", [Bound i]))
wenzelm@13000
   375
  | fastype_of1 (_, Var (_,T)) = T
lcp@61
   376
  | fastype_of1 (Ts, Abs (_,T,u)) = T --> fastype_of1 (T::Ts, u);
lcp@61
   377
lcp@61
   378
fun fastype_of t : typ = fastype_of1 ([],t);
clasohm@0
   379
wenzelm@16678
   380
(*Determine the argument type of a function*)
wenzelm@16678
   381
fun argument_type_of tm =
wenzelm@16678
   382
  let
wenzelm@16678
   383
    fun argT i (Type ("fun", [T, U])) = if i = 0 then T else argT (i - 1) U
wenzelm@16678
   384
      | argT _ T = raise TYPE ("argument_type_of", [T], []);
wenzelm@16678
   385
wenzelm@16678
   386
    fun arg 0 _ (Abs (_, T, _)) = T
wenzelm@16678
   387
      | arg i Ts (Abs (_, T, t)) = arg (i - 1) (T :: Ts) t
wenzelm@16678
   388
      | arg i Ts (t $ _) = arg (i + 1) Ts t
wenzelm@16678
   389
      | arg i Ts a = argT i (fastype_of1 (Ts, a));
wenzelm@16678
   390
  in arg 0 [] tm end;
wenzelm@16678
   391
clasohm@0
   392
wenzelm@19473
   393
val list_abs = uncurry (fold_rev (fn (x, T) => fn t => Abs (x, T, t)));
wenzelm@10806
   394
haftmann@18927
   395
fun strip_abs (Abs (a, T, t)) =
haftmann@18927
   396
      let val (a', t') = strip_abs t
haftmann@18927
   397
      in ((a, T) :: a', t') end
haftmann@18927
   398
  | strip_abs t = ([], t);
haftmann@18927
   399
clasohm@0
   400
(* maps  (x1,...,xn)t   to   t  *)
wenzelm@13000
   401
fun strip_abs_body (Abs(_,_,t))  =  strip_abs_body t
clasohm@0
   402
  | strip_abs_body u  =  u;
clasohm@0
   403
clasohm@0
   404
(* maps  (x1,...,xn)t   to   [x1, ..., xn]  *)
wenzelm@13000
   405
fun strip_abs_vars (Abs(a,T,t))  =  (a,T) :: strip_abs_vars t
clasohm@0
   406
  | strip_abs_vars u  =  [] : (string*typ) list;
clasohm@0
   407
clasohm@0
   408
clasohm@0
   409
fun strip_qnt_body qnt =
clasohm@0
   410
let fun strip(tm as Const(c,_)$Abs(_,_,t)) = if c=qnt then strip t else tm
clasohm@0
   411
      | strip t = t
clasohm@0
   412
in strip end;
clasohm@0
   413
clasohm@0
   414
fun strip_qnt_vars qnt =
clasohm@0
   415
let fun strip(Const(c,_)$Abs(a,T,t)) = if c=qnt then (a,T)::strip t else []
clasohm@0
   416
      | strip t  =  [] : (string*typ) list
clasohm@0
   417
in strip end;
clasohm@0
   418
clasohm@0
   419
clasohm@0
   420
(* maps   (f, [t1,...,tn])  to  f(t1,...,tn) *)
skalberg@15570
   421
val list_comb : term * term list -> term = Library.foldl (op $);
clasohm@0
   422
clasohm@0
   423
clasohm@0
   424
(* maps   f(t1,...,tn)  to  (f, [t1,...,tn]) ; naturally tail-recursive*)
wenzelm@13000
   425
fun strip_comb u : term * term list =
clasohm@0
   426
    let fun stripc (f$t, ts) = stripc (f, t::ts)
wenzelm@13000
   427
        |   stripc  x =  x
clasohm@0
   428
    in  stripc(u,[])  end;
clasohm@0
   429
clasohm@0
   430
clasohm@0
   431
(* maps   f(t1,...,tn)  to  f , which is never a combination *)
clasohm@0
   432
fun head_of (f$t) = head_of f
clasohm@0
   433
  | head_of u = u;
clasohm@0
   434
clasohm@0
   435
wenzelm@16599
   436
(*number of atoms and abstractions in a term*)
wenzelm@16599
   437
fun size_of_term tm =
wenzelm@16599
   438
  let
wenzelm@16678
   439
    fun add_size (t $ u, n) = add_size (t, add_size (u, n))
wenzelm@16678
   440
      | add_size (Abs (_ ,_, t), n) = add_size (t, n + 1)
wenzelm@16678
   441
      | add_size (_, n) = n + 1;
wenzelm@16678
   442
  in add_size (tm, 0) end;
clasohm@0
   443
haftmann@18847
   444
fun map_atyps f (Type (a, Ts)) = Type (a, map (map_atyps f) Ts)
haftmann@18976
   445
  | map_atyps f T = f T;
haftmann@18847
   446
haftmann@18847
   447
fun map_aterms f (t $ u) = map_aterms f t $ map_aterms f u
haftmann@18847
   448
  | map_aterms f (Abs (a, T, t)) = Abs (a, T, map_aterms f t)
haftmann@18847
   449
  | map_aterms f t = f t;
haftmann@18847
   450
wenzelm@18981
   451
fun map_type_tvar f = map_atyps (fn TVar x => f x | T => T);
wenzelm@18981
   452
fun map_type_tfree f = map_atyps (fn TFree x => f x | T => T);
nipkow@949
   453
clasohm@0
   454
fun map_term_types f =
wenzelm@16678
   455
  let
wenzelm@16678
   456
    fun map_aux (Const (a, T)) = Const (a, f T)
wenzelm@16678
   457
      | map_aux (Free (a, T)) = Free (a, f T)
wenzelm@16678
   458
      | map_aux (Var (v, T)) = Var (v, f T)
wenzelm@16678
   459
      | map_aux (t as Bound _)  = t
wenzelm@16678
   460
      | map_aux (Abs (a, T, t)) = Abs (a, f T, map_aux t)
wenzelm@16678
   461
      | map_aux (t $ u) = map_aux t $ map_aux u;
wenzelm@16678
   462
  in map_aux end;
clasohm@0
   463
clasohm@0
   464
(* iterate a function over all types in a term *)
clasohm@0
   465
fun it_term_types f =
clasohm@0
   466
let fun iter(Const(_,T), a) = f(T,a)
clasohm@0
   467
      | iter(Free(_,T), a) = f(T,a)
clasohm@0
   468
      | iter(Var(_,T), a) = f(T,a)
clasohm@0
   469
      | iter(Abs(_,T,t), a) = iter(t,f(T,a))
clasohm@0
   470
      | iter(f$u, a) = iter(f, iter(u, a))
clasohm@0
   471
      | iter(Bound _, a) = a
clasohm@0
   472
in iter end
clasohm@0
   473
clasohm@0
   474
wenzelm@16943
   475
(* fold types and terms *)
wenzelm@16943
   476
wenzelm@16943
   477
(*fold atoms of type*)
wenzelm@16943
   478
fun fold_atyps f (Type (_, Ts)) = fold (fold_atyps f) Ts
wenzelm@16943
   479
  | fold_atyps f T = f T;
wenzelm@16943
   480
wenzelm@16943
   481
(*fold atoms of term*)
wenzelm@16943
   482
fun fold_aterms f (t $ u) = fold_aterms f t #> fold_aterms f u
wenzelm@16943
   483
  | fold_aterms f (Abs (_, _, t)) = fold_aterms f t
wenzelm@16943
   484
  | fold_aterms f a = f a;
wenzelm@16943
   485
wenzelm@16943
   486
(*fold types of term*)
wenzelm@16943
   487
fun fold_term_types f (t as Const (_, T)) = f t T
wenzelm@16943
   488
  | fold_term_types f (t as Free (_, T)) = f t T
wenzelm@16943
   489
  | fold_term_types f (t as Var (_, T)) = f t T
wenzelm@16943
   490
  | fold_term_types f (Bound _) = I
wenzelm@16943
   491
  | fold_term_types f (t as Abs (_, T, b)) = f t T #> fold_term_types f b
wenzelm@16943
   492
  | fold_term_types f (t $ u) = fold_term_types f t #> fold_term_types f u;
wenzelm@16943
   493
wenzelm@16943
   494
fun fold_types f = fold_term_types (K f);
wenzelm@16943
   495
wenzelm@16943
   496
(*collect variables*)
wenzelm@16943
   497
val add_tvarsT = fold_atyps (fn TVar v => insert (op =) v | _ => I);
wenzelm@16943
   498
val add_tvars = fold_types add_tvarsT;
wenzelm@16943
   499
val add_vars = fold_aterms (fn Var v => insert (op =) v | _ => I);
wenzelm@16943
   500
val add_tfreesT = fold_atyps (fn TFree v => insert (op =) v | _ => I);
wenzelm@16943
   501
val add_tfrees = fold_types add_tfreesT;
wenzelm@16943
   502
val add_frees = fold_aterms (fn Free v => insert (op =) v | _ => I);
wenzelm@16943
   503
wenzelm@16943
   504
(*collect variable names*)
wenzelm@16943
   505
val add_term_varnames = fold_aterms (fn Var (xi, _) => insert (op =) xi | _ => I);
wenzelm@16943
   506
fun term_varnames t = add_term_varnames t [];
wenzelm@16943
   507
wenzelm@18149
   508
fun find_free t x =
wenzelm@18149
   509
  let
wenzelm@18149
   510
    exception Found of term;
wenzelm@18149
   511
    fun find (t as Free (x', _)) = if x = x' then raise Found t else I
wenzelm@18149
   512
      | find _ = I;
wenzelm@18149
   513
  in (fold_aterms find t (); NONE) handle Found v => SOME v end;
wenzelm@18149
   514
wenzelm@18149
   515
wenzelm@16943
   516
wenzelm@16678
   517
(** Comparing terms, types, sorts etc. **)
wenzelm@16537
   518
wenzelm@16678
   519
(* fast syntactic comparison *)
wenzelm@16678
   520
wenzelm@16678
   521
fun fast_indexname_ord ((x, i), (y, j)) =
wenzelm@16678
   522
  (case int_ord (i, j) of EQUAL => fast_string_ord (x, y) | ord => ord);
wenzelm@16537
   523
wenzelm@16599
   524
fun sort_ord SS =
wenzelm@16599
   525
  if pointer_eq SS then EQUAL
wenzelm@16990
   526
  else dict_ord fast_string_ord SS;
wenzelm@16678
   527
wenzelm@16678
   528
local
wenzelm@16537
   529
wenzelm@16678
   530
fun cons_nr (TVar _) = 0
wenzelm@16678
   531
  | cons_nr (TFree _) = 1
wenzelm@16678
   532
  | cons_nr (Type _) = 2;
wenzelm@16537
   533
wenzelm@16678
   534
in
wenzelm@16537
   535
wenzelm@16537
   536
fun typ_ord TU =
wenzelm@16537
   537
  if pointer_eq TU then EQUAL
wenzelm@16537
   538
  else
wenzelm@16537
   539
    (case TU of
wenzelm@16678
   540
      (Type (a, Ts), Type (b, Us)) =>
wenzelm@16990
   541
        (case fast_string_ord (a, b) of EQUAL => dict_ord typ_ord (Ts, Us) | ord => ord)
wenzelm@16678
   542
    | (TFree (a, S), TFree (b, S')) =>
wenzelm@16678
   543
        (case fast_string_ord (a, b) of EQUAL => sort_ord (S, S') | ord => ord)
wenzelm@16678
   544
    | (TVar (xi, S), TVar (yj, S')) =>
wenzelm@16678
   545
        (case fast_indexname_ord (xi, yj) of EQUAL => sort_ord (S, S') | ord => ord)
wenzelm@16678
   546
    | (T, U) => int_ord (cons_nr T, cons_nr U));
wenzelm@16678
   547
wenzelm@16678
   548
end;
wenzelm@16678
   549
wenzelm@16678
   550
local
wenzelm@16678
   551
wenzelm@16678
   552
fun cons_nr (Const _) = 0
wenzelm@16678
   553
  | cons_nr (Free _) = 1
wenzelm@16678
   554
  | cons_nr (Var _) = 2
wenzelm@16678
   555
  | cons_nr (Bound _) = 3
wenzelm@16678
   556
  | cons_nr (Abs _) = 4
wenzelm@16678
   557
  | cons_nr (_ $ _) = 5;
wenzelm@16678
   558
wenzelm@16678
   559
fun struct_ord (Abs (_, _, t), Abs (_, _, u)) = struct_ord (t, u)
wenzelm@16678
   560
  | struct_ord (t1 $ t2, u1 $ u2) =
wenzelm@16678
   561
      (case struct_ord (t1, u1) of EQUAL => struct_ord (t2, u2) | ord => ord)
wenzelm@16678
   562
  | struct_ord (t, u) = int_ord (cons_nr t, cons_nr u);
wenzelm@16678
   563
wenzelm@16678
   564
fun atoms_ord (Abs (_, _, t), Abs (_, _, u)) = atoms_ord (t, u)
wenzelm@16678
   565
  | atoms_ord (t1 $ t2, u1 $ u2) =
wenzelm@16678
   566
      (case atoms_ord (t1, u1) of EQUAL => atoms_ord (t2, u2) | ord => ord)
wenzelm@16678
   567
  | atoms_ord (Const (a, _), Const (b, _)) = fast_string_ord (a, b)
wenzelm@16678
   568
  | atoms_ord (Free (x, _), Free (y, _)) = fast_string_ord (x, y)
wenzelm@16678
   569
  | atoms_ord (Var (xi, _), Var (yj, _)) = fast_indexname_ord (xi, yj)
wenzelm@16678
   570
  | atoms_ord (Bound i, Bound j) = int_ord (i, j)
wenzelm@16678
   571
  | atoms_ord _ = sys_error "atoms_ord";
wenzelm@16678
   572
wenzelm@16678
   573
fun types_ord (Abs (_, T, t), Abs (_, U, u)) =
wenzelm@16678
   574
      (case typ_ord (T, U) of EQUAL => types_ord (t, u) | ord => ord)
wenzelm@16678
   575
  | types_ord (t1 $ t2, u1 $ u2) =
wenzelm@16678
   576
      (case types_ord (t1, u1) of EQUAL => types_ord (t2, u2) | ord => ord)
wenzelm@16678
   577
  | types_ord (Const (_, T), Const (_, U)) = typ_ord (T, U)
wenzelm@16678
   578
  | types_ord (Free (_, T), Free (_, U)) = typ_ord (T, U)
wenzelm@16678
   579
  | types_ord (Var (_, T), Var (_, U)) = typ_ord (T, U)
wenzelm@16678
   580
  | types_ord (Bound _, Bound _) = EQUAL
wenzelm@16678
   581
  | types_ord _ = sys_error "types_ord";
wenzelm@16678
   582
wenzelm@16678
   583
in
wenzelm@16678
   584
wenzelm@16678
   585
fun fast_term_ord tu =
wenzelm@16678
   586
  if pointer_eq tu then EQUAL
wenzelm@16678
   587
  else
wenzelm@16678
   588
    (case struct_ord tu of
wenzelm@16678
   589
      EQUAL => (case atoms_ord tu of EQUAL => types_ord tu | ord => ord)
wenzelm@16678
   590
    | ord => ord);
wenzelm@16678
   591
wenzelm@16678
   592
fun op aconv tu = (fast_term_ord tu = EQUAL);
wenzelm@16678
   593
fun aconvs ts_us = (list_ord fast_term_ord ts_us = EQUAL);
wenzelm@16678
   594
wenzelm@16678
   595
structure Vartab = TableFun(type key = indexname val ord = fast_indexname_ord);
wenzelm@16678
   596
structure Typtab = TableFun(type key = typ val ord = typ_ord);
wenzelm@16678
   597
structure Termtab = TableFun(type key = term val ord = fast_term_ord);
wenzelm@16678
   598
wenzelm@16678
   599
end;
wenzelm@16537
   600
wenzelm@16537
   601
wenzelm@16537
   602
(* term_ord *)
wenzelm@16537
   603
wenzelm@16537
   604
(*a linear well-founded AC-compatible ordering for terms:
wenzelm@16537
   605
  s < t <=> 1. size(s) < size(t) or
wenzelm@16537
   606
            2. size(s) = size(t) and s=f(...) and t=g(...) and f<g or
wenzelm@16537
   607
            3. size(s) = size(t) and s=f(s1..sn) and t=f(t1..tn) and
wenzelm@16537
   608
               (s1..sn) < (t1..tn) (lexicographically)*)
wenzelm@16678
   609
wenzelm@16678
   610
fun indexname_ord ((x, i), (y, j)) =
wenzelm@16678
   611
  (case int_ord (i, j) of EQUAL => string_ord (x, y) | ord => ord);
wenzelm@16678
   612
wenzelm@16667
   613
local
wenzelm@16667
   614
wenzelm@16667
   615
fun hd_depth (t $ _, n) = hd_depth (t, n + 1)
wenzelm@16667
   616
  | hd_depth p = p;
wenzelm@16537
   617
wenzelm@16537
   618
fun dest_hd (Const (a, T)) = (((a, 0), T), 0)
wenzelm@16537
   619
  | dest_hd (Free (a, T)) = (((a, 0), T), 1)
wenzelm@16537
   620
  | dest_hd (Var v) = (v, 2)
wenzelm@16537
   621
  | dest_hd (Bound i) = ((("", i), dummyT), 3)
wenzelm@16537
   622
  | dest_hd (Abs (_, T, _)) = ((("", 0), T), 4);
wenzelm@16537
   623
wenzelm@16667
   624
in
wenzelm@16667
   625
wenzelm@16537
   626
fun term_ord tu =
wenzelm@16537
   627
  if pointer_eq tu then EQUAL
wenzelm@16537
   628
  else
wenzelm@16537
   629
    (case tu of
wenzelm@16537
   630
      (Abs (_, T, t), Abs(_, U, u)) =>
wenzelm@16537
   631
        (case term_ord (t, u) of EQUAL => typ_ord (T, U) | ord => ord)
wenzelm@16667
   632
    | (t, u) =>
wenzelm@16537
   633
        (case int_ord (size_of_term t, size_of_term u) of
wenzelm@16537
   634
          EQUAL =>
wenzelm@16943
   635
            (case prod_ord hd_ord int_ord (hd_depth (t, 0), hd_depth (u, 0)) of
wenzelm@16943
   636
              EQUAL => args_ord (t, u) | ord => ord)
wenzelm@16537
   637
        | ord => ord))
wenzelm@16537
   638
and hd_ord (f, g) =
wenzelm@16537
   639
  prod_ord (prod_ord indexname_ord typ_ord) int_ord (dest_hd f, dest_hd g)
wenzelm@16667
   640
and args_ord (f $ t, g $ u) =
wenzelm@16667
   641
      (case args_ord (f, g) of EQUAL => term_ord (t, u) | ord => ord)
wenzelm@16667
   642
  | args_ord _ = EQUAL;
wenzelm@16537
   643
wenzelm@16537
   644
fun termless tu = (term_ord tu = LESS);
wenzelm@16537
   645
wenzelm@16667
   646
end;
wenzelm@16667
   647
wenzelm@16667
   648
wenzelm@16667
   649
(** Lexicographic path order on terms **)
wenzelm@16667
   650
wenzelm@16667
   651
(*
nipkow@16570
   652
  See Baader & Nipkow, Term rewriting, CUP 1998.
nipkow@16570
   653
  Without variables.  Const, Var, Bound, Free and Abs are treated all as
nipkow@16570
   654
  constants.
nipkow@16570
   655
nipkow@16570
   656
  f_ord maps strings to integers and serves two purposes:
nipkow@16570
   657
  - Predicate on constant symbols.  Those that are not recognised by f_ord
nipkow@16570
   658
    must be mapped to ~1.
nipkow@16570
   659
  - Order on the recognised symbols.  These must be mapped to distinct
nipkow@16570
   660
    integers >= 0.
nipkow@16570
   661
wenzelm@16667
   662
*)
nipkow@16570
   663
nipkow@16570
   664
local
wenzelm@16667
   665
fun dest_hd f_ord (Const (a, T)) =
nipkow@16570
   666
      let val ord = f_ord a in
nipkow@16570
   667
        if ord = ~1 then ((1, ((a, 0), T)), 0) else ((0, (("", ord), T)), 0)
nipkow@16570
   668
      end
nipkow@16570
   669
  | dest_hd _ (Free (a, T)) = ((1, ((a, 0), T)), 0)
nipkow@16570
   670
  | dest_hd _ (Var v) = ((1, v), 1)
nipkow@16570
   671
  | dest_hd _ (Bound i) = ((1, (("", i), dummyT)), 2)
nipkow@16570
   672
  | dest_hd _ (Abs (_, T, _)) = ((1, (("", 0), T)), 3);
nipkow@16570
   673
nipkow@16570
   674
fun term_lpo f_ord (s, t) =
nipkow@16570
   675
  let val (f, ss) = strip_comb s and (g, ts) = strip_comb t in
nipkow@16570
   676
    if forall (fn si => term_lpo f_ord (si, t) = LESS) ss
nipkow@16570
   677
    then case hd_ord f_ord (f, g) of
wenzelm@16667
   678
        GREATER =>
wenzelm@16667
   679
          if forall (fn ti => term_lpo f_ord (s, ti) = GREATER) ts
wenzelm@16667
   680
          then GREATER else LESS
nipkow@16570
   681
      | EQUAL =>
wenzelm@16667
   682
          if forall (fn ti => term_lpo f_ord (s, ti) = GREATER) ts
wenzelm@16667
   683
          then list_ord (term_lpo f_ord) (ss, ts)
wenzelm@16667
   684
          else LESS
nipkow@16570
   685
      | LESS => LESS
nipkow@16570
   686
    else GREATER
nipkow@16570
   687
  end
nipkow@16570
   688
and hd_ord f_ord (f, g) = case (f, g) of
nipkow@16570
   689
    (Abs (_, T, t), Abs (_, U, u)) =>
nipkow@16570
   690
      (case term_lpo f_ord (t, u) of EQUAL => typ_ord (T, U) | ord => ord)
nipkow@16570
   691
  | (_, _) => prod_ord (prod_ord int_ord
nipkow@16570
   692
                  (prod_ord indexname_ord typ_ord)) int_ord
nipkow@16570
   693
                (dest_hd f_ord f, dest_hd f_ord g)
nipkow@16570
   694
in
nipkow@16570
   695
val term_lpo = term_lpo
nipkow@16570
   696
end;
nipkow@16570
   697
wenzelm@16537
   698
clasohm@0
   699
(** Connectives of higher order logic **)
clasohm@0
   700
wenzelm@19394
   701
fun aT S = TFree ("'a", S);
wenzelm@19394
   702
wenzelm@375
   703
fun itselfT ty = Type ("itself", [ty]);
wenzelm@14854
   704
val a_itselfT = itselfT (TFree ("'a", []));
wenzelm@375
   705
clasohm@0
   706
val propT : typ = Type("prop",[]);
clasohm@0
   707
clasohm@0
   708
val implies = Const("==>", propT-->propT-->propT);
clasohm@0
   709
clasohm@0
   710
fun all T = Const("all", (T-->propT)-->propT);
clasohm@0
   711
clasohm@0
   712
fun equals T = Const("==", T-->T-->propT);
clasohm@0
   713
clasohm@0
   714
(* maps  !!x1...xn. t   to   t  *)
wenzelm@13000
   715
fun strip_all_body (Const("all",_)$Abs(_,_,t))  =  strip_all_body t
clasohm@0
   716
  | strip_all_body t  =  t;
clasohm@0
   717
clasohm@0
   718
(* maps  !!x1...xn. t   to   [x1, ..., xn]  *)
clasohm@0
   719
fun strip_all_vars (Const("all",_)$Abs(a,T,t))  =
wenzelm@13000
   720
                (a,T) :: strip_all_vars t
clasohm@0
   721
  | strip_all_vars t  =  [] : (string*typ) list;
clasohm@0
   722
clasohm@0
   723
(*increments a term's non-local bound variables
clasohm@0
   724
  required when moving a term within abstractions
clasohm@0
   725
     inc is  increment for bound variables
clasohm@0
   726
     lev is  level at which a bound variable is considered 'loose'*)
wenzelm@13000
   727
fun incr_bv (inc, lev, u as Bound i) = if i>=lev then Bound(i+inc) else u
clasohm@0
   728
  | incr_bv (inc, lev, Abs(a,T,body)) =
wenzelm@9536
   729
        Abs(a, T, incr_bv(inc,lev+1,body))
wenzelm@13000
   730
  | incr_bv (inc, lev, f$t) =
clasohm@0
   731
      incr_bv(inc,lev,f) $ incr_bv(inc,lev,t)
clasohm@0
   732
  | incr_bv (inc, lev, u) = u;
clasohm@0
   733
clasohm@0
   734
fun incr_boundvars  0  t = t
clasohm@0
   735
  | incr_boundvars inc t = incr_bv(inc,0,t);
clasohm@0
   736
wenzelm@12981
   737
(*Scan a pair of terms; while they are similar,
wenzelm@12981
   738
  accumulate corresponding bound vars in "al"*)
wenzelm@12981
   739
fun match_bvs(Abs(x,_,s),Abs(y,_,t), al) =
wenzelm@12981
   740
      match_bvs(s, t, if x="" orelse y="" then al
wenzelm@12981
   741
                                          else (x,y)::al)
wenzelm@12981
   742
  | match_bvs(f$s, g$t, al) = match_bvs(f,g,match_bvs(s,t,al))
wenzelm@12981
   743
  | match_bvs(_,_,al) = al;
wenzelm@12981
   744
wenzelm@12981
   745
(* strip abstractions created by parameters *)
wenzelm@12981
   746
fun match_bvars((s,t),al) = match_bvs(strip_abs_body s, strip_abs_body t, al);
wenzelm@12981
   747
wenzelm@12981
   748
fun rename_abs pat obj t =
wenzelm@12981
   749
  let
wenzelm@12981
   750
    val ren = match_bvs (pat, obj, []);
wenzelm@12981
   751
    fun ren_abs (Abs (x, T, b)) =
wenzelm@18942
   752
          Abs (the_default x (AList.lookup (op =) ren x), T, ren_abs b)
wenzelm@12981
   753
      | ren_abs (f $ t) = ren_abs f $ ren_abs t
wenzelm@12981
   754
      | ren_abs t = t
skalberg@15531
   755
  in if null ren then NONE else SOME (ren_abs t) end;
clasohm@0
   756
clasohm@0
   757
(*Accumulate all 'loose' bound vars referring to level 'lev' or beyond.
clasohm@0
   758
   (Bound 0) is loose at level 0 *)
wenzelm@13000
   759
fun add_loose_bnos (Bound i, lev, js) =
wenzelm@9536
   760
        if i<lev then js  else  (i-lev) ins_int js
clasohm@0
   761
  | add_loose_bnos (Abs (_,_,t), lev, js) = add_loose_bnos (t, lev+1, js)
clasohm@0
   762
  | add_loose_bnos (f$t, lev, js) =
wenzelm@13000
   763
        add_loose_bnos (f, lev, add_loose_bnos (t, lev, js))
clasohm@0
   764
  | add_loose_bnos (_, _, js) = js;
clasohm@0
   765
clasohm@0
   766
fun loose_bnos t = add_loose_bnos (t, 0, []);
clasohm@0
   767
clasohm@0
   768
(* loose_bvar(t,k) iff t contains a 'loose' bound variable referring to
clasohm@0
   769
   level k or beyond. *)
clasohm@0
   770
fun loose_bvar(Bound i,k) = i >= k
clasohm@0
   771
  | loose_bvar(f$t, k) = loose_bvar(f,k) orelse loose_bvar(t,k)
clasohm@0
   772
  | loose_bvar(Abs(_,_,t),k) = loose_bvar(t,k+1)
clasohm@0
   773
  | loose_bvar _ = false;
clasohm@0
   774
nipkow@2792
   775
fun loose_bvar1(Bound i,k) = i = k
nipkow@2792
   776
  | loose_bvar1(f$t, k) = loose_bvar1(f,k) orelse loose_bvar1(t,k)
nipkow@2792
   777
  | loose_bvar1(Abs(_,_,t),k) = loose_bvar1(t,k+1)
nipkow@2792
   778
  | loose_bvar1 _ = false;
clasohm@0
   779
clasohm@0
   780
(*Substitute arguments for loose bound variables.
clasohm@0
   781
  Beta-reduction of arg(n-1)...arg0 into t replacing (Bound i) with (argi).
wenzelm@4626
   782
  Note that for ((%x y. c) a b), the bound vars in c are x=1 and y=0
wenzelm@9536
   783
        and the appropriate call is  subst_bounds([b,a], c) .
clasohm@0
   784
  Loose bound variables >=n are reduced by "n" to
clasohm@0
   785
     compensate for the disappearance of lambdas.
clasohm@0
   786
*)
wenzelm@13000
   787
fun subst_bounds (args: term list, t) : term =
wenzelm@19065
   788
  let
wenzelm@19065
   789
    exception SAME;
wenzelm@19065
   790
    val n = length args;
wenzelm@19065
   791
    fun subst (t as Bound i, lev) =
wenzelm@19065
   792
         (if i < lev then raise SAME   (*var is locally bound*)
wenzelm@19065
   793
          else incr_boundvars lev (List.nth (args, i - lev))
wenzelm@19065
   794
            handle Subscript => Bound (i - n))  (*loose: change it*)
wenzelm@19065
   795
      | subst (Abs (a, T, body), lev) = Abs (a, T, subst (body, lev + 1))
wenzelm@19065
   796
      | subst (f $ t, lev) =
wenzelm@19065
   797
          (subst (f, lev) $ (subst (t, lev) handle SAME => t) handle SAME => f $ subst (t, lev))
wenzelm@19065
   798
      | subst _ = raise SAME;
wenzelm@19065
   799
  in case args of [] => t | _ => (subst (t, 0) handle SAME => t) end;
clasohm@0
   800
paulson@2192
   801
(*Special case: one argument*)
wenzelm@13000
   802
fun subst_bound (arg, t) : term =
wenzelm@19065
   803
  let
wenzelm@19065
   804
    exception SAME;
wenzelm@19065
   805
    fun subst (Bound i, lev) =
wenzelm@19065
   806
          if i < lev then raise SAME   (*var is locally bound*)
wenzelm@19065
   807
          else if i = lev then incr_boundvars lev arg
wenzelm@19065
   808
          else Bound (i - 1)   (*loose: change it*)
wenzelm@19065
   809
      | subst (Abs (a, T, body), lev) = Abs (a, T, subst (body, lev + 1))
wenzelm@19065
   810
      | subst (f $ t, lev) =
wenzelm@19065
   811
          (subst (f, lev) $ (subst (t, lev) handle SAME => t) handle SAME => f $ subst (t, lev))
wenzelm@19065
   812
      | subst _ = raise SAME;
wenzelm@19065
   813
  in subst (t, 0) handle SAME => t end;
paulson@2192
   814
clasohm@0
   815
(*beta-reduce if possible, else form application*)
paulson@2192
   816
fun betapply (Abs(_,_,t), u) = subst_bound (u,t)
clasohm@0
   817
  | betapply (f,u) = f$u;
clasohm@0
   818
wenzelm@18183
   819
val betapplys = Library.foldl betapply;
wenzelm@18183
   820
wenzelm@14786
   821
wenzelm@16882
   822
(** Specialized equality, membership, insertion etc. **)
paulson@2192
   823
wenzelm@16882
   824
(* indexnames *)
wenzelm@16882
   825
wenzelm@16724
   826
fun eq_ix ((x, i): indexname, (y, j)) = i = j andalso x = y;
paulson@2192
   827
wenzelm@2959
   828
fun mem_ix (_, []) = false
wenzelm@16882
   829
  | mem_ix (x, y :: ys) = eq_ix (x, y) orelse mem_ix (x, ys);
paulson@2192
   830
wenzelm@16882
   831
fun ins_ix (x, xs) = if mem_ix (x, xs) then xs else x :: xs;
paulson@2192
   832
clasohm@0
   833
wenzelm@16882
   834
(* variables *)
wenzelm@16882
   835
wenzelm@16943
   836
fun eq_tvar ((xi, S: sort), (xi', S')) = eq_ix (xi, xi') andalso S = S';
wenzelm@16943
   837
fun eq_var ((xi, T: typ), (xi', T')) = eq_ix (xi, xi') andalso T = T';
wenzelm@16943
   838
wenzelm@16943
   839
val tvar_ord = prod_ord indexname_ord sort_ord;
wenzelm@16943
   840
val var_ord = prod_ord indexname_ord typ_ord;
wenzelm@16882
   841
wenzelm@16882
   842
wenzelm@16882
   843
(* terms *)
paulson@2176
   844
paulson@2176
   845
fun mem_term (_, []) = false
wenzelm@16882
   846
  | mem_term (t, t'::ts) = t aconv t' orelse mem_term (t, ts);
paulson@2176
   847
paulson@2176
   848
fun ins_term(t,ts) = if mem_term(t,ts) then ts else t :: ts;
paulson@2176
   849
wenzelm@16882
   850
wenzelm@13000
   851
(*A fast unification filter: true unless the two terms cannot be unified.
clasohm@0
   852
  Terms must be NORMAL.  Treats all Vars as distinct. *)
clasohm@0
   853
fun could_unify (t,u) =
clasohm@0
   854
  let fun matchrands (f$t, g$u) = could_unify(t,u) andalso  matchrands(f,g)
wenzelm@9536
   855
        | matchrands _ = true
clasohm@0
   856
  in case (head_of t , head_of u) of
wenzelm@9536
   857
        (_, Var _) => true
clasohm@0
   858
      | (Var _, _) => true
clasohm@0
   859
      | (Const(a,_), Const(b,_)) =>  a=b andalso matchrands(t,u)
clasohm@0
   860
      | (Free(a,_), Free(b,_)) =>  a=b andalso matchrands(t,u)
clasohm@0
   861
      | (Bound i, Bound j) =>  i=j andalso matchrands(t,u)
clasohm@0
   862
      | (Abs _, _) =>  true   (*because of possible eta equality*)
clasohm@0
   863
      | (_, Abs _) =>  true
clasohm@0
   864
      | _ => false
clasohm@0
   865
  end;
clasohm@0
   866
clasohm@0
   867
(*Substitute new for free occurrences of old in a term*)
clasohm@0
   868
fun subst_free [] = (fn t=>t)
clasohm@0
   869
  | subst_free pairs =
wenzelm@13000
   870
      let fun substf u =
haftmann@17314
   871
            case AList.lookup (op aconv) pairs u of
skalberg@15531
   872
                SOME u' => u'
skalberg@15531
   873
              | NONE => (case u of Abs(a,T,t) => Abs(a, T, substf t)
wenzelm@9536
   874
                                 | t$u' => substf t $ substf u'
wenzelm@9536
   875
                                 | _ => u)
clasohm@0
   876
      in  substf  end;
clasohm@0
   877
clasohm@0
   878
(*a total, irreflexive ordering on index names*)
clasohm@0
   879
fun xless ((a,i), (b,j): indexname) = i<j  orelse  (i=j andalso a<b);
clasohm@0
   880
clasohm@0
   881
wenzelm@13000
   882
(*Abstraction of the term "body" over its occurrences of v,
clasohm@0
   883
    which must contain no loose bound variables.
clasohm@0
   884
  The resulting term is ready to become the body of an Abs.*)
wenzelm@16882
   885
fun abstract_over (v, body) =
wenzelm@16882
   886
  let
wenzelm@16990
   887
    exception SAME;
wenzelm@16990
   888
    fun abs lev tm =
wenzelm@16990
   889
      if v aconv tm then Bound lev
wenzelm@16882
   890
      else
wenzelm@16990
   891
        (case tm of
wenzelm@16990
   892
          Abs (a, T, t) => Abs (a, T, abs (lev + 1) t)
wenzelm@16990
   893
        | t $ u => (abs lev t $ (abs lev u handle SAME => u) handle SAME => t $ abs lev u)
wenzelm@16990
   894
        | _ => raise SAME);
wenzelm@16990
   895
  in abs 0 body handle SAME => body end;
clasohm@0
   896
wenzelm@18975
   897
fun lambda (v as Const (x, T)) t = Abs (NameSpace.base x, T, abstract_over (v, t))
wenzelm@18942
   898
  | lambda (v as Free (x, T)) t = Abs (x, T, abstract_over (v, t))
berghofe@13665
   899
  | lambda (v as Var ((x, _), T)) t = Abs (x, T, abstract_over (v, t))
berghofe@13665
   900
  | lambda v t = raise TERM ("lambda", [v, t]);
clasohm@0
   901
clasohm@0
   902
(*Form an abstraction over a free variable.*)
clasohm@0
   903
fun absfree (a,T,body) = Abs(a, T, abstract_over (Free(a,T), body));
wenzelm@17786
   904
fun absdummy (T, body) = Abs ("uu", T, body);
clasohm@0
   905
clasohm@0
   906
(*Abstraction over a list of free variables*)
clasohm@0
   907
fun list_abs_free ([ ] ,     t) = t
wenzelm@13000
   908
  | list_abs_free ((a,T)::vars, t) =
clasohm@0
   909
      absfree(a, T, list_abs_free(vars,t));
clasohm@0
   910
clasohm@0
   911
(*Quantification over a list of free variables*)
clasohm@0
   912
fun list_all_free ([], t: term) = t
wenzelm@13000
   913
  | list_all_free ((a,T)::vars, t) =
clasohm@0
   914
        (all T) $ (absfree(a, T, list_all_free(vars,t)));
clasohm@0
   915
clasohm@0
   916
(*Quantification over a list of variables (already bound in body) *)
clasohm@0
   917
fun list_all ([], t) = t
wenzelm@13000
   918
  | list_all ((a,T)::vars, t) =
clasohm@0
   919
        (all T) $ (Abs(a, T, list_all(vars,t)));
clasohm@0
   920
wenzelm@16678
   921
(*Replace the ATOMIC term ti by ui;    inst = [(t1,u1), ..., (tn,un)].
clasohm@0
   922
  A simultaneous substitution:  [ (a,b), (b,a) ] swaps a and b.  *)
wenzelm@16678
   923
fun subst_atomic [] tm = tm
wenzelm@16678
   924
  | subst_atomic inst tm =
wenzelm@16678
   925
      let
wenzelm@16678
   926
        fun subst (Abs (a, T, body)) = Abs (a, T, subst body)
wenzelm@16678
   927
          | subst (t $ u) = subst t $ subst u
wenzelm@18942
   928
          | subst t = the_default t (AList.lookup (op aconv) inst t);
wenzelm@16678
   929
      in subst tm end;
clasohm@0
   930
wenzelm@16678
   931
(*Replace the ATOMIC type Ti by Ui;    inst = [(T1,U1), ..., (Tn,Un)].*)
wenzelm@16678
   932
fun typ_subst_atomic [] ty = ty
wenzelm@16678
   933
  | typ_subst_atomic inst ty =
wenzelm@16678
   934
      let
wenzelm@16678
   935
        fun subst (Type (a, Ts)) = Type (a, map subst Ts)
wenzelm@18942
   936
          | subst T = the_default T (AList.lookup (op = : typ * typ -> bool) inst T);
wenzelm@16678
   937
      in subst ty end;
berghofe@15797
   938
wenzelm@16678
   939
fun subst_atomic_types [] tm = tm
wenzelm@16678
   940
  | subst_atomic_types inst tm = map_term_types (typ_subst_atomic inst) tm;
wenzelm@16678
   941
wenzelm@16678
   942
fun typ_subst_TVars [] ty = ty
wenzelm@16678
   943
  | typ_subst_TVars inst ty =
wenzelm@16678
   944
      let
wenzelm@16678
   945
        fun subst (Type (a, Ts)) = Type (a, map subst Ts)
wenzelm@18942
   946
          | subst (T as TVar (xi, _)) = the_default T (AList.lookup (op =) inst xi)
wenzelm@16678
   947
          | subst T = T;
wenzelm@16678
   948
      in subst ty end;
clasohm@0
   949
wenzelm@16678
   950
fun subst_TVars [] tm = tm
wenzelm@16678
   951
  | subst_TVars inst tm = map_term_types (typ_subst_TVars inst) tm;
clasohm@0
   952
wenzelm@16678
   953
(*see also Envir.norm_term*)
wenzelm@16678
   954
fun subst_Vars [] tm = tm
wenzelm@16678
   955
  | subst_Vars inst tm =
wenzelm@16678
   956
      let
wenzelm@18942
   957
        fun subst (t as Var (xi, _)) = the_default t (AList.lookup (op =) inst xi)
wenzelm@16678
   958
          | subst (Abs (a, T, t)) = Abs (a, T, subst t)
wenzelm@16678
   959
          | subst (t $ u) = subst t $ subst u
wenzelm@16678
   960
          | subst t = t;
wenzelm@16678
   961
      in subst tm end;
clasohm@0
   962
wenzelm@16678
   963
(*see also Envir.norm_term*)
wenzelm@16678
   964
fun subst_vars ([], []) tm = tm
wenzelm@16678
   965
  | subst_vars ([], inst) tm = subst_Vars inst tm
wenzelm@16678
   966
  | subst_vars (instT, inst) tm =
wenzelm@16678
   967
      let
wenzelm@16678
   968
        fun subst (Const (a, T)) = Const (a, typ_subst_TVars instT T)
wenzelm@16678
   969
          | subst (Free (a, T)) = Free (a, typ_subst_TVars instT T)
wenzelm@16678
   970
          | subst (t as Var (xi, T)) =
haftmann@17271
   971
              (case AList.lookup (op =) inst xi of
wenzelm@16678
   972
                NONE => Var (xi, typ_subst_TVars instT T)
wenzelm@16678
   973
              | SOME t => t)
wenzelm@16678
   974
          | subst (t as Bound _) = t
wenzelm@16678
   975
          | subst (Abs (a, T, t)) = Abs (a, typ_subst_TVars instT T, subst t)
wenzelm@16678
   976
          | subst (t $ u) = subst t $ subst u;
wenzelm@16678
   977
      in subst tm end;
clasohm@0
   978
clasohm@0
   979
wenzelm@16943
   980
(* instantiation of schematic variables (types before terms) *)
wenzelm@16882
   981
wenzelm@16882
   982
local exception SAME in
wenzelm@16882
   983
wenzelm@16943
   984
fun instantiateT_same [] _ = raise SAME
wenzelm@16943
   985
  | instantiateT_same instT ty =
wenzelm@16882
   986
      let
wenzelm@16882
   987
        fun subst_typ (Type (a, Ts)) = Type (a, subst_typs Ts)
wenzelm@16882
   988
          | subst_typ (TVar v) =
haftmann@17314
   989
              (case AList.lookup eq_tvar instT v of
wenzelm@16882
   990
                SOME T => T
wenzelm@16882
   991
              | NONE => raise SAME)
wenzelm@16882
   992
          | subst_typ _ = raise SAME
wenzelm@16882
   993
        and subst_typs (T :: Ts) =
wenzelm@16882
   994
            (subst_typ T :: (subst_typs Ts handle SAME => Ts)
wenzelm@16882
   995
              handle SAME => T :: subst_typs Ts)
wenzelm@16882
   996
          | subst_typs [] = raise SAME;
wenzelm@16882
   997
      in subst_typ ty end;
wenzelm@16882
   998
wenzelm@16882
   999
fun instantiate ([], []) tm = tm
wenzelm@16882
  1000
  | instantiate (instT, inst) tm =
wenzelm@16882
  1001
      let
wenzelm@16943
  1002
        val substT = instantiateT_same instT;
wenzelm@16943
  1003
        fun subst (Const (c, T)) = Const (c, substT T)
wenzelm@16943
  1004
          | subst (Free (x, T)) = Free (x, substT T)
wenzelm@16882
  1005
          | subst (Var (xi, T)) =
wenzelm@16943
  1006
              let val (T', same) = (substT T, false) handle SAME => (T, true) in
haftmann@17314
  1007
                (case AList.lookup eq_var inst (xi, T') of
wenzelm@16882
  1008
                   SOME t => t
wenzelm@16882
  1009
                 | NONE => if same then raise SAME else Var (xi, T'))
wenzelm@16882
  1010
              end
wenzelm@16882
  1011
          | subst (Bound _) = raise SAME
wenzelm@16882
  1012
          | subst (Abs (x, T, t)) =
wenzelm@16943
  1013
              (Abs (x, substT T, subst t handle SAME => t)
wenzelm@16882
  1014
                handle SAME => Abs (x, T, subst t))
wenzelm@16882
  1015
          | subst (t $ u) = (subst t $ (subst u handle SAME => u) handle SAME => t $ subst u);
wenzelm@16882
  1016
      in subst tm handle SAME => tm end;
wenzelm@16882
  1017
wenzelm@16882
  1018
fun instantiateT instT ty =
wenzelm@16943
  1019
  instantiateT_same instT ty handle SAME => ty;
wenzelm@16882
  1020
wenzelm@16882
  1021
end;
wenzelm@16882
  1022
wenzelm@16882
  1023
paulson@15573
  1024
(** Identifying first-order terms **)
paulson@15573
  1025
paulson@15573
  1026
(*Argument Ts is a reverse list of binder types, needed if term t contains Bound vars*)
paulson@15573
  1027
fun has_not_funtype Ts t = not (is_funtype (fastype_of1 (Ts,t)));
paulson@15573
  1028
wenzelm@16537
  1029
(*First order means in all terms of the form f(t1,...,tn) no argument has a
paulson@16589
  1030
  function type. The supplied quantifiers are excluded: their argument always
paulson@16589
  1031
  has a function type through a recursive call into its body.*)
wenzelm@16667
  1032
fun is_first_order quants =
paulson@16589
  1033
  let fun first_order1 Ts (Abs (_,T,body)) = first_order1 (T::Ts) body
wenzelm@16667
  1034
        | first_order1 Ts (Const(q,_) $ Abs(a,T,body)) =
wenzelm@16667
  1035
            q mem_string quants  andalso   (*it is a known quantifier*)
paulson@16589
  1036
            not (is_funtype T)   andalso first_order1 (T::Ts) body
wenzelm@16667
  1037
        | first_order1 Ts t =
wenzelm@16667
  1038
            case strip_comb t of
wenzelm@16667
  1039
                 (Var _, ts) => forall (first_order1 Ts andf has_not_funtype Ts) ts
wenzelm@16667
  1040
               | (Free _, ts) => forall (first_order1 Ts andf has_not_funtype Ts) ts
wenzelm@16667
  1041
               | (Const _, ts) => forall (first_order1 Ts andf has_not_funtype Ts) ts
wenzelm@16667
  1042
               | (Bound _, ts) => forall (first_order1 Ts andf has_not_funtype Ts) ts
wenzelm@16667
  1043
               | (Abs _, ts) => false (*not in beta-normal form*)
wenzelm@16667
  1044
               | _ => error "first_order: unexpected case"
paulson@16589
  1045
    in  first_order1 []  end;
paulson@15573
  1046
wenzelm@16710
  1047
wenzelm@16990
  1048
(* maximum index of typs and terms *)
clasohm@0
  1049
wenzelm@16710
  1050
fun maxidx_typ (TVar ((_, j), _)) i = Int.max (i, j)
wenzelm@16710
  1051
  | maxidx_typ (Type (_, Ts)) i = maxidx_typs Ts i
wenzelm@16710
  1052
  | maxidx_typ (TFree _) i = i
wenzelm@16710
  1053
and maxidx_typs [] i = i
wenzelm@16710
  1054
  | maxidx_typs (T :: Ts) i = maxidx_typs Ts (maxidx_typ T i);
clasohm@0
  1055
wenzelm@16710
  1056
fun maxidx_term (Var ((_, j), T)) i = maxidx_typ T (Int.max (i, j))
wenzelm@16710
  1057
  | maxidx_term (Const (_, T)) i = maxidx_typ T i
wenzelm@16710
  1058
  | maxidx_term (Free (_, T)) i = maxidx_typ T i
wenzelm@16710
  1059
  | maxidx_term (Bound _) i = i
wenzelm@16710
  1060
  | maxidx_term (Abs (_, T, t)) i = maxidx_term t (maxidx_typ T i)
wenzelm@16710
  1061
  | maxidx_term (t $ u) i = maxidx_term u (maxidx_term t i);
clasohm@0
  1062
wenzelm@16710
  1063
fun maxidx_of_typ T = maxidx_typ T ~1;
wenzelm@16710
  1064
fun maxidx_of_typs Ts = maxidx_typs Ts ~1;
wenzelm@16710
  1065
fun maxidx_of_term t = maxidx_term t ~1;
berghofe@13665
  1066
clasohm@0
  1067
clasohm@0
  1068
clasohm@0
  1069
(**** Syntax-related declarations ****)
clasohm@0
  1070
clasohm@0
  1071
(*** Printing ***)
clasohm@0
  1072
wenzelm@19014
  1073
(*Makes a variant of a name distinct from already used names.  First
wenzelm@19014
  1074
  attaches the suffix and then increments this; preserves a suffix of
wenzelm@19014
  1075
  underscores "_". *)
wenzelm@19014
  1076
fun variant_name used name =
wenzelm@12306
  1077
  let
wenzelm@19014
  1078
    val (c, u) = pairself implode (Library.take_suffix (fn s => s = "_") (Symbol.explode name));
wenzelm@19014
  1079
    fun vary2 c = if used (c ^ u) then vary2 (Symbol.bump_string c) else c;
wenzelm@19014
  1080
    fun vary1 c = if used (c ^ u) then vary2 (Symbol.bump_init c) else c;
wenzelm@12306
  1081
  in vary1 (if c = "" then "u" else c) ^ u end;
clasohm@0
  1082
wenzelm@19014
  1083
fun variant used_names = variant_name (member (op =) used_names);
wenzelm@19014
  1084
clasohm@0
  1085
(*Create variants of the list of names, with priority to the first ones*)
clasohm@0
  1086
fun variantlist ([], used) = []
wenzelm@13000
  1087
  | variantlist(b::bs, used) =
clasohm@0
  1088
      let val b' = variant used b
clasohm@0
  1089
      in  b' :: variantlist (bs, b'::used)  end;
clasohm@0
  1090
wenzelm@14695
  1091
(*Invent fresh names*)
wenzelm@14695
  1092
fun invent_names _ _ 0 = []
wenzelm@14695
  1093
  | invent_names used a n =
wenzelm@14695
  1094
      let val b = Symbol.bump_string a in
wenzelm@14695
  1095
        if a mem_string used then invent_names used b n
wenzelm@14695
  1096
        else a :: invent_names used b (n - 1)
wenzelm@14695
  1097
      end;
wenzelm@11353
  1098
wenzelm@16537
  1099
wenzelm@4017
  1100
(** Consts etc. **)
wenzelm@4017
  1101
wenzelm@18995
  1102
fun add_term_consts (Const (c, _), cs) = insert (op =) c cs
wenzelm@4017
  1103
  | add_term_consts (t $ u, cs) = add_term_consts (t, add_term_consts (u, cs))
wenzelm@4017
  1104
  | add_term_consts (Abs (_, _, t), cs) = add_term_consts (t, cs)
wenzelm@4017
  1105
  | add_term_consts (_, cs) = cs;
wenzelm@4017
  1106
nipkow@13646
  1107
fun term_consts t = add_term_consts(t,[]);
nipkow@13646
  1108
wenzelm@16943
  1109
fun exists_subterm P =
wenzelm@16943
  1110
  let
wenzelm@16943
  1111
    fun ex tm = P tm orelse
wenzelm@16943
  1112
      (case tm of
wenzelm@16943
  1113
        t $ u => ex t orelse ex u
wenzelm@16943
  1114
      | Abs (_, _, t) => ex t
wenzelm@16943
  1115
      | _ => false);
wenzelm@16943
  1116
  in ex end;
obua@16108
  1117
wenzelm@16943
  1118
fun exists_Const P = exists_subterm (fn Const c => P c | _ => false);
nipkow@4631
  1119
wenzelm@4017
  1120
clasohm@0
  1121
(** TFrees and TVars **)
clasohm@0
  1122
wenzelm@12802
  1123
(*Accumulates the names of Frees in the term, suppressing duplicates.*)
wenzelm@12802
  1124
fun add_term_free_names (Free(a,_), bs) = a ins_string bs
wenzelm@12802
  1125
  | add_term_free_names (f$u, bs) = add_term_free_names (f, add_term_free_names(u, bs))
wenzelm@12802
  1126
  | add_term_free_names (Abs(_,_,t), bs) = add_term_free_names(t,bs)
wenzelm@12802
  1127
  | add_term_free_names (_, bs) = bs;
wenzelm@12802
  1128
clasohm@0
  1129
(*Accumulates the names in the term, suppressing duplicates.
clasohm@0
  1130
  Includes Frees and Consts.  For choosing unambiguous bound var names.*)
wenzelm@10666
  1131
fun add_term_names (Const(a,_), bs) = NameSpace.base a ins_string bs
paulson@2176
  1132
  | add_term_names (Free(a,_), bs) = a ins_string bs
clasohm@0
  1133
  | add_term_names (f$u, bs) = add_term_names (f, add_term_names(u, bs))
clasohm@0
  1134
  | add_term_names (Abs(_,_,t), bs) = add_term_names(t,bs)
clasohm@0
  1135
  | add_term_names (_, bs) = bs;
clasohm@0
  1136
clasohm@0
  1137
(*Accumulates the TVars in a type, suppressing duplicates. *)
skalberg@15574
  1138
fun add_typ_tvars(Type(_,Ts),vs) = foldr add_typ_tvars vs Ts
clasohm@0
  1139
  | add_typ_tvars(TFree(_),vs) = vs
wenzelm@16294
  1140
  | add_typ_tvars(TVar(v),vs) = insert (op =) v vs;
clasohm@0
  1141
clasohm@0
  1142
(*Accumulates the TFrees in a type, suppressing duplicates. *)
skalberg@15574
  1143
fun add_typ_tfree_names(Type(_,Ts),fs) = foldr add_typ_tfree_names fs Ts
paulson@2176
  1144
  | add_typ_tfree_names(TFree(f,_),fs) = f ins_string fs
clasohm@0
  1145
  | add_typ_tfree_names(TVar(_),fs) = fs;
clasohm@0
  1146
skalberg@15574
  1147
fun add_typ_tfrees(Type(_,Ts),fs) = foldr add_typ_tfrees fs Ts
wenzelm@16294
  1148
  | add_typ_tfrees(TFree(f),fs) = insert (op =) f fs
clasohm@0
  1149
  | add_typ_tfrees(TVar(_),fs) = fs;
clasohm@0
  1150
skalberg@15574
  1151
fun add_typ_varnames(Type(_,Ts),nms) = foldr add_typ_varnames nms Ts
paulson@2176
  1152
  | add_typ_varnames(TFree(nm,_),nms) = nm ins_string nms
paulson@2176
  1153
  | add_typ_varnames(TVar((nm,_),_),nms) = nm ins_string nms;
nipkow@949
  1154
clasohm@0
  1155
(*Accumulates the TVars in a term, suppressing duplicates. *)
clasohm@0
  1156
val add_term_tvars = it_term_types add_typ_tvars;
clasohm@0
  1157
clasohm@0
  1158
(*Accumulates the TFrees in a term, suppressing duplicates. *)
clasohm@0
  1159
val add_term_tfrees = it_term_types add_typ_tfrees;
clasohm@0
  1160
val add_term_tfree_names = it_term_types add_typ_tfree_names;
clasohm@0
  1161
nipkow@949
  1162
val add_term_tvarnames = it_term_types add_typ_varnames;
nipkow@949
  1163
clasohm@0
  1164
(*Non-list versions*)
clasohm@0
  1165
fun typ_tfrees T = add_typ_tfrees(T,[]);
clasohm@0
  1166
fun typ_tvars T = add_typ_tvars(T,[]);
clasohm@0
  1167
fun term_tfrees t = add_term_tfrees(t,[]);
clasohm@0
  1168
fun term_tvars t = add_term_tvars(t,[]);
clasohm@0
  1169
nipkow@949
  1170
(*special code to enforce left-to-right collection of TVar-indexnames*)
nipkow@949
  1171
skalberg@15570
  1172
fun add_typ_ixns(ixns,Type(_,Ts)) = Library.foldl add_typ_ixns (ixns,Ts)
wenzelm@13000
  1173
  | add_typ_ixns(ixns,TVar(ixn,_)) = if mem_ix (ixn, ixns) then ixns
wenzelm@9536
  1174
                                     else ixns@[ixn]
nipkow@949
  1175
  | add_typ_ixns(ixns,TFree(_)) = ixns;
nipkow@949
  1176
nipkow@949
  1177
fun add_term_tvar_ixns(Const(_,T),ixns) = add_typ_ixns(ixns,T)
nipkow@949
  1178
  | add_term_tvar_ixns(Free(_,T),ixns) = add_typ_ixns(ixns,T)
nipkow@949
  1179
  | add_term_tvar_ixns(Var(_,T),ixns) = add_typ_ixns(ixns,T)
nipkow@949
  1180
  | add_term_tvar_ixns(Bound _,ixns) = ixns
nipkow@949
  1181
  | add_term_tvar_ixns(Abs(_,T,t),ixns) =
nipkow@949
  1182
      add_term_tvar_ixns(t,add_typ_ixns(ixns,T))
nipkow@949
  1183
  | add_term_tvar_ixns(f$t,ixns) =
nipkow@949
  1184
      add_term_tvar_ixns(t,add_term_tvar_ixns(f,ixns));
nipkow@949
  1185
wenzelm@16537
  1186
clasohm@0
  1187
(** Frees and Vars **)
clasohm@0
  1188
clasohm@0
  1189
(*Accumulates the Vars in the term, suppressing duplicates*)
clasohm@0
  1190
fun add_term_vars (t, vars: term list) = case t of
wenzelm@16990
  1191
    Var   _ => OrdList.insert term_ord t vars
clasohm@0
  1192
  | Abs (_,_,body) => add_term_vars(body,vars)
clasohm@0
  1193
  | f$t =>  add_term_vars (f, add_term_vars(t, vars))
clasohm@0
  1194
  | _ => vars;
clasohm@0
  1195
clasohm@0
  1196
fun term_vars t = add_term_vars(t,[]);
clasohm@0
  1197
clasohm@0
  1198
(*Accumulates the Frees in the term, suppressing duplicates*)
clasohm@0
  1199
fun add_term_frees (t, frees: term list) = case t of
wenzelm@16990
  1200
    Free   _ => OrdList.insert term_ord t frees
clasohm@0
  1201
  | Abs (_,_,body) => add_term_frees(body,frees)
clasohm@0
  1202
  | f$t =>  add_term_frees (f, add_term_frees(t, frees))
clasohm@0
  1203
  | _ => frees;
clasohm@0
  1204
clasohm@0
  1205
fun term_frees t = add_term_frees(t,[]);
clasohm@0
  1206
clasohm@0
  1207
(*Given an abstraction over P, replaces the bound variable by a Free variable
wenzelm@17851
  1208
  having a unique name -- SLOW!*)
clasohm@0
  1209
fun variant_abs (a,T,P) =
clasohm@0
  1210
  let val b = variant (add_term_names(P,[])) a
paulson@2192
  1211
  in  (b,  subst_bound (Free(b,T), P))  end;
clasohm@0
  1212
wenzelm@16678
  1213
fun dest_abs (x, T, body) =
wenzelm@16678
  1214
  let
wenzelm@16678
  1215
    fun name_clash (Free (y, _)) = (x = y)
wenzelm@16678
  1216
      | name_clash (t $ u) = name_clash t orelse name_clash u
wenzelm@16678
  1217
      | name_clash (Abs (_, _, t)) = name_clash t
wenzelm@16678
  1218
      | name_clash _ = false;
wenzelm@16678
  1219
  in
wenzelm@16678
  1220
    if name_clash body then
wenzelm@16678
  1221
      dest_abs (variant [x] x, T, body)    (*potentially slow, but rarely happens*)
wenzelm@16678
  1222
    else (x, subst_bound (Free (x, T), body))
wenzelm@16678
  1223
  end;
wenzelm@16678
  1224
wenzelm@16990
  1225
(*names for numbered variables --
wenzelm@16990
  1226
  preserves order wrt. int_ord vs. string_ord, avoids allocating new strings*)
wenzelm@16990
  1227
local
wenzelm@16990
  1228
  val small_int = Vector.tabulate (1000, fn i =>
wenzelm@16990
  1229
    let val leading = if i < 10 then "00" else if i < 100 then "0" else ""
wenzelm@16990
  1230
    in ":" ^ leading ^ string_of_int i end);
wenzelm@16990
  1231
in
wenzelm@16990
  1232
  fun bound n =
wenzelm@16990
  1233
    if n < 1000 then Vector.sub (small_int, n)
wenzelm@16990
  1234
    else ":" ^ bound (n div 1000) ^ Vector.sub (small_int, n mod 1000);
wenzelm@16990
  1235
end;
wenzelm@16990
  1236
wenzelm@16990
  1237
val is_bound = String.isPrefix ":";
wenzelm@16943
  1238
clasohm@0
  1239
(* renames and reverses the strings in vars away from names *)
clasohm@0
  1240
fun rename_aTs names vars : (string*typ)list =
clasohm@0
  1241
  let fun rename_aT (vars,(a,T)) =
wenzelm@9536
  1242
                (variant (map #1 vars @ names) a, T) :: vars
skalberg@15570
  1243
  in Library.foldl rename_aT ([],vars) end;
clasohm@0
  1244
clasohm@0
  1245
fun rename_wrt_term t = rename_aTs (add_term_names(t,[]));
clasohm@1364
  1246
paulson@1417
  1247
wenzelm@16943
  1248
(* zero var indexes *)
wenzelm@4286
  1249
wenzelm@16943
  1250
fun zero_var_inst vars =
wenzelm@16943
  1251
  fold (fn v as ((x, i), X) => fn (used, inst) =>
wenzelm@16943
  1252
    let
wenzelm@17642
  1253
      val x' = variant used (if is_bound x then "u" else x);
wenzelm@16943
  1254
      val used' = x' :: used;
wenzelm@16943
  1255
    in if x = x' andalso i = 0 then (used', inst) else (used', (v, ((x', 0), X)) :: inst) end)
wenzelm@16943
  1256
  vars ([], []) |> #2;
wenzelm@4286
  1257
wenzelm@16943
  1258
fun zero_var_indexesT ty =
wenzelm@16943
  1259
  instantiateT (map (apsnd TVar) (zero_var_inst (sort tvar_ord (add_tvarsT ty [])))) ty;
haftmann@16790
  1260
wenzelm@16943
  1261
fun zero_var_indexes_inst tm =
wenzelm@16943
  1262
  let
wenzelm@16943
  1263
    val instT = map (apsnd TVar) (zero_var_inst (sort tvar_ord (fold_types add_tvarsT tm [])));
wenzelm@16943
  1264
    val inst =
wenzelm@16943
  1265
      add_vars tm [] |> map (apsnd (instantiateT instT))
wenzelm@16943
  1266
      |> sort var_ord |> zero_var_inst |> map (apsnd Var);
wenzelm@16943
  1267
  in (instT, inst) end;
wenzelm@12499
  1268
wenzelm@16943
  1269
fun zero_var_indexes tm = instantiate (zero_var_indexes_inst tm) tm;
wenzelm@4286
  1270
paulson@1417
  1271
wenzelm@9536
  1272
(* dummy patterns *)
wenzelm@9536
  1273
wenzelm@9536
  1274
val dummy_patternN = "dummy_pattern";
wenzelm@9536
  1275
wenzelm@18253
  1276
fun dummy_pattern T = Const (dummy_patternN, T);
wenzelm@18253
  1277
wenzelm@9536
  1278
fun is_dummy_pattern (Const ("dummy_pattern", _)) = true
wenzelm@9536
  1279
  | is_dummy_pattern _ = false;
wenzelm@9536
  1280
wenzelm@9536
  1281
fun no_dummy_patterns tm =
haftmann@16787
  1282
  if not (fold_aterms (fn t => fn b => b orelse is_dummy_pattern t) tm false) then tm
wenzelm@9536
  1283
  else raise TERM ("Illegal occurrence of '_' dummy pattern", [tm]);
wenzelm@9536
  1284
wenzelm@11903
  1285
fun replace_dummy Ts (i, Const ("dummy_pattern", T)) =
wenzelm@11903
  1286
      (i + 1, list_comb (Var (("_dummy_", i), Ts ---> T), map Bound (0 upto length Ts - 1)))
wenzelm@11903
  1287
  | replace_dummy Ts (i, Abs (x, T, t)) =
wenzelm@11903
  1288
      let val (i', t') = replace_dummy (T :: Ts) (i, t)
wenzelm@11903
  1289
      in (i', Abs (x, T, t')) end
wenzelm@11903
  1290
  | replace_dummy Ts (i, t $ u) =
wenzelm@11903
  1291
      let val (i', t') = replace_dummy Ts (i, t); val (i'', u') = replace_dummy Ts (i', u)
wenzelm@11903
  1292
      in (i'', t' $ u') end
wenzelm@11903
  1293
  | replace_dummy _ (i, a) = (i, a);
wenzelm@11903
  1294
wenzelm@11903
  1295
val replace_dummy_patterns = replace_dummy [];
wenzelm@9536
  1296
wenzelm@10552
  1297
fun is_replaced_dummy_pattern ("_dummy_", _) = true
wenzelm@10552
  1298
  | is_replaced_dummy_pattern _ = false;
wenzelm@9536
  1299
wenzelm@16035
  1300
fun show_dummy_patterns (Var (("_dummy_", _), T)) = Const ("dummy_pattern", T)
wenzelm@16035
  1301
  | show_dummy_patterns (t $ u) = show_dummy_patterns t $ show_dummy_patterns u
wenzelm@16035
  1302
  | show_dummy_patterns (Abs (x, T, t)) = Abs (x, T, show_dummy_patterns t)
wenzelm@16035
  1303
  | show_dummy_patterns a = a;
wenzelm@16035
  1304
wenzelm@13484
  1305
wenzelm@13484
  1306
(* adhoc freezing *)
wenzelm@13484
  1307
wenzelm@13484
  1308
fun adhoc_freeze_vars tm =
wenzelm@13484
  1309
  let
wenzelm@13484
  1310
    fun mk_inst (var as Var ((a, i), T)) =
wenzelm@13484
  1311
      let val x = a ^ Library.gensym "_" ^ string_of_int i
wenzelm@13484
  1312
      in ((var,  Free(x, T)), x) end;
wenzelm@13484
  1313
    val (insts, xs) = split_list (map mk_inst (term_vars tm));
wenzelm@13484
  1314
  in (subst_atomic insts tm, xs) end;
wenzelm@13484
  1315
wenzelm@13484
  1316
wenzelm@15986
  1317
val show_question_marks = ref true;
berghofe@15472
  1318
wenzelm@14786
  1319
fun string_of_vname (x, i) =
wenzelm@14786
  1320
  let
wenzelm@15986
  1321
    val question_mark = if ! show_question_marks then "?" else "";
wenzelm@15986
  1322
    val idx = string_of_int i;
wenzelm@15986
  1323
    val dot =
wenzelm@15986
  1324
      (case rev (Symbol.explode x) of
wenzelm@15986
  1325
        _ :: "\\<^isub>" :: _ => false
wenzelm@15986
  1326
      | _ :: "\\<^isup>" :: _ => false
wenzelm@15986
  1327
      | c :: _ => Symbol.is_digit c
wenzelm@15986
  1328
      | _ => true);
wenzelm@14786
  1329
  in
wenzelm@15986
  1330
    if dot then question_mark ^ x ^ "." ^ idx
wenzelm@15986
  1331
    else if i <> 0 then question_mark ^ x ^ idx
wenzelm@15986
  1332
    else question_mark ^ x
wenzelm@14786
  1333
  end;
wenzelm@14786
  1334
wenzelm@14786
  1335
fun string_of_vname' (x, ~1) = x
wenzelm@14786
  1336
  | string_of_vname' xi = string_of_vname xi;
wenzelm@14786
  1337
haftmann@19455
  1338
fun str_of_sort [] = "{}"
haftmann@19455
  1339
  | str_of_sort [c] = c
haftmann@19455
  1340
  | str_of_sort cs = (enclose "{" "}" o commas) cs
wenzelm@17777
  1341
haftmann@19455
  1342
fun str_of_typ (Type ("fun", [ty1, ty2])) =
haftmann@19455
  1343
      "(" ^ str_of_typ ty1 ^ " => " ^ str_of_typ ty2 ^ ")"
haftmann@19455
  1344
  | str_of_typ (Type ("dummy", [])) =
haftmann@19455
  1345
      "_"
haftmann@19455
  1346
  | str_of_typ (Type (tyco, _)) =
haftmann@19455
  1347
      tyco
haftmann@19455
  1348
  | str_of_typ (Type (tyco, tys)) =
haftmann@19455
  1349
      (enclose "(" ")" o space_implode " ") (tyco :: map str_of_typ tys)
haftmann@19455
  1350
  | str_of_typ (TFree (v, sort)) =
haftmann@19455
  1351
      v ^ "::" ^ str_of_sort sort
haftmann@19455
  1352
  | str_of_typ (TVar (vi, sort)) =
haftmann@19455
  1353
      string_of_vname vi ^ "::" ^ str_of_sort sort;
haftmann@19455
  1354
haftmann@19455
  1355
val str_of_term =
haftmann@19455
  1356
  let
haftmann@19455
  1357
    fun typed (s, ty) = s ^ "::" ^ str_of_typ ty;
haftmann@19455
  1358
    fun bound vs i = case AList.lookup (op =) vs i
haftmann@19455
  1359
     of SOME v => enclose "[" "]" (string_of_int i ^ " ~> " ^ v)
haftmann@19455
  1360
      | NONE => (enclose "[" "]" o string_of_int) i
haftmann@19455
  1361
    fun str vs (Const (c, _)) = c
haftmann@19455
  1362
      | str vs (Free (v, ty)) = typed (v, ty)
haftmann@19455
  1363
      | str vs (Var (vi, ty)) = typed (string_of_vname vi, ty)
haftmann@19455
  1364
      | str vs (Bound i) = bound vs i
haftmann@19455
  1365
      | str vs (Abs (x, ty, t)) = "(%" ^ typed (x, ty) ^ ". " ^ str ((length vs, x)::vs) t ^ ")"
haftmann@19455
  1366
      | str vs (t1 $ t2) = "(" ^ str vs t1 ^ " " ^ str vs t2 ^ ")";
haftmann@19455
  1367
  in str [] end;
wenzelm@17777
  1368
clasohm@1364
  1369
end;
clasohm@1364
  1370
wenzelm@4444
  1371
structure BasicTerm: BASIC_TERM = Term;
wenzelm@4444
  1372
open BasicTerm;