src/Pure/term.ML
author wenzelm
Sat Jun 17 19:37:50 2006 +0200 (2006-06-17)
changeset 19909 6b5574d64aa4
parent 19647 043921b0e587
child 20001 392e39bd1811
permissions -rw-r--r--
added exists_subtype;
added internal/skolem (from Syntax/lexicon.ML);
added generalize(T);
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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_subtype: (typ -> bool) -> typ -> bool
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  val exists_subterm: (term -> bool) -> term -> bool
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  val exists_Const: (string * typ -> bool) -> term -> bool
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  val add_term_free_names: term * string list -> string list
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  val add_typ_tvars: typ * (indexname * sort) list -> (indexname * sort) list
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  val add_typ_tfree_names: typ * string list -> string list
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  val add_typ_tfrees: typ * (string * sort) list -> (string * sort) list
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  val add_typ_varnames: typ * string list -> string list
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  val add_term_tvars: term * (indexname * sort) list -> (indexname * sort) list
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  val add_term_tfrees: term * (string * sort) list -> (string * sort) list
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  val add_term_tfree_names: term * string list -> string list
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  val 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 internal: string -> string
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  val dest_internal: string -> string
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  val skolem: string -> string
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  val dest_skolem: string -> string
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  val generalize: string list * string list -> int -> term -> term
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  val generalizeT: string list -> int -> typ -> typ
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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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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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   324
clasohm@0
   325
fun dest_Free (Free x) =  x
clasohm@0
   326
  | dest_Free t = raise TERM("dest_Free", [t]);
clasohm@0
   327
clasohm@0
   328
fun dest_Var (Var x) =  x
clasohm@0
   329
  | dest_Var t = raise TERM("dest_Var", [t]);
clasohm@0
   330
clasohm@0
   331
paulson@4464
   332
fun domain_type (Type("fun", [T,_])) = T
paulson@4464
   333
and range_type  (Type("fun", [_,T])) = T;
paulson@4064
   334
clasohm@0
   335
(* maps  [T1,...,Tn]--->T  to the list  [T1,T2,...,Tn]*)
clasohm@0
   336
fun binder_types (Type("fun",[S,T])) = S :: binder_types T
clasohm@0
   337
  | binder_types _   =  [];
clasohm@0
   338
clasohm@0
   339
(* maps  [T1,...,Tn]--->T  to T*)
clasohm@0
   340
fun body_type (Type("fun",[S,T])) = body_type T
clasohm@0
   341
  | body_type T   =  T;
clasohm@0
   342
clasohm@0
   343
(* maps  [T1,...,Tn]--->T  to   ([T1,T2,...,Tn], T)  *)
clasohm@0
   344
fun strip_type T : typ list * typ =
clasohm@0
   345
  (binder_types T, body_type T);
clasohm@0
   346
clasohm@0
   347
clasohm@0
   348
(*Compute the type of the term, checking that combinations are well-typed
clasohm@0
   349
  Ts = [T0,T1,...] holds types of bound variables 0, 1, ...*)
clasohm@0
   350
fun type_of1 (Ts, Const (_,T)) = T
clasohm@0
   351
  | type_of1 (Ts, Free  (_,T)) = T
skalberg@15570
   352
  | type_of1 (Ts, Bound i) = (List.nth (Ts,i)
skalberg@15570
   353
        handle Subscript => raise TYPE("type_of: bound variable", [], [Bound i]))
clasohm@0
   354
  | type_of1 (Ts, Var (_,T)) = T
clasohm@0
   355
  | type_of1 (Ts, Abs (_,T,body)) = T --> type_of1(T::Ts, body)
wenzelm@13000
   356
  | type_of1 (Ts, f$u) =
clasohm@0
   357
      let val U = type_of1(Ts,u)
clasohm@0
   358
          and T = type_of1(Ts,f)
clasohm@0
   359
      in case T of
wenzelm@9536
   360
            Type("fun",[T1,T2]) =>
wenzelm@9536
   361
              if T1=U then T2  else raise TYPE
wenzelm@9536
   362
                    ("type_of: type mismatch in application", [T1,U], [f$u])
wenzelm@13000
   363
          | _ => raise TYPE
wenzelm@9536
   364
                    ("type_of: function type is expected in application",
wenzelm@9536
   365
                     [T,U], [f$u])
clasohm@0
   366
      end;
clasohm@0
   367
clasohm@0
   368
fun type_of t : typ = type_of1 ([],t);
clasohm@0
   369
clasohm@0
   370
(*Determines the type of a term, with minimal checking*)
wenzelm@13000
   371
fun fastype_of1 (Ts, f$u) =
lcp@61
   372
    (case fastype_of1 (Ts,f) of
wenzelm@9536
   373
        Type("fun",[_,T]) => T
wenzelm@9536
   374
        | _ => raise TERM("fastype_of: expected function type", [f$u]))
lcp@61
   375
  | fastype_of1 (_, Const (_,T)) = T
lcp@61
   376
  | fastype_of1 (_, Free (_,T)) = T
skalberg@15570
   377
  | fastype_of1 (Ts, Bound i) = (List.nth(Ts,i)
skalberg@15570
   378
         handle Subscript => raise TERM("fastype_of: Bound", [Bound i]))
wenzelm@13000
   379
  | fastype_of1 (_, Var (_,T)) = T
lcp@61
   380
  | fastype_of1 (Ts, Abs (_,T,u)) = T --> fastype_of1 (T::Ts, u);
lcp@61
   381
lcp@61
   382
fun fastype_of t : typ = fastype_of1 ([],t);
clasohm@0
   383
wenzelm@16678
   384
(*Determine the argument type of a function*)
wenzelm@16678
   385
fun argument_type_of tm =
wenzelm@16678
   386
  let
wenzelm@16678
   387
    fun argT i (Type ("fun", [T, U])) = if i = 0 then T else argT (i - 1) U
wenzelm@16678
   388
      | argT _ T = raise TYPE ("argument_type_of", [T], []);
wenzelm@16678
   389
wenzelm@16678
   390
    fun arg 0 _ (Abs (_, T, _)) = T
wenzelm@16678
   391
      | arg i Ts (Abs (_, T, t)) = arg (i - 1) (T :: Ts) t
wenzelm@16678
   392
      | arg i Ts (t $ _) = arg (i + 1) Ts t
wenzelm@16678
   393
      | arg i Ts a = argT i (fastype_of1 (Ts, a));
wenzelm@16678
   394
  in arg 0 [] tm end;
wenzelm@16678
   395
clasohm@0
   396
wenzelm@19473
   397
val list_abs = uncurry (fold_rev (fn (x, T) => fn t => Abs (x, T, t)));
wenzelm@10806
   398
haftmann@18927
   399
fun strip_abs (Abs (a, T, t)) =
haftmann@18927
   400
      let val (a', t') = strip_abs t
haftmann@18927
   401
      in ((a, T) :: a', t') end
haftmann@18927
   402
  | strip_abs t = ([], t);
haftmann@18927
   403
clasohm@0
   404
(* maps  (x1,...,xn)t   to   t  *)
wenzelm@13000
   405
fun strip_abs_body (Abs(_,_,t))  =  strip_abs_body t
clasohm@0
   406
  | strip_abs_body u  =  u;
clasohm@0
   407
clasohm@0
   408
(* maps  (x1,...,xn)t   to   [x1, ..., xn]  *)
wenzelm@13000
   409
fun strip_abs_vars (Abs(a,T,t))  =  (a,T) :: strip_abs_vars t
clasohm@0
   410
  | strip_abs_vars u  =  [] : (string*typ) list;
clasohm@0
   411
clasohm@0
   412
clasohm@0
   413
fun strip_qnt_body qnt =
clasohm@0
   414
let fun strip(tm as Const(c,_)$Abs(_,_,t)) = if c=qnt then strip t else tm
clasohm@0
   415
      | strip t = t
clasohm@0
   416
in strip end;
clasohm@0
   417
clasohm@0
   418
fun strip_qnt_vars qnt =
clasohm@0
   419
let fun strip(Const(c,_)$Abs(a,T,t)) = if c=qnt then (a,T)::strip t else []
clasohm@0
   420
      | strip t  =  [] : (string*typ) list
clasohm@0
   421
in strip end;
clasohm@0
   422
clasohm@0
   423
clasohm@0
   424
(* maps   (f, [t1,...,tn])  to  f(t1,...,tn) *)
skalberg@15570
   425
val list_comb : term * term list -> term = Library.foldl (op $);
clasohm@0
   426
clasohm@0
   427
clasohm@0
   428
(* maps   f(t1,...,tn)  to  (f, [t1,...,tn]) ; naturally tail-recursive*)
wenzelm@13000
   429
fun strip_comb u : term * term list =
clasohm@0
   430
    let fun stripc (f$t, ts) = stripc (f, t::ts)
wenzelm@13000
   431
        |   stripc  x =  x
clasohm@0
   432
    in  stripc(u,[])  end;
clasohm@0
   433
clasohm@0
   434
clasohm@0
   435
(* maps   f(t1,...,tn)  to  f , which is never a combination *)
clasohm@0
   436
fun head_of (f$t) = head_of f
clasohm@0
   437
  | head_of u = u;
clasohm@0
   438
clasohm@0
   439
wenzelm@16599
   440
(*number of atoms and abstractions in a term*)
wenzelm@16599
   441
fun size_of_term tm =
wenzelm@16599
   442
  let
wenzelm@16678
   443
    fun add_size (t $ u, n) = add_size (t, add_size (u, n))
wenzelm@16678
   444
      | add_size (Abs (_ ,_, t), n) = add_size (t, n + 1)
wenzelm@16678
   445
      | add_size (_, n) = n + 1;
wenzelm@16678
   446
  in add_size (tm, 0) end;
clasohm@0
   447
haftmann@18847
   448
fun map_atyps f (Type (a, Ts)) = Type (a, map (map_atyps f) Ts)
haftmann@18976
   449
  | map_atyps f T = f T;
haftmann@18847
   450
haftmann@18847
   451
fun map_aterms f (t $ u) = map_aterms f t $ map_aterms f u
haftmann@18847
   452
  | map_aterms f (Abs (a, T, t)) = Abs (a, T, map_aterms f t)
haftmann@18847
   453
  | map_aterms f t = f t;
haftmann@18847
   454
wenzelm@18981
   455
fun map_type_tvar f = map_atyps (fn TVar x => f x | T => T);
wenzelm@18981
   456
fun map_type_tfree f = map_atyps (fn TFree x => f x | T => T);
nipkow@949
   457
clasohm@0
   458
fun map_term_types f =
wenzelm@16678
   459
  let
wenzelm@16678
   460
    fun map_aux (Const (a, T)) = Const (a, f T)
wenzelm@16678
   461
      | map_aux (Free (a, T)) = Free (a, f T)
wenzelm@16678
   462
      | map_aux (Var (v, T)) = Var (v, f T)
wenzelm@16678
   463
      | map_aux (t as Bound _)  = t
wenzelm@16678
   464
      | map_aux (Abs (a, T, t)) = Abs (a, f T, map_aux t)
wenzelm@16678
   465
      | map_aux (t $ u) = map_aux t $ map_aux u;
wenzelm@16678
   466
  in map_aux end;
clasohm@0
   467
clasohm@0
   468
(* iterate a function over all types in a term *)
clasohm@0
   469
fun it_term_types f =
clasohm@0
   470
let fun iter(Const(_,T), a) = f(T,a)
clasohm@0
   471
      | iter(Free(_,T), a) = f(T,a)
clasohm@0
   472
      | iter(Var(_,T), a) = f(T,a)
clasohm@0
   473
      | iter(Abs(_,T,t), a) = iter(t,f(T,a))
clasohm@0
   474
      | iter(f$u, a) = iter(f, iter(u, a))
clasohm@0
   475
      | iter(Bound _, a) = a
clasohm@0
   476
in iter end
clasohm@0
   477
clasohm@0
   478
wenzelm@16943
   479
(* fold types and terms *)
wenzelm@16943
   480
wenzelm@16943
   481
(*fold atoms of type*)
wenzelm@16943
   482
fun fold_atyps f (Type (_, Ts)) = fold (fold_atyps f) Ts
wenzelm@16943
   483
  | fold_atyps f T = f T;
wenzelm@16943
   484
wenzelm@16943
   485
(*fold atoms of term*)
wenzelm@16943
   486
fun fold_aterms f (t $ u) = fold_aterms f t #> fold_aterms f u
wenzelm@16943
   487
  | fold_aterms f (Abs (_, _, t)) = fold_aterms f t
wenzelm@16943
   488
  | fold_aterms f a = f a;
wenzelm@16943
   489
wenzelm@16943
   490
(*fold types of term*)
wenzelm@16943
   491
fun fold_term_types f (t as Const (_, T)) = f t T
wenzelm@16943
   492
  | fold_term_types f (t as Free (_, T)) = f t T
wenzelm@16943
   493
  | fold_term_types f (t as Var (_, T)) = f t T
wenzelm@16943
   494
  | fold_term_types f (Bound _) = I
wenzelm@16943
   495
  | fold_term_types f (t as Abs (_, T, b)) = f t T #> fold_term_types f b
wenzelm@16943
   496
  | fold_term_types f (t $ u) = fold_term_types f t #> fold_term_types f u;
wenzelm@16943
   497
wenzelm@16943
   498
fun fold_types f = fold_term_types (K f);
wenzelm@16943
   499
wenzelm@16943
   500
(*collect variables*)
wenzelm@16943
   501
val add_tvarsT = fold_atyps (fn TVar v => insert (op =) v | _ => I);
wenzelm@16943
   502
val add_tvars = fold_types add_tvarsT;
wenzelm@16943
   503
val add_vars = fold_aterms (fn Var v => insert (op =) v | _ => I);
wenzelm@16943
   504
val add_tfreesT = fold_atyps (fn TFree v => insert (op =) v | _ => I);
wenzelm@16943
   505
val add_tfrees = fold_types add_tfreesT;
wenzelm@16943
   506
val add_frees = fold_aterms (fn Free v => insert (op =) v | _ => I);
wenzelm@16943
   507
wenzelm@16943
   508
(*collect variable names*)
wenzelm@16943
   509
val add_term_varnames = fold_aterms (fn Var (xi, _) => insert (op =) xi | _ => I);
wenzelm@16943
   510
fun term_varnames t = add_term_varnames t [];
wenzelm@16943
   511
wenzelm@18149
   512
fun find_free t x =
wenzelm@18149
   513
  let
wenzelm@18149
   514
    exception Found of term;
wenzelm@18149
   515
    fun find (t as Free (x', _)) = if x = x' then raise Found t else I
wenzelm@18149
   516
      | find _ = I;
wenzelm@18149
   517
  in (fold_aterms find t (); NONE) handle Found v => SOME v end;
wenzelm@18149
   518
wenzelm@18149
   519
wenzelm@16943
   520
wenzelm@16678
   521
(** Comparing terms, types, sorts etc. **)
wenzelm@16537
   522
wenzelm@16678
   523
(* fast syntactic comparison *)
wenzelm@16678
   524
wenzelm@16678
   525
fun fast_indexname_ord ((x, i), (y, j)) =
wenzelm@16678
   526
  (case int_ord (i, j) of EQUAL => fast_string_ord (x, y) | ord => ord);
wenzelm@16537
   527
wenzelm@16599
   528
fun sort_ord SS =
wenzelm@16599
   529
  if pointer_eq SS then EQUAL
wenzelm@16990
   530
  else dict_ord fast_string_ord SS;
wenzelm@16678
   531
wenzelm@16678
   532
local
wenzelm@16537
   533
wenzelm@16678
   534
fun cons_nr (TVar _) = 0
wenzelm@16678
   535
  | cons_nr (TFree _) = 1
wenzelm@16678
   536
  | cons_nr (Type _) = 2;
wenzelm@16537
   537
wenzelm@16678
   538
in
wenzelm@16537
   539
wenzelm@16537
   540
fun typ_ord TU =
wenzelm@16537
   541
  if pointer_eq TU then EQUAL
wenzelm@16537
   542
  else
wenzelm@16537
   543
    (case TU of
wenzelm@16678
   544
      (Type (a, Ts), Type (b, Us)) =>
wenzelm@16990
   545
        (case fast_string_ord (a, b) of EQUAL => dict_ord typ_ord (Ts, Us) | ord => ord)
wenzelm@16678
   546
    | (TFree (a, S), TFree (b, S')) =>
wenzelm@16678
   547
        (case fast_string_ord (a, b) of EQUAL => sort_ord (S, S') | ord => ord)
wenzelm@16678
   548
    | (TVar (xi, S), TVar (yj, S')) =>
wenzelm@16678
   549
        (case fast_indexname_ord (xi, yj) of EQUAL => sort_ord (S, S') | ord => ord)
wenzelm@16678
   550
    | (T, U) => int_ord (cons_nr T, cons_nr U));
wenzelm@16678
   551
wenzelm@16678
   552
end;
wenzelm@16678
   553
wenzelm@16678
   554
local
wenzelm@16678
   555
wenzelm@16678
   556
fun cons_nr (Const _) = 0
wenzelm@16678
   557
  | cons_nr (Free _) = 1
wenzelm@16678
   558
  | cons_nr (Var _) = 2
wenzelm@16678
   559
  | cons_nr (Bound _) = 3
wenzelm@16678
   560
  | cons_nr (Abs _) = 4
wenzelm@16678
   561
  | cons_nr (_ $ _) = 5;
wenzelm@16678
   562
wenzelm@16678
   563
fun struct_ord (Abs (_, _, t), Abs (_, _, u)) = struct_ord (t, u)
wenzelm@16678
   564
  | struct_ord (t1 $ t2, u1 $ u2) =
wenzelm@16678
   565
      (case struct_ord (t1, u1) of EQUAL => struct_ord (t2, u2) | ord => ord)
wenzelm@16678
   566
  | struct_ord (t, u) = int_ord (cons_nr t, cons_nr u);
wenzelm@16678
   567
wenzelm@16678
   568
fun atoms_ord (Abs (_, _, t), Abs (_, _, u)) = atoms_ord (t, u)
wenzelm@16678
   569
  | atoms_ord (t1 $ t2, u1 $ u2) =
wenzelm@16678
   570
      (case atoms_ord (t1, u1) of EQUAL => atoms_ord (t2, u2) | ord => ord)
wenzelm@16678
   571
  | atoms_ord (Const (a, _), Const (b, _)) = fast_string_ord (a, b)
wenzelm@16678
   572
  | atoms_ord (Free (x, _), Free (y, _)) = fast_string_ord (x, y)
wenzelm@16678
   573
  | atoms_ord (Var (xi, _), Var (yj, _)) = fast_indexname_ord (xi, yj)
wenzelm@16678
   574
  | atoms_ord (Bound i, Bound j) = int_ord (i, j)
wenzelm@16678
   575
  | atoms_ord _ = sys_error "atoms_ord";
wenzelm@16678
   576
wenzelm@16678
   577
fun types_ord (Abs (_, T, t), Abs (_, U, u)) =
wenzelm@16678
   578
      (case typ_ord (T, U) of EQUAL => types_ord (t, u) | ord => ord)
wenzelm@16678
   579
  | types_ord (t1 $ t2, u1 $ u2) =
wenzelm@16678
   580
      (case types_ord (t1, u1) of EQUAL => types_ord (t2, u2) | ord => ord)
wenzelm@16678
   581
  | types_ord (Const (_, T), Const (_, U)) = typ_ord (T, U)
wenzelm@16678
   582
  | types_ord (Free (_, T), Free (_, U)) = typ_ord (T, U)
wenzelm@16678
   583
  | types_ord (Var (_, T), Var (_, U)) = typ_ord (T, U)
wenzelm@16678
   584
  | types_ord (Bound _, Bound _) = EQUAL
wenzelm@16678
   585
  | types_ord _ = sys_error "types_ord";
wenzelm@16678
   586
wenzelm@16678
   587
in
wenzelm@16678
   588
wenzelm@16678
   589
fun fast_term_ord tu =
wenzelm@16678
   590
  if pointer_eq tu then EQUAL
wenzelm@16678
   591
  else
wenzelm@16678
   592
    (case struct_ord tu of
wenzelm@16678
   593
      EQUAL => (case atoms_ord tu of EQUAL => types_ord tu | ord => ord)
wenzelm@16678
   594
    | ord => ord);
wenzelm@16678
   595
wenzelm@16678
   596
fun op aconv tu = (fast_term_ord tu = EQUAL);
wenzelm@16678
   597
fun aconvs ts_us = (list_ord fast_term_ord ts_us = EQUAL);
wenzelm@16678
   598
wenzelm@16678
   599
structure Vartab = TableFun(type key = indexname val ord = fast_indexname_ord);
wenzelm@16678
   600
structure Typtab = TableFun(type key = typ val ord = typ_ord);
wenzelm@16678
   601
structure Termtab = TableFun(type key = term val ord = fast_term_ord);
wenzelm@16678
   602
wenzelm@16678
   603
end;
wenzelm@16537
   604
wenzelm@16537
   605
wenzelm@16537
   606
(* term_ord *)
wenzelm@16537
   607
wenzelm@16537
   608
(*a linear well-founded AC-compatible ordering for terms:
wenzelm@16537
   609
  s < t <=> 1. size(s) < size(t) or
wenzelm@16537
   610
            2. size(s) = size(t) and s=f(...) and t=g(...) and f<g or
wenzelm@16537
   611
            3. size(s) = size(t) and s=f(s1..sn) and t=f(t1..tn) and
wenzelm@16537
   612
               (s1..sn) < (t1..tn) (lexicographically)*)
wenzelm@16678
   613
wenzelm@16678
   614
fun indexname_ord ((x, i), (y, j)) =
wenzelm@16678
   615
  (case int_ord (i, j) of EQUAL => string_ord (x, y) | ord => ord);
wenzelm@16678
   616
wenzelm@16667
   617
local
wenzelm@16667
   618
wenzelm@16667
   619
fun hd_depth (t $ _, n) = hd_depth (t, n + 1)
wenzelm@16667
   620
  | hd_depth p = p;
wenzelm@16537
   621
wenzelm@16537
   622
fun dest_hd (Const (a, T)) = (((a, 0), T), 0)
wenzelm@16537
   623
  | dest_hd (Free (a, T)) = (((a, 0), T), 1)
wenzelm@16537
   624
  | dest_hd (Var v) = (v, 2)
wenzelm@16537
   625
  | dest_hd (Bound i) = ((("", i), dummyT), 3)
wenzelm@16537
   626
  | dest_hd (Abs (_, T, _)) = ((("", 0), T), 4);
wenzelm@16537
   627
wenzelm@16667
   628
in
wenzelm@16667
   629
wenzelm@16537
   630
fun term_ord tu =
wenzelm@16537
   631
  if pointer_eq tu then EQUAL
wenzelm@16537
   632
  else
wenzelm@16537
   633
    (case tu of
wenzelm@16537
   634
      (Abs (_, T, t), Abs(_, U, u)) =>
wenzelm@16537
   635
        (case term_ord (t, u) of EQUAL => typ_ord (T, U) | ord => ord)
wenzelm@16667
   636
    | (t, u) =>
wenzelm@16537
   637
        (case int_ord (size_of_term t, size_of_term u) of
wenzelm@16537
   638
          EQUAL =>
wenzelm@16943
   639
            (case prod_ord hd_ord int_ord (hd_depth (t, 0), hd_depth (u, 0)) of
wenzelm@16943
   640
              EQUAL => args_ord (t, u) | ord => ord)
wenzelm@16537
   641
        | ord => ord))
wenzelm@16537
   642
and hd_ord (f, g) =
wenzelm@16537
   643
  prod_ord (prod_ord indexname_ord typ_ord) int_ord (dest_hd f, dest_hd g)
wenzelm@16667
   644
and args_ord (f $ t, g $ u) =
wenzelm@16667
   645
      (case args_ord (f, g) of EQUAL => term_ord (t, u) | ord => ord)
wenzelm@16667
   646
  | args_ord _ = EQUAL;
wenzelm@16537
   647
wenzelm@16537
   648
fun termless tu = (term_ord tu = LESS);
wenzelm@16537
   649
wenzelm@16667
   650
end;
wenzelm@16667
   651
wenzelm@16667
   652
wenzelm@16667
   653
(** Lexicographic path order on terms **)
wenzelm@16667
   654
wenzelm@16667
   655
(*
nipkow@16570
   656
  See Baader & Nipkow, Term rewriting, CUP 1998.
nipkow@16570
   657
  Without variables.  Const, Var, Bound, Free and Abs are treated all as
nipkow@16570
   658
  constants.
nipkow@16570
   659
nipkow@16570
   660
  f_ord maps strings to integers and serves two purposes:
nipkow@16570
   661
  - Predicate on constant symbols.  Those that are not recognised by f_ord
nipkow@16570
   662
    must be mapped to ~1.
nipkow@16570
   663
  - Order on the recognised symbols.  These must be mapped to distinct
nipkow@16570
   664
    integers >= 0.
nipkow@16570
   665
wenzelm@16667
   666
*)
nipkow@16570
   667
nipkow@16570
   668
local
wenzelm@16667
   669
fun dest_hd f_ord (Const (a, T)) =
nipkow@16570
   670
      let val ord = f_ord a in
nipkow@16570
   671
        if ord = ~1 then ((1, ((a, 0), T)), 0) else ((0, (("", ord), T)), 0)
nipkow@16570
   672
      end
nipkow@16570
   673
  | dest_hd _ (Free (a, T)) = ((1, ((a, 0), T)), 0)
nipkow@16570
   674
  | dest_hd _ (Var v) = ((1, v), 1)
nipkow@16570
   675
  | dest_hd _ (Bound i) = ((1, (("", i), dummyT)), 2)
nipkow@16570
   676
  | dest_hd _ (Abs (_, T, _)) = ((1, (("", 0), T)), 3);
nipkow@16570
   677
nipkow@16570
   678
fun term_lpo f_ord (s, t) =
nipkow@16570
   679
  let val (f, ss) = strip_comb s and (g, ts) = strip_comb t in
nipkow@16570
   680
    if forall (fn si => term_lpo f_ord (si, t) = LESS) ss
nipkow@16570
   681
    then case hd_ord f_ord (f, g) of
wenzelm@16667
   682
        GREATER =>
wenzelm@16667
   683
          if forall (fn ti => term_lpo f_ord (s, ti) = GREATER) ts
wenzelm@16667
   684
          then GREATER else LESS
nipkow@16570
   685
      | EQUAL =>
wenzelm@16667
   686
          if forall (fn ti => term_lpo f_ord (s, ti) = GREATER) ts
wenzelm@16667
   687
          then list_ord (term_lpo f_ord) (ss, ts)
wenzelm@16667
   688
          else LESS
nipkow@16570
   689
      | LESS => LESS
nipkow@16570
   690
    else GREATER
nipkow@16570
   691
  end
nipkow@16570
   692
and hd_ord f_ord (f, g) = case (f, g) of
nipkow@16570
   693
    (Abs (_, T, t), Abs (_, U, u)) =>
nipkow@16570
   694
      (case term_lpo f_ord (t, u) of EQUAL => typ_ord (T, U) | ord => ord)
nipkow@16570
   695
  | (_, _) => prod_ord (prod_ord int_ord
nipkow@16570
   696
                  (prod_ord indexname_ord typ_ord)) int_ord
nipkow@16570
   697
                (dest_hd f_ord f, dest_hd f_ord g)
nipkow@16570
   698
in
nipkow@16570
   699
val term_lpo = term_lpo
nipkow@16570
   700
end;
nipkow@16570
   701
wenzelm@16537
   702
clasohm@0
   703
(** Connectives of higher order logic **)
clasohm@0
   704
wenzelm@19394
   705
fun aT S = TFree ("'a", S);
wenzelm@19394
   706
wenzelm@375
   707
fun itselfT ty = Type ("itself", [ty]);
wenzelm@14854
   708
val a_itselfT = itselfT (TFree ("'a", []));
wenzelm@375
   709
clasohm@0
   710
val propT : typ = Type("prop",[]);
clasohm@0
   711
clasohm@0
   712
val implies = Const("==>", propT-->propT-->propT);
clasohm@0
   713
clasohm@0
   714
fun all T = Const("all", (T-->propT)-->propT);
clasohm@0
   715
clasohm@0
   716
fun equals T = Const("==", T-->T-->propT);
clasohm@0
   717
clasohm@0
   718
(* maps  !!x1...xn. t   to   t  *)
wenzelm@13000
   719
fun strip_all_body (Const("all",_)$Abs(_,_,t))  =  strip_all_body t
clasohm@0
   720
  | strip_all_body t  =  t;
clasohm@0
   721
clasohm@0
   722
(* maps  !!x1...xn. t   to   [x1, ..., xn]  *)
clasohm@0
   723
fun strip_all_vars (Const("all",_)$Abs(a,T,t))  =
wenzelm@13000
   724
                (a,T) :: strip_all_vars t
clasohm@0
   725
  | strip_all_vars t  =  [] : (string*typ) list;
clasohm@0
   726
clasohm@0
   727
(*increments a term's non-local bound variables
clasohm@0
   728
  required when moving a term within abstractions
clasohm@0
   729
     inc is  increment for bound variables
clasohm@0
   730
     lev is  level at which a bound variable is considered 'loose'*)
wenzelm@13000
   731
fun incr_bv (inc, lev, u as Bound i) = if i>=lev then Bound(i+inc) else u
clasohm@0
   732
  | incr_bv (inc, lev, Abs(a,T,body)) =
wenzelm@9536
   733
        Abs(a, T, incr_bv(inc,lev+1,body))
wenzelm@13000
   734
  | incr_bv (inc, lev, f$t) =
clasohm@0
   735
      incr_bv(inc,lev,f) $ incr_bv(inc,lev,t)
clasohm@0
   736
  | incr_bv (inc, lev, u) = u;
clasohm@0
   737
clasohm@0
   738
fun incr_boundvars  0  t = t
clasohm@0
   739
  | incr_boundvars inc t = incr_bv(inc,0,t);
clasohm@0
   740
wenzelm@12981
   741
(*Scan a pair of terms; while they are similar,
wenzelm@12981
   742
  accumulate corresponding bound vars in "al"*)
wenzelm@12981
   743
fun match_bvs(Abs(x,_,s),Abs(y,_,t), al) =
wenzelm@12981
   744
      match_bvs(s, t, if x="" orelse y="" then al
wenzelm@12981
   745
                                          else (x,y)::al)
wenzelm@12981
   746
  | match_bvs(f$s, g$t, al) = match_bvs(f,g,match_bvs(s,t,al))
wenzelm@12981
   747
  | match_bvs(_,_,al) = al;
wenzelm@12981
   748
wenzelm@12981
   749
(* strip abstractions created by parameters *)
wenzelm@12981
   750
fun match_bvars((s,t),al) = match_bvs(strip_abs_body s, strip_abs_body t, al);
wenzelm@12981
   751
wenzelm@12981
   752
fun rename_abs pat obj t =
wenzelm@12981
   753
  let
wenzelm@12981
   754
    val ren = match_bvs (pat, obj, []);
wenzelm@12981
   755
    fun ren_abs (Abs (x, T, b)) =
wenzelm@18942
   756
          Abs (the_default x (AList.lookup (op =) ren x), T, ren_abs b)
wenzelm@12981
   757
      | ren_abs (f $ t) = ren_abs f $ ren_abs t
wenzelm@12981
   758
      | ren_abs t = t
skalberg@15531
   759
  in if null ren then NONE else SOME (ren_abs t) end;
clasohm@0
   760
clasohm@0
   761
(*Accumulate all 'loose' bound vars referring to level 'lev' or beyond.
clasohm@0
   762
   (Bound 0) is loose at level 0 *)
wenzelm@13000
   763
fun add_loose_bnos (Bound i, lev, js) =
wenzelm@9536
   764
        if i<lev then js  else  (i-lev) ins_int js
clasohm@0
   765
  | add_loose_bnos (Abs (_,_,t), lev, js) = add_loose_bnos (t, lev+1, js)
clasohm@0
   766
  | add_loose_bnos (f$t, lev, js) =
wenzelm@13000
   767
        add_loose_bnos (f, lev, add_loose_bnos (t, lev, js))
clasohm@0
   768
  | add_loose_bnos (_, _, js) = js;
clasohm@0
   769
clasohm@0
   770
fun loose_bnos t = add_loose_bnos (t, 0, []);
clasohm@0
   771
clasohm@0
   772
(* loose_bvar(t,k) iff t contains a 'loose' bound variable referring to
clasohm@0
   773
   level k or beyond. *)
clasohm@0
   774
fun loose_bvar(Bound i,k) = i >= k
clasohm@0
   775
  | loose_bvar(f$t, k) = loose_bvar(f,k) orelse loose_bvar(t,k)
clasohm@0
   776
  | loose_bvar(Abs(_,_,t),k) = loose_bvar(t,k+1)
clasohm@0
   777
  | loose_bvar _ = false;
clasohm@0
   778
nipkow@2792
   779
fun loose_bvar1(Bound i,k) = i = k
nipkow@2792
   780
  | loose_bvar1(f$t, k) = loose_bvar1(f,k) orelse loose_bvar1(t,k)
nipkow@2792
   781
  | loose_bvar1(Abs(_,_,t),k) = loose_bvar1(t,k+1)
nipkow@2792
   782
  | loose_bvar1 _ = false;
clasohm@0
   783
clasohm@0
   784
(*Substitute arguments for loose bound variables.
clasohm@0
   785
  Beta-reduction of arg(n-1)...arg0 into t replacing (Bound i) with (argi).
wenzelm@4626
   786
  Note that for ((%x y. c) a b), the bound vars in c are x=1 and y=0
wenzelm@9536
   787
        and the appropriate call is  subst_bounds([b,a], c) .
clasohm@0
   788
  Loose bound variables >=n are reduced by "n" to
clasohm@0
   789
     compensate for the disappearance of lambdas.
clasohm@0
   790
*)
wenzelm@13000
   791
fun subst_bounds (args: term list, t) : term =
wenzelm@19065
   792
  let
wenzelm@19065
   793
    exception SAME;
wenzelm@19065
   794
    val n = length args;
wenzelm@19065
   795
    fun subst (t as Bound i, lev) =
wenzelm@19065
   796
         (if i < lev then raise SAME   (*var is locally bound*)
wenzelm@19065
   797
          else incr_boundvars lev (List.nth (args, i - lev))
wenzelm@19065
   798
            handle Subscript => Bound (i - n))  (*loose: change it*)
wenzelm@19065
   799
      | subst (Abs (a, T, body), lev) = Abs (a, T, subst (body, lev + 1))
wenzelm@19065
   800
      | subst (f $ t, lev) =
wenzelm@19065
   801
          (subst (f, lev) $ (subst (t, lev) handle SAME => t) handle SAME => f $ subst (t, lev))
wenzelm@19065
   802
      | subst _ = raise SAME;
wenzelm@19065
   803
  in case args of [] => t | _ => (subst (t, 0) handle SAME => t) end;
clasohm@0
   804
paulson@2192
   805
(*Special case: one argument*)
wenzelm@13000
   806
fun subst_bound (arg, t) : term =
wenzelm@19065
   807
  let
wenzelm@19065
   808
    exception SAME;
wenzelm@19065
   809
    fun subst (Bound i, lev) =
wenzelm@19065
   810
          if i < lev then raise SAME   (*var is locally bound*)
wenzelm@19065
   811
          else if i = lev then incr_boundvars lev arg
wenzelm@19065
   812
          else Bound (i - 1)   (*loose: change it*)
wenzelm@19065
   813
      | subst (Abs (a, T, body), lev) = Abs (a, T, subst (body, lev + 1))
wenzelm@19065
   814
      | subst (f $ t, lev) =
wenzelm@19065
   815
          (subst (f, lev) $ (subst (t, lev) handle SAME => t) handle SAME => f $ subst (t, lev))
wenzelm@19065
   816
      | subst _ = raise SAME;
wenzelm@19065
   817
  in subst (t, 0) handle SAME => t end;
paulson@2192
   818
clasohm@0
   819
(*beta-reduce if possible, else form application*)
paulson@2192
   820
fun betapply (Abs(_,_,t), u) = subst_bound (u,t)
clasohm@0
   821
  | betapply (f,u) = f$u;
clasohm@0
   822
wenzelm@18183
   823
val betapplys = Library.foldl betapply;
wenzelm@18183
   824
wenzelm@14786
   825
wenzelm@16882
   826
(** Specialized equality, membership, insertion etc. **)
paulson@2192
   827
wenzelm@16882
   828
(* indexnames *)
wenzelm@16882
   829
wenzelm@16724
   830
fun eq_ix ((x, i): indexname, (y, j)) = i = j andalso x = y;
paulson@2192
   831
wenzelm@2959
   832
fun mem_ix (_, []) = false
wenzelm@16882
   833
  | mem_ix (x, y :: ys) = eq_ix (x, y) orelse mem_ix (x, ys);
paulson@2192
   834
wenzelm@16882
   835
fun ins_ix (x, xs) = if mem_ix (x, xs) then xs else x :: xs;
paulson@2192
   836
clasohm@0
   837
wenzelm@16882
   838
(* variables *)
wenzelm@16882
   839
wenzelm@16943
   840
fun eq_tvar ((xi, S: sort), (xi', S')) = eq_ix (xi, xi') andalso S = S';
wenzelm@16943
   841
fun eq_var ((xi, T: typ), (xi', T')) = eq_ix (xi, xi') andalso T = T';
wenzelm@16943
   842
wenzelm@16943
   843
val tvar_ord = prod_ord indexname_ord sort_ord;
wenzelm@16943
   844
val var_ord = prod_ord indexname_ord typ_ord;
wenzelm@16882
   845
wenzelm@16882
   846
wenzelm@16882
   847
(* terms *)
paulson@2176
   848
paulson@2176
   849
fun mem_term (_, []) = false
wenzelm@16882
   850
  | mem_term (t, t'::ts) = t aconv t' orelse mem_term (t, ts);
paulson@2176
   851
paulson@2176
   852
fun ins_term(t,ts) = if mem_term(t,ts) then ts else t :: ts;
paulson@2176
   853
wenzelm@16882
   854
wenzelm@13000
   855
(*A fast unification filter: true unless the two terms cannot be unified.
clasohm@0
   856
  Terms must be NORMAL.  Treats all Vars as distinct. *)
clasohm@0
   857
fun could_unify (t,u) =
clasohm@0
   858
  let fun matchrands (f$t, g$u) = could_unify(t,u) andalso  matchrands(f,g)
wenzelm@9536
   859
        | matchrands _ = true
clasohm@0
   860
  in case (head_of t , head_of u) of
wenzelm@9536
   861
        (_, Var _) => true
clasohm@0
   862
      | (Var _, _) => true
clasohm@0
   863
      | (Const(a,_), Const(b,_)) =>  a=b andalso matchrands(t,u)
clasohm@0
   864
      | (Free(a,_), Free(b,_)) =>  a=b andalso matchrands(t,u)
clasohm@0
   865
      | (Bound i, Bound j) =>  i=j andalso matchrands(t,u)
clasohm@0
   866
      | (Abs _, _) =>  true   (*because of possible eta equality*)
clasohm@0
   867
      | (_, Abs _) =>  true
clasohm@0
   868
      | _ => false
clasohm@0
   869
  end;
clasohm@0
   870
clasohm@0
   871
(*Substitute new for free occurrences of old in a term*)
clasohm@0
   872
fun subst_free [] = (fn t=>t)
clasohm@0
   873
  | subst_free pairs =
wenzelm@13000
   874
      let fun substf u =
haftmann@17314
   875
            case AList.lookup (op aconv) pairs u of
skalberg@15531
   876
                SOME u' => u'
skalberg@15531
   877
              | NONE => (case u of Abs(a,T,t) => Abs(a, T, substf t)
wenzelm@9536
   878
                                 | t$u' => substf t $ substf u'
wenzelm@9536
   879
                                 | _ => u)
clasohm@0
   880
      in  substf  end;
clasohm@0
   881
clasohm@0
   882
(*a total, irreflexive ordering on index names*)
clasohm@0
   883
fun xless ((a,i), (b,j): indexname) = i<j  orelse  (i=j andalso a<b);
clasohm@0
   884
clasohm@0
   885
wenzelm@13000
   886
(*Abstraction of the term "body" over its occurrences of v,
clasohm@0
   887
    which must contain no loose bound variables.
clasohm@0
   888
  The resulting term is ready to become the body of an Abs.*)
wenzelm@16882
   889
fun abstract_over (v, body) =
wenzelm@16882
   890
  let
wenzelm@16990
   891
    exception SAME;
wenzelm@16990
   892
    fun abs lev tm =
wenzelm@16990
   893
      if v aconv tm then Bound lev
wenzelm@16882
   894
      else
wenzelm@16990
   895
        (case tm of
wenzelm@16990
   896
          Abs (a, T, t) => Abs (a, T, abs (lev + 1) t)
wenzelm@16990
   897
        | t $ u => (abs lev t $ (abs lev u handle SAME => u) handle SAME => t $ abs lev u)
wenzelm@16990
   898
        | _ => raise SAME);
wenzelm@16990
   899
  in abs 0 body handle SAME => body end;
clasohm@0
   900
wenzelm@18975
   901
fun lambda (v as Const (x, T)) t = Abs (NameSpace.base x, T, abstract_over (v, t))
wenzelm@18942
   902
  | lambda (v as Free (x, T)) t = Abs (x, T, abstract_over (v, t))
berghofe@13665
   903
  | lambda (v as Var ((x, _), T)) t = Abs (x, T, abstract_over (v, t))
berghofe@13665
   904
  | lambda v t = raise TERM ("lambda", [v, t]);
clasohm@0
   905
clasohm@0
   906
(*Form an abstraction over a free variable.*)
clasohm@0
   907
fun absfree (a,T,body) = Abs(a, T, abstract_over (Free(a,T), body));
wenzelm@17786
   908
fun absdummy (T, body) = Abs ("uu", T, body);
clasohm@0
   909
clasohm@0
   910
(*Abstraction over a list of free variables*)
clasohm@0
   911
fun list_abs_free ([ ] ,     t) = t
wenzelm@13000
   912
  | list_abs_free ((a,T)::vars, t) =
clasohm@0
   913
      absfree(a, T, list_abs_free(vars,t));
clasohm@0
   914
clasohm@0
   915
(*Quantification over a list of free variables*)
clasohm@0
   916
fun list_all_free ([], t: term) = t
wenzelm@13000
   917
  | list_all_free ((a,T)::vars, t) =
clasohm@0
   918
        (all T) $ (absfree(a, T, list_all_free(vars,t)));
clasohm@0
   919
clasohm@0
   920
(*Quantification over a list of variables (already bound in body) *)
clasohm@0
   921
fun list_all ([], t) = t
wenzelm@13000
   922
  | list_all ((a,T)::vars, t) =
clasohm@0
   923
        (all T) $ (Abs(a, T, list_all(vars,t)));
clasohm@0
   924
wenzelm@16678
   925
(*Replace the ATOMIC term ti by ui;    inst = [(t1,u1), ..., (tn,un)].
clasohm@0
   926
  A simultaneous substitution:  [ (a,b), (b,a) ] swaps a and b.  *)
wenzelm@16678
   927
fun subst_atomic [] tm = tm
wenzelm@16678
   928
  | subst_atomic inst tm =
wenzelm@16678
   929
      let
wenzelm@16678
   930
        fun subst (Abs (a, T, body)) = Abs (a, T, subst body)
wenzelm@16678
   931
          | subst (t $ u) = subst t $ subst u
wenzelm@18942
   932
          | subst t = the_default t (AList.lookup (op aconv) inst t);
wenzelm@16678
   933
      in subst tm end;
clasohm@0
   934
wenzelm@16678
   935
(*Replace the ATOMIC type Ti by Ui;    inst = [(T1,U1), ..., (Tn,Un)].*)
wenzelm@16678
   936
fun typ_subst_atomic [] ty = ty
wenzelm@16678
   937
  | typ_subst_atomic inst ty =
wenzelm@16678
   938
      let
wenzelm@16678
   939
        fun subst (Type (a, Ts)) = Type (a, map subst Ts)
wenzelm@18942
   940
          | subst T = the_default T (AList.lookup (op = : typ * typ -> bool) inst T);
wenzelm@16678
   941
      in subst ty end;
berghofe@15797
   942
wenzelm@16678
   943
fun subst_atomic_types [] tm = tm
wenzelm@16678
   944
  | subst_atomic_types inst tm = map_term_types (typ_subst_atomic inst) tm;
wenzelm@16678
   945
wenzelm@16678
   946
fun typ_subst_TVars [] ty = ty
wenzelm@16678
   947
  | typ_subst_TVars inst ty =
wenzelm@16678
   948
      let
wenzelm@16678
   949
        fun subst (Type (a, Ts)) = Type (a, map subst Ts)
wenzelm@18942
   950
          | subst (T as TVar (xi, _)) = the_default T (AList.lookup (op =) inst xi)
wenzelm@16678
   951
          | subst T = T;
wenzelm@16678
   952
      in subst ty end;
clasohm@0
   953
wenzelm@16678
   954
fun subst_TVars [] tm = tm
wenzelm@16678
   955
  | subst_TVars inst tm = map_term_types (typ_subst_TVars inst) tm;
clasohm@0
   956
wenzelm@16678
   957
(*see also Envir.norm_term*)
wenzelm@16678
   958
fun subst_Vars [] tm = tm
wenzelm@16678
   959
  | subst_Vars inst tm =
wenzelm@16678
   960
      let
wenzelm@18942
   961
        fun subst (t as Var (xi, _)) = the_default t (AList.lookup (op =) inst xi)
wenzelm@16678
   962
          | subst (Abs (a, T, t)) = Abs (a, T, subst t)
wenzelm@16678
   963
          | subst (t $ u) = subst t $ subst u
wenzelm@16678
   964
          | subst t = t;
wenzelm@16678
   965
      in subst tm end;
clasohm@0
   966
wenzelm@16678
   967
(*see also Envir.norm_term*)
wenzelm@16678
   968
fun subst_vars ([], []) tm = tm
wenzelm@16678
   969
  | subst_vars ([], inst) tm = subst_Vars inst tm
wenzelm@16678
   970
  | subst_vars (instT, inst) tm =
wenzelm@16678
   971
      let
wenzelm@16678
   972
        fun subst (Const (a, T)) = Const (a, typ_subst_TVars instT T)
wenzelm@16678
   973
          | subst (Free (a, T)) = Free (a, typ_subst_TVars instT T)
wenzelm@16678
   974
          | subst (t as Var (xi, T)) =
haftmann@17271
   975
              (case AList.lookup (op =) inst xi of
wenzelm@16678
   976
                NONE => Var (xi, typ_subst_TVars instT T)
wenzelm@16678
   977
              | SOME t => t)
wenzelm@16678
   978
          | subst (t as Bound _) = t
wenzelm@16678
   979
          | subst (Abs (a, T, t)) = Abs (a, typ_subst_TVars instT T, subst t)
wenzelm@16678
   980
          | subst (t $ u) = subst t $ subst u;
wenzelm@16678
   981
      in subst tm end;
clasohm@0
   982
clasohm@0
   983
wenzelm@19909
   984
(* internal identifiers *)
wenzelm@19909
   985
wenzelm@19909
   986
val internal = suffix "_";
wenzelm@19909
   987
val dest_internal = unsuffix "_";
wenzelm@19909
   988
wenzelm@19909
   989
val skolem = suffix "__";
wenzelm@19909
   990
val dest_skolem = unsuffix "__";
wenzelm@19909
   991
wenzelm@19909
   992
wenzelm@19909
   993
(* generalization of fixed variables *)
wenzelm@19909
   994
wenzelm@19909
   995
local exception SAME in
wenzelm@19909
   996
wenzelm@19909
   997
fun generalizeT_same [] _ _ = raise SAME
wenzelm@19909
   998
  | generalizeT_same tfrees idx ty =
wenzelm@19909
   999
      let
wenzelm@19909
  1000
        fun gen_typ (Type (a, Ts)) = Type (a, gen_typs Ts)
wenzelm@19909
  1001
          | gen_typ (TFree (a, S)) =
wenzelm@19909
  1002
              if member (op =) tfrees a then TVar ((a, idx), S)
wenzelm@19909
  1003
              else raise SAME
wenzelm@19909
  1004
          | gen_typ _ = raise SAME
wenzelm@19909
  1005
        and gen_typs (T :: Ts) =
wenzelm@19909
  1006
            (gen_typ T :: (gen_typs Ts handle SAME => Ts)
wenzelm@19909
  1007
              handle SAME => T :: gen_typs Ts)
wenzelm@19909
  1008
          | gen_typs [] = raise SAME;
wenzelm@19909
  1009
      in gen_typ ty end;
wenzelm@19909
  1010
wenzelm@19909
  1011
fun generalize ([], []) _ tm = tm
wenzelm@19909
  1012
  | generalize (tfrees, frees) idx tm =
wenzelm@19909
  1013
      let
wenzelm@19909
  1014
        fun var ((x, i), T) =
wenzelm@19909
  1015
          (case try dest_internal x of
wenzelm@19909
  1016
            NONE => Var ((x, i), T)
wenzelm@19909
  1017
          | SOME x' => var ((x', i + 1), T));
wenzelm@19909
  1018
wenzelm@19909
  1019
        val genT = generalizeT_same tfrees idx;
wenzelm@19909
  1020
        fun gen (Free (x, T)) =
wenzelm@19909
  1021
              if member (op =) frees x then var ((x, idx), genT T handle SAME => T)
wenzelm@19909
  1022
              else Free (x, genT T)
wenzelm@19909
  1023
          | gen (Var (xi, T)) = Var (xi, genT T)
wenzelm@19909
  1024
          | gen (Const (c, T)) = Const (c, genT T)
wenzelm@19909
  1025
          | gen (Bound _) = raise SAME
wenzelm@19909
  1026
          | gen (Abs (x, T, t)) =
wenzelm@19909
  1027
              (Abs (x, genT T, gen t handle SAME => t)
wenzelm@19909
  1028
                handle SAME => Abs (x, T, gen t))
wenzelm@19909
  1029
          | gen (t $ u) = (gen t $ (gen u handle SAME => u) handle SAME => t $ gen u);
wenzelm@19909
  1030
      in gen tm handle SAME => tm end;
wenzelm@19909
  1031
wenzelm@19909
  1032
fun generalizeT tfrees i ty =
wenzelm@19909
  1033
  generalizeT_same tfrees i ty handle SAME => ty;
wenzelm@19909
  1034
wenzelm@19909
  1035
end;
wenzelm@19909
  1036
wenzelm@19909
  1037
wenzelm@16943
  1038
(* instantiation of schematic variables (types before terms) *)
wenzelm@16882
  1039
wenzelm@16882
  1040
local exception SAME in
wenzelm@16882
  1041
wenzelm@16943
  1042
fun instantiateT_same [] _ = raise SAME
wenzelm@16943
  1043
  | instantiateT_same instT ty =
wenzelm@16882
  1044
      let
wenzelm@16882
  1045
        fun subst_typ (Type (a, Ts)) = Type (a, subst_typs Ts)
wenzelm@16882
  1046
          | subst_typ (TVar v) =
haftmann@17314
  1047
              (case AList.lookup eq_tvar instT v of
wenzelm@16882
  1048
                SOME T => T
wenzelm@16882
  1049
              | NONE => raise SAME)
wenzelm@16882
  1050
          | subst_typ _ = raise SAME
wenzelm@16882
  1051
        and subst_typs (T :: Ts) =
wenzelm@16882
  1052
            (subst_typ T :: (subst_typs Ts handle SAME => Ts)
wenzelm@16882
  1053
              handle SAME => T :: subst_typs Ts)
wenzelm@16882
  1054
          | subst_typs [] = raise SAME;
wenzelm@16882
  1055
      in subst_typ ty end;
wenzelm@16882
  1056
wenzelm@16882
  1057
fun instantiate ([], []) tm = tm
wenzelm@16882
  1058
  | instantiate (instT, inst) tm =
wenzelm@16882
  1059
      let
wenzelm@16943
  1060
        val substT = instantiateT_same instT;
wenzelm@16943
  1061
        fun subst (Const (c, T)) = Const (c, substT T)
wenzelm@16943
  1062
          | subst (Free (x, T)) = Free (x, substT T)
wenzelm@16882
  1063
          | subst (Var (xi, T)) =
wenzelm@16943
  1064
              let val (T', same) = (substT T, false) handle SAME => (T, true) in
haftmann@17314
  1065
                (case AList.lookup eq_var inst (xi, T') of
wenzelm@16882
  1066
                   SOME t => t
wenzelm@16882
  1067
                 | NONE => if same then raise SAME else Var (xi, T'))
wenzelm@16882
  1068
              end
wenzelm@16882
  1069
          | subst (Bound _) = raise SAME
wenzelm@16882
  1070
          | subst (Abs (x, T, t)) =
wenzelm@16943
  1071
              (Abs (x, substT T, subst t handle SAME => t)
wenzelm@16882
  1072
                handle SAME => Abs (x, T, subst t))
wenzelm@16882
  1073
          | subst (t $ u) = (subst t $ (subst u handle SAME => u) handle SAME => t $ subst u);
wenzelm@16882
  1074
      in subst tm handle SAME => tm end;
wenzelm@16882
  1075
wenzelm@16882
  1076
fun instantiateT instT ty =
wenzelm@16943
  1077
  instantiateT_same instT ty handle SAME => ty;
wenzelm@16882
  1078
wenzelm@16882
  1079
end;
wenzelm@16882
  1080
wenzelm@16882
  1081
paulson@15573
  1082
(** Identifying first-order terms **)
paulson@15573
  1083
paulson@15573
  1084
(*Argument Ts is a reverse list of binder types, needed if term t contains Bound vars*)
paulson@15573
  1085
fun has_not_funtype Ts t = not (is_funtype (fastype_of1 (Ts,t)));
paulson@15573
  1086
wenzelm@16537
  1087
(*First order means in all terms of the form f(t1,...,tn) no argument has a
paulson@16589
  1088
  function type. The supplied quantifiers are excluded: their argument always
paulson@16589
  1089
  has a function type through a recursive call into its body.*)
wenzelm@16667
  1090
fun is_first_order quants =
paulson@16589
  1091
  let fun first_order1 Ts (Abs (_,T,body)) = first_order1 (T::Ts) body
wenzelm@16667
  1092
        | first_order1 Ts (Const(q,_) $ Abs(a,T,body)) =
wenzelm@16667
  1093
            q mem_string quants  andalso   (*it is a known quantifier*)
paulson@16589
  1094
            not (is_funtype T)   andalso first_order1 (T::Ts) body
wenzelm@16667
  1095
        | first_order1 Ts t =
wenzelm@16667
  1096
            case strip_comb t of
wenzelm@16667
  1097
                 (Var _, ts) => forall (first_order1 Ts andf has_not_funtype Ts) ts
wenzelm@16667
  1098
               | (Free _, ts) => forall (first_order1 Ts andf has_not_funtype Ts) ts
wenzelm@16667
  1099
               | (Const _, ts) => forall (first_order1 Ts andf has_not_funtype Ts) ts
wenzelm@16667
  1100
               | (Bound _, ts) => forall (first_order1 Ts andf has_not_funtype Ts) ts
wenzelm@16667
  1101
               | (Abs _, ts) => false (*not in beta-normal form*)
wenzelm@16667
  1102
               | _ => error "first_order: unexpected case"
paulson@16589
  1103
    in  first_order1 []  end;
paulson@15573
  1104
wenzelm@16710
  1105
wenzelm@16990
  1106
(* maximum index of typs and terms *)
clasohm@0
  1107
wenzelm@16710
  1108
fun maxidx_typ (TVar ((_, j), _)) i = Int.max (i, j)
wenzelm@16710
  1109
  | maxidx_typ (Type (_, Ts)) i = maxidx_typs Ts i
wenzelm@16710
  1110
  | maxidx_typ (TFree _) i = i
wenzelm@16710
  1111
and maxidx_typs [] i = i
wenzelm@16710
  1112
  | maxidx_typs (T :: Ts) i = maxidx_typs Ts (maxidx_typ T i);
clasohm@0
  1113
wenzelm@16710
  1114
fun maxidx_term (Var ((_, j), T)) i = maxidx_typ T (Int.max (i, j))
wenzelm@16710
  1115
  | maxidx_term (Const (_, T)) i = maxidx_typ T i
wenzelm@16710
  1116
  | maxidx_term (Free (_, T)) i = maxidx_typ T i
wenzelm@16710
  1117
  | maxidx_term (Bound _) i = i
wenzelm@16710
  1118
  | maxidx_term (Abs (_, T, t)) i = maxidx_term t (maxidx_typ T i)
wenzelm@16710
  1119
  | maxidx_term (t $ u) i = maxidx_term u (maxidx_term t i);
clasohm@0
  1120
wenzelm@16710
  1121
fun maxidx_of_typ T = maxidx_typ T ~1;
wenzelm@16710
  1122
fun maxidx_of_typs Ts = maxidx_typs Ts ~1;
wenzelm@16710
  1123
fun maxidx_of_term t = maxidx_term t ~1;
berghofe@13665
  1124
clasohm@0
  1125
clasohm@0
  1126
clasohm@0
  1127
(**** Syntax-related declarations ****)
clasohm@0
  1128
clasohm@0
  1129
(*** Printing ***)
clasohm@0
  1130
wenzelm@19014
  1131
(*Makes a variant of a name distinct from already used names.  First
wenzelm@19014
  1132
  attaches the suffix and then increments this; preserves a suffix of
wenzelm@19014
  1133
  underscores "_". *)
wenzelm@19014
  1134
fun variant_name used name =
wenzelm@12306
  1135
  let
wenzelm@19014
  1136
    val (c, u) = pairself implode (Library.take_suffix (fn s => s = "_") (Symbol.explode name));
wenzelm@19014
  1137
    fun vary2 c = if used (c ^ u) then vary2 (Symbol.bump_string c) else c;
wenzelm@19014
  1138
    fun vary1 c = if used (c ^ u) then vary2 (Symbol.bump_init c) else c;
wenzelm@12306
  1139
  in vary1 (if c = "" then "u" else c) ^ u end;
clasohm@0
  1140
wenzelm@19014
  1141
fun variant used_names = variant_name (member (op =) used_names);
wenzelm@19014
  1142
clasohm@0
  1143
(*Create variants of the list of names, with priority to the first ones*)
clasohm@0
  1144
fun variantlist ([], used) = []
wenzelm@13000
  1145
  | variantlist(b::bs, used) =
clasohm@0
  1146
      let val b' = variant used b
clasohm@0
  1147
      in  b' :: variantlist (bs, b'::used)  end;
clasohm@0
  1148
wenzelm@14695
  1149
(*Invent fresh names*)
wenzelm@14695
  1150
fun invent_names _ _ 0 = []
wenzelm@14695
  1151
  | invent_names used a n =
wenzelm@14695
  1152
      let val b = Symbol.bump_string a in
wenzelm@14695
  1153
        if a mem_string used then invent_names used b n
wenzelm@14695
  1154
        else a :: invent_names used b (n - 1)
wenzelm@14695
  1155
      end;
wenzelm@11353
  1156
wenzelm@16537
  1157
wenzelm@19909
  1158
(* substructure *)
wenzelm@4017
  1159
wenzelm@19909
  1160
fun exists_subtype P =
wenzelm@19909
  1161
  let
wenzelm@19909
  1162
    fun ex ty = P ty orelse
wenzelm@19909
  1163
      (case ty of Type (_, Ts) => exists ex Ts | _ => false);
wenzelm@19909
  1164
  in ex end;
nipkow@13646
  1165
wenzelm@16943
  1166
fun exists_subterm P =
wenzelm@16943
  1167
  let
wenzelm@16943
  1168
    fun ex tm = P tm orelse
wenzelm@16943
  1169
      (case tm of
wenzelm@16943
  1170
        t $ u => ex t orelse ex u
wenzelm@16943
  1171
      | Abs (_, _, t) => ex t
wenzelm@16943
  1172
      | _ => false);
wenzelm@16943
  1173
  in ex end;
obua@16108
  1174
wenzelm@19909
  1175
wenzelm@19909
  1176
(** Consts etc. **)
wenzelm@19909
  1177
wenzelm@19909
  1178
fun add_term_consts (Const (c, _), cs) = insert (op =) c cs
wenzelm@19909
  1179
  | add_term_consts (t $ u, cs) = add_term_consts (t, add_term_consts (u, cs))
wenzelm@19909
  1180
  | add_term_consts (Abs (_, _, t), cs) = add_term_consts (t, cs)
wenzelm@19909
  1181
  | add_term_consts (_, cs) = cs;
wenzelm@19909
  1182
wenzelm@19909
  1183
fun term_consts t = add_term_consts(t,[]);
wenzelm@19909
  1184
wenzelm@16943
  1185
fun exists_Const P = exists_subterm (fn Const c => P c | _ => false);
nipkow@4631
  1186
wenzelm@4017
  1187
clasohm@0
  1188
(** TFrees and TVars **)
clasohm@0
  1189
wenzelm@12802
  1190
(*Accumulates the names of Frees in the term, suppressing duplicates.*)
wenzelm@12802
  1191
fun add_term_free_names (Free(a,_), bs) = a ins_string bs
wenzelm@12802
  1192
  | add_term_free_names (f$u, bs) = add_term_free_names (f, add_term_free_names(u, bs))
wenzelm@12802
  1193
  | add_term_free_names (Abs(_,_,t), bs) = add_term_free_names(t,bs)
wenzelm@12802
  1194
  | add_term_free_names (_, bs) = bs;
wenzelm@12802
  1195
clasohm@0
  1196
(*Accumulates the names in the term, suppressing duplicates.
clasohm@0
  1197
  Includes Frees and Consts.  For choosing unambiguous bound var names.*)
wenzelm@10666
  1198
fun add_term_names (Const(a,_), bs) = NameSpace.base a ins_string bs
paulson@2176
  1199
  | add_term_names (Free(a,_), bs) = a ins_string bs
clasohm@0
  1200
  | add_term_names (f$u, bs) = add_term_names (f, add_term_names(u, bs))
clasohm@0
  1201
  | add_term_names (Abs(_,_,t), bs) = add_term_names(t,bs)
clasohm@0
  1202
  | add_term_names (_, bs) = bs;
clasohm@0
  1203
clasohm@0
  1204
(*Accumulates the TVars in a type, suppressing duplicates. *)
skalberg@15574
  1205
fun add_typ_tvars(Type(_,Ts),vs) = foldr add_typ_tvars vs Ts
clasohm@0
  1206
  | add_typ_tvars(TFree(_),vs) = vs
wenzelm@16294
  1207
  | add_typ_tvars(TVar(v),vs) = insert (op =) v vs;
clasohm@0
  1208
clasohm@0
  1209
(*Accumulates the TFrees in a type, suppressing duplicates. *)
skalberg@15574
  1210
fun add_typ_tfree_names(Type(_,Ts),fs) = foldr add_typ_tfree_names fs Ts
paulson@2176
  1211
  | add_typ_tfree_names(TFree(f,_),fs) = f ins_string fs
clasohm@0
  1212
  | add_typ_tfree_names(TVar(_),fs) = fs;
clasohm@0
  1213
skalberg@15574
  1214
fun add_typ_tfrees(Type(_,Ts),fs) = foldr add_typ_tfrees fs Ts
wenzelm@16294
  1215
  | add_typ_tfrees(TFree(f),fs) = insert (op =) f fs
clasohm@0
  1216
  | add_typ_tfrees(TVar(_),fs) = fs;
clasohm@0
  1217
skalberg@15574
  1218
fun add_typ_varnames(Type(_,Ts),nms) = foldr add_typ_varnames nms Ts
paulson@2176
  1219
  | add_typ_varnames(TFree(nm,_),nms) = nm ins_string nms
paulson@2176
  1220
  | add_typ_varnames(TVar((nm,_),_),nms) = nm ins_string nms;
nipkow@949
  1221
clasohm@0
  1222
(*Accumulates the TVars in a term, suppressing duplicates. *)
clasohm@0
  1223
val add_term_tvars = it_term_types add_typ_tvars;
clasohm@0
  1224
clasohm@0
  1225
(*Accumulates the TFrees in a term, suppressing duplicates. *)
clasohm@0
  1226
val add_term_tfrees = it_term_types add_typ_tfrees;
clasohm@0
  1227
val add_term_tfree_names = it_term_types add_typ_tfree_names;
clasohm@0
  1228
nipkow@949
  1229
val add_term_tvarnames = it_term_types add_typ_varnames;
nipkow@949
  1230
clasohm@0
  1231
(*Non-list versions*)
clasohm@0
  1232
fun typ_tfrees T = add_typ_tfrees(T,[]);
clasohm@0
  1233
fun typ_tvars T = add_typ_tvars(T,[]);
clasohm@0
  1234
fun term_tfrees t = add_term_tfrees(t,[]);
clasohm@0
  1235
fun term_tvars t = add_term_tvars(t,[]);
clasohm@0
  1236
nipkow@949
  1237
(*special code to enforce left-to-right collection of TVar-indexnames*)
nipkow@949
  1238
skalberg@15570
  1239
fun add_typ_ixns(ixns,Type(_,Ts)) = Library.foldl add_typ_ixns (ixns,Ts)
wenzelm@13000
  1240
  | add_typ_ixns(ixns,TVar(ixn,_)) = if mem_ix (ixn, ixns) then ixns
wenzelm@9536
  1241
                                     else ixns@[ixn]
nipkow@949
  1242
  | add_typ_ixns(ixns,TFree(_)) = ixns;
nipkow@949
  1243
nipkow@949
  1244
fun add_term_tvar_ixns(Const(_,T),ixns) = add_typ_ixns(ixns,T)
nipkow@949
  1245
  | add_term_tvar_ixns(Free(_,T),ixns) = add_typ_ixns(ixns,T)
nipkow@949
  1246
  | add_term_tvar_ixns(Var(_,T),ixns) = add_typ_ixns(ixns,T)
nipkow@949
  1247
  | add_term_tvar_ixns(Bound _,ixns) = ixns
nipkow@949
  1248
  | add_term_tvar_ixns(Abs(_,T,t),ixns) =
nipkow@949
  1249
      add_term_tvar_ixns(t,add_typ_ixns(ixns,T))
nipkow@949
  1250
  | add_term_tvar_ixns(f$t,ixns) =
nipkow@949
  1251
      add_term_tvar_ixns(t,add_term_tvar_ixns(f,ixns));
nipkow@949
  1252
wenzelm@16537
  1253
clasohm@0
  1254
(** Frees and Vars **)
clasohm@0
  1255
clasohm@0
  1256
(*Accumulates the Vars in the term, suppressing duplicates*)
clasohm@0
  1257
fun add_term_vars (t, vars: term list) = case t of
wenzelm@16990
  1258
    Var   _ => OrdList.insert term_ord t vars
clasohm@0
  1259
  | Abs (_,_,body) => add_term_vars(body,vars)
clasohm@0
  1260
  | f$t =>  add_term_vars (f, add_term_vars(t, vars))
clasohm@0
  1261
  | _ => vars;
clasohm@0
  1262
clasohm@0
  1263
fun term_vars t = add_term_vars(t,[]);
clasohm@0
  1264
clasohm@0
  1265
(*Accumulates the Frees in the term, suppressing duplicates*)
clasohm@0
  1266
fun add_term_frees (t, frees: term list) = case t of
wenzelm@16990
  1267
    Free   _ => OrdList.insert term_ord t frees
clasohm@0
  1268
  | Abs (_,_,body) => add_term_frees(body,frees)
clasohm@0
  1269
  | f$t =>  add_term_frees (f, add_term_frees(t, frees))
clasohm@0
  1270
  | _ => frees;
clasohm@0
  1271
clasohm@0
  1272
fun term_frees t = add_term_frees(t,[]);
clasohm@0
  1273
clasohm@0
  1274
(*Given an abstraction over P, replaces the bound variable by a Free variable
wenzelm@17851
  1275
  having a unique name -- SLOW!*)
clasohm@0
  1276
fun variant_abs (a,T,P) =
clasohm@0
  1277
  let val b = variant (add_term_names(P,[])) a
paulson@2192
  1278
  in  (b,  subst_bound (Free(b,T), P))  end;
clasohm@0
  1279
wenzelm@16678
  1280
fun dest_abs (x, T, body) =
wenzelm@16678
  1281
  let
wenzelm@16678
  1282
    fun name_clash (Free (y, _)) = (x = y)
wenzelm@16678
  1283
      | name_clash (t $ u) = name_clash t orelse name_clash u
wenzelm@16678
  1284
      | name_clash (Abs (_, _, t)) = name_clash t
wenzelm@16678
  1285
      | name_clash _ = false;
wenzelm@16678
  1286
  in
wenzelm@16678
  1287
    if name_clash body then
wenzelm@16678
  1288
      dest_abs (variant [x] x, T, body)    (*potentially slow, but rarely happens*)
wenzelm@16678
  1289
    else (x, subst_bound (Free (x, T), body))
wenzelm@16678
  1290
  end;
wenzelm@16678
  1291
wenzelm@16990
  1292
(*names for numbered variables --
wenzelm@16990
  1293
  preserves order wrt. int_ord vs. string_ord, avoids allocating new strings*)
wenzelm@16990
  1294
local
wenzelm@16990
  1295
  val small_int = Vector.tabulate (1000, fn i =>
wenzelm@16990
  1296
    let val leading = if i < 10 then "00" else if i < 100 then "0" else ""
wenzelm@16990
  1297
    in ":" ^ leading ^ string_of_int i end);
wenzelm@16990
  1298
in
wenzelm@16990
  1299
  fun bound n =
wenzelm@16990
  1300
    if n < 1000 then Vector.sub (small_int, n)
wenzelm@16990
  1301
    else ":" ^ bound (n div 1000) ^ Vector.sub (small_int, n mod 1000);
wenzelm@16990
  1302
end;
wenzelm@16990
  1303
wenzelm@16990
  1304
val is_bound = String.isPrefix ":";
wenzelm@16943
  1305
clasohm@0
  1306
(* renames and reverses the strings in vars away from names *)
clasohm@0
  1307
fun rename_aTs names vars : (string*typ)list =
clasohm@0
  1308
  let fun rename_aT (vars,(a,T)) =
wenzelm@9536
  1309
                (variant (map #1 vars @ names) a, T) :: vars
skalberg@15570
  1310
  in Library.foldl rename_aT ([],vars) end;
clasohm@0
  1311
clasohm@0
  1312
fun rename_wrt_term t = rename_aTs (add_term_names(t,[]));
clasohm@1364
  1313
paulson@1417
  1314
wenzelm@16943
  1315
(* zero var indexes *)
wenzelm@4286
  1316
wenzelm@16943
  1317
fun zero_var_inst vars =
wenzelm@16943
  1318
  fold (fn v as ((x, i), X) => fn (used, inst) =>
wenzelm@16943
  1319
    let
wenzelm@17642
  1320
      val x' = variant used (if is_bound x then "u" else x);
wenzelm@16943
  1321
      val used' = x' :: used;
wenzelm@16943
  1322
    in if x = x' andalso i = 0 then (used', inst) else (used', (v, ((x', 0), X)) :: inst) end)
wenzelm@16943
  1323
  vars ([], []) |> #2;
wenzelm@4286
  1324
wenzelm@16943
  1325
fun zero_var_indexesT ty =
wenzelm@16943
  1326
  instantiateT (map (apsnd TVar) (zero_var_inst (sort tvar_ord (add_tvarsT ty [])))) ty;
haftmann@16790
  1327
wenzelm@16943
  1328
fun zero_var_indexes_inst tm =
wenzelm@16943
  1329
  let
wenzelm@16943
  1330
    val instT = map (apsnd TVar) (zero_var_inst (sort tvar_ord (fold_types add_tvarsT tm [])));
wenzelm@16943
  1331
    val inst =
wenzelm@16943
  1332
      add_vars tm [] |> map (apsnd (instantiateT instT))
wenzelm@16943
  1333
      |> sort var_ord |> zero_var_inst |> map (apsnd Var);
wenzelm@16943
  1334
  in (instT, inst) end;
wenzelm@12499
  1335
wenzelm@16943
  1336
fun zero_var_indexes tm = instantiate (zero_var_indexes_inst tm) tm;
wenzelm@4286
  1337
paulson@1417
  1338
wenzelm@9536
  1339
(* dummy patterns *)
wenzelm@9536
  1340
wenzelm@9536
  1341
val dummy_patternN = "dummy_pattern";
wenzelm@9536
  1342
wenzelm@18253
  1343
fun dummy_pattern T = Const (dummy_patternN, T);
wenzelm@18253
  1344
wenzelm@9536
  1345
fun is_dummy_pattern (Const ("dummy_pattern", _)) = true
wenzelm@9536
  1346
  | is_dummy_pattern _ = false;
wenzelm@9536
  1347
wenzelm@9536
  1348
fun no_dummy_patterns tm =
haftmann@16787
  1349
  if not (fold_aterms (fn t => fn b => b orelse is_dummy_pattern t) tm false) then tm
wenzelm@9536
  1350
  else raise TERM ("Illegal occurrence of '_' dummy pattern", [tm]);
wenzelm@9536
  1351
wenzelm@11903
  1352
fun replace_dummy Ts (i, Const ("dummy_pattern", T)) =
wenzelm@11903
  1353
      (i + 1, list_comb (Var (("_dummy_", i), Ts ---> T), map Bound (0 upto length Ts - 1)))
wenzelm@11903
  1354
  | replace_dummy Ts (i, Abs (x, T, t)) =
wenzelm@11903
  1355
      let val (i', t') = replace_dummy (T :: Ts) (i, t)
wenzelm@11903
  1356
      in (i', Abs (x, T, t')) end
wenzelm@11903
  1357
  | replace_dummy Ts (i, t $ u) =
wenzelm@11903
  1358
      let val (i', t') = replace_dummy Ts (i, t); val (i'', u') = replace_dummy Ts (i', u)
wenzelm@11903
  1359
      in (i'', t' $ u') end
wenzelm@11903
  1360
  | replace_dummy _ (i, a) = (i, a);
wenzelm@11903
  1361
wenzelm@11903
  1362
val replace_dummy_patterns = replace_dummy [];
wenzelm@9536
  1363
wenzelm@10552
  1364
fun is_replaced_dummy_pattern ("_dummy_", _) = true
wenzelm@10552
  1365
  | is_replaced_dummy_pattern _ = false;
wenzelm@9536
  1366
wenzelm@16035
  1367
fun show_dummy_patterns (Var (("_dummy_", _), T)) = Const ("dummy_pattern", T)
wenzelm@16035
  1368
  | show_dummy_patterns (t $ u) = show_dummy_patterns t $ show_dummy_patterns u
wenzelm@16035
  1369
  | show_dummy_patterns (Abs (x, T, t)) = Abs (x, T, show_dummy_patterns t)
wenzelm@16035
  1370
  | show_dummy_patterns a = a;
wenzelm@16035
  1371
wenzelm@13484
  1372
wenzelm@13484
  1373
(* adhoc freezing *)
wenzelm@13484
  1374
wenzelm@13484
  1375
fun adhoc_freeze_vars tm =
wenzelm@13484
  1376
  let
wenzelm@13484
  1377
    fun mk_inst (var as Var ((a, i), T)) =
wenzelm@13484
  1378
      let val x = a ^ Library.gensym "_" ^ string_of_int i
wenzelm@13484
  1379
      in ((var,  Free(x, T)), x) end;
wenzelm@13484
  1380
    val (insts, xs) = split_list (map mk_inst (term_vars tm));
wenzelm@13484
  1381
  in (subst_atomic insts tm, xs) end;
wenzelm@13484
  1382
wenzelm@13484
  1383
wenzelm@15986
  1384
val show_question_marks = ref true;
berghofe@15472
  1385
wenzelm@14786
  1386
fun string_of_vname (x, i) =
wenzelm@14786
  1387
  let
wenzelm@15986
  1388
    val question_mark = if ! show_question_marks then "?" else "";
wenzelm@15986
  1389
    val idx = string_of_int i;
wenzelm@15986
  1390
    val dot =
wenzelm@15986
  1391
      (case rev (Symbol.explode x) of
wenzelm@15986
  1392
        _ :: "\\<^isub>" :: _ => false
wenzelm@15986
  1393
      | _ :: "\\<^isup>" :: _ => false
wenzelm@15986
  1394
      | c :: _ => Symbol.is_digit c
wenzelm@15986
  1395
      | _ => true);
wenzelm@14786
  1396
  in
wenzelm@15986
  1397
    if dot then question_mark ^ x ^ "." ^ idx
wenzelm@15986
  1398
    else if i <> 0 then question_mark ^ x ^ idx
wenzelm@15986
  1399
    else question_mark ^ x
wenzelm@14786
  1400
  end;
wenzelm@14786
  1401
wenzelm@14786
  1402
fun string_of_vname' (x, ~1) = x
wenzelm@14786
  1403
  | string_of_vname' xi = string_of_vname xi;
wenzelm@14786
  1404
clasohm@1364
  1405
end;
clasohm@1364
  1406
wenzelm@4444
  1407
structure BasicTerm: BASIC_TERM = Term;
wenzelm@4444
  1408
open BasicTerm;