src/Pure/term.ML
author wenzelm
Thu Jan 01 14:23:38 2009 +0100 (2009-01-01)
changeset 29286 5de880bda02d
parent 29280 c5531bf7c6b2
child 29882 29154e67731d
permissions -rw-r--r--
added canonical add_const_names, add_consts;
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(*  Title:      Pure/term.ML
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    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
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    Author:     Makarius
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Simply typed lambda-calculus: types, terms, and basic operations.
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*)
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infix 9 $;
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infixr 5 -->;
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infixr --->;
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infix aconv;
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signature BASIC_TERM =
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sig
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  eqtype indexname
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  eqtype class
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  eqtype sort
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  eqtype arity
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  datatype typ =
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    Type  of string * typ list |
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    TFree of string * sort |
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    TVar  of indexname * sort
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  datatype term =
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    Const of string * typ |
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    Free of string * typ |
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    Var of indexname * typ |
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    Bound of int |
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    Abs of string * typ * term |
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    $ of term * term
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  exception TYPE of string * typ list * term list
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  exception TERM of string * term list
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  val dummyS: sort
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  val dummyT: typ
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  val no_dummyT: typ -> typ
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  val --> : typ * typ -> typ
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  val ---> : typ list * typ -> typ
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  val dest_Type: typ -> string * typ list
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  val dest_TVar: typ -> indexname * sort
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  val dest_TFree: typ -> string * sort
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  val is_Bound: term -> bool
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  val is_Const: term -> bool
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  val is_Free: term -> bool
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  val is_Var: term -> bool
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  val is_TVar: typ -> bool
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  val dest_Const: term -> string * typ
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  val dest_Free: term -> string * typ
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  val dest_Var: term -> indexname * typ
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  val domain_type: typ -> typ
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  val range_type: typ -> typ
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  val binder_types: typ -> typ list
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  val body_type: typ -> typ
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  val strip_type: typ -> typ list * typ
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  val type_of1: typ list * term -> typ
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  val type_of: term -> typ
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  val fastype_of1: typ list * term -> typ
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  val fastype_of: term -> typ
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  val list_abs: (string * typ) list * term -> term
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  val strip_abs: term -> (string * typ) list * term
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  val strip_abs_body: term -> term
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  val strip_abs_vars: term -> (string * typ) list
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  val strip_qnt_body: string -> term -> term
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  val strip_qnt_vars: string -> term -> (string * typ) list
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  val list_comb: term * term list -> term
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  val strip_comb: term -> term * term list
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  val head_of: term -> term
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  val size_of_term: term -> int
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  val map_atyps: (typ -> typ) -> typ -> typ
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  val map_aterms: (term -> term) -> term -> term
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  val map_type_tvar: (indexname * sort -> typ) -> typ -> typ
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  val map_type_tfree: (string * sort -> typ) -> typ -> typ
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  val map_types: (typ -> typ) -> term -> term
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  val fold_atyps: (typ -> 'a -> 'a) -> typ -> 'a -> 'a
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  val fold_aterms: (term -> 'a -> 'a) -> term -> 'a -> 'a
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  val fold_term_types: (term -> typ -> 'a -> 'a) -> term -> 'a -> 'a
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  val fold_types: (typ -> 'a -> 'a) -> term -> 'a -> 'a
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  val burrow_types: (typ list -> typ list) -> term list -> term list
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  val aconv: term * term -> bool
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  val propT: typ
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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 subst_free: (term * term) list -> term -> term
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  val abstract_over: term * term -> term
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  val lambda: term -> term -> term
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  val absfree: string * typ * term -> term
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  val absdummy: typ * term -> term
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  val list_abs_free: (string * typ) list * term -> term
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  val list_all_free: (string * typ) list * term -> term
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  val list_all: (string * typ) list * term -> term
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  val subst_atomic: (term * term) list -> term -> term
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  val typ_subst_atomic: (typ * typ) list -> typ -> typ
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  val subst_atomic_types: (typ * typ) list -> term -> term
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  val typ_subst_TVars: (indexname * typ) list -> typ -> typ
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  val subst_TVars: (indexname * typ) list -> term -> term
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  val subst_Vars: (indexname * term) list -> term -> term
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  val subst_vars: (indexname * typ) list * (indexname * term) list -> term -> term
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  val is_first_order: string list -> term -> bool
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  val maxidx_of_typ: typ -> int
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  val maxidx_of_typs: typ list -> int
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  val maxidx_of_term: term -> int
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  val exists_subtype: (typ -> bool) -> typ -> bool
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  val exists_type: (typ -> bool) -> term -> bool
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  val exists_subterm: (term -> bool) -> term -> bool
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  val exists_Const: (string * typ -> bool) -> term -> bool
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  val 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 all: typ -> term
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  val argument_type_of: term -> int -> typ
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  val add_tvar_namesT: typ -> indexname list -> indexname list
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  val add_tvar_names: term -> indexname list -> indexname list
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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_var_names: term -> indexname list -> indexname list
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  val add_vars: term -> (indexname * typ) list -> (indexname * typ) list
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  val add_tfree_namesT: typ -> string list -> string list
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  val add_tfree_names: term -> string list -> string 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_free_names: term -> string list -> string list
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  val add_frees: term -> (string * typ) list -> (string * typ) list
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  val add_const_names: term -> string list -> string list
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  val add_consts: term -> (string * typ) list -> (string * typ) list
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  val hidden_polymorphism: term -> (indexname * sort) list
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  val declare_typ_names: typ -> Name.context -> Name.context
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  val declare_term_names: term -> Name.context -> Name.context
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  val declare_term_frees: term -> Name.context -> Name.context
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  val variant_frees: term -> (string * 'a) list -> (string * 'a) list
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  val rename_wrt_term: term -> (string * 'a) list -> (string * 'a) list
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  val eq_ix: indexname * indexname -> bool
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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 could_unify: term * term -> bool
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  val strip_abs_eta: int -> term -> (string * typ) list * term
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  val match_bvars: (term * term) * (string * string) list -> (string * string) list
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  val map_abs_vars: (string -> string) -> term -> term
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  val rename_abs: term -> term -> term -> term option
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  val close_schematic_term: term -> term
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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 has_abs: term -> bool
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  val dest_abs: string * typ * term -> string * term
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  val dummy_patternN: string
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  val dummy_pattern: typ -> term
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  val is_dummy_pattern: term -> bool
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  val free_dummy_patterns: term -> Name.context -> term * Name.context
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  val no_dummy_patterns: term -> term
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  val replace_dummy_patterns: term -> int -> term * int
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  val is_replaced_dummy_pattern: indexname -> bool
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  val show_dummy_patterns: term -> term
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  val string_of_vname: indexname -> string
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  val string_of_vname': indexname -> string
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end;
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structure Term: TERM =
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struct
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(*Indexnames can be quickly renamed by adding an offset to the integer part,
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  for resolution.*)
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type indexname = string * int;
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(* Types are classified by sorts. *)
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type class = string;
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type sort  = class list;
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type arity = string * sort list * sort;
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(* The sorts attached to TFrees and TVars specify the sort of that variable *)
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datatype typ = Type  of string * typ list
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             | TFree of string * sort
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             | TVar  of indexname * sort;
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(*Terms.  Bound variables are indicated by depth number.
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  Free variables, (scheme) variables and constants have names.
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  An term is "closed" if every bound variable of level "lev"
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  is enclosed by at least "lev" abstractions.
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  It is possible to create meaningless terms containing loose bound vars
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  or type mismatches.  But such terms are not allowed in rules. *)
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datatype term =
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    Const of string * typ
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  | Free  of string * typ
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  | Var   of indexname * typ
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  | Bound of int
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  | Abs   of string*typ*term
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  | op $  of term*term;
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(*Errors involving type mismatches*)
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exception TYPE of string * typ list * term list;
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(*Errors errors involving terms*)
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exception TERM of string * term list;
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(*Note variable naming conventions!
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    a,b,c: string
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    f,g,h: functions (including terms of function type)
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    i,j,m,n: int
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    t,u: term
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    v,w: indexnames
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    x,y: any
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    A,B,C: term (denoting formulae)
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    T,U: typ
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*)
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(** Types **)
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(*dummies for type-inference etc.*)
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val dummyS = [""];
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val dummyT = Type ("dummy", []);
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fun no_dummyT typ =
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  let
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    fun check (T as Type ("dummy", _)) =
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          raise TYPE ("Illegal occurrence of '_' dummy type", [T], [])
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      | check (Type (_, Ts)) = List.app check Ts
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      | check _ = ();
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  in check typ; typ end;
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fun S --> T = Type("fun",[S,T]);
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(*handy for multiple args: [T1,...,Tn]--->T  gives  T1-->(T2--> ... -->T)*)
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val op ---> = Library.foldr (op -->);
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fun dest_Type (Type x) = x
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  | dest_Type T = raise TYPE ("dest_Type", [T], []);
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fun dest_TVar (TVar x) = x
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  | dest_TVar T = raise TYPE ("dest_TVar", [T], []);
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fun dest_TFree (TFree x) = x
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  | dest_TFree T = raise TYPE ("dest_TFree", [T], []);
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(** Discriminators **)
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fun is_Bound (Bound _) = true
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  | is_Bound _         = false;
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fun is_Const (Const _) = true
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  | is_Const _ = false;
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fun is_Free (Free _) = true
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  | is_Free _ = false;
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fun is_Var (Var _) = true
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  | is_Var _ = false;
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fun is_TVar (TVar _) = true
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  | is_TVar _ = false;
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(** Destructors **)
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fun dest_Const (Const x) =  x
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  | dest_Const t = raise TERM("dest_Const", [t]);
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fun dest_Free (Free x) =  x
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  | dest_Free t = raise TERM("dest_Free", [t]);
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fun dest_Var (Var x) =  x
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  | dest_Var t = raise TERM("dest_Var", [t]);
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fun domain_type (Type("fun", [T,_])) = T
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and range_type  (Type("fun", [_,T])) = T;
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(* maps  [T1,...,Tn]--->T  to the list  [T1,T2,...,Tn]*)
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fun binder_types (Type("fun",[S,T])) = S :: binder_types T
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  | binder_types _   =  [];
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(* maps  [T1,...,Tn]--->T  to T*)
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fun body_type (Type("fun",[S,T])) = body_type T
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  | body_type T   =  T;
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(* maps  [T1,...,Tn]--->T  to   ([T1,T2,...,Tn], T)  *)
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fun strip_type T : typ list * typ =
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  (binder_types T, body_type T);
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(*Compute the type of the term, checking that combinations are well-typed
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  Ts = [T0,T1,...] holds types of bound variables 0, 1, ...*)
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fun type_of1 (Ts, Const (_,T)) = T
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  | type_of1 (Ts, Free  (_,T)) = T
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  | type_of1 (Ts, Bound i) = (List.nth (Ts,i)
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        handle Subscript => raise TYPE("type_of: bound variable", [], [Bound i]))
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  | type_of1 (Ts, Var (_,T)) = T
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  | type_of1 (Ts, Abs (_,T,body)) = T --> type_of1(T::Ts, body)
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  | type_of1 (Ts, f$u) =
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      let val U = type_of1(Ts,u)
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          and T = type_of1(Ts,f)
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      in case T of
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            Type("fun",[T1,T2]) =>
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              if T1=U then T2  else raise TYPE
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                    ("type_of: type mismatch in application", [T1,U], [f$u])
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          | _ => raise TYPE
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                    ("type_of: function type is expected in application",
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                     [T,U], [f$u])
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      end;
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fun type_of t : typ = type_of1 ([],t);
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(*Determines the type of a term, with minimal checking*)
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fun fastype_of1 (Ts, f$u) =
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    (case fastype_of1 (Ts,f) of
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        Type("fun",[_,T]) => T
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        | _ => raise TERM("fastype_of: expected function type", [f$u]))
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  | fastype_of1 (_, Const (_,T)) = T
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  | fastype_of1 (_, Free (_,T)) = T
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  | fastype_of1 (Ts, Bound i) = (List.nth(Ts,i)
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         handle Subscript => raise TERM("fastype_of: Bound", [Bound i]))
wenzelm@13000
   326
  | fastype_of1 (_, Var (_,T)) = T
lcp@61
   327
  | fastype_of1 (Ts, Abs (_,T,u)) = T --> fastype_of1 (T::Ts, u);
lcp@61
   328
lcp@61
   329
fun fastype_of t : typ = fastype_of1 ([],t);
clasohm@0
   330
wenzelm@16678
   331
(*Determine the argument type of a function*)
wenzelm@22908
   332
fun argument_type_of tm k =
wenzelm@16678
   333
  let
wenzelm@16678
   334
    fun argT i (Type ("fun", [T, U])) = if i = 0 then T else argT (i - 1) U
wenzelm@16678
   335
      | argT _ T = raise TYPE ("argument_type_of", [T], []);
wenzelm@16678
   336
wenzelm@16678
   337
    fun arg 0 _ (Abs (_, T, _)) = T
wenzelm@16678
   338
      | arg i Ts (Abs (_, T, t)) = arg (i - 1) (T :: Ts) t
wenzelm@16678
   339
      | arg i Ts (t $ _) = arg (i + 1) Ts t
wenzelm@16678
   340
      | arg i Ts a = argT i (fastype_of1 (Ts, a));
wenzelm@22908
   341
  in arg k [] tm end;
wenzelm@16678
   342
clasohm@0
   343
wenzelm@19473
   344
val list_abs = uncurry (fold_rev (fn (x, T) => fn t => Abs (x, T, t)));
wenzelm@10806
   345
haftmann@18927
   346
fun strip_abs (Abs (a, T, t)) =
haftmann@18927
   347
      let val (a', t') = strip_abs t
haftmann@18927
   348
      in ((a, T) :: a', t') end
haftmann@18927
   349
  | strip_abs t = ([], t);
haftmann@18927
   350
clasohm@0
   351
(* maps  (x1,...,xn)t   to   t  *)
wenzelm@13000
   352
fun strip_abs_body (Abs(_,_,t))  =  strip_abs_body t
clasohm@0
   353
  | strip_abs_body u  =  u;
clasohm@0
   354
clasohm@0
   355
(* maps  (x1,...,xn)t   to   [x1, ..., xn]  *)
wenzelm@13000
   356
fun strip_abs_vars (Abs(a,T,t))  =  (a,T) :: strip_abs_vars t
clasohm@0
   357
  | strip_abs_vars u  =  [] : (string*typ) list;
clasohm@0
   358
clasohm@0
   359
clasohm@0
   360
fun strip_qnt_body qnt =
clasohm@0
   361
let fun strip(tm as Const(c,_)$Abs(_,_,t)) = if c=qnt then strip t else tm
clasohm@0
   362
      | strip t = t
clasohm@0
   363
in strip end;
clasohm@0
   364
clasohm@0
   365
fun strip_qnt_vars qnt =
clasohm@0
   366
let fun strip(Const(c,_)$Abs(a,T,t)) = if c=qnt then (a,T)::strip t else []
clasohm@0
   367
      | strip t  =  [] : (string*typ) list
clasohm@0
   368
in strip end;
clasohm@0
   369
clasohm@0
   370
clasohm@0
   371
(* maps   (f, [t1,...,tn])  to  f(t1,...,tn) *)
skalberg@15570
   372
val list_comb : term * term list -> term = Library.foldl (op $);
clasohm@0
   373
clasohm@0
   374
clasohm@0
   375
(* maps   f(t1,...,tn)  to  (f, [t1,...,tn]) ; naturally tail-recursive*)
wenzelm@13000
   376
fun strip_comb u : term * term list =
clasohm@0
   377
    let fun stripc (f$t, ts) = stripc (f, t::ts)
wenzelm@13000
   378
        |   stripc  x =  x
clasohm@0
   379
    in  stripc(u,[])  end;
clasohm@0
   380
clasohm@0
   381
clasohm@0
   382
(* maps   f(t1,...,tn)  to  f , which is never a combination *)
clasohm@0
   383
fun head_of (f$t) = head_of f
clasohm@0
   384
  | head_of u = u;
clasohm@0
   385
wenzelm@16599
   386
(*number of atoms and abstractions in a term*)
wenzelm@16599
   387
fun size_of_term tm =
wenzelm@16599
   388
  let
wenzelm@16678
   389
    fun add_size (t $ u, n) = add_size (t, add_size (u, n))
wenzelm@16678
   390
      | add_size (Abs (_ ,_, t), n) = add_size (t, n + 1)
wenzelm@16678
   391
      | add_size (_, n) = n + 1;
wenzelm@16678
   392
  in add_size (tm, 0) end;
clasohm@0
   393
haftmann@18847
   394
fun map_atyps f (Type (a, Ts)) = Type (a, map (map_atyps f) Ts)
haftmann@18976
   395
  | map_atyps f T = f T;
haftmann@18847
   396
haftmann@18847
   397
fun map_aterms f (t $ u) = map_aterms f t $ map_aterms f u
haftmann@18847
   398
  | map_aterms f (Abs (a, T, t)) = Abs (a, T, map_aterms f t)
haftmann@18847
   399
  | map_aterms f t = f t;
haftmann@18847
   400
wenzelm@18981
   401
fun map_type_tvar f = map_atyps (fn TVar x => f x | T => T);
wenzelm@18981
   402
fun map_type_tfree f = map_atyps (fn TFree x => f x | T => T);
nipkow@949
   403
wenzelm@20548
   404
fun map_types f =
wenzelm@16678
   405
  let
wenzelm@16678
   406
    fun map_aux (Const (a, T)) = Const (a, f T)
wenzelm@16678
   407
      | map_aux (Free (a, T)) = Free (a, f T)
wenzelm@16678
   408
      | map_aux (Var (v, T)) = Var (v, f T)
wenzelm@16678
   409
      | map_aux (t as Bound _)  = t
wenzelm@16678
   410
      | map_aux (Abs (a, T, t)) = Abs (a, f T, map_aux t)
wenzelm@16678
   411
      | map_aux (t $ u) = map_aux t $ map_aux u;
wenzelm@16678
   412
  in map_aux end;
clasohm@0
   413
clasohm@0
   414
wenzelm@16943
   415
(* fold types and terms *)
wenzelm@16943
   416
wenzelm@16943
   417
fun fold_atyps f (Type (_, Ts)) = fold (fold_atyps f) Ts
wenzelm@16943
   418
  | fold_atyps f T = f T;
wenzelm@16943
   419
wenzelm@16943
   420
fun fold_aterms f (t $ u) = fold_aterms f t #> fold_aterms f u
wenzelm@16943
   421
  | fold_aterms f (Abs (_, _, t)) = fold_aterms f t
wenzelm@16943
   422
  | fold_aterms f a = f a;
wenzelm@16943
   423
wenzelm@16943
   424
fun fold_term_types f (t as Const (_, T)) = f t T
wenzelm@16943
   425
  | fold_term_types f (t as Free (_, T)) = f t T
wenzelm@16943
   426
  | fold_term_types f (t as Var (_, T)) = f t T
wenzelm@16943
   427
  | fold_term_types f (Bound _) = I
wenzelm@16943
   428
  | fold_term_types f (t as Abs (_, T, b)) = f t T #> fold_term_types f b
wenzelm@16943
   429
  | fold_term_types f (t $ u) = fold_term_types f t #> fold_term_types f u;
wenzelm@16943
   430
wenzelm@16943
   431
fun fold_types f = fold_term_types (K f);
wenzelm@16943
   432
wenzelm@24483
   433
fun replace_types (Const (c, _)) (T :: Ts) = (Const (c, T), Ts)
wenzelm@24483
   434
  | replace_types (Free (x, _)) (T :: Ts) = (Free (x, T), Ts)
wenzelm@24483
   435
  | replace_types (Var (xi, _)) (T :: Ts) = (Var (xi, T), Ts)
wenzelm@24483
   436
  | replace_types (Bound i) Ts = (Bound i, Ts)
wenzelm@24483
   437
  | replace_types (Abs (x, _, b)) (T :: Ts) =
wenzelm@24483
   438
      let val (b', Ts') = replace_types b Ts
wenzelm@24483
   439
      in (Abs (x, T, b'), Ts') end
wenzelm@24483
   440
  | replace_types (t $ u) Ts =
wenzelm@24483
   441
      let
wenzelm@24483
   442
        val (t', Ts') = replace_types t Ts;
wenzelm@24483
   443
        val (u', Ts'') = replace_types u Ts';
wenzelm@24483
   444
      in (t' $ u', Ts'') end;
wenzelm@24483
   445
wenzelm@24483
   446
fun burrow_types f ts =
wenzelm@24483
   447
  let
wenzelm@24483
   448
    val Ts = rev (fold (fold_types cons) ts []);
wenzelm@24483
   449
    val Ts' = f Ts;
wenzelm@24483
   450
    val (ts', []) = fold_map replace_types ts Ts';
wenzelm@24483
   451
  in ts' end;
wenzelm@24483
   452
wenzelm@16943
   453
(*collect variables*)
wenzelm@29257
   454
val add_tvar_namesT = fold_atyps (fn TVar (xi, _) => insert (op =) xi | _ => I);
wenzelm@29257
   455
val add_tvar_names = fold_types add_tvar_namesT;
wenzelm@16943
   456
val add_tvarsT = fold_atyps (fn TVar v => insert (op =) v | _ => I);
wenzelm@16943
   457
val add_tvars = fold_types add_tvarsT;
wenzelm@29257
   458
val add_var_names = fold_aterms (fn Var (xi, _) => insert (op =) xi | _ => I);
wenzelm@16943
   459
val add_vars = fold_aterms (fn Var v => insert (op =) v | _ => I);
wenzelm@29257
   460
val add_tfree_namesT = fold_atyps (fn TFree (xi, _) => insert (op =) xi | _ => I);
wenzelm@29257
   461
val add_tfree_names = fold_types add_tfree_namesT;
wenzelm@16943
   462
val add_tfreesT = fold_atyps (fn TFree v => insert (op =) v | _ => I);
wenzelm@16943
   463
val add_tfrees = fold_types add_tfreesT;
wenzelm@29257
   464
val add_free_names = fold_aterms (fn Free (x, _) => insert (op =) x | _ => I);
wenzelm@16943
   465
val add_frees = fold_aterms (fn Free v => insert (op =) v | _ => I);
wenzelm@29286
   466
val add_const_names = fold_aterms (fn Const (c, _) => insert (op =) c | _ => I);
wenzelm@29286
   467
val add_consts = fold_aterms (fn Const c => insert (op =) c | _ => I);
wenzelm@16943
   468
wenzelm@25050
   469
(*extra type variables in a term, not covered by its type*)
wenzelm@25050
   470
fun hidden_polymorphism t =
wenzelm@21682
   471
  let
wenzelm@25050
   472
    val T = fastype_of t;
wenzelm@21682
   473
    val tvarsT = add_tvarsT T [];
wenzelm@21682
   474
    val extra_tvars = fold_types (fold_atyps
wenzelm@21682
   475
      (fn TVar v => if member (op =) tvarsT v then I else insert (op =) v | _ => I)) t [];
wenzelm@21682
   476
  in extra_tvars end;
wenzelm@21682
   477
wenzelm@16943
   478
wenzelm@29278
   479
(* renaming variables *)
wenzelm@29278
   480
wenzelm@29278
   481
val declare_typ_names = fold_atyps (fn TFree (a, _) => Name.declare a | _ => I);
wenzelm@29278
   482
wenzelm@29278
   483
fun declare_term_names tm =
wenzelm@29278
   484
  fold_aterms
wenzelm@29278
   485
    (fn Const (a, _) => Name.declare (NameSpace.base a)
wenzelm@29278
   486
      | Free (a, _) => Name.declare a
wenzelm@29278
   487
      | _ => I) tm #>
wenzelm@29278
   488
  fold_types declare_typ_names tm;
wenzelm@29278
   489
wenzelm@29278
   490
val declare_term_frees = fold_aterms (fn Free (x, _) => Name.declare x | _ => I);
wenzelm@29278
   491
wenzelm@29278
   492
fun variant_frees t frees =
wenzelm@29278
   493
  fst (Name.variants (map fst frees) (declare_term_names t Name.context)) ~~ map snd frees;
wenzelm@29278
   494
wenzelm@29278
   495
fun rename_wrt_term t frees = rev (variant_frees t frees);  (*reversed result!*)
wenzelm@29278
   496
wenzelm@29278
   497
wenzelm@25050
   498
wenzelm@29269
   499
(** Comparing terms **)
wenzelm@29269
   500
wenzelm@29269
   501
(* variables *)
wenzelm@29269
   502
wenzelm@29269
   503
fun eq_ix ((x, i): indexname, (y, j)) = i = j andalso x = y;
wenzelm@16537
   504
wenzelm@29269
   505
fun eq_tvar ((xi, S: sort), (xi', S')) = eq_ix (xi, xi') andalso S = S';
wenzelm@29269
   506
fun eq_var ((xi, T: typ), (xi', T')) = eq_ix (xi, xi') andalso T = T';
wenzelm@29269
   507
wenzelm@29269
   508
wenzelm@29269
   509
(* alpha equivalence *)
wenzelm@20511
   510
wenzelm@20511
   511
fun tm1 aconv tm2 =
wenzelm@20511
   512
  pointer_eq (tm1, tm2) orelse
wenzelm@20511
   513
    (case (tm1, tm2) of
wenzelm@20511
   514
      (t1 $ u1, t2 $ u2) => t1 aconv t2 andalso u1 aconv u2
wenzelm@20511
   515
    | (Abs (_, T1, t1), Abs (_, T2, t2)) => t1 aconv t2 andalso T1 = T2
wenzelm@20511
   516
    | (a1, a2) => a1 = a2);
wenzelm@20511
   517
wenzelm@20511
   518
wenzelm@29269
   519
(*A fast unification filter: true unless the two terms cannot be unified.
wenzelm@29269
   520
  Terms must be NORMAL.  Treats all Vars as distinct. *)
wenzelm@29269
   521
fun could_unify (t, u) =
wenzelm@29269
   522
  let
wenzelm@29269
   523
    fun matchrands (f $ t) (g $ u) = could_unify (t, u) andalso matchrands f g
wenzelm@29269
   524
      | matchrands _ _ = true;
wenzelm@29269
   525
  in
wenzelm@29269
   526
    case (head_of t, head_of u) of
wenzelm@29269
   527
      (_, Var _) => true
wenzelm@29269
   528
    | (Var _, _) => true
wenzelm@29269
   529
    | (Const (a, _), Const (b, _)) => a = b andalso matchrands t u
wenzelm@29269
   530
    | (Free (a, _), Free (b, _)) => a = b andalso matchrands t u
wenzelm@29269
   531
    | (Bound i, Bound j) => i = j andalso matchrands t u
wenzelm@29269
   532
    | (Abs _, _) => true   (*because of possible eta equality*)
wenzelm@29269
   533
    | (_, Abs _) => true
wenzelm@29269
   534
    | _ => false
wenzelm@29269
   535
  end;
wenzelm@16678
   536
nipkow@16570
   537
wenzelm@16537
   538
clasohm@0
   539
(** Connectives of higher order logic **)
clasohm@0
   540
wenzelm@24850
   541
fun aT S = TFree (Name.aT, S);
wenzelm@19394
   542
wenzelm@375
   543
fun itselfT ty = Type ("itself", [ty]);
wenzelm@24850
   544
val a_itselfT = itselfT (TFree (Name.aT, []));
wenzelm@375
   545
clasohm@0
   546
val propT : typ = Type("prop",[]);
clasohm@0
   547
clasohm@0
   548
fun all T = Const("all", (T-->propT)-->propT);
clasohm@0
   549
clasohm@0
   550
(* maps  !!x1...xn. t   to   t  *)
wenzelm@13000
   551
fun strip_all_body (Const("all",_)$Abs(_,_,t))  =  strip_all_body t
clasohm@0
   552
  | strip_all_body t  =  t;
clasohm@0
   553
clasohm@0
   554
(* maps  !!x1...xn. t   to   [x1, ..., xn]  *)
clasohm@0
   555
fun strip_all_vars (Const("all",_)$Abs(a,T,t))  =
wenzelm@13000
   556
                (a,T) :: strip_all_vars t
clasohm@0
   557
  | strip_all_vars t  =  [] : (string*typ) list;
clasohm@0
   558
clasohm@0
   559
(*increments a term's non-local bound variables
clasohm@0
   560
  required when moving a term within abstractions
clasohm@0
   561
     inc is  increment for bound variables
clasohm@0
   562
     lev is  level at which a bound variable is considered 'loose'*)
wenzelm@13000
   563
fun incr_bv (inc, lev, u as Bound i) = if i>=lev then Bound(i+inc) else u
clasohm@0
   564
  | incr_bv (inc, lev, Abs(a,T,body)) =
wenzelm@9536
   565
        Abs(a, T, incr_bv(inc,lev+1,body))
wenzelm@13000
   566
  | incr_bv (inc, lev, f$t) =
clasohm@0
   567
      incr_bv(inc,lev,f) $ incr_bv(inc,lev,t)
clasohm@0
   568
  | incr_bv (inc, lev, u) = u;
clasohm@0
   569
clasohm@0
   570
fun incr_boundvars  0  t = t
clasohm@0
   571
  | incr_boundvars inc t = incr_bv(inc,0,t);
clasohm@0
   572
wenzelm@12981
   573
(*Scan a pair of terms; while they are similar,
wenzelm@12981
   574
  accumulate corresponding bound vars in "al"*)
wenzelm@12981
   575
fun match_bvs(Abs(x,_,s),Abs(y,_,t), al) =
wenzelm@12981
   576
      match_bvs(s, t, if x="" orelse y="" then al
wenzelm@12981
   577
                                          else (x,y)::al)
wenzelm@12981
   578
  | match_bvs(f$s, g$t, al) = match_bvs(f,g,match_bvs(s,t,al))
wenzelm@12981
   579
  | match_bvs(_,_,al) = al;
wenzelm@12981
   580
wenzelm@12981
   581
(* strip abstractions created by parameters *)
wenzelm@12981
   582
fun match_bvars((s,t),al) = match_bvs(strip_abs_body s, strip_abs_body t, al);
wenzelm@12981
   583
haftmann@22031
   584
fun map_abs_vars f (t $ u) = map_abs_vars f t $ map_abs_vars f u
haftmann@22031
   585
  | map_abs_vars f (Abs (a, T, t)) = Abs (f a, T, map_abs_vars f t)
haftmann@22031
   586
  | map_abs_vars f t = t;
haftmann@22031
   587
wenzelm@12981
   588
fun rename_abs pat obj t =
wenzelm@12981
   589
  let
wenzelm@12981
   590
    val ren = match_bvs (pat, obj, []);
wenzelm@12981
   591
    fun ren_abs (Abs (x, T, b)) =
wenzelm@18942
   592
          Abs (the_default x (AList.lookup (op =) ren x), T, ren_abs b)
wenzelm@12981
   593
      | ren_abs (f $ t) = ren_abs f $ ren_abs t
wenzelm@12981
   594
      | ren_abs t = t
skalberg@15531
   595
  in if null ren then NONE else SOME (ren_abs t) end;
clasohm@0
   596
clasohm@0
   597
(*Accumulate all 'loose' bound vars referring to level 'lev' or beyond.
clasohm@0
   598
   (Bound 0) is loose at level 0 *)
wenzelm@13000
   599
fun add_loose_bnos (Bound i, lev, js) =
haftmann@20854
   600
        if i<lev then js else insert (op =) (i - lev) js
clasohm@0
   601
  | add_loose_bnos (Abs (_,_,t), lev, js) = add_loose_bnos (t, lev+1, js)
clasohm@0
   602
  | add_loose_bnos (f$t, lev, js) =
wenzelm@13000
   603
        add_loose_bnos (f, lev, add_loose_bnos (t, lev, js))
clasohm@0
   604
  | add_loose_bnos (_, _, js) = js;
clasohm@0
   605
clasohm@0
   606
fun loose_bnos t = add_loose_bnos (t, 0, []);
clasohm@0
   607
clasohm@0
   608
(* loose_bvar(t,k) iff t contains a 'loose' bound variable referring to
clasohm@0
   609
   level k or beyond. *)
clasohm@0
   610
fun loose_bvar(Bound i,k) = i >= k
clasohm@0
   611
  | loose_bvar(f$t, k) = loose_bvar(f,k) orelse loose_bvar(t,k)
clasohm@0
   612
  | loose_bvar(Abs(_,_,t),k) = loose_bvar(t,k+1)
clasohm@0
   613
  | loose_bvar _ = false;
clasohm@0
   614
nipkow@2792
   615
fun loose_bvar1(Bound i,k) = i = k
nipkow@2792
   616
  | loose_bvar1(f$t, k) = loose_bvar1(f,k) orelse loose_bvar1(t,k)
nipkow@2792
   617
  | loose_bvar1(Abs(_,_,t),k) = loose_bvar1(t,k+1)
nipkow@2792
   618
  | loose_bvar1 _ = false;
clasohm@0
   619
clasohm@0
   620
(*Substitute arguments for loose bound variables.
clasohm@0
   621
  Beta-reduction of arg(n-1)...arg0 into t replacing (Bound i) with (argi).
wenzelm@4626
   622
  Note that for ((%x y. c) a b), the bound vars in c are x=1 and y=0
wenzelm@9536
   623
        and the appropriate call is  subst_bounds([b,a], c) .
clasohm@0
   624
  Loose bound variables >=n are reduced by "n" to
clasohm@0
   625
     compensate for the disappearance of lambdas.
clasohm@0
   626
*)
wenzelm@13000
   627
fun subst_bounds (args: term list, t) : term =
wenzelm@19065
   628
  let
wenzelm@19065
   629
    exception SAME;
wenzelm@19065
   630
    val n = length args;
wenzelm@19065
   631
    fun subst (t as Bound i, lev) =
wenzelm@19065
   632
         (if i < lev then raise SAME   (*var is locally bound*)
wenzelm@19065
   633
          else incr_boundvars lev (List.nth (args, i - lev))
wenzelm@19065
   634
            handle Subscript => Bound (i - n))  (*loose: change it*)
wenzelm@19065
   635
      | subst (Abs (a, T, body), lev) = Abs (a, T, subst (body, lev + 1))
wenzelm@19065
   636
      | subst (f $ t, lev) =
wenzelm@19065
   637
          (subst (f, lev) $ (subst (t, lev) handle SAME => t) handle SAME => f $ subst (t, lev))
wenzelm@19065
   638
      | subst _ = raise SAME;
wenzelm@19065
   639
  in case args of [] => t | _ => (subst (t, 0) handle SAME => t) end;
clasohm@0
   640
paulson@2192
   641
(*Special case: one argument*)
wenzelm@13000
   642
fun subst_bound (arg, t) : term =
wenzelm@19065
   643
  let
wenzelm@19065
   644
    exception SAME;
wenzelm@19065
   645
    fun subst (Bound i, lev) =
wenzelm@19065
   646
          if i < lev then raise SAME   (*var is locally bound*)
wenzelm@19065
   647
          else if i = lev then incr_boundvars lev arg
wenzelm@19065
   648
          else Bound (i - 1)   (*loose: change it*)
wenzelm@19065
   649
      | subst (Abs (a, T, body), lev) = Abs (a, T, subst (body, lev + 1))
wenzelm@19065
   650
      | subst (f $ t, lev) =
wenzelm@19065
   651
          (subst (f, lev) $ (subst (t, lev) handle SAME => t) handle SAME => f $ subst (t, lev))
wenzelm@19065
   652
      | subst _ = raise SAME;
wenzelm@19065
   653
  in subst (t, 0) handle SAME => t end;
paulson@2192
   654
clasohm@0
   655
(*beta-reduce if possible, else form application*)
paulson@2192
   656
fun betapply (Abs(_,_,t), u) = subst_bound (u,t)
clasohm@0
   657
  | betapply (f,u) = f$u;
clasohm@0
   658
wenzelm@18183
   659
val betapplys = Library.foldl betapply;
wenzelm@18183
   660
wenzelm@14786
   661
haftmann@20109
   662
(*unfolding abstractions with substitution
haftmann@20109
   663
  of bound variables and implicit eta-expansion*)
haftmann@20109
   664
fun strip_abs_eta k t =
haftmann@20109
   665
  let
wenzelm@29278
   666
    val used = fold_aterms declare_term_frees t Name.context;
haftmann@20109
   667
    fun strip_abs t (0, used) = (([], t), (0, used))
haftmann@20109
   668
      | strip_abs (Abs (v, T, t)) (k, used) =
haftmann@20109
   669
          let
wenzelm@20122
   670
            val ([v'], used') = Name.variants [v] used;
haftmann@21013
   671
            val t' = subst_bound (Free (v', T), t);
wenzelm@20122
   672
            val ((vs, t''), (k', used'')) = strip_abs t' (k - 1, used');
wenzelm@20122
   673
          in (((v', T) :: vs, t''), (k', used'')) end
haftmann@20109
   674
      | strip_abs t (k, used) = (([], t), (k, used));
haftmann@20109
   675
    fun expand_eta [] t _ = ([], t)
haftmann@20109
   676
      | expand_eta (T::Ts) t used =
haftmann@20109
   677
          let
wenzelm@20122
   678
            val ([v], used') = Name.variants [""] used;
wenzelm@20122
   679
            val (vs, t') = expand_eta Ts (t $ Free (v, T)) used';
haftmann@20109
   680
          in ((v, T) :: vs, t') end;
haftmann@20109
   681
    val ((vs1, t'), (k', used')) = strip_abs t (k, used);
haftmann@20109
   682
    val Ts = (fst o chop k' o fst o strip_type o fastype_of) t';
haftmann@20109
   683
    val (vs2, t'') = expand_eta Ts t' used';
haftmann@20109
   684
  in (vs1 @ vs2, t'') end;
haftmann@20109
   685
haftmann@20109
   686
clasohm@0
   687
(*Substitute new for free occurrences of old in a term*)
wenzelm@29256
   688
fun subst_free [] = I
clasohm@0
   689
  | subst_free pairs =
wenzelm@13000
   690
      let fun substf u =
haftmann@17314
   691
            case AList.lookup (op aconv) pairs u of
skalberg@15531
   692
                SOME u' => u'
skalberg@15531
   693
              | NONE => (case u of Abs(a,T,t) => Abs(a, T, substf t)
wenzelm@9536
   694
                                 | t$u' => substf t $ substf u'
wenzelm@9536
   695
                                 | _ => u)
clasohm@0
   696
      in  substf  end;
clasohm@0
   697
wenzelm@13000
   698
(*Abstraction of the term "body" over its occurrences of v,
clasohm@0
   699
    which must contain no loose bound variables.
clasohm@0
   700
  The resulting term is ready to become the body of an Abs.*)
wenzelm@16882
   701
fun abstract_over (v, body) =
wenzelm@16882
   702
  let
wenzelm@16990
   703
    exception SAME;
wenzelm@16990
   704
    fun abs lev tm =
wenzelm@16990
   705
      if v aconv tm then Bound lev
wenzelm@16882
   706
      else
wenzelm@16990
   707
        (case tm of
wenzelm@16990
   708
          Abs (a, T, t) => Abs (a, T, abs (lev + 1) t)
wenzelm@16990
   709
        | t $ u => (abs lev t $ (abs lev u handle SAME => u) handle SAME => t $ abs lev u)
wenzelm@16990
   710
        | _ => raise SAME);
wenzelm@16990
   711
  in abs 0 body handle SAME => body end;
clasohm@0
   712
wenzelm@21975
   713
fun lambda v t =
wenzelm@21975
   714
  let val x =
wenzelm@21975
   715
    (case v of
wenzelm@21975
   716
      Const (x, _) => NameSpace.base x
wenzelm@21975
   717
    | Free (x, _) => x
wenzelm@21975
   718
    | Var ((x, _), _) => x
wenzelm@24850
   719
    | _ => Name.uu)
wenzelm@21975
   720
  in Abs (x, fastype_of v, abstract_over (v, t)) end;
clasohm@0
   721
clasohm@0
   722
(*Form an abstraction over a free variable.*)
wenzelm@21975
   723
fun absfree (a,T,body) = Abs (a, T, abstract_over (Free (a, T), body));
wenzelm@24850
   724
fun absdummy (T, body) = Abs (Name.internal Name.uu, T, body);
clasohm@0
   725
clasohm@0
   726
(*Abstraction over a list of free variables*)
clasohm@0
   727
fun list_abs_free ([ ] ,     t) = t
wenzelm@13000
   728
  | list_abs_free ((a,T)::vars, t) =
clasohm@0
   729
      absfree(a, T, list_abs_free(vars,t));
clasohm@0
   730
clasohm@0
   731
(*Quantification over a list of free variables*)
clasohm@0
   732
fun list_all_free ([], t: term) = t
wenzelm@13000
   733
  | list_all_free ((a,T)::vars, t) =
clasohm@0
   734
        (all T) $ (absfree(a, T, list_all_free(vars,t)));
clasohm@0
   735
clasohm@0
   736
(*Quantification over a list of variables (already bound in body) *)
clasohm@0
   737
fun list_all ([], t) = t
wenzelm@13000
   738
  | list_all ((a,T)::vars, t) =
clasohm@0
   739
        (all T) $ (Abs(a, T, list_all(vars,t)));
clasohm@0
   740
wenzelm@16678
   741
(*Replace the ATOMIC term ti by ui;    inst = [(t1,u1), ..., (tn,un)].
clasohm@0
   742
  A simultaneous substitution:  [ (a,b), (b,a) ] swaps a and b.  *)
wenzelm@16678
   743
fun subst_atomic [] tm = tm
wenzelm@16678
   744
  | subst_atomic inst tm =
wenzelm@16678
   745
      let
wenzelm@16678
   746
        fun subst (Abs (a, T, body)) = Abs (a, T, subst body)
wenzelm@16678
   747
          | subst (t $ u) = subst t $ subst u
wenzelm@18942
   748
          | subst t = the_default t (AList.lookup (op aconv) inst t);
wenzelm@16678
   749
      in subst tm end;
clasohm@0
   750
wenzelm@16678
   751
(*Replace the ATOMIC type Ti by Ui;    inst = [(T1,U1), ..., (Tn,Un)].*)
wenzelm@16678
   752
fun typ_subst_atomic [] ty = ty
wenzelm@16678
   753
  | typ_subst_atomic inst ty =
wenzelm@16678
   754
      let
wenzelm@16678
   755
        fun subst (Type (a, Ts)) = Type (a, map subst Ts)
wenzelm@18942
   756
          | subst T = the_default T (AList.lookup (op = : typ * typ -> bool) inst T);
wenzelm@16678
   757
      in subst ty end;
berghofe@15797
   758
wenzelm@16678
   759
fun subst_atomic_types [] tm = tm
wenzelm@20548
   760
  | subst_atomic_types inst tm = map_types (typ_subst_atomic inst) tm;
wenzelm@16678
   761
wenzelm@16678
   762
fun typ_subst_TVars [] ty = ty
wenzelm@16678
   763
  | typ_subst_TVars inst ty =
wenzelm@16678
   764
      let
wenzelm@16678
   765
        fun subst (Type (a, Ts)) = Type (a, map subst Ts)
wenzelm@18942
   766
          | subst (T as TVar (xi, _)) = the_default T (AList.lookup (op =) inst xi)
wenzelm@16678
   767
          | subst T = T;
wenzelm@16678
   768
      in subst ty end;
clasohm@0
   769
wenzelm@16678
   770
fun subst_TVars [] tm = tm
wenzelm@20548
   771
  | subst_TVars inst tm = map_types (typ_subst_TVars inst) tm;
clasohm@0
   772
wenzelm@16678
   773
fun subst_Vars [] tm = tm
wenzelm@16678
   774
  | subst_Vars inst tm =
wenzelm@16678
   775
      let
wenzelm@18942
   776
        fun subst (t as Var (xi, _)) = the_default t (AList.lookup (op =) inst xi)
wenzelm@16678
   777
          | subst (Abs (a, T, t)) = Abs (a, T, subst t)
wenzelm@16678
   778
          | subst (t $ u) = subst t $ subst u
wenzelm@16678
   779
          | subst t = t;
wenzelm@16678
   780
      in subst tm end;
clasohm@0
   781
wenzelm@16678
   782
fun subst_vars ([], []) tm = tm
wenzelm@16678
   783
  | subst_vars ([], inst) tm = subst_Vars inst tm
wenzelm@16678
   784
  | subst_vars (instT, inst) tm =
wenzelm@16678
   785
      let
wenzelm@16678
   786
        fun subst (Const (a, T)) = Const (a, typ_subst_TVars instT T)
wenzelm@16678
   787
          | subst (Free (a, T)) = Free (a, typ_subst_TVars instT T)
wenzelm@16678
   788
          | subst (t as Var (xi, T)) =
haftmann@17271
   789
              (case AList.lookup (op =) inst xi of
wenzelm@16678
   790
                NONE => Var (xi, typ_subst_TVars instT T)
wenzelm@16678
   791
              | SOME t => t)
wenzelm@16678
   792
          | subst (t as Bound _) = t
wenzelm@16678
   793
          | subst (Abs (a, T, t)) = Abs (a, typ_subst_TVars instT T, subst t)
wenzelm@16678
   794
          | subst (t $ u) = subst t $ subst u;
wenzelm@16678
   795
      in subst tm end;
clasohm@0
   796
wenzelm@25050
   797
fun close_schematic_term t =
wenzelm@25050
   798
  let
wenzelm@25050
   799
    val extra_types = map (fn v => Const ("TYPE", itselfT (TVar v))) (hidden_polymorphism t);
wenzelm@25050
   800
    val extra_terms = map Var (rev (add_vars t []));
wenzelm@25050
   801
  in fold_rev lambda (extra_types @ extra_terms) t end;
wenzelm@25050
   802
wenzelm@25050
   803
clasohm@0
   804
paulson@15573
   805
(** Identifying first-order terms **)
paulson@15573
   806
wenzelm@20199
   807
(*Differs from proofterm/is_fun in its treatment of TVar*)
wenzelm@29256
   808
fun is_funtype (Type ("fun", [_, _])) = true
wenzelm@20199
   809
  | is_funtype _ = false;
wenzelm@20199
   810
paulson@15573
   811
(*Argument Ts is a reverse list of binder types, needed if term t contains Bound vars*)
wenzelm@29256
   812
fun has_not_funtype Ts t = not (is_funtype (fastype_of1 (Ts, t)));
paulson@15573
   813
wenzelm@16537
   814
(*First order means in all terms of the form f(t1,...,tn) no argument has a
paulson@16589
   815
  function type. The supplied quantifiers are excluded: their argument always
paulson@16589
   816
  has a function type through a recursive call into its body.*)
wenzelm@16667
   817
fun is_first_order quants =
paulson@16589
   818
  let fun first_order1 Ts (Abs (_,T,body)) = first_order1 (T::Ts) body
wenzelm@16667
   819
        | first_order1 Ts (Const(q,_) $ Abs(a,T,body)) =
wenzelm@20664
   820
            member (op =) quants q  andalso   (*it is a known quantifier*)
paulson@16589
   821
            not (is_funtype T)   andalso first_order1 (T::Ts) body
wenzelm@16667
   822
        | first_order1 Ts t =
wenzelm@16667
   823
            case strip_comb t of
wenzelm@16667
   824
                 (Var _, ts) => forall (first_order1 Ts andf has_not_funtype Ts) ts
wenzelm@16667
   825
               | (Free _, ts) => forall (first_order1 Ts andf has_not_funtype Ts) ts
wenzelm@16667
   826
               | (Const _, ts) => forall (first_order1 Ts andf has_not_funtype Ts) ts
wenzelm@16667
   827
               | (Bound _, ts) => forall (first_order1 Ts andf has_not_funtype Ts) ts
wenzelm@16667
   828
               | (Abs _, ts) => false (*not in beta-normal form*)
wenzelm@16667
   829
               | _ => error "first_order: unexpected case"
paulson@16589
   830
    in  first_order1 []  end;
paulson@15573
   831
wenzelm@16710
   832
wenzelm@16990
   833
(* maximum index of typs and terms *)
clasohm@0
   834
wenzelm@16710
   835
fun maxidx_typ (TVar ((_, j), _)) i = Int.max (i, j)
wenzelm@16710
   836
  | maxidx_typ (Type (_, Ts)) i = maxidx_typs Ts i
wenzelm@16710
   837
  | maxidx_typ (TFree _) i = i
wenzelm@16710
   838
and maxidx_typs [] i = i
wenzelm@16710
   839
  | maxidx_typs (T :: Ts) i = maxidx_typs Ts (maxidx_typ T i);
clasohm@0
   840
wenzelm@16710
   841
fun maxidx_term (Var ((_, j), T)) i = maxidx_typ T (Int.max (i, j))
wenzelm@16710
   842
  | maxidx_term (Const (_, T)) i = maxidx_typ T i
wenzelm@16710
   843
  | maxidx_term (Free (_, T)) i = maxidx_typ T i
wenzelm@16710
   844
  | maxidx_term (Bound _) i = i
wenzelm@16710
   845
  | maxidx_term (Abs (_, T, t)) i = maxidx_term t (maxidx_typ T i)
wenzelm@16710
   846
  | maxidx_term (t $ u) i = maxidx_term u (maxidx_term t i);
clasohm@0
   847
wenzelm@16710
   848
fun maxidx_of_typ T = maxidx_typ T ~1;
wenzelm@16710
   849
fun maxidx_of_typs Ts = maxidx_typs Ts ~1;
wenzelm@16710
   850
fun maxidx_of_term t = maxidx_term t ~1;
berghofe@13665
   851
clasohm@0
   852
clasohm@0
   853
wenzelm@29270
   854
(** misc syntax operations **)
clasohm@0
   855
wenzelm@19909
   856
(* substructure *)
wenzelm@4017
   857
wenzelm@19909
   858
fun exists_subtype P =
wenzelm@19909
   859
  let
wenzelm@19909
   860
    fun ex ty = P ty orelse
wenzelm@19909
   861
      (case ty of Type (_, Ts) => exists ex Ts | _ => false);
wenzelm@19909
   862
  in ex end;
nipkow@13646
   863
wenzelm@20531
   864
fun exists_type P =
wenzelm@20531
   865
  let
wenzelm@20531
   866
    fun ex (Const (_, T)) = P T
wenzelm@20531
   867
      | ex (Free (_, T)) = P T
wenzelm@20531
   868
      | ex (Var (_, T)) = P T
wenzelm@20531
   869
      | ex (Bound _) = false
wenzelm@20531
   870
      | ex (Abs (_, T, t)) = P T orelse ex t
wenzelm@20531
   871
      | ex (t $ u) = ex t orelse ex u;
wenzelm@20531
   872
  in ex end;
wenzelm@20531
   873
wenzelm@16943
   874
fun exists_subterm P =
wenzelm@16943
   875
  let
wenzelm@16943
   876
    fun ex tm = P tm orelse
wenzelm@16943
   877
      (case tm of
wenzelm@16943
   878
        t $ u => ex t orelse ex u
wenzelm@16943
   879
      | Abs (_, _, t) => ex t
wenzelm@16943
   880
      | _ => false);
wenzelm@16943
   881
  in ex end;
obua@16108
   882
wenzelm@29270
   883
fun exists_Const P = exists_subterm (fn Const c => P c | _ => false);
wenzelm@29270
   884
wenzelm@24671
   885
fun has_abs (Abs _) = true
wenzelm@24671
   886
  | has_abs (t $ u) = has_abs t orelse has_abs u
wenzelm@24671
   887
  | has_abs _ = false;
wenzelm@24671
   888
wenzelm@24671
   889
wenzelm@20199
   890
(* dest abstraction *)
clasohm@0
   891
wenzelm@16678
   892
fun dest_abs (x, T, body) =
wenzelm@16678
   893
  let
wenzelm@16678
   894
    fun name_clash (Free (y, _)) = (x = y)
wenzelm@16678
   895
      | name_clash (t $ u) = name_clash t orelse name_clash u
wenzelm@16678
   896
      | name_clash (Abs (_, _, t)) = name_clash t
wenzelm@16678
   897
      | name_clash _ = false;
wenzelm@16678
   898
  in
wenzelm@27335
   899
    if name_clash body then dest_abs (Name.variant [x] x, T, body)    (*potentially slow*)
wenzelm@16678
   900
    else (x, subst_bound (Free (x, T), body))
wenzelm@16678
   901
  end;
wenzelm@16678
   902
wenzelm@20160
   903
wenzelm@9536
   904
(* dummy patterns *)
wenzelm@9536
   905
wenzelm@9536
   906
val dummy_patternN = "dummy_pattern";
wenzelm@9536
   907
wenzelm@18253
   908
fun dummy_pattern T = Const (dummy_patternN, T);
wenzelm@18253
   909
wenzelm@9536
   910
fun is_dummy_pattern (Const ("dummy_pattern", _)) = true
wenzelm@9536
   911
  | is_dummy_pattern _ = false;
wenzelm@9536
   912
wenzelm@9536
   913
fun no_dummy_patterns tm =
haftmann@16787
   914
  if not (fold_aterms (fn t => fn b => b orelse is_dummy_pattern t) tm false) then tm
wenzelm@9536
   915
  else raise TERM ("Illegal occurrence of '_' dummy pattern", [tm]);
wenzelm@9536
   916
wenzelm@24733
   917
fun free_dummy_patterns (Const ("dummy_pattern", T)) used =
wenzelm@24850
   918
      let val [x] = Name.invents used Name.uu 1
wenzelm@24733
   919
      in (Free (Name.internal x, T), Name.declare x used) end
wenzelm@24733
   920
  | free_dummy_patterns (Abs (x, T, b)) used =
wenzelm@24733
   921
      let val (b', used') = free_dummy_patterns b used
wenzelm@24733
   922
      in (Abs (x, T, b'), used') end
wenzelm@24733
   923
  | free_dummy_patterns (t $ u) used =
wenzelm@24733
   924
      let
wenzelm@24733
   925
        val (t', used') = free_dummy_patterns t used;
wenzelm@24733
   926
        val (u', used'') = free_dummy_patterns u used';
wenzelm@24733
   927
      in (t' $ u', used'') end
wenzelm@24733
   928
  | free_dummy_patterns a used = (a, used);
wenzelm@24733
   929
wenzelm@24762
   930
fun replace_dummy Ts (Const ("dummy_pattern", T)) i =
wenzelm@24762
   931
      (list_comb (Var (("_dummy_", i), Ts ---> T), map Bound (0 upto length Ts - 1)), i + 1)
wenzelm@24762
   932
  | replace_dummy Ts (Abs (x, T, t)) i =
wenzelm@24762
   933
      let val (t', i') = replace_dummy (T :: Ts) t i
wenzelm@24762
   934
      in (Abs (x, T, t'), i') end
wenzelm@24762
   935
  | replace_dummy Ts (t $ u) i =
wenzelm@24762
   936
      let
wenzelm@24762
   937
        val (t', i') = replace_dummy Ts t i;
wenzelm@24762
   938
        val (u', i'') = replace_dummy Ts u i';
wenzelm@24762
   939
      in (t' $ u', i'') end
wenzelm@24762
   940
  | replace_dummy _ a i = (a, i);
wenzelm@11903
   941
wenzelm@11903
   942
val replace_dummy_patterns = replace_dummy [];
wenzelm@9536
   943
wenzelm@10552
   944
fun is_replaced_dummy_pattern ("_dummy_", _) = true
wenzelm@10552
   945
  | is_replaced_dummy_pattern _ = false;
wenzelm@9536
   946
wenzelm@16035
   947
fun show_dummy_patterns (Var (("_dummy_", _), T)) = Const ("dummy_pattern", T)
wenzelm@16035
   948
  | show_dummy_patterns (t $ u) = show_dummy_patterns t $ show_dummy_patterns u
wenzelm@16035
   949
  | show_dummy_patterns (Abs (x, T, t)) = Abs (x, T, show_dummy_patterns t)
wenzelm@16035
   950
  | show_dummy_patterns a = a;
wenzelm@16035
   951
wenzelm@13484
   952
wenzelm@20100
   953
(* display variables *)
wenzelm@20100
   954
wenzelm@15986
   955
val show_question_marks = ref true;
berghofe@15472
   956
wenzelm@14786
   957
fun string_of_vname (x, i) =
wenzelm@14786
   958
  let
wenzelm@15986
   959
    val question_mark = if ! show_question_marks then "?" else "";
wenzelm@15986
   960
    val idx = string_of_int i;
wenzelm@15986
   961
    val dot =
wenzelm@15986
   962
      (case rev (Symbol.explode x) of
wenzelm@15986
   963
        _ :: "\\<^isub>" :: _ => false
wenzelm@15986
   964
      | _ :: "\\<^isup>" :: _ => false
wenzelm@15986
   965
      | c :: _ => Symbol.is_digit c
wenzelm@15986
   966
      | _ => true);
wenzelm@14786
   967
  in
wenzelm@15986
   968
    if dot then question_mark ^ x ^ "." ^ idx
wenzelm@15986
   969
    else if i <> 0 then question_mark ^ x ^ idx
wenzelm@15986
   970
    else question_mark ^ x
wenzelm@14786
   971
  end;
wenzelm@14786
   972
wenzelm@14786
   973
fun string_of_vname' (x, ~1) = x
wenzelm@14786
   974
  | string_of_vname' xi = string_of_vname xi;
wenzelm@14786
   975
clasohm@1364
   976
end;
clasohm@1364
   977
wenzelm@4444
   978
structure BasicTerm: BASIC_TERM = Term;
wenzelm@4444
   979
open BasicTerm;