src/Pure/term.ML
author wenzelm
Wed Nov 16 17:45:29 2005 +0100 (2005-11-16)
changeset 18183 a9f67248996a
parent 18149 c6899e23b5ff
child 18253 0626a0a217ec
permissions -rw-r--r--
added betapplys;
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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_body: term -> term
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  val strip_abs_vars: term -> (string * typ) list
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  val strip_qnt_body: string -> term -> term
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  val strip_qnt_vars: string -> term -> (string * typ) list
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  val list_comb: term * term list -> term
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  val strip_comb: term -> term * term list
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  val head_of: term -> term
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  val size_of_term: term -> int
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  val map_type_tvar: (indexname * sort -> typ) -> typ -> typ
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  val map_type_tfree: (string * sort -> typ) -> typ -> typ
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  val map_term_types: (typ -> typ) -> term -> term
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  val it_term_types: (typ * 'a -> 'a) -> term * 'a -> 'a
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  val 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 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 itselfT: typ -> typ
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  val a_itselfT: typ
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  val propT: typ
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  val implies: term
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  val all: typ -> term
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  val equals: typ -> term
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  val strip_all_body: term -> term
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  val strip_all_vars: term -> (string * typ) list
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  val incr_bv: int * int * term -> term
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  val incr_boundvars: int -> term -> term
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  val add_loose_bnos: term * int * int list -> int list
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  val loose_bnos: term -> int list
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  val loose_bvar: term * int -> bool
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  val loose_bvar1: term * int -> bool
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  val subst_bounds: term list * term -> term
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  val subst_bound: term * term -> term
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  val 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_typ_classes: typ * class list -> class list
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  val add_typ_tycons: typ * string list -> string list
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  val add_term_classes: term * class list -> class list
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  val add_term_tycons: term * string list -> string list
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  val add_term_consts: term * string list -> string list
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  val term_consts: term -> string list
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  val 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 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 invent_names: string list -> string -> int -> string list
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  val map_typ: (string -> string) -> (string -> string) -> typ -> typ
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  val map_term: (string -> string) -> (string -> string) -> (string -> string) -> term -> term
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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 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_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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paulson@4464
   326
fun domain_type (Type("fun", [T,_])) = T
paulson@4464
   327
and range_type  (Type("fun", [_,T])) = T;
paulson@4064
   328
clasohm@0
   329
(* maps  [T1,...,Tn]--->T  to the list  [T1,T2,...,Tn]*)
clasohm@0
   330
fun binder_types (Type("fun",[S,T])) = S :: binder_types T
clasohm@0
   331
  | binder_types _   =  [];
clasohm@0
   332
clasohm@0
   333
(* maps  [T1,...,Tn]--->T  to T*)
clasohm@0
   334
fun body_type (Type("fun",[S,T])) = body_type T
clasohm@0
   335
  | body_type T   =  T;
clasohm@0
   336
clasohm@0
   337
(* maps  [T1,...,Tn]--->T  to   ([T1,T2,...,Tn], T)  *)
clasohm@0
   338
fun strip_type T : typ list * typ =
clasohm@0
   339
  (binder_types T, body_type T);
clasohm@0
   340
clasohm@0
   341
clasohm@0
   342
(*Compute the type of the term, checking that combinations are well-typed
clasohm@0
   343
  Ts = [T0,T1,...] holds types of bound variables 0, 1, ...*)
clasohm@0
   344
fun type_of1 (Ts, Const (_,T)) = T
clasohm@0
   345
  | type_of1 (Ts, Free  (_,T)) = T
skalberg@15570
   346
  | type_of1 (Ts, Bound i) = (List.nth (Ts,i)
skalberg@15570
   347
        handle Subscript => raise TYPE("type_of: bound variable", [], [Bound i]))
clasohm@0
   348
  | type_of1 (Ts, Var (_,T)) = T
clasohm@0
   349
  | type_of1 (Ts, Abs (_,T,body)) = T --> type_of1(T::Ts, body)
wenzelm@13000
   350
  | type_of1 (Ts, f$u) =
clasohm@0
   351
      let val U = type_of1(Ts,u)
clasohm@0
   352
          and T = type_of1(Ts,f)
clasohm@0
   353
      in case T of
wenzelm@9536
   354
            Type("fun",[T1,T2]) =>
wenzelm@9536
   355
              if T1=U then T2  else raise TYPE
wenzelm@9536
   356
                    ("type_of: type mismatch in application", [T1,U], [f$u])
wenzelm@13000
   357
          | _ => raise TYPE
wenzelm@9536
   358
                    ("type_of: function type is expected in application",
wenzelm@9536
   359
                     [T,U], [f$u])
clasohm@0
   360
      end;
clasohm@0
   361
clasohm@0
   362
fun type_of t : typ = type_of1 ([],t);
clasohm@0
   363
clasohm@0
   364
(*Determines the type of a term, with minimal checking*)
wenzelm@13000
   365
fun fastype_of1 (Ts, f$u) =
lcp@61
   366
    (case fastype_of1 (Ts,f) of
wenzelm@9536
   367
        Type("fun",[_,T]) => T
wenzelm@9536
   368
        | _ => raise TERM("fastype_of: expected function type", [f$u]))
lcp@61
   369
  | fastype_of1 (_, Const (_,T)) = T
lcp@61
   370
  | fastype_of1 (_, Free (_,T)) = T
skalberg@15570
   371
  | fastype_of1 (Ts, Bound i) = (List.nth(Ts,i)
skalberg@15570
   372
         handle Subscript => raise TERM("fastype_of: Bound", [Bound i]))
wenzelm@13000
   373
  | fastype_of1 (_, Var (_,T)) = T
lcp@61
   374
  | fastype_of1 (Ts, Abs (_,T,u)) = T --> fastype_of1 (T::Ts, u);
lcp@61
   375
lcp@61
   376
fun fastype_of t : typ = fastype_of1 ([],t);
clasohm@0
   377
wenzelm@16678
   378
(*Determine the argument type of a function*)
wenzelm@16678
   379
fun argument_type_of tm =
wenzelm@16678
   380
  let
wenzelm@16678
   381
    fun argT i (Type ("fun", [T, U])) = if i = 0 then T else argT (i - 1) U
wenzelm@16678
   382
      | argT _ T = raise TYPE ("argument_type_of", [T], []);
wenzelm@16678
   383
wenzelm@16678
   384
    fun arg 0 _ (Abs (_, T, _)) = T
wenzelm@16678
   385
      | arg i Ts (Abs (_, T, t)) = arg (i - 1) (T :: Ts) t
wenzelm@16678
   386
      | arg i Ts (t $ _) = arg (i + 1) Ts t
wenzelm@16678
   387
      | arg i Ts a = argT i (fastype_of1 (Ts, a));
wenzelm@16678
   388
  in arg 0 [] tm end;
wenzelm@16678
   389
clasohm@0
   390
skalberg@15570
   391
val list_abs = Library.foldr (fn ((x, T), t) => Abs (x, T, t));
wenzelm@10806
   392
clasohm@0
   393
(* maps  (x1,...,xn)t   to   t  *)
wenzelm@13000
   394
fun strip_abs_body (Abs(_,_,t))  =  strip_abs_body t
clasohm@0
   395
  | strip_abs_body u  =  u;
clasohm@0
   396
clasohm@0
   397
(* maps  (x1,...,xn)t   to   [x1, ..., xn]  *)
wenzelm@13000
   398
fun strip_abs_vars (Abs(a,T,t))  =  (a,T) :: strip_abs_vars t
clasohm@0
   399
  | strip_abs_vars u  =  [] : (string*typ) list;
clasohm@0
   400
clasohm@0
   401
clasohm@0
   402
fun strip_qnt_body qnt =
clasohm@0
   403
let fun strip(tm as Const(c,_)$Abs(_,_,t)) = if c=qnt then strip t else tm
clasohm@0
   404
      | strip t = t
clasohm@0
   405
in strip end;
clasohm@0
   406
clasohm@0
   407
fun strip_qnt_vars qnt =
clasohm@0
   408
let fun strip(Const(c,_)$Abs(a,T,t)) = if c=qnt then (a,T)::strip t else []
clasohm@0
   409
      | strip t  =  [] : (string*typ) list
clasohm@0
   410
in strip end;
clasohm@0
   411
clasohm@0
   412
clasohm@0
   413
(* maps   (f, [t1,...,tn])  to  f(t1,...,tn) *)
skalberg@15570
   414
val list_comb : term * term list -> term = Library.foldl (op $);
clasohm@0
   415
clasohm@0
   416
clasohm@0
   417
(* maps   f(t1,...,tn)  to  (f, [t1,...,tn]) ; naturally tail-recursive*)
wenzelm@13000
   418
fun strip_comb u : term * term list =
clasohm@0
   419
    let fun stripc (f$t, ts) = stripc (f, t::ts)
wenzelm@13000
   420
        |   stripc  x =  x
clasohm@0
   421
    in  stripc(u,[])  end;
clasohm@0
   422
clasohm@0
   423
clasohm@0
   424
(* maps   f(t1,...,tn)  to  f , which is never a combination *)
clasohm@0
   425
fun head_of (f$t) = head_of f
clasohm@0
   426
  | head_of u = u;
clasohm@0
   427
clasohm@0
   428
wenzelm@16599
   429
(*number of atoms and abstractions in a term*)
wenzelm@16599
   430
fun size_of_term tm =
wenzelm@16599
   431
  let
wenzelm@16678
   432
    fun add_size (t $ u, n) = add_size (t, add_size (u, n))
wenzelm@16678
   433
      | add_size (Abs (_ ,_, t), n) = add_size (t, n + 1)
wenzelm@16678
   434
      | add_size (_, n) = n + 1;
wenzelm@16678
   435
  in add_size (tm, 0) end;
clasohm@0
   436
wenzelm@16678
   437
fun map_type_tvar f =
wenzelm@16678
   438
  let
wenzelm@16678
   439
    fun map_aux (Type (a, Ts)) = Type (a, map map_aux Ts)
wenzelm@16678
   440
      | map_aux (TVar x) = f x
wenzelm@16678
   441
      | map_aux T = T;
wenzelm@16678
   442
  in map_aux end;
nipkow@949
   443
wenzelm@16678
   444
fun map_type_tfree f =
wenzelm@16678
   445
  let
wenzelm@16678
   446
    fun map_aux (Type (a, Ts)) = Type (a, map map_aux Ts)
wenzelm@16678
   447
      | map_aux (TFree x) = f x
wenzelm@16678
   448
      | map_aux T = T;
wenzelm@16678
   449
  in map_aux end;
nipkow@949
   450
clasohm@0
   451
fun map_term_types f =
wenzelm@16678
   452
  let
wenzelm@16678
   453
    fun map_aux (Const (a, T)) = Const (a, f T)
wenzelm@16678
   454
      | map_aux (Free (a, T)) = Free (a, f T)
wenzelm@16678
   455
      | map_aux (Var (v, T)) = Var (v, f T)
wenzelm@16678
   456
      | map_aux (t as Bound _)  = t
wenzelm@16678
   457
      | map_aux (Abs (a, T, t)) = Abs (a, f T, map_aux t)
wenzelm@16678
   458
      | map_aux (t $ u) = map_aux t $ map_aux u;
wenzelm@16678
   459
  in map_aux end;
clasohm@0
   460
clasohm@0
   461
(* iterate a function over all types in a term *)
clasohm@0
   462
fun it_term_types f =
clasohm@0
   463
let fun iter(Const(_,T), a) = f(T,a)
clasohm@0
   464
      | iter(Free(_,T), a) = f(T,a)
clasohm@0
   465
      | iter(Var(_,T), a) = f(T,a)
clasohm@0
   466
      | iter(Abs(_,T,t), a) = iter(t,f(T,a))
clasohm@0
   467
      | iter(f$u, a) = iter(f, iter(u, a))
clasohm@0
   468
      | iter(Bound _, a) = a
clasohm@0
   469
in iter end
clasohm@0
   470
clasohm@0
   471
wenzelm@16943
   472
(* fold types and terms *)
wenzelm@16943
   473
wenzelm@16943
   474
(*fold atoms of type*)
wenzelm@16943
   475
fun fold_atyps f (Type (_, Ts)) = fold (fold_atyps f) Ts
wenzelm@16943
   476
  | fold_atyps f T = f T;
wenzelm@16943
   477
wenzelm@16943
   478
(*fold atoms of term*)
wenzelm@16943
   479
fun fold_aterms f (t $ u) = fold_aterms f t #> fold_aterms f u
wenzelm@16943
   480
  | fold_aterms f (Abs (_, _, t)) = fold_aterms f t
wenzelm@16943
   481
  | fold_aterms f a = f a;
wenzelm@16943
   482
wenzelm@16943
   483
(*fold types of term*)
wenzelm@16943
   484
fun fold_term_types f (t as Const (_, T)) = f t T
wenzelm@16943
   485
  | fold_term_types f (t as Free (_, T)) = f t T
wenzelm@16943
   486
  | fold_term_types f (t as Var (_, T)) = f t T
wenzelm@16943
   487
  | fold_term_types f (Bound _) = I
wenzelm@16943
   488
  | fold_term_types f (t as Abs (_, T, b)) = f t T #> fold_term_types f b
wenzelm@16943
   489
  | fold_term_types f (t $ u) = fold_term_types f t #> fold_term_types f u;
wenzelm@16943
   490
wenzelm@16943
   491
fun fold_types f = fold_term_types (K f);
wenzelm@16943
   492
wenzelm@16943
   493
(*collect variables*)
wenzelm@16943
   494
val add_tvarsT = fold_atyps (fn TVar v => insert (op =) v | _ => I);
wenzelm@16943
   495
val add_tvars = fold_types add_tvarsT;
wenzelm@16943
   496
val add_vars = fold_aterms (fn Var v => insert (op =) v | _ => I);
wenzelm@16943
   497
val add_tfreesT = fold_atyps (fn TFree v => insert (op =) v | _ => I);
wenzelm@16943
   498
val add_tfrees = fold_types add_tfreesT;
wenzelm@16943
   499
val add_frees = fold_aterms (fn Free v => insert (op =) v | _ => I);
wenzelm@16943
   500
wenzelm@16943
   501
(*collect variable names*)
wenzelm@16943
   502
val add_term_varnames = fold_aterms (fn Var (xi, _) => insert (op =) xi | _ => I);
wenzelm@16943
   503
fun term_varnames t = add_term_varnames t [];
wenzelm@16943
   504
wenzelm@18149
   505
fun find_free t x =
wenzelm@18149
   506
  let
wenzelm@18149
   507
    exception Found of term;
wenzelm@18149
   508
    fun find (t as Free (x', _)) = if x = x' then raise Found t else I
wenzelm@18149
   509
      | find _ = I;
wenzelm@18149
   510
  in (fold_aterms find t (); NONE) handle Found v => SOME v end;
wenzelm@18149
   511
wenzelm@18149
   512
wenzelm@16943
   513
wenzelm@16678
   514
(** Comparing terms, types, sorts etc. **)
wenzelm@16537
   515
wenzelm@16678
   516
(* fast syntactic comparison *)
wenzelm@16678
   517
wenzelm@16678
   518
fun fast_indexname_ord ((x, i), (y, j)) =
wenzelm@16678
   519
  (case int_ord (i, j) of EQUAL => fast_string_ord (x, y) | ord => ord);
wenzelm@16537
   520
wenzelm@16599
   521
fun sort_ord SS =
wenzelm@16599
   522
  if pointer_eq SS then EQUAL
wenzelm@16990
   523
  else dict_ord fast_string_ord SS;
wenzelm@16678
   524
wenzelm@16678
   525
local
wenzelm@16537
   526
wenzelm@16678
   527
fun cons_nr (TVar _) = 0
wenzelm@16678
   528
  | cons_nr (TFree _) = 1
wenzelm@16678
   529
  | cons_nr (Type _) = 2;
wenzelm@16537
   530
wenzelm@16678
   531
in
wenzelm@16537
   532
wenzelm@16537
   533
fun typ_ord TU =
wenzelm@16537
   534
  if pointer_eq TU then EQUAL
wenzelm@16537
   535
  else
wenzelm@16537
   536
    (case TU of
wenzelm@16678
   537
      (Type (a, Ts), Type (b, Us)) =>
wenzelm@16990
   538
        (case fast_string_ord (a, b) of EQUAL => dict_ord typ_ord (Ts, Us) | ord => ord)
wenzelm@16678
   539
    | (TFree (a, S), TFree (b, S')) =>
wenzelm@16678
   540
        (case fast_string_ord (a, b) of EQUAL => sort_ord (S, S') | ord => ord)
wenzelm@16678
   541
    | (TVar (xi, S), TVar (yj, S')) =>
wenzelm@16678
   542
        (case fast_indexname_ord (xi, yj) of EQUAL => sort_ord (S, S') | ord => ord)
wenzelm@16678
   543
    | (T, U) => int_ord (cons_nr T, cons_nr U));
wenzelm@16678
   544
wenzelm@16678
   545
end;
wenzelm@16678
   546
wenzelm@16678
   547
local
wenzelm@16678
   548
wenzelm@16678
   549
fun cons_nr (Const _) = 0
wenzelm@16678
   550
  | cons_nr (Free _) = 1
wenzelm@16678
   551
  | cons_nr (Var _) = 2
wenzelm@16678
   552
  | cons_nr (Bound _) = 3
wenzelm@16678
   553
  | cons_nr (Abs _) = 4
wenzelm@16678
   554
  | cons_nr (_ $ _) = 5;
wenzelm@16678
   555
wenzelm@16678
   556
fun struct_ord (Abs (_, _, t), Abs (_, _, u)) = struct_ord (t, u)
wenzelm@16678
   557
  | struct_ord (t1 $ t2, u1 $ u2) =
wenzelm@16678
   558
      (case struct_ord (t1, u1) of EQUAL => struct_ord (t2, u2) | ord => ord)
wenzelm@16678
   559
  | struct_ord (t, u) = int_ord (cons_nr t, cons_nr u);
wenzelm@16678
   560
wenzelm@16678
   561
fun atoms_ord (Abs (_, _, t), Abs (_, _, u)) = atoms_ord (t, u)
wenzelm@16678
   562
  | atoms_ord (t1 $ t2, u1 $ u2) =
wenzelm@16678
   563
      (case atoms_ord (t1, u1) of EQUAL => atoms_ord (t2, u2) | ord => ord)
wenzelm@16678
   564
  | atoms_ord (Const (a, _), Const (b, _)) = fast_string_ord (a, b)
wenzelm@16678
   565
  | atoms_ord (Free (x, _), Free (y, _)) = fast_string_ord (x, y)
wenzelm@16678
   566
  | atoms_ord (Var (xi, _), Var (yj, _)) = fast_indexname_ord (xi, yj)
wenzelm@16678
   567
  | atoms_ord (Bound i, Bound j) = int_ord (i, j)
wenzelm@16678
   568
  | atoms_ord _ = sys_error "atoms_ord";
wenzelm@16678
   569
wenzelm@16678
   570
fun types_ord (Abs (_, T, t), Abs (_, U, u)) =
wenzelm@16678
   571
      (case typ_ord (T, U) of EQUAL => types_ord (t, u) | ord => ord)
wenzelm@16678
   572
  | types_ord (t1 $ t2, u1 $ u2) =
wenzelm@16678
   573
      (case types_ord (t1, u1) of EQUAL => types_ord (t2, u2) | ord => ord)
wenzelm@16678
   574
  | types_ord (Const (_, T), Const (_, U)) = typ_ord (T, U)
wenzelm@16678
   575
  | types_ord (Free (_, T), Free (_, U)) = typ_ord (T, U)
wenzelm@16678
   576
  | types_ord (Var (_, T), Var (_, U)) = typ_ord (T, U)
wenzelm@16678
   577
  | types_ord (Bound _, Bound _) = EQUAL
wenzelm@16678
   578
  | types_ord _ = sys_error "types_ord";
wenzelm@16678
   579
wenzelm@16678
   580
in
wenzelm@16678
   581
wenzelm@16678
   582
fun fast_term_ord tu =
wenzelm@16678
   583
  if pointer_eq tu then EQUAL
wenzelm@16678
   584
  else
wenzelm@16678
   585
    (case struct_ord tu of
wenzelm@16678
   586
      EQUAL => (case atoms_ord tu of EQUAL => types_ord tu | ord => ord)
wenzelm@16678
   587
    | ord => ord);
wenzelm@16678
   588
wenzelm@16678
   589
fun op aconv tu = (fast_term_ord tu = EQUAL);
wenzelm@16678
   590
fun aconvs ts_us = (list_ord fast_term_ord ts_us = EQUAL);
wenzelm@16678
   591
wenzelm@16678
   592
structure Vartab = TableFun(type key = indexname val ord = fast_indexname_ord);
wenzelm@16678
   593
structure Typtab = TableFun(type key = typ val ord = typ_ord);
wenzelm@16678
   594
structure Termtab = TableFun(type key = term val ord = fast_term_ord);
wenzelm@16678
   595
wenzelm@16678
   596
end;
wenzelm@16537
   597
wenzelm@16537
   598
wenzelm@16537
   599
(* term_ord *)
wenzelm@16537
   600
wenzelm@16537
   601
(*a linear well-founded AC-compatible ordering for terms:
wenzelm@16537
   602
  s < t <=> 1. size(s) < size(t) or
wenzelm@16537
   603
            2. size(s) = size(t) and s=f(...) and t=g(...) and f<g or
wenzelm@16537
   604
            3. size(s) = size(t) and s=f(s1..sn) and t=f(t1..tn) and
wenzelm@16537
   605
               (s1..sn) < (t1..tn) (lexicographically)*)
wenzelm@16678
   606
wenzelm@16678
   607
fun indexname_ord ((x, i), (y, j)) =
wenzelm@16678
   608
  (case int_ord (i, j) of EQUAL => string_ord (x, y) | ord => ord);
wenzelm@16678
   609
wenzelm@16667
   610
local
wenzelm@16667
   611
wenzelm@16667
   612
fun hd_depth (t $ _, n) = hd_depth (t, n + 1)
wenzelm@16667
   613
  | hd_depth p = p;
wenzelm@16537
   614
wenzelm@16537
   615
fun dest_hd (Const (a, T)) = (((a, 0), T), 0)
wenzelm@16537
   616
  | dest_hd (Free (a, T)) = (((a, 0), T), 1)
wenzelm@16537
   617
  | dest_hd (Var v) = (v, 2)
wenzelm@16537
   618
  | dest_hd (Bound i) = ((("", i), dummyT), 3)
wenzelm@16537
   619
  | dest_hd (Abs (_, T, _)) = ((("", 0), T), 4);
wenzelm@16537
   620
wenzelm@16667
   621
in
wenzelm@16667
   622
wenzelm@16537
   623
fun term_ord tu =
wenzelm@16537
   624
  if pointer_eq tu then EQUAL
wenzelm@16537
   625
  else
wenzelm@16537
   626
    (case tu of
wenzelm@16537
   627
      (Abs (_, T, t), Abs(_, U, u)) =>
wenzelm@16537
   628
        (case term_ord (t, u) of EQUAL => typ_ord (T, U) | ord => ord)
wenzelm@16667
   629
    | (t, u) =>
wenzelm@16537
   630
        (case int_ord (size_of_term t, size_of_term u) of
wenzelm@16537
   631
          EQUAL =>
wenzelm@16943
   632
            (case prod_ord hd_ord int_ord (hd_depth (t, 0), hd_depth (u, 0)) of
wenzelm@16943
   633
              EQUAL => args_ord (t, u) | ord => ord)
wenzelm@16537
   634
        | ord => ord))
wenzelm@16537
   635
and hd_ord (f, g) =
wenzelm@16537
   636
  prod_ord (prod_ord indexname_ord typ_ord) int_ord (dest_hd f, dest_hd g)
wenzelm@16667
   637
and args_ord (f $ t, g $ u) =
wenzelm@16667
   638
      (case args_ord (f, g) of EQUAL => term_ord (t, u) | ord => ord)
wenzelm@16667
   639
  | args_ord _ = EQUAL;
wenzelm@16537
   640
wenzelm@16537
   641
fun termless tu = (term_ord tu = LESS);
wenzelm@16537
   642
wenzelm@16667
   643
end;
wenzelm@16667
   644
wenzelm@16667
   645
wenzelm@16667
   646
(** Lexicographic path order on terms **)
wenzelm@16667
   647
wenzelm@16667
   648
(*
nipkow@16570
   649
  See Baader & Nipkow, Term rewriting, CUP 1998.
nipkow@16570
   650
  Without variables.  Const, Var, Bound, Free and Abs are treated all as
nipkow@16570
   651
  constants.
nipkow@16570
   652
nipkow@16570
   653
  f_ord maps strings to integers and serves two purposes:
nipkow@16570
   654
  - Predicate on constant symbols.  Those that are not recognised by f_ord
nipkow@16570
   655
    must be mapped to ~1.
nipkow@16570
   656
  - Order on the recognised symbols.  These must be mapped to distinct
nipkow@16570
   657
    integers >= 0.
nipkow@16570
   658
wenzelm@16667
   659
*)
nipkow@16570
   660
nipkow@16570
   661
local
wenzelm@16667
   662
fun dest_hd f_ord (Const (a, T)) =
nipkow@16570
   663
      let val ord = f_ord a in
nipkow@16570
   664
        if ord = ~1 then ((1, ((a, 0), T)), 0) else ((0, (("", ord), T)), 0)
nipkow@16570
   665
      end
nipkow@16570
   666
  | dest_hd _ (Free (a, T)) = ((1, ((a, 0), T)), 0)
nipkow@16570
   667
  | dest_hd _ (Var v) = ((1, v), 1)
nipkow@16570
   668
  | dest_hd _ (Bound i) = ((1, (("", i), dummyT)), 2)
nipkow@16570
   669
  | dest_hd _ (Abs (_, T, _)) = ((1, (("", 0), T)), 3);
nipkow@16570
   670
nipkow@16570
   671
fun term_lpo f_ord (s, t) =
nipkow@16570
   672
  let val (f, ss) = strip_comb s and (g, ts) = strip_comb t in
nipkow@16570
   673
    if forall (fn si => term_lpo f_ord (si, t) = LESS) ss
nipkow@16570
   674
    then case hd_ord f_ord (f, g) of
wenzelm@16667
   675
        GREATER =>
wenzelm@16667
   676
          if forall (fn ti => term_lpo f_ord (s, ti) = GREATER) ts
wenzelm@16667
   677
          then GREATER else LESS
nipkow@16570
   678
      | EQUAL =>
wenzelm@16667
   679
          if forall (fn ti => term_lpo f_ord (s, ti) = GREATER) ts
wenzelm@16667
   680
          then list_ord (term_lpo f_ord) (ss, ts)
wenzelm@16667
   681
          else LESS
nipkow@16570
   682
      | LESS => LESS
nipkow@16570
   683
    else GREATER
nipkow@16570
   684
  end
nipkow@16570
   685
and hd_ord f_ord (f, g) = case (f, g) of
nipkow@16570
   686
    (Abs (_, T, t), Abs (_, U, u)) =>
nipkow@16570
   687
      (case term_lpo f_ord (t, u) of EQUAL => typ_ord (T, U) | ord => ord)
nipkow@16570
   688
  | (_, _) => prod_ord (prod_ord int_ord
nipkow@16570
   689
                  (prod_ord indexname_ord typ_ord)) int_ord
nipkow@16570
   690
                (dest_hd f_ord f, dest_hd f_ord g)
nipkow@16570
   691
in
nipkow@16570
   692
val term_lpo = term_lpo
nipkow@16570
   693
end;
nipkow@16570
   694
wenzelm@16537
   695
clasohm@0
   696
(** Connectives of higher order logic **)
clasohm@0
   697
wenzelm@375
   698
fun itselfT ty = Type ("itself", [ty]);
wenzelm@14854
   699
val a_itselfT = itselfT (TFree ("'a", []));
wenzelm@375
   700
clasohm@0
   701
val propT : typ = Type("prop",[]);
clasohm@0
   702
clasohm@0
   703
val implies = Const("==>", propT-->propT-->propT);
clasohm@0
   704
clasohm@0
   705
fun all T = Const("all", (T-->propT)-->propT);
clasohm@0
   706
clasohm@0
   707
fun equals T = Const("==", T-->T-->propT);
clasohm@0
   708
clasohm@0
   709
(* maps  !!x1...xn. t   to   t  *)
wenzelm@13000
   710
fun strip_all_body (Const("all",_)$Abs(_,_,t))  =  strip_all_body t
clasohm@0
   711
  | strip_all_body t  =  t;
clasohm@0
   712
clasohm@0
   713
(* maps  !!x1...xn. t   to   [x1, ..., xn]  *)
clasohm@0
   714
fun strip_all_vars (Const("all",_)$Abs(a,T,t))  =
wenzelm@13000
   715
                (a,T) :: strip_all_vars t
clasohm@0
   716
  | strip_all_vars t  =  [] : (string*typ) list;
clasohm@0
   717
clasohm@0
   718
(*increments a term's non-local bound variables
clasohm@0
   719
  required when moving a term within abstractions
clasohm@0
   720
     inc is  increment for bound variables
clasohm@0
   721
     lev is  level at which a bound variable is considered 'loose'*)
wenzelm@13000
   722
fun incr_bv (inc, lev, u as Bound i) = if i>=lev then Bound(i+inc) else u
clasohm@0
   723
  | incr_bv (inc, lev, Abs(a,T,body)) =
wenzelm@9536
   724
        Abs(a, T, incr_bv(inc,lev+1,body))
wenzelm@13000
   725
  | incr_bv (inc, lev, f$t) =
clasohm@0
   726
      incr_bv(inc,lev,f) $ incr_bv(inc,lev,t)
clasohm@0
   727
  | incr_bv (inc, lev, u) = u;
clasohm@0
   728
clasohm@0
   729
fun incr_boundvars  0  t = t
clasohm@0
   730
  | incr_boundvars inc t = incr_bv(inc,0,t);
clasohm@0
   731
wenzelm@12981
   732
(*Scan a pair of terms; while they are similar,
wenzelm@12981
   733
  accumulate corresponding bound vars in "al"*)
wenzelm@12981
   734
fun match_bvs(Abs(x,_,s),Abs(y,_,t), al) =
wenzelm@12981
   735
      match_bvs(s, t, if x="" orelse y="" then al
wenzelm@12981
   736
                                          else (x,y)::al)
wenzelm@12981
   737
  | match_bvs(f$s, g$t, al) = match_bvs(f,g,match_bvs(s,t,al))
wenzelm@12981
   738
  | match_bvs(_,_,al) = al;
wenzelm@12981
   739
wenzelm@12981
   740
(* strip abstractions created by parameters *)
wenzelm@12981
   741
fun match_bvars((s,t),al) = match_bvs(strip_abs_body s, strip_abs_body t, al);
wenzelm@12981
   742
wenzelm@12981
   743
fun rename_abs pat obj t =
wenzelm@12981
   744
  let
wenzelm@12981
   745
    val ren = match_bvs (pat, obj, []);
wenzelm@12981
   746
    fun ren_abs (Abs (x, T, b)) =
haftmann@17271
   747
          Abs (if_none (AList.lookup (op =) ren x) x, T, ren_abs b)
wenzelm@12981
   748
      | ren_abs (f $ t) = ren_abs f $ ren_abs t
wenzelm@12981
   749
      | ren_abs t = t
skalberg@15531
   750
  in if null ren then NONE else SOME (ren_abs t) end;
clasohm@0
   751
clasohm@0
   752
(*Accumulate all 'loose' bound vars referring to level 'lev' or beyond.
clasohm@0
   753
   (Bound 0) is loose at level 0 *)
wenzelm@13000
   754
fun add_loose_bnos (Bound i, lev, js) =
wenzelm@9536
   755
        if i<lev then js  else  (i-lev) ins_int js
clasohm@0
   756
  | add_loose_bnos (Abs (_,_,t), lev, js) = add_loose_bnos (t, lev+1, js)
clasohm@0
   757
  | add_loose_bnos (f$t, lev, js) =
wenzelm@13000
   758
        add_loose_bnos (f, lev, add_loose_bnos (t, lev, js))
clasohm@0
   759
  | add_loose_bnos (_, _, js) = js;
clasohm@0
   760
clasohm@0
   761
fun loose_bnos t = add_loose_bnos (t, 0, []);
clasohm@0
   762
clasohm@0
   763
(* loose_bvar(t,k) iff t contains a 'loose' bound variable referring to
clasohm@0
   764
   level k or beyond. *)
clasohm@0
   765
fun loose_bvar(Bound i,k) = i >= k
clasohm@0
   766
  | loose_bvar(f$t, k) = loose_bvar(f,k) orelse loose_bvar(t,k)
clasohm@0
   767
  | loose_bvar(Abs(_,_,t),k) = loose_bvar(t,k+1)
clasohm@0
   768
  | loose_bvar _ = false;
clasohm@0
   769
nipkow@2792
   770
fun loose_bvar1(Bound i,k) = i = k
nipkow@2792
   771
  | loose_bvar1(f$t, k) = loose_bvar1(f,k) orelse loose_bvar1(t,k)
nipkow@2792
   772
  | loose_bvar1(Abs(_,_,t),k) = loose_bvar1(t,k+1)
nipkow@2792
   773
  | loose_bvar1 _ = false;
clasohm@0
   774
clasohm@0
   775
(*Substitute arguments for loose bound variables.
clasohm@0
   776
  Beta-reduction of arg(n-1)...arg0 into t replacing (Bound i) with (argi).
wenzelm@4626
   777
  Note that for ((%x y. c) a b), the bound vars in c are x=1 and y=0
wenzelm@9536
   778
        and the appropriate call is  subst_bounds([b,a], c) .
clasohm@0
   779
  Loose bound variables >=n are reduced by "n" to
clasohm@0
   780
     compensate for the disappearance of lambdas.
clasohm@0
   781
*)
wenzelm@13000
   782
fun subst_bounds (args: term list, t) : term =
clasohm@0
   783
  let val n = length args;
clasohm@0
   784
      fun subst (t as Bound i, lev) =
wenzelm@9536
   785
           (if i<lev then  t    (*var is locally bound*)
wenzelm@9536
   786
            else  incr_boundvars lev (List.nth(args, i-lev))
wenzelm@9536
   787
                    handle Subscript => Bound(i-n)  (*loose: change it*))
wenzelm@9536
   788
        | subst (Abs(a,T,body), lev) = Abs(a, T,  subst(body,lev+1))
wenzelm@9536
   789
        | subst (f$t, lev) =  subst(f,lev)  $  subst(t,lev)
wenzelm@9536
   790
        | subst (t,lev) = t
clasohm@0
   791
  in   case args of [] => t  | _ => subst (t,0)  end;
clasohm@0
   792
paulson@2192
   793
(*Special case: one argument*)
wenzelm@13000
   794
fun subst_bound (arg, t) : term =
paulson@2192
   795
  let fun subst (t as Bound i, lev) =
wenzelm@9536
   796
            if i<lev then  t    (*var is locally bound*)
wenzelm@9536
   797
            else  if i=lev then incr_boundvars lev arg
wenzelm@9536
   798
                           else Bound(i-1)  (*loose: change it*)
wenzelm@9536
   799
        | subst (Abs(a,T,body), lev) = Abs(a, T,  subst(body,lev+1))
wenzelm@9536
   800
        | subst (f$t, lev) =  subst(f,lev)  $  subst(t,lev)
wenzelm@9536
   801
        | subst (t,lev) = t
paulson@2192
   802
  in  subst (t,0)  end;
paulson@2192
   803
clasohm@0
   804
(*beta-reduce if possible, else form application*)
paulson@2192
   805
fun betapply (Abs(_,_,t), u) = subst_bound (u,t)
clasohm@0
   806
  | betapply (f,u) = f$u;
clasohm@0
   807
wenzelm@18183
   808
val betapplys = Library.foldl betapply;
wenzelm@18183
   809
wenzelm@14786
   810
wenzelm@16882
   811
(** Specialized equality, membership, insertion etc. **)
paulson@2192
   812
wenzelm@16882
   813
(* indexnames *)
wenzelm@16882
   814
wenzelm@16724
   815
fun eq_ix ((x, i): indexname, (y, j)) = i = j andalso x = y;
paulson@2192
   816
wenzelm@2959
   817
fun mem_ix (_, []) = false
wenzelm@16882
   818
  | mem_ix (x, y :: ys) = eq_ix (x, y) orelse mem_ix (x, ys);
paulson@2192
   819
wenzelm@16882
   820
fun ins_ix (x, xs) = if mem_ix (x, xs) then xs else x :: xs;
paulson@2192
   821
clasohm@0
   822
wenzelm@16882
   823
(* variables *)
wenzelm@16882
   824
wenzelm@16943
   825
fun eq_tvar ((xi, S: sort), (xi', S')) = eq_ix (xi, xi') andalso S = S';
wenzelm@16943
   826
fun eq_var ((xi, T: typ), (xi', T')) = eq_ix (xi, xi') andalso T = T';
wenzelm@16943
   827
wenzelm@16943
   828
val tvar_ord = prod_ord indexname_ord sort_ord;
wenzelm@16943
   829
val var_ord = prod_ord indexname_ord typ_ord;
wenzelm@16882
   830
wenzelm@16882
   831
wenzelm@16882
   832
(* terms *)
paulson@2176
   833
paulson@2176
   834
fun mem_term (_, []) = false
wenzelm@16882
   835
  | mem_term (t, t'::ts) = t aconv t' orelse mem_term (t, ts);
paulson@2176
   836
paulson@2176
   837
fun ins_term(t,ts) = if mem_term(t,ts) then ts else t :: ts;
paulson@2176
   838
wenzelm@16882
   839
wenzelm@13000
   840
(*A fast unification filter: true unless the two terms cannot be unified.
clasohm@0
   841
  Terms must be NORMAL.  Treats all Vars as distinct. *)
clasohm@0
   842
fun could_unify (t,u) =
clasohm@0
   843
  let fun matchrands (f$t, g$u) = could_unify(t,u) andalso  matchrands(f,g)
wenzelm@9536
   844
        | matchrands _ = true
clasohm@0
   845
  in case (head_of t , head_of u) of
wenzelm@9536
   846
        (_, Var _) => true
clasohm@0
   847
      | (Var _, _) => true
clasohm@0
   848
      | (Const(a,_), Const(b,_)) =>  a=b andalso matchrands(t,u)
clasohm@0
   849
      | (Free(a,_), Free(b,_)) =>  a=b andalso matchrands(t,u)
clasohm@0
   850
      | (Bound i, Bound j) =>  i=j andalso matchrands(t,u)
clasohm@0
   851
      | (Abs _, _) =>  true   (*because of possible eta equality*)
clasohm@0
   852
      | (_, Abs _) =>  true
clasohm@0
   853
      | _ => false
clasohm@0
   854
  end;
clasohm@0
   855
clasohm@0
   856
(*Substitute new for free occurrences of old in a term*)
clasohm@0
   857
fun subst_free [] = (fn t=>t)
clasohm@0
   858
  | subst_free pairs =
wenzelm@13000
   859
      let fun substf u =
haftmann@17314
   860
            case AList.lookup (op aconv) pairs u of
skalberg@15531
   861
                SOME u' => u'
skalberg@15531
   862
              | NONE => (case u of Abs(a,T,t) => Abs(a, T, substf t)
wenzelm@9536
   863
                                 | t$u' => substf t $ substf u'
wenzelm@9536
   864
                                 | _ => u)
clasohm@0
   865
      in  substf  end;
clasohm@0
   866
clasohm@0
   867
(*a total, irreflexive ordering on index names*)
clasohm@0
   868
fun xless ((a,i), (b,j): indexname) = i<j  orelse  (i=j andalso a<b);
clasohm@0
   869
clasohm@0
   870
wenzelm@13000
   871
(*Abstraction of the term "body" over its occurrences of v,
clasohm@0
   872
    which must contain no loose bound variables.
clasohm@0
   873
  The resulting term is ready to become the body of an Abs.*)
wenzelm@16882
   874
fun abstract_over (v, body) =
wenzelm@16882
   875
  let
wenzelm@16990
   876
    exception SAME;
wenzelm@16990
   877
    fun abs lev tm =
wenzelm@16990
   878
      if v aconv tm then Bound lev
wenzelm@16882
   879
      else
wenzelm@16990
   880
        (case tm of
wenzelm@16990
   881
          Abs (a, T, t) => Abs (a, T, abs (lev + 1) t)
wenzelm@16990
   882
        | t $ u => (abs lev t $ (abs lev u handle SAME => u) handle SAME => t $ abs lev u)
wenzelm@16990
   883
        | _ => raise SAME);
wenzelm@16990
   884
  in abs 0 body handle SAME => body end;
clasohm@0
   885
berghofe@13665
   886
fun lambda (v as Free (x, T)) t = Abs (x, T, abstract_over (v, t))
berghofe@13665
   887
  | lambda (v as Var ((x, _), T)) t = Abs (x, T, abstract_over (v, t))
berghofe@13665
   888
  | lambda v t = raise TERM ("lambda", [v, t]);
clasohm@0
   889
clasohm@0
   890
(*Form an abstraction over a free variable.*)
clasohm@0
   891
fun absfree (a,T,body) = Abs(a, T, abstract_over (Free(a,T), body));
wenzelm@17786
   892
fun absdummy (T, body) = Abs ("uu", T, body);
clasohm@0
   893
clasohm@0
   894
(*Abstraction over a list of free variables*)
clasohm@0
   895
fun list_abs_free ([ ] ,     t) = t
wenzelm@13000
   896
  | list_abs_free ((a,T)::vars, t) =
clasohm@0
   897
      absfree(a, T, list_abs_free(vars,t));
clasohm@0
   898
clasohm@0
   899
(*Quantification over a list of free variables*)
clasohm@0
   900
fun list_all_free ([], t: term) = t
wenzelm@13000
   901
  | list_all_free ((a,T)::vars, t) =
clasohm@0
   902
        (all T) $ (absfree(a, T, list_all_free(vars,t)));
clasohm@0
   903
clasohm@0
   904
(*Quantification over a list of variables (already bound in body) *)
clasohm@0
   905
fun list_all ([], t) = t
wenzelm@13000
   906
  | list_all ((a,T)::vars, t) =
clasohm@0
   907
        (all T) $ (Abs(a, T, list_all(vars,t)));
clasohm@0
   908
wenzelm@16678
   909
(*Replace the ATOMIC term ti by ui;    inst = [(t1,u1), ..., (tn,un)].
clasohm@0
   910
  A simultaneous substitution:  [ (a,b), (b,a) ] swaps a and b.  *)
wenzelm@16678
   911
fun subst_atomic [] tm = tm
wenzelm@16678
   912
  | subst_atomic inst tm =
wenzelm@16678
   913
      let
wenzelm@16678
   914
        fun subst (Abs (a, T, body)) = Abs (a, T, subst body)
wenzelm@16678
   915
          | subst (t $ u) = subst t $ subst u
haftmann@17314
   916
          | subst t = if_none (AList.lookup (op aconv) inst t) t;
wenzelm@16678
   917
      in subst tm end;
clasohm@0
   918
wenzelm@16678
   919
(*Replace the ATOMIC type Ti by Ui;    inst = [(T1,U1), ..., (Tn,Un)].*)
wenzelm@16678
   920
fun typ_subst_atomic [] ty = ty
wenzelm@16678
   921
  | typ_subst_atomic inst ty =
wenzelm@16678
   922
      let
wenzelm@16678
   923
        fun subst (Type (a, Ts)) = Type (a, map subst Ts)
haftmann@17314
   924
          | subst T = if_none (AList.lookup (op = : typ * typ -> bool) inst T) T;
wenzelm@16678
   925
      in subst ty end;
berghofe@15797
   926
wenzelm@16678
   927
fun subst_atomic_types [] tm = tm
wenzelm@16678
   928
  | subst_atomic_types inst tm = map_term_types (typ_subst_atomic inst) tm;
wenzelm@16678
   929
wenzelm@16678
   930
fun typ_subst_TVars [] ty = ty
wenzelm@16678
   931
  | typ_subst_TVars inst ty =
wenzelm@16678
   932
      let
wenzelm@16678
   933
        fun subst (Type (a, Ts)) = Type (a, map subst Ts)
haftmann@17271
   934
          | subst (T as TVar (xi, _)) = if_none (AList.lookup (op =) inst xi) T
wenzelm@16678
   935
          | subst T = T;
wenzelm@16678
   936
      in subst ty end;
clasohm@0
   937
wenzelm@16678
   938
fun subst_TVars [] tm = tm
wenzelm@16678
   939
  | subst_TVars inst tm = map_term_types (typ_subst_TVars inst) tm;
clasohm@0
   940
wenzelm@16678
   941
(*see also Envir.norm_term*)
wenzelm@16678
   942
fun subst_Vars [] tm = tm
wenzelm@16678
   943
  | subst_Vars inst tm =
wenzelm@16678
   944
      let
haftmann@17271
   945
        fun subst (t as Var (xi, _)) = if_none (AList.lookup (op =) inst xi) t
wenzelm@16678
   946
          | subst (Abs (a, T, t)) = Abs (a, T, subst t)
wenzelm@16678
   947
          | subst (t $ u) = subst t $ subst u
wenzelm@16678
   948
          | subst t = t;
wenzelm@16678
   949
      in subst tm end;
clasohm@0
   950
wenzelm@16678
   951
(*see also Envir.norm_term*)
wenzelm@16678
   952
fun subst_vars ([], []) tm = tm
wenzelm@16678
   953
  | subst_vars ([], inst) tm = subst_Vars inst tm
wenzelm@16678
   954
  | subst_vars (instT, inst) tm =
wenzelm@16678
   955
      let
wenzelm@16678
   956
        fun subst (Const (a, T)) = Const (a, typ_subst_TVars instT T)
wenzelm@16678
   957
          | subst (Free (a, T)) = Free (a, typ_subst_TVars instT T)
wenzelm@16678
   958
          | subst (t as Var (xi, T)) =
haftmann@17271
   959
              (case AList.lookup (op =) inst xi of
wenzelm@16678
   960
                NONE => Var (xi, typ_subst_TVars instT T)
wenzelm@16678
   961
              | SOME t => t)
wenzelm@16678
   962
          | subst (t as Bound _) = t
wenzelm@16678
   963
          | subst (Abs (a, T, t)) = Abs (a, typ_subst_TVars instT T, subst t)
wenzelm@16678
   964
          | subst (t $ u) = subst t $ subst u;
wenzelm@16678
   965
      in subst tm end;
clasohm@0
   966
clasohm@0
   967
wenzelm@16943
   968
(* instantiation of schematic variables (types before terms) *)
wenzelm@16882
   969
wenzelm@16882
   970
local exception SAME in
wenzelm@16882
   971
wenzelm@16943
   972
fun instantiateT_same [] _ = raise SAME
wenzelm@16943
   973
  | instantiateT_same instT ty =
wenzelm@16882
   974
      let
wenzelm@16882
   975
        fun subst_typ (Type (a, Ts)) = Type (a, subst_typs Ts)
wenzelm@16882
   976
          | subst_typ (TVar v) =
haftmann@17314
   977
              (case AList.lookup eq_tvar instT v of
wenzelm@16882
   978
                SOME T => T
wenzelm@16882
   979
              | NONE => raise SAME)
wenzelm@16882
   980
          | subst_typ _ = raise SAME
wenzelm@16882
   981
        and subst_typs (T :: Ts) =
wenzelm@16882
   982
            (subst_typ T :: (subst_typs Ts handle SAME => Ts)
wenzelm@16882
   983
              handle SAME => T :: subst_typs Ts)
wenzelm@16882
   984
          | subst_typs [] = raise SAME;
wenzelm@16882
   985
      in subst_typ ty end;
wenzelm@16882
   986
wenzelm@16882
   987
fun instantiate ([], []) tm = tm
wenzelm@16882
   988
  | instantiate (instT, inst) tm =
wenzelm@16882
   989
      let
wenzelm@16943
   990
        val substT = instantiateT_same instT;
wenzelm@16943
   991
        fun subst (Const (c, T)) = Const (c, substT T)
wenzelm@16943
   992
          | subst (Free (x, T)) = Free (x, substT T)
wenzelm@16882
   993
          | subst (Var (xi, T)) =
wenzelm@16943
   994
              let val (T', same) = (substT T, false) handle SAME => (T, true) in
haftmann@17314
   995
                (case AList.lookup eq_var inst (xi, T') of
wenzelm@16882
   996
                   SOME t => t
wenzelm@16882
   997
                 | NONE => if same then raise SAME else Var (xi, T'))
wenzelm@16882
   998
              end
wenzelm@16882
   999
          | subst (Bound _) = raise SAME
wenzelm@16882
  1000
          | subst (Abs (x, T, t)) =
wenzelm@16943
  1001
              (Abs (x, substT T, subst t handle SAME => t)
wenzelm@16882
  1002
                handle SAME => Abs (x, T, subst t))
wenzelm@16882
  1003
          | subst (t $ u) = (subst t $ (subst u handle SAME => u) handle SAME => t $ subst u);
wenzelm@16882
  1004
      in subst tm handle SAME => tm end;
wenzelm@16882
  1005
wenzelm@16882
  1006
fun instantiateT instT ty =
wenzelm@16943
  1007
  instantiateT_same instT ty handle SAME => ty;
wenzelm@16882
  1008
wenzelm@16882
  1009
end;
wenzelm@16882
  1010
wenzelm@16882
  1011
paulson@15573
  1012
(** Identifying first-order terms **)
paulson@15573
  1013
paulson@15573
  1014
(*Argument Ts is a reverse list of binder types, needed if term t contains Bound vars*)
paulson@15573
  1015
fun has_not_funtype Ts t = not (is_funtype (fastype_of1 (Ts,t)));
paulson@15573
  1016
wenzelm@16537
  1017
(*First order means in all terms of the form f(t1,...,tn) no argument has a
paulson@16589
  1018
  function type. The supplied quantifiers are excluded: their argument always
paulson@16589
  1019
  has a function type through a recursive call into its body.*)
wenzelm@16667
  1020
fun is_first_order quants =
paulson@16589
  1021
  let fun first_order1 Ts (Abs (_,T,body)) = first_order1 (T::Ts) body
wenzelm@16667
  1022
        | first_order1 Ts (Const(q,_) $ Abs(a,T,body)) =
wenzelm@16667
  1023
            q mem_string quants  andalso   (*it is a known quantifier*)
paulson@16589
  1024
            not (is_funtype T)   andalso first_order1 (T::Ts) body
wenzelm@16667
  1025
        | first_order1 Ts t =
wenzelm@16667
  1026
            case strip_comb t of
wenzelm@16667
  1027
                 (Var _, ts) => forall (first_order1 Ts andf has_not_funtype Ts) ts
wenzelm@16667
  1028
               | (Free _, ts) => forall (first_order1 Ts andf has_not_funtype Ts) ts
wenzelm@16667
  1029
               | (Const _, ts) => forall (first_order1 Ts andf has_not_funtype Ts) ts
wenzelm@16667
  1030
               | (Bound _, ts) => forall (first_order1 Ts andf has_not_funtype Ts) ts
wenzelm@16667
  1031
               | (Abs _, ts) => false (*not in beta-normal form*)
wenzelm@16667
  1032
               | _ => error "first_order: unexpected case"
paulson@16589
  1033
    in  first_order1 []  end;
paulson@15573
  1034
wenzelm@16710
  1035
wenzelm@16990
  1036
(* maximum index of typs and terms *)
clasohm@0
  1037
wenzelm@16710
  1038
fun maxidx_typ (TVar ((_, j), _)) i = Int.max (i, j)
wenzelm@16710
  1039
  | maxidx_typ (Type (_, Ts)) i = maxidx_typs Ts i
wenzelm@16710
  1040
  | maxidx_typ (TFree _) i = i
wenzelm@16710
  1041
and maxidx_typs [] i = i
wenzelm@16710
  1042
  | maxidx_typs (T :: Ts) i = maxidx_typs Ts (maxidx_typ T i);
clasohm@0
  1043
wenzelm@16710
  1044
fun maxidx_term (Var ((_, j), T)) i = maxidx_typ T (Int.max (i, j))
wenzelm@16710
  1045
  | maxidx_term (Const (_, T)) i = maxidx_typ T i
wenzelm@16710
  1046
  | maxidx_term (Free (_, T)) i = maxidx_typ T i
wenzelm@16710
  1047
  | maxidx_term (Bound _) i = i
wenzelm@16710
  1048
  | maxidx_term (Abs (_, T, t)) i = maxidx_term t (maxidx_typ T i)
wenzelm@16710
  1049
  | maxidx_term (t $ u) i = maxidx_term u (maxidx_term t i);
clasohm@0
  1050
wenzelm@16710
  1051
fun maxidx_of_typ T = maxidx_typ T ~1;
wenzelm@16710
  1052
fun maxidx_of_typs Ts = maxidx_typs Ts ~1;
wenzelm@16710
  1053
fun maxidx_of_term t = maxidx_term t ~1;
berghofe@13665
  1054
clasohm@0
  1055
clasohm@0
  1056
clasohm@0
  1057
(**** Syntax-related declarations ****)
clasohm@0
  1058
clasohm@0
  1059
(*** Printing ***)
clasohm@0
  1060
wenzelm@16943
  1061
(*Makes a variant of a name distinct from the names in 'used'.
wenzelm@14676
  1062
  First attaches the suffix and then increments this;
wenzelm@12306
  1063
  preserves a suffix of underscores "_". *)
wenzelm@16943
  1064
fun variant used name =
wenzelm@12306
  1065
  let
wenzelm@12306
  1066
    val (c, u) = pairself implode (Library.take_suffix (equal "_") (Symbol.explode name));
wenzelm@16943
  1067
    fun vary2 c = if ((c ^ u) mem_string used) then vary2 (Symbol.bump_string c) else c;
wenzelm@16943
  1068
    fun vary1 c = if ((c ^ u) mem_string used) then vary2 (Symbol.bump_init c) else c;
wenzelm@12306
  1069
  in vary1 (if c = "" then "u" else c) ^ u end;
clasohm@0
  1070
clasohm@0
  1071
(*Create variants of the list of names, with priority to the first ones*)
clasohm@0
  1072
fun variantlist ([], used) = []
wenzelm@13000
  1073
  | variantlist(b::bs, used) =
clasohm@0
  1074
      let val b' = variant used b
clasohm@0
  1075
      in  b' :: variantlist (bs, b'::used)  end;
clasohm@0
  1076
wenzelm@14695
  1077
(*Invent fresh names*)
wenzelm@14695
  1078
fun invent_names _ _ 0 = []
wenzelm@14695
  1079
  | invent_names used a n =
wenzelm@14695
  1080
      let val b = Symbol.bump_string a in
wenzelm@14695
  1081
        if a mem_string used then invent_names used b n
wenzelm@14695
  1082
        else a :: invent_names used b (n - 1)
wenzelm@14695
  1083
      end;
wenzelm@11353
  1084
wenzelm@16537
  1085
wenzelm@4017
  1086
(** Consts etc. **)
wenzelm@4017
  1087
skalberg@15574
  1088
fun add_typ_classes (Type (_, Ts), cs) = foldr add_typ_classes cs Ts
wenzelm@4017
  1089
  | add_typ_classes (TFree (_, S), cs) = S union cs
wenzelm@4017
  1090
  | add_typ_classes (TVar (_, S), cs) = S union cs;
wenzelm@4017
  1091
wenzelm@16294
  1092
fun add_typ_tycons (Type (c, Ts), cs) = foldr add_typ_tycons (c ins_string cs) Ts
wenzelm@4017
  1093
  | add_typ_tycons (_, cs) = cs;
wenzelm@4017
  1094
wenzelm@4017
  1095
val add_term_classes = it_term_types add_typ_classes;
wenzelm@4017
  1096
val add_term_tycons = it_term_types add_typ_tycons;
wenzelm@4017
  1097
wenzelm@9319
  1098
fun add_term_consts (Const (c, _), cs) = c ins_string cs
wenzelm@4017
  1099
  | add_term_consts (t $ u, cs) = add_term_consts (t, add_term_consts (u, cs))
wenzelm@4017
  1100
  | add_term_consts (Abs (_, _, t), cs) = add_term_consts (t, cs)
wenzelm@4017
  1101
  | add_term_consts (_, cs) = cs;
wenzelm@4017
  1102
nipkow@13646
  1103
fun term_consts t = add_term_consts(t,[]);
nipkow@13646
  1104
wenzelm@16943
  1105
fun exists_subterm P =
wenzelm@16943
  1106
  let
wenzelm@16943
  1107
    fun ex tm = P tm orelse
wenzelm@16943
  1108
      (case tm of
wenzelm@16943
  1109
        t $ u => ex t orelse ex u
wenzelm@16943
  1110
      | Abs (_, _, t) => ex t
wenzelm@16943
  1111
      | _ => false);
wenzelm@16943
  1112
  in ex end;
obua@16108
  1113
wenzelm@16943
  1114
fun exists_Const P = exists_subterm (fn Const c => P c | _ => false);
nipkow@4631
  1115
wenzelm@4017
  1116
(*map classes, tycons*)
wenzelm@4017
  1117
fun map_typ f g (Type (c, Ts)) = Type (g c, map (map_typ f g) Ts)
wenzelm@4017
  1118
  | map_typ f _ (TFree (x, S)) = TFree (x, map f S)
wenzelm@4017
  1119
  | map_typ f _ (TVar (xi, S)) = TVar (xi, map f S);
wenzelm@4017
  1120
wenzelm@4017
  1121
(*map classes, tycons, consts*)
wenzelm@4017
  1122
fun map_term f g h (Const (c, T)) = Const (h c, map_typ f g T)
wenzelm@4017
  1123
  | map_term f g _ (Free (x, T)) = Free (x, map_typ f g T)
wenzelm@4017
  1124
  | map_term f g _ (Var (xi, T)) = Var (xi, map_typ f g T)
wenzelm@4017
  1125
  | map_term _ _ _ (t as Bound _) = t
wenzelm@4017
  1126
  | map_term f g h (Abs (x, T, t)) = Abs (x, map_typ f g T, map_term f g h t)
wenzelm@4017
  1127
  | map_term f g h (t $ u) = map_term f g h t $ map_term f g h u;
wenzelm@4017
  1128
wenzelm@4017
  1129
clasohm@0
  1130
(** TFrees and TVars **)
clasohm@0
  1131
wenzelm@12802
  1132
(*Accumulates the names of Frees in the term, suppressing duplicates.*)
wenzelm@12802
  1133
fun add_term_free_names (Free(a,_), bs) = a ins_string bs
wenzelm@12802
  1134
  | add_term_free_names (f$u, bs) = add_term_free_names (f, add_term_free_names(u, bs))
wenzelm@12802
  1135
  | add_term_free_names (Abs(_,_,t), bs) = add_term_free_names(t,bs)
wenzelm@12802
  1136
  | add_term_free_names (_, bs) = bs;
wenzelm@12802
  1137
clasohm@0
  1138
(*Accumulates the names in the term, suppressing duplicates.
clasohm@0
  1139
  Includes Frees and Consts.  For choosing unambiguous bound var names.*)
wenzelm@10666
  1140
fun add_term_names (Const(a,_), bs) = NameSpace.base a ins_string bs
paulson@2176
  1141
  | add_term_names (Free(a,_), bs) = a ins_string bs
clasohm@0
  1142
  | add_term_names (f$u, bs) = add_term_names (f, add_term_names(u, bs))
clasohm@0
  1143
  | add_term_names (Abs(_,_,t), bs) = add_term_names(t,bs)
clasohm@0
  1144
  | add_term_names (_, bs) = bs;
clasohm@0
  1145
clasohm@0
  1146
(*Accumulates the TVars in a type, suppressing duplicates. *)
skalberg@15574
  1147
fun add_typ_tvars(Type(_,Ts),vs) = foldr add_typ_tvars vs Ts
clasohm@0
  1148
  | add_typ_tvars(TFree(_),vs) = vs
wenzelm@16294
  1149
  | add_typ_tvars(TVar(v),vs) = insert (op =) v vs;
clasohm@0
  1150
clasohm@0
  1151
(*Accumulates the TFrees in a type, suppressing duplicates. *)
skalberg@15574
  1152
fun add_typ_tfree_names(Type(_,Ts),fs) = foldr add_typ_tfree_names fs Ts
paulson@2176
  1153
  | add_typ_tfree_names(TFree(f,_),fs) = f ins_string fs
clasohm@0
  1154
  | add_typ_tfree_names(TVar(_),fs) = fs;
clasohm@0
  1155
skalberg@15574
  1156
fun add_typ_tfrees(Type(_,Ts),fs) = foldr add_typ_tfrees fs Ts
wenzelm@16294
  1157
  | add_typ_tfrees(TFree(f),fs) = insert (op =) f fs
clasohm@0
  1158
  | add_typ_tfrees(TVar(_),fs) = fs;
clasohm@0
  1159
skalberg@15574
  1160
fun add_typ_varnames(Type(_,Ts),nms) = foldr add_typ_varnames nms Ts
paulson@2176
  1161
  | add_typ_varnames(TFree(nm,_),nms) = nm ins_string nms
paulson@2176
  1162
  | add_typ_varnames(TVar((nm,_),_),nms) = nm ins_string nms;
nipkow@949
  1163
clasohm@0
  1164
(*Accumulates the TVars in a term, suppressing duplicates. *)
clasohm@0
  1165
val add_term_tvars = it_term_types add_typ_tvars;
clasohm@0
  1166
clasohm@0
  1167
(*Accumulates the TFrees in a term, suppressing duplicates. *)
clasohm@0
  1168
val add_term_tfrees = it_term_types add_typ_tfrees;
clasohm@0
  1169
val add_term_tfree_names = it_term_types add_typ_tfree_names;
clasohm@0
  1170
nipkow@949
  1171
val add_term_tvarnames = it_term_types add_typ_varnames;
nipkow@949
  1172
clasohm@0
  1173
(*Non-list versions*)
clasohm@0
  1174
fun typ_tfrees T = add_typ_tfrees(T,[]);
clasohm@0
  1175
fun typ_tvars T = add_typ_tvars(T,[]);
clasohm@0
  1176
fun term_tfrees t = add_term_tfrees(t,[]);
clasohm@0
  1177
fun term_tvars t = add_term_tvars(t,[]);
clasohm@0
  1178
nipkow@949
  1179
(*special code to enforce left-to-right collection of TVar-indexnames*)
nipkow@949
  1180
skalberg@15570
  1181
fun add_typ_ixns(ixns,Type(_,Ts)) = Library.foldl add_typ_ixns (ixns,Ts)
wenzelm@13000
  1182
  | add_typ_ixns(ixns,TVar(ixn,_)) = if mem_ix (ixn, ixns) then ixns
wenzelm@9536
  1183
                                     else ixns@[ixn]
nipkow@949
  1184
  | add_typ_ixns(ixns,TFree(_)) = ixns;
nipkow@949
  1185
nipkow@949
  1186
fun add_term_tvar_ixns(Const(_,T),ixns) = add_typ_ixns(ixns,T)
nipkow@949
  1187
  | add_term_tvar_ixns(Free(_,T),ixns) = add_typ_ixns(ixns,T)
nipkow@949
  1188
  | add_term_tvar_ixns(Var(_,T),ixns) = add_typ_ixns(ixns,T)
nipkow@949
  1189
  | add_term_tvar_ixns(Bound _,ixns) = ixns
nipkow@949
  1190
  | add_term_tvar_ixns(Abs(_,T,t),ixns) =
nipkow@949
  1191
      add_term_tvar_ixns(t,add_typ_ixns(ixns,T))
nipkow@949
  1192
  | add_term_tvar_ixns(f$t,ixns) =
nipkow@949
  1193
      add_term_tvar_ixns(t,add_term_tvar_ixns(f,ixns));
nipkow@949
  1194
wenzelm@16537
  1195
clasohm@0
  1196
(** Frees and Vars **)
clasohm@0
  1197
clasohm@0
  1198
(*Accumulates the Vars in the term, suppressing duplicates*)
clasohm@0
  1199
fun add_term_vars (t, vars: term list) = case t of
wenzelm@16990
  1200
    Var   _ => OrdList.insert term_ord t vars
clasohm@0
  1201
  | Abs (_,_,body) => add_term_vars(body,vars)
clasohm@0
  1202
  | f$t =>  add_term_vars (f, add_term_vars(t, vars))
clasohm@0
  1203
  | _ => vars;
clasohm@0
  1204
clasohm@0
  1205
fun term_vars t = add_term_vars(t,[]);
clasohm@0
  1206
clasohm@0
  1207
(*Accumulates the Frees in the term, suppressing duplicates*)
clasohm@0
  1208
fun add_term_frees (t, frees: term list) = case t of
wenzelm@16990
  1209
    Free   _ => OrdList.insert term_ord t frees
clasohm@0
  1210
  | Abs (_,_,body) => add_term_frees(body,frees)
clasohm@0
  1211
  | f$t =>  add_term_frees (f, add_term_frees(t, frees))
clasohm@0
  1212
  | _ => frees;
clasohm@0
  1213
clasohm@0
  1214
fun term_frees t = add_term_frees(t,[]);
clasohm@0
  1215
clasohm@0
  1216
(*Given an abstraction over P, replaces the bound variable by a Free variable
wenzelm@17851
  1217
  having a unique name -- SLOW!*)
clasohm@0
  1218
fun variant_abs (a,T,P) =
clasohm@0
  1219
  let val b = variant (add_term_names(P,[])) a
paulson@2192
  1220
  in  (b,  subst_bound (Free(b,T), P))  end;
clasohm@0
  1221
wenzelm@16678
  1222
fun dest_abs (x, T, body) =
wenzelm@16678
  1223
  let
wenzelm@16678
  1224
    fun name_clash (Free (y, _)) = (x = y)
wenzelm@16678
  1225
      | name_clash (t $ u) = name_clash t orelse name_clash u
wenzelm@16678
  1226
      | name_clash (Abs (_, _, t)) = name_clash t
wenzelm@16678
  1227
      | name_clash _ = false;
wenzelm@16678
  1228
  in
wenzelm@16678
  1229
    if name_clash body then
wenzelm@16678
  1230
      dest_abs (variant [x] x, T, body)    (*potentially slow, but rarely happens*)
wenzelm@16678
  1231
    else (x, subst_bound (Free (x, T), body))
wenzelm@16678
  1232
  end;
wenzelm@16678
  1233
wenzelm@16990
  1234
(*names for numbered variables --
wenzelm@16990
  1235
  preserves order wrt. int_ord vs. string_ord, avoids allocating new strings*)
wenzelm@16990
  1236
local
wenzelm@16990
  1237
  val small_int = Vector.tabulate (1000, fn i =>
wenzelm@16990
  1238
    let val leading = if i < 10 then "00" else if i < 100 then "0" else ""
wenzelm@16990
  1239
    in ":" ^ leading ^ string_of_int i end);
wenzelm@16990
  1240
in
wenzelm@16990
  1241
  fun bound n =
wenzelm@16990
  1242
    if n < 1000 then Vector.sub (small_int, n)
wenzelm@16990
  1243
    else ":" ^ bound (n div 1000) ^ Vector.sub (small_int, n mod 1000);
wenzelm@16990
  1244
end;
wenzelm@16990
  1245
wenzelm@16990
  1246
val is_bound = String.isPrefix ":";
wenzelm@16943
  1247
clasohm@0
  1248
(* renames and reverses the strings in vars away from names *)
clasohm@0
  1249
fun rename_aTs names vars : (string*typ)list =
clasohm@0
  1250
  let fun rename_aT (vars,(a,T)) =
wenzelm@9536
  1251
                (variant (map #1 vars @ names) a, T) :: vars
skalberg@15570
  1252
  in Library.foldl rename_aT ([],vars) end;
clasohm@0
  1253
clasohm@0
  1254
fun rename_wrt_term t = rename_aTs (add_term_names(t,[]));
clasohm@1364
  1255
paulson@1417
  1256
wenzelm@16943
  1257
(* zero var indexes *)
wenzelm@4286
  1258
wenzelm@16943
  1259
fun zero_var_inst vars =
wenzelm@16943
  1260
  fold (fn v as ((x, i), X) => fn (used, inst) =>
wenzelm@16943
  1261
    let
wenzelm@17642
  1262
      val x' = variant used (if is_bound x then "u" else x);
wenzelm@16943
  1263
      val used' = x' :: used;
wenzelm@16943
  1264
    in if x = x' andalso i = 0 then (used', inst) else (used', (v, ((x', 0), X)) :: inst) end)
wenzelm@16943
  1265
  vars ([], []) |> #2;
wenzelm@4286
  1266
wenzelm@16943
  1267
fun zero_var_indexesT ty =
wenzelm@16943
  1268
  instantiateT (map (apsnd TVar) (zero_var_inst (sort tvar_ord (add_tvarsT ty [])))) ty;
haftmann@16790
  1269
wenzelm@16943
  1270
fun zero_var_indexes_inst tm =
wenzelm@16943
  1271
  let
wenzelm@16943
  1272
    val instT = map (apsnd TVar) (zero_var_inst (sort tvar_ord (fold_types add_tvarsT tm [])));
wenzelm@16943
  1273
    val inst =
wenzelm@16943
  1274
      add_vars tm [] |> map (apsnd (instantiateT instT))
wenzelm@16943
  1275
      |> sort var_ord |> zero_var_inst |> map (apsnd Var);
wenzelm@16943
  1276
  in (instT, inst) end;
wenzelm@12499
  1277
wenzelm@16943
  1278
fun zero_var_indexes tm = instantiate (zero_var_indexes_inst tm) tm;
wenzelm@4286
  1279
paulson@1417
  1280
wenzelm@9536
  1281
(* dummy patterns *)
wenzelm@9536
  1282
wenzelm@9536
  1283
val dummy_patternN = "dummy_pattern";
wenzelm@9536
  1284
wenzelm@9536
  1285
fun is_dummy_pattern (Const ("dummy_pattern", _)) = true
wenzelm@9536
  1286
  | is_dummy_pattern _ = false;
wenzelm@9536
  1287
wenzelm@9536
  1288
fun no_dummy_patterns tm =
haftmann@16787
  1289
  if not (fold_aterms (fn t => fn b => b orelse is_dummy_pattern t) tm false) then tm
wenzelm@9536
  1290
  else raise TERM ("Illegal occurrence of '_' dummy pattern", [tm]);
wenzelm@9536
  1291
wenzelm@11903
  1292
fun replace_dummy Ts (i, Const ("dummy_pattern", T)) =
wenzelm@11903
  1293
      (i + 1, list_comb (Var (("_dummy_", i), Ts ---> T), map Bound (0 upto length Ts - 1)))
wenzelm@11903
  1294
  | replace_dummy Ts (i, Abs (x, T, t)) =
wenzelm@11903
  1295
      let val (i', t') = replace_dummy (T :: Ts) (i, t)
wenzelm@11903
  1296
      in (i', Abs (x, T, t')) end
wenzelm@11903
  1297
  | replace_dummy Ts (i, t $ u) =
wenzelm@11903
  1298
      let val (i', t') = replace_dummy Ts (i, t); val (i'', u') = replace_dummy Ts (i', u)
wenzelm@11903
  1299
      in (i'', t' $ u') end
wenzelm@11903
  1300
  | replace_dummy _ (i, a) = (i, a);
wenzelm@11903
  1301
wenzelm@11903
  1302
val replace_dummy_patterns = replace_dummy [];
wenzelm@9536
  1303
wenzelm@10552
  1304
fun is_replaced_dummy_pattern ("_dummy_", _) = true
wenzelm@10552
  1305
  | is_replaced_dummy_pattern _ = false;
wenzelm@9536
  1306
wenzelm@16035
  1307
fun show_dummy_patterns (Var (("_dummy_", _), T)) = Const ("dummy_pattern", T)
wenzelm@16035
  1308
  | show_dummy_patterns (t $ u) = show_dummy_patterns t $ show_dummy_patterns u
wenzelm@16035
  1309
  | show_dummy_patterns (Abs (x, T, t)) = Abs (x, T, show_dummy_patterns t)
wenzelm@16035
  1310
  | show_dummy_patterns a = a;
wenzelm@16035
  1311
wenzelm@13484
  1312
wenzelm@13484
  1313
(* adhoc freezing *)
wenzelm@13484
  1314
wenzelm@13484
  1315
fun adhoc_freeze_vars tm =
wenzelm@13484
  1316
  let
wenzelm@13484
  1317
    fun mk_inst (var as Var ((a, i), T)) =
wenzelm@13484
  1318
      let val x = a ^ Library.gensym "_" ^ string_of_int i
wenzelm@13484
  1319
      in ((var,  Free(x, T)), x) end;
wenzelm@13484
  1320
    val (insts, xs) = split_list (map mk_inst (term_vars tm));
wenzelm@13484
  1321
  in (subst_atomic insts tm, xs) end;
wenzelm@13484
  1322
wenzelm@13484
  1323
wenzelm@14786
  1324
(* string_of_vname *)
wenzelm@14786
  1325
wenzelm@15986
  1326
val show_question_marks = ref true;
berghofe@15472
  1327
wenzelm@14786
  1328
fun string_of_vname (x, i) =
wenzelm@14786
  1329
  let
wenzelm@15986
  1330
    val question_mark = if ! show_question_marks then "?" else "";
wenzelm@15986
  1331
    val idx = string_of_int i;
wenzelm@15986
  1332
    val dot =
wenzelm@15986
  1333
      (case rev (Symbol.explode x) of
wenzelm@15986
  1334
        _ :: "\\<^isub>" :: _ => false
wenzelm@15986
  1335
      | _ :: "\\<^isup>" :: _ => false
wenzelm@15986
  1336
      | c :: _ => Symbol.is_digit c
wenzelm@15986
  1337
      | _ => true);
wenzelm@14786
  1338
  in
wenzelm@15986
  1339
    if dot then question_mark ^ x ^ "." ^ idx
wenzelm@15986
  1340
    else if i <> 0 then question_mark ^ x ^ idx
wenzelm@15986
  1341
    else question_mark ^ x
wenzelm@14786
  1342
  end;
wenzelm@14786
  1343
wenzelm@14786
  1344
fun string_of_vname' (x, ~1) = x
wenzelm@14786
  1345
  | string_of_vname' xi = string_of_vname xi;
wenzelm@14786
  1346
wenzelm@17777
  1347
wenzelm@17777
  1348
(* str_of_term *)
wenzelm@17777
  1349
wenzelm@17777
  1350
fun str_of_term (Const (c, _)) = c
wenzelm@17777
  1351
  | str_of_term (Free (x, _)) = x
wenzelm@17777
  1352
  | str_of_term (Var (xi, _)) = string_of_vname xi
wenzelm@17777
  1353
  | str_of_term (Bound i) = string_of_int i
wenzelm@17777
  1354
  | str_of_term (Abs (x, _, t)) = "%" ^ x ^ ". " ^ str_of_term t
wenzelm@17777
  1355
  | str_of_term (t $ u) = "(" ^ str_of_term t ^ " " ^ str_of_term u ^ ")";
wenzelm@17777
  1356
clasohm@1364
  1357
end;
clasohm@1364
  1358
wenzelm@4444
  1359
structure BasicTerm: BASIC_TERM = Term;
wenzelm@4444
  1360
open BasicTerm;