src/Pure/term.ML
author wenzelm
Sat Nov 04 15:24:40 2017 +0100 (19 months ago)
changeset 67003 49850a679c2c
parent 63619 9c870388e87a
child 67703 8c4806fe827f
permissions -rw-r--r--
more robust sorted_entries;
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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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  type indexname = string * int
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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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  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 dest_comb: term -> term * term
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  val domain_type: typ -> typ
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  val range_type: typ -> typ
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  val dest_funT: typ -> 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 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 size_of_typ: typ -> 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_atyps_sorts: (typ * sort -> '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 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 fold_subtypes: (typ -> 'a -> 'a) -> typ -> 'a -> 'a
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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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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 -> int -> typ
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  val abs: string * typ -> term -> term
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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 aconv_untyped: term * term -> 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 is_open: term -> bool
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  val is_dependent: term -> bool
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  val term_name: term -> string
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  val dependent_lambda_name: string * term -> term -> term
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  val lambda_name: string * term -> term -> term
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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 could_beta_contract: term -> bool
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  val could_eta_contract: term -> bool
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  val could_beta_eta_contract: term -> bool
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  val dest_abs: string * typ * term -> string * term
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  val dummy_pattern: typ -> term
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  val dummy: term
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  val dummy_prop: 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 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 dest_comb (t1 $ t2) = (t1, t2)
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  | dest_comb t = raise TERM("dest_comb", [t]);
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fun domain_type (Type ("fun", [T, _])) = T;
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fun range_type (Type ("fun", [_, U])) = U;
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fun dest_funT (Type ("fun", [T, U])) = (T, U)
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  | dest_funT T = raise TYPE ("dest_funT", [T], []);
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(*maps  [T1,...,Tn]--->T  to the list  [T1,T2,...,Tn]*)
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fun binder_types (Type ("fun", [T, U])) = T :: binder_types U
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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", [_, U])) = body_type U
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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 = (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) = (nth Ts i
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        handle General.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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   327
                     [T,U], [f$u])
clasohm@0
   328
      end;
clasohm@0
   329
clasohm@0
   330
fun type_of t : typ = type_of1 ([],t);
clasohm@0
   331
clasohm@0
   332
(*Determines the type of a term, with minimal checking*)
wenzelm@13000
   333
fun fastype_of1 (Ts, f$u) =
lcp@61
   334
    (case fastype_of1 (Ts,f) of
wenzelm@9536
   335
        Type("fun",[_,T]) => T
wenzelm@9536
   336
        | _ => raise TERM("fastype_of: expected function type", [f$u]))
lcp@61
   337
  | fastype_of1 (_, Const (_,T)) = T
lcp@61
   338
  | fastype_of1 (_, Free (_,T)) = T
wenzelm@30146
   339
  | fastype_of1 (Ts, Bound i) = (nth Ts i
wenzelm@43278
   340
         handle General.Subscript => raise TERM("fastype_of: Bound", [Bound i]))
wenzelm@13000
   341
  | fastype_of1 (_, Var (_,T)) = T
lcp@61
   342
  | fastype_of1 (Ts, Abs (_,T,u)) = T --> fastype_of1 (T::Ts, u);
lcp@61
   343
lcp@61
   344
fun fastype_of t : typ = fastype_of1 ([],t);
clasohm@0
   345
wenzelm@16678
   346
(*Determine the argument type of a function*)
wenzelm@22908
   347
fun argument_type_of tm k =
wenzelm@16678
   348
  let
wenzelm@16678
   349
    fun argT i (Type ("fun", [T, U])) = if i = 0 then T else argT (i - 1) U
wenzelm@16678
   350
      | argT _ T = raise TYPE ("argument_type_of", [T], []);
wenzelm@16678
   351
wenzelm@16678
   352
    fun arg 0 _ (Abs (_, T, _)) = T
wenzelm@16678
   353
      | arg i Ts (Abs (_, T, t)) = arg (i - 1) (T :: Ts) t
wenzelm@16678
   354
      | arg i Ts (t $ _) = arg (i + 1) Ts t
wenzelm@16678
   355
      | arg i Ts a = argT i (fastype_of1 (Ts, a));
wenzelm@22908
   356
  in arg k [] tm end;
wenzelm@16678
   357
clasohm@0
   358
wenzelm@46219
   359
fun abs (x, T) t = Abs (x, T, t);
wenzelm@10806
   360
haftmann@18927
   361
fun strip_abs (Abs (a, T, t)) =
haftmann@18927
   362
      let val (a', t') = strip_abs t
haftmann@18927
   363
      in ((a, T) :: a', t') end
haftmann@18927
   364
  | strip_abs t = ([], t);
haftmann@18927
   365
wenzelm@63611
   366
(*maps  (x1,...,xn)t   to   t*)
wenzelm@13000
   367
fun strip_abs_body (Abs(_,_,t))  =  strip_abs_body t
clasohm@0
   368
  | strip_abs_body u  =  u;
clasohm@0
   369
wenzelm@63611
   370
(*maps  (x1,...,xn)t   to   [x1, ..., xn]*)
wenzelm@13000
   371
fun strip_abs_vars (Abs(a,T,t))  =  (a,T) :: strip_abs_vars t
clasohm@0
   372
  | strip_abs_vars u  =  [] : (string*typ) list;
clasohm@0
   373
clasohm@0
   374
clasohm@0
   375
fun strip_qnt_body qnt =
clasohm@0
   376
let fun strip(tm as Const(c,_)$Abs(_,_,t)) = if c=qnt then strip t else tm
clasohm@0
   377
      | strip t = t
clasohm@0
   378
in strip end;
clasohm@0
   379
clasohm@0
   380
fun strip_qnt_vars qnt =
clasohm@0
   381
let fun strip(Const(c,_)$Abs(a,T,t)) = if c=qnt then (a,T)::strip t else []
clasohm@0
   382
      | strip t  =  [] : (string*typ) list
clasohm@0
   383
in strip end;
clasohm@0
   384
clasohm@0
   385
wenzelm@63611
   386
(*maps   (f, [t1,...,tn])  to  f(t1,...,tn)*)
skalberg@15570
   387
val list_comb : term * term list -> term = Library.foldl (op $);
clasohm@0
   388
clasohm@0
   389
wenzelm@63611
   390
(*maps   f(t1,...,tn)  to  (f, [t1,...,tn]) ; naturally tail-recursive*)
wenzelm@13000
   391
fun strip_comb u : term * term list =
clasohm@0
   392
    let fun stripc (f$t, ts) = stripc (f, t::ts)
wenzelm@13000
   393
        |   stripc  x =  x
clasohm@0
   394
    in  stripc(u,[])  end;
clasohm@0
   395
clasohm@0
   396
wenzelm@63611
   397
(*maps   f(t1,...,tn)  to  f , which is never a combination*)
clasohm@0
   398
fun head_of (f$t) = head_of f
clasohm@0
   399
  | head_of u = u;
clasohm@0
   400
wenzelm@16599
   401
(*number of atoms and abstractions in a term*)
wenzelm@16599
   402
fun size_of_term tm =
wenzelm@16599
   403
  let
wenzelm@30144
   404
    fun add_size (t $ u) n = add_size t (add_size u n)
wenzelm@30144
   405
      | add_size (Abs (_ ,_, t)) n = add_size t (n + 1)
wenzelm@30144
   406
      | add_size _ n = n + 1;
wenzelm@30144
   407
  in add_size tm 0 end;
clasohm@0
   408
wenzelm@30144
   409
(*number of atoms and constructors in a type*)
kleing@29882
   410
fun size_of_typ ty =
kleing@29882
   411
  let
wenzelm@30144
   412
    fun add_size (Type (_, tys)) n = fold add_size tys (n + 1)
wenzelm@30144
   413
      | add_size _ n = n + 1;
wenzelm@30144
   414
  in add_size ty 0 end;
kleing@29882
   415
haftmann@18847
   416
fun map_atyps f (Type (a, Ts)) = Type (a, map (map_atyps f) Ts)
haftmann@18976
   417
  | map_atyps f T = f T;
haftmann@18847
   418
haftmann@18847
   419
fun map_aterms f (t $ u) = map_aterms f t $ map_aterms f u
haftmann@18847
   420
  | map_aterms f (Abs (a, T, t)) = Abs (a, T, map_aterms f t)
haftmann@18847
   421
  | map_aterms f t = f t;
haftmann@18847
   422
wenzelm@18981
   423
fun map_type_tvar f = map_atyps (fn TVar x => f x | T => T);
wenzelm@18981
   424
fun map_type_tfree f = map_atyps (fn TFree x => f x | T => T);
nipkow@949
   425
wenzelm@20548
   426
fun map_types f =
wenzelm@16678
   427
  let
wenzelm@16678
   428
    fun map_aux (Const (a, T)) = Const (a, f T)
wenzelm@16678
   429
      | map_aux (Free (a, T)) = Free (a, f T)
wenzelm@16678
   430
      | map_aux (Var (v, T)) = Var (v, f T)
wenzelm@39293
   431
      | map_aux (Bound i) = Bound i
wenzelm@16678
   432
      | map_aux (Abs (a, T, t)) = Abs (a, f T, map_aux t)
wenzelm@16678
   433
      | map_aux (t $ u) = map_aux t $ map_aux u;
wenzelm@16678
   434
  in map_aux end;
clasohm@0
   435
clasohm@0
   436
wenzelm@16943
   437
(* fold types and terms *)
wenzelm@16943
   438
wenzelm@16943
   439
fun fold_atyps f (Type (_, Ts)) = fold (fold_atyps f) Ts
wenzelm@16943
   440
  | fold_atyps f T = f T;
wenzelm@16943
   441
wenzelm@35986
   442
fun fold_atyps_sorts f =
wenzelm@35986
   443
  fold_atyps (fn T as TFree (_, S) => f (T, S) | T as TVar (_, S) => f (T, S));
wenzelm@35986
   444
wenzelm@16943
   445
fun fold_aterms f (t $ u) = fold_aterms f t #> fold_aterms f u
wenzelm@16943
   446
  | fold_aterms f (Abs (_, _, t)) = fold_aterms f t
wenzelm@16943
   447
  | fold_aterms f a = f a;
wenzelm@16943
   448
wenzelm@16943
   449
fun fold_term_types f (t as Const (_, T)) = f t T
wenzelm@16943
   450
  | fold_term_types f (t as Free (_, T)) = f t T
wenzelm@16943
   451
  | fold_term_types f (t as Var (_, T)) = f t T
wenzelm@16943
   452
  | fold_term_types f (Bound _) = I
wenzelm@16943
   453
  | fold_term_types f (t as Abs (_, T, b)) = f t T #> fold_term_types f b
wenzelm@16943
   454
  | fold_term_types f (t $ u) = fold_term_types f t #> fold_term_types f u;
wenzelm@16943
   455
wenzelm@16943
   456
fun fold_types f = fold_term_types (K f);
wenzelm@16943
   457
wenzelm@24483
   458
fun replace_types (Const (c, _)) (T :: Ts) = (Const (c, T), Ts)
wenzelm@24483
   459
  | replace_types (Free (x, _)) (T :: Ts) = (Free (x, T), Ts)
wenzelm@24483
   460
  | replace_types (Var (xi, _)) (T :: Ts) = (Var (xi, T), Ts)
wenzelm@24483
   461
  | replace_types (Bound i) Ts = (Bound i, Ts)
wenzelm@24483
   462
  | replace_types (Abs (x, _, b)) (T :: Ts) =
wenzelm@24483
   463
      let val (b', Ts') = replace_types b Ts
wenzelm@24483
   464
      in (Abs (x, T, b'), Ts') end
wenzelm@24483
   465
  | replace_types (t $ u) Ts =
wenzelm@24483
   466
      let
wenzelm@24483
   467
        val (t', Ts') = replace_types t Ts;
wenzelm@24483
   468
        val (u', Ts'') = replace_types u Ts';
wenzelm@24483
   469
      in (t' $ u', Ts'') end;
wenzelm@24483
   470
wenzelm@24483
   471
fun burrow_types f ts =
wenzelm@24483
   472
  let
wenzelm@49674
   473
    val Ts = rev ((fold o fold_types) cons ts []);
wenzelm@24483
   474
    val Ts' = f Ts;
wenzelm@24483
   475
    val (ts', []) = fold_map replace_types ts Ts';
wenzelm@24483
   476
  in ts' end;
wenzelm@24483
   477
wenzelm@16943
   478
(*collect variables*)
wenzelm@29257
   479
val add_tvar_namesT = fold_atyps (fn TVar (xi, _) => insert (op =) xi | _ => I);
wenzelm@29257
   480
val add_tvar_names = fold_types add_tvar_namesT;
wenzelm@16943
   481
val add_tvarsT = fold_atyps (fn TVar v => insert (op =) v | _ => I);
wenzelm@16943
   482
val add_tvars = fold_types add_tvarsT;
wenzelm@29257
   483
val add_var_names = fold_aterms (fn Var (xi, _) => insert (op =) xi | _ => I);
wenzelm@16943
   484
val add_vars = fold_aterms (fn Var v => insert (op =) v | _ => I);
wenzelm@33697
   485
val add_tfree_namesT = fold_atyps (fn TFree (a, _) => insert (op =) a | _ => I);
wenzelm@29257
   486
val add_tfree_names = fold_types add_tfree_namesT;
wenzelm@16943
   487
val add_tfreesT = fold_atyps (fn TFree v => insert (op =) v | _ => I);
wenzelm@16943
   488
val add_tfrees = fold_types add_tfreesT;
wenzelm@29257
   489
val add_free_names = fold_aterms (fn Free (x, _) => insert (op =) x | _ => I);
wenzelm@16943
   490
val add_frees = fold_aterms (fn Free v => insert (op =) v | _ => I);
wenzelm@29286
   491
val add_const_names = fold_aterms (fn Const (c, _) => insert (op =) c | _ => I);
wenzelm@29286
   492
val add_consts = fold_aterms (fn Const c => insert (op =) c | _ => I);
wenzelm@16943
   493
wenzelm@25050
   494
(*extra type variables in a term, not covered by its type*)
wenzelm@25050
   495
fun hidden_polymorphism t =
wenzelm@21682
   496
  let
wenzelm@25050
   497
    val T = fastype_of t;
wenzelm@21682
   498
    val tvarsT = add_tvarsT T [];
wenzelm@21682
   499
    val extra_tvars = fold_types (fold_atyps
wenzelm@21682
   500
      (fn TVar v => if member (op =) tvarsT v then I else insert (op =) v | _ => I)) t [];
wenzelm@21682
   501
  in extra_tvars end;
wenzelm@21682
   502
wenzelm@16943
   503
wenzelm@29278
   504
(* renaming variables *)
wenzelm@29278
   505
wenzelm@29278
   506
val declare_typ_names = fold_atyps (fn TFree (a, _) => Name.declare a | _ => I);
wenzelm@29278
   507
wenzelm@29278
   508
fun declare_term_names tm =
wenzelm@29278
   509
  fold_aterms
wenzelm@30364
   510
    (fn Const (a, _) => Name.declare (Long_Name.base_name a)
wenzelm@29278
   511
      | Free (a, _) => Name.declare a
wenzelm@29278
   512
      | _ => I) tm #>
wenzelm@29278
   513
  fold_types declare_typ_names tm;
wenzelm@29278
   514
wenzelm@29278
   515
val declare_term_frees = fold_aterms (fn Free (x, _) => Name.declare x | _ => I);
wenzelm@29278
   516
wenzelm@29278
   517
fun variant_frees t frees =
wenzelm@43326
   518
  fst (fold_map Name.variant (map fst frees) (declare_term_names t Name.context)) ~~
wenzelm@43326
   519
    map snd frees;
wenzelm@29278
   520
wenzelm@29278
   521
fun rename_wrt_term t frees = rev (variant_frees t frees);  (*reversed result!*)
wenzelm@29278
   522
wenzelm@29278
   523
wenzelm@25050
   524
wenzelm@29269
   525
(** Comparing terms **)
wenzelm@29269
   526
wenzelm@29269
   527
(* variables *)
wenzelm@29269
   528
wenzelm@29269
   529
fun eq_ix ((x, i): indexname, (y, j)) = i = j andalso x = y;
wenzelm@16537
   530
wenzelm@29269
   531
fun eq_tvar ((xi, S: sort), (xi', S')) = eq_ix (xi, xi') andalso S = S';
wenzelm@29269
   532
fun eq_var ((xi, T: typ), (xi', T')) = eq_ix (xi, xi') andalso T = T';
wenzelm@29269
   533
wenzelm@29269
   534
wenzelm@29269
   535
(* alpha equivalence *)
wenzelm@20511
   536
wenzelm@20511
   537
fun tm1 aconv tm2 =
wenzelm@20511
   538
  pointer_eq (tm1, tm2) orelse
wenzelm@20511
   539
    (case (tm1, tm2) of
wenzelm@20511
   540
      (t1 $ u1, t2 $ u2) => t1 aconv t2 andalso u1 aconv u2
wenzelm@20511
   541
    | (Abs (_, T1, t1), Abs (_, T2, t2)) => t1 aconv t2 andalso T1 = T2
wenzelm@20511
   542
    | (a1, a2) => a1 = a2);
wenzelm@20511
   543
wenzelm@33537
   544
fun aconv_untyped (tm1, tm2) =
wenzelm@33537
   545
  pointer_eq (tm1, tm2) orelse
wenzelm@33537
   546
    (case (tm1, tm2) of
wenzelm@33537
   547
      (t1 $ u1, t2 $ u2) => aconv_untyped (t1, t2) andalso aconv_untyped (u1, u2)
wenzelm@33537
   548
    | (Abs (_, _, t1), Abs (_, _, t2)) => aconv_untyped (t1, t2)
wenzelm@33537
   549
    | (Const (a, _), Const (b, _)) => a = b
wenzelm@33537
   550
    | (Free (x, _), Free (y, _)) => x = y
wenzelm@33537
   551
    | (Var (xi, _), Var (yj, _)) => xi = yj
wenzelm@33537
   552
    | (Bound i, Bound j) => i = j
wenzelm@33537
   553
    | _ => false);
wenzelm@33537
   554
wenzelm@20511
   555
wenzelm@29269
   556
(*A fast unification filter: true unless the two terms cannot be unified.
wenzelm@29269
   557
  Terms must be NORMAL.  Treats all Vars as distinct. *)
wenzelm@29269
   558
fun could_unify (t, u) =
wenzelm@29269
   559
  let
wenzelm@29269
   560
    fun matchrands (f $ t) (g $ u) = could_unify (t, u) andalso matchrands f g
wenzelm@29269
   561
      | matchrands _ _ = true;
wenzelm@29269
   562
  in
wenzelm@29269
   563
    case (head_of t, head_of u) of
wenzelm@29269
   564
      (_, Var _) => true
wenzelm@29269
   565
    | (Var _, _) => true
wenzelm@29269
   566
    | (Const (a, _), Const (b, _)) => a = b andalso matchrands t u
wenzelm@29269
   567
    | (Free (a, _), Free (b, _)) => a = b andalso matchrands t u
wenzelm@29269
   568
    | (Bound i, Bound j) => i = j andalso matchrands t u
wenzelm@29269
   569
    | (Abs _, _) => true   (*because of possible eta equality*)
wenzelm@29269
   570
    | (_, Abs _) => true
wenzelm@29269
   571
    | _ => false
wenzelm@29269
   572
  end;
wenzelm@16678
   573
nipkow@16570
   574
wenzelm@16537
   575
clasohm@0
   576
(** Connectives of higher order logic **)
clasohm@0
   577
wenzelm@24850
   578
fun aT S = TFree (Name.aT, S);
wenzelm@19394
   579
wenzelm@375
   580
fun itselfT ty = Type ("itself", [ty]);
wenzelm@24850
   581
val a_itselfT = itselfT (TFree (Name.aT, []));
wenzelm@375
   582
wenzelm@46217
   583
val propT : typ = Type ("prop",[]);
clasohm@0
   584
wenzelm@63611
   585
(*maps  !!x1...xn. t   to   t*)
wenzelm@60311
   586
fun strip_all_body (Const ("Pure.all", _) $ Abs (_, _, t)) = strip_all_body t
wenzelm@60311
   587
  | strip_all_body t = t;
clasohm@0
   588
wenzelm@63611
   589
(*maps  !!x1...xn. t   to   [x1, ..., xn]*)
wenzelm@60311
   590
fun strip_all_vars (Const ("Pure.all", _) $ Abs (a, T, t)) = (a, T) :: strip_all_vars t
wenzelm@60311
   591
  | strip_all_vars t = [];
clasohm@0
   592
clasohm@0
   593
(*increments a term's non-local bound variables
clasohm@0
   594
  required when moving a term within abstractions
clasohm@0
   595
     inc is  increment for bound variables
clasohm@0
   596
     lev is  level at which a bound variable is considered 'loose'*)
wenzelm@13000
   597
fun incr_bv (inc, lev, u as Bound i) = if i>=lev then Bound(i+inc) else u
clasohm@0
   598
  | incr_bv (inc, lev, Abs(a,T,body)) =
wenzelm@9536
   599
        Abs(a, T, incr_bv(inc,lev+1,body))
wenzelm@13000
   600
  | incr_bv (inc, lev, f$t) =
clasohm@0
   601
      incr_bv(inc,lev,f) $ incr_bv(inc,lev,t)
clasohm@0
   602
  | incr_bv (inc, lev, u) = u;
clasohm@0
   603
clasohm@0
   604
fun incr_boundvars  0  t = t
clasohm@0
   605
  | incr_boundvars inc t = incr_bv(inc,0,t);
clasohm@0
   606
wenzelm@12981
   607
(*Scan a pair of terms; while they are similar,
wenzelm@12981
   608
  accumulate corresponding bound vars in "al"*)
wenzelm@12981
   609
fun match_bvs(Abs(x,_,s),Abs(y,_,t), al) =
wenzelm@12981
   610
      match_bvs(s, t, if x="" orelse y="" then al
wenzelm@12981
   611
                                          else (x,y)::al)
wenzelm@12981
   612
  | match_bvs(f$s, g$t, al) = match_bvs(f,g,match_bvs(s,t,al))
wenzelm@12981
   613
  | match_bvs(_,_,al) = al;
wenzelm@12981
   614
wenzelm@12981
   615
(* strip abstractions created by parameters *)
wenzelm@48263
   616
fun match_bvars (s,t) al = match_bvs(strip_abs_body s, strip_abs_body t, al);
wenzelm@12981
   617
haftmann@22031
   618
fun map_abs_vars f (t $ u) = map_abs_vars f t $ map_abs_vars f u
haftmann@22031
   619
  | map_abs_vars f (Abs (a, T, t)) = Abs (f a, T, map_abs_vars f t)
haftmann@22031
   620
  | map_abs_vars f t = t;
haftmann@22031
   621
wenzelm@12981
   622
fun rename_abs pat obj t =
wenzelm@12981
   623
  let
wenzelm@12981
   624
    val ren = match_bvs (pat, obj, []);
wenzelm@12981
   625
    fun ren_abs (Abs (x, T, b)) =
wenzelm@18942
   626
          Abs (the_default x (AList.lookup (op =) ren x), T, ren_abs b)
wenzelm@12981
   627
      | ren_abs (f $ t) = ren_abs f $ ren_abs t
wenzelm@12981
   628
      | ren_abs t = t
skalberg@15531
   629
  in if null ren then NONE else SOME (ren_abs t) end;
clasohm@0
   630
clasohm@0
   631
(*Accumulate all 'loose' bound vars referring to level 'lev' or beyond.
clasohm@0
   632
   (Bound 0) is loose at level 0 *)
wenzelm@13000
   633
fun add_loose_bnos (Bound i, lev, js) =
haftmann@20854
   634
        if i<lev then js else insert (op =) (i - lev) js
clasohm@0
   635
  | add_loose_bnos (Abs (_,_,t), lev, js) = add_loose_bnos (t, lev+1, js)
clasohm@0
   636
  | add_loose_bnos (f$t, lev, js) =
wenzelm@13000
   637
        add_loose_bnos (f, lev, add_loose_bnos (t, lev, js))
clasohm@0
   638
  | add_loose_bnos (_, _, js) = js;
clasohm@0
   639
clasohm@0
   640
fun loose_bnos t = add_loose_bnos (t, 0, []);
clasohm@0
   641
clasohm@0
   642
(* loose_bvar(t,k) iff t contains a 'loose' bound variable referring to
clasohm@0
   643
   level k or beyond. *)
clasohm@0
   644
fun loose_bvar(Bound i,k) = i >= k
clasohm@0
   645
  | loose_bvar(f$t, k) = loose_bvar(f,k) orelse loose_bvar(t,k)
clasohm@0
   646
  | loose_bvar(Abs(_,_,t),k) = loose_bvar(t,k+1)
clasohm@0
   647
  | loose_bvar _ = false;
clasohm@0
   648
nipkow@2792
   649
fun loose_bvar1(Bound i,k) = i = k
nipkow@2792
   650
  | loose_bvar1(f$t, k) = loose_bvar1(f,k) orelse loose_bvar1(t,k)
nipkow@2792
   651
  | loose_bvar1(Abs(_,_,t),k) = loose_bvar1(t,k+1)
nipkow@2792
   652
  | loose_bvar1 _ = false;
clasohm@0
   653
wenzelm@42083
   654
fun is_open t = loose_bvar (t, 0);
wenzelm@42083
   655
fun is_dependent t = loose_bvar1 (t, 0);
wenzelm@42083
   656
clasohm@0
   657
(*Substitute arguments for loose bound variables.
clasohm@0
   658
  Beta-reduction of arg(n-1)...arg0 into t replacing (Bound i) with (argi).
wenzelm@4626
   659
  Note that for ((%x y. c) a b), the bound vars in c are x=1 and y=0
wenzelm@9536
   660
        and the appropriate call is  subst_bounds([b,a], c) .
clasohm@0
   661
  Loose bound variables >=n are reduced by "n" to
clasohm@0
   662
     compensate for the disappearance of lambdas.
clasohm@0
   663
*)
wenzelm@13000
   664
fun subst_bounds (args: term list, t) : term =
wenzelm@19065
   665
  let
wenzelm@19065
   666
    val n = length args;
wenzelm@19065
   667
    fun subst (t as Bound i, lev) =
wenzelm@32020
   668
         (if i < lev then raise Same.SAME   (*var is locally bound*)
wenzelm@30146
   669
          else incr_boundvars lev (nth args (i - lev))
wenzelm@43278
   670
            handle General.Subscript => Bound (i - n))  (*loose: change it*)
wenzelm@19065
   671
      | subst (Abs (a, T, body), lev) = Abs (a, T, subst (body, lev + 1))
wenzelm@19065
   672
      | subst (f $ t, lev) =
wenzelm@32020
   673
          (subst (f, lev) $ (subst (t, lev) handle Same.SAME => t)
wenzelm@32020
   674
            handle Same.SAME => f $ subst (t, lev))
wenzelm@32020
   675
      | subst _ = raise Same.SAME;
wenzelm@32020
   676
  in case args of [] => t | _ => (subst (t, 0) handle Same.SAME => t) end;
clasohm@0
   677
paulson@2192
   678
(*Special case: one argument*)
wenzelm@13000
   679
fun subst_bound (arg, t) : term =
wenzelm@19065
   680
  let
wenzelm@19065
   681
    fun subst (Bound i, lev) =
wenzelm@32020
   682
          if i < lev then raise Same.SAME   (*var is locally bound*)
wenzelm@19065
   683
          else if i = lev then incr_boundvars lev arg
wenzelm@19065
   684
          else Bound (i - 1)   (*loose: change it*)
wenzelm@19065
   685
      | subst (Abs (a, T, body), lev) = Abs (a, T, subst (body, lev + 1))
wenzelm@19065
   686
      | subst (f $ t, lev) =
wenzelm@32020
   687
          (subst (f, lev) $ (subst (t, lev) handle Same.SAME => t)
wenzelm@32020
   688
            handle Same.SAME => f $ subst (t, lev))
wenzelm@32020
   689
      | subst _ = raise Same.SAME;
wenzelm@32020
   690
  in subst (t, 0) handle Same.SAME => t end;
paulson@2192
   691
clasohm@0
   692
(*beta-reduce if possible, else form application*)
paulson@2192
   693
fun betapply (Abs(_,_,t), u) = subst_bound (u,t)
clasohm@0
   694
  | betapply (f,u) = f$u;
clasohm@0
   695
wenzelm@18183
   696
val betapplys = Library.foldl betapply;
wenzelm@18183
   697
wenzelm@14786
   698
haftmann@20109
   699
(*unfolding abstractions with substitution
haftmann@20109
   700
  of bound variables and implicit eta-expansion*)
haftmann@20109
   701
fun strip_abs_eta k t =
haftmann@20109
   702
  let
wenzelm@29278
   703
    val used = fold_aterms declare_term_frees t Name.context;
haftmann@20109
   704
    fun strip_abs t (0, used) = (([], t), (0, used))
haftmann@20109
   705
      | strip_abs (Abs (v, T, t)) (k, used) =
haftmann@20109
   706
          let
wenzelm@43326
   707
            val (v', used') = Name.variant v used;
haftmann@21013
   708
            val t' = subst_bound (Free (v', T), t);
wenzelm@20122
   709
            val ((vs, t''), (k', used'')) = strip_abs t' (k - 1, used');
wenzelm@20122
   710
          in (((v', T) :: vs, t''), (k', used'')) end
haftmann@20109
   711
      | strip_abs t (k, used) = (([], t), (k, used));
haftmann@20109
   712
    fun expand_eta [] t _ = ([], t)
haftmann@20109
   713
      | expand_eta (T::Ts) t used =
haftmann@20109
   714
          let
wenzelm@43326
   715
            val (v, used') = Name.variant "" used;
wenzelm@20122
   716
            val (vs, t') = expand_eta Ts (t $ Free (v, T)) used';
haftmann@20109
   717
          in ((v, T) :: vs, t') end;
haftmann@20109
   718
    val ((vs1, t'), (k', used')) = strip_abs t (k, used);
wenzelm@40844
   719
    val Ts = fst (chop k' (binder_types (fastype_of t')));
haftmann@20109
   720
    val (vs2, t'') = expand_eta Ts t' used';
haftmann@20109
   721
  in (vs1 @ vs2, t'') end;
haftmann@20109
   722
haftmann@20109
   723
clasohm@0
   724
(*Substitute new for free occurrences of old in a term*)
wenzelm@29256
   725
fun subst_free [] = I
clasohm@0
   726
  | subst_free pairs =
wenzelm@13000
   727
      let fun substf u =
haftmann@17314
   728
            case AList.lookup (op aconv) pairs u of
skalberg@15531
   729
                SOME u' => u'
skalberg@15531
   730
              | NONE => (case u of Abs(a,T,t) => Abs(a, T, substf t)
wenzelm@9536
   731
                                 | t$u' => substf t $ substf u'
wenzelm@9536
   732
                                 | _ => u)
clasohm@0
   733
      in  substf  end;
clasohm@0
   734
wenzelm@13000
   735
(*Abstraction of the term "body" over its occurrences of v,
clasohm@0
   736
    which must contain no loose bound variables.
clasohm@0
   737
  The resulting term is ready to become the body of an Abs.*)
wenzelm@16882
   738
fun abstract_over (v, body) =
wenzelm@16882
   739
  let
wenzelm@16990
   740
    fun abs lev tm =
wenzelm@16990
   741
      if v aconv tm then Bound lev
wenzelm@16882
   742
      else
wenzelm@16990
   743
        (case tm of
wenzelm@16990
   744
          Abs (a, T, t) => Abs (a, T, abs (lev + 1) t)
wenzelm@32020
   745
        | t $ u =>
wenzelm@32020
   746
            (abs lev t $ (abs lev u handle Same.SAME => u)
wenzelm@32020
   747
              handle Same.SAME => t $ abs lev u)
wenzelm@32020
   748
        | _ => raise Same.SAME);
wenzelm@32020
   749
  in abs 0 body handle Same.SAME => body end;
clasohm@0
   750
wenzelm@32198
   751
fun term_name (Const (x, _)) = Long_Name.base_name x
wenzelm@32198
   752
  | term_name (Free (x, _)) = x
wenzelm@32198
   753
  | term_name (Var ((x, _), _)) = x
wenzelm@32198
   754
  | term_name _ = Name.uu;
wenzelm@32198
   755
wenzelm@60404
   756
fun dependent_lambda_name (x, v) t =
wenzelm@60404
   757
  let val t' = abstract_over (v, t)
wenzelm@60404
   758
  in if is_dependent t' then Abs (if x = "" then term_name v else x, fastype_of v, t') else t end;
wenzelm@60404
   759
wenzelm@32198
   760
fun lambda_name (x, v) t =
wenzelm@32198
   761
  Abs (if x = "" then term_name v else x, fastype_of v, abstract_over (v, t));
wenzelm@32198
   762
wenzelm@32198
   763
fun lambda v t = lambda_name ("", v) t;
clasohm@0
   764
wenzelm@44241
   765
fun absfree (a, T) body = Abs (a, T, abstract_over (Free (a, T), body));
wenzelm@44241
   766
fun absdummy T body = Abs (Name.uu_, T, body);
clasohm@0
   767
wenzelm@16678
   768
(*Replace the ATOMIC term ti by ui;    inst = [(t1,u1), ..., (tn,un)].
clasohm@0
   769
  A simultaneous substitution:  [ (a,b), (b,a) ] swaps a and b.  *)
wenzelm@16678
   770
fun subst_atomic [] tm = tm
wenzelm@16678
   771
  | subst_atomic inst tm =
wenzelm@16678
   772
      let
wenzelm@16678
   773
        fun subst (Abs (a, T, body)) = Abs (a, T, subst body)
wenzelm@16678
   774
          | subst (t $ u) = subst t $ subst u
wenzelm@18942
   775
          | subst t = the_default t (AList.lookup (op aconv) inst t);
wenzelm@16678
   776
      in subst tm end;
clasohm@0
   777
wenzelm@16678
   778
(*Replace the ATOMIC type Ti by Ui;    inst = [(T1,U1), ..., (Tn,Un)].*)
wenzelm@16678
   779
fun typ_subst_atomic [] ty = ty
wenzelm@16678
   780
  | typ_subst_atomic inst ty =
wenzelm@16678
   781
      let
wenzelm@16678
   782
        fun subst (Type (a, Ts)) = Type (a, map subst Ts)
wenzelm@18942
   783
          | subst T = the_default T (AList.lookup (op = : typ * typ -> bool) inst T);
wenzelm@16678
   784
      in subst ty end;
berghofe@15797
   785
wenzelm@16678
   786
fun subst_atomic_types [] tm = tm
wenzelm@20548
   787
  | subst_atomic_types inst tm = map_types (typ_subst_atomic inst) tm;
wenzelm@16678
   788
wenzelm@16678
   789
fun typ_subst_TVars [] ty = ty
wenzelm@16678
   790
  | typ_subst_TVars inst ty =
wenzelm@16678
   791
      let
wenzelm@16678
   792
        fun subst (Type (a, Ts)) = Type (a, map subst Ts)
wenzelm@18942
   793
          | subst (T as TVar (xi, _)) = the_default T (AList.lookup (op =) inst xi)
wenzelm@16678
   794
          | subst T = T;
wenzelm@16678
   795
      in subst ty end;
clasohm@0
   796
wenzelm@16678
   797
fun subst_TVars [] tm = tm
wenzelm@20548
   798
  | subst_TVars inst tm = map_types (typ_subst_TVars inst) tm;
clasohm@0
   799
wenzelm@16678
   800
fun subst_Vars [] tm = tm
wenzelm@16678
   801
  | subst_Vars inst tm =
wenzelm@16678
   802
      let
wenzelm@18942
   803
        fun subst (t as Var (xi, _)) = the_default t (AList.lookup (op =) inst xi)
wenzelm@16678
   804
          | subst (Abs (a, T, t)) = Abs (a, T, subst t)
wenzelm@16678
   805
          | subst (t $ u) = subst t $ subst u
wenzelm@16678
   806
          | subst t = t;
wenzelm@16678
   807
      in subst tm end;
clasohm@0
   808
wenzelm@16678
   809
fun subst_vars ([], []) tm = tm
wenzelm@16678
   810
  | subst_vars ([], inst) tm = subst_Vars inst tm
wenzelm@16678
   811
  | subst_vars (instT, inst) tm =
wenzelm@16678
   812
      let
wenzelm@16678
   813
        fun subst (Const (a, T)) = Const (a, typ_subst_TVars instT T)
wenzelm@16678
   814
          | subst (Free (a, T)) = Free (a, typ_subst_TVars instT T)
wenzelm@32784
   815
          | subst (Var (xi, T)) =
haftmann@17271
   816
              (case AList.lookup (op =) inst xi of
wenzelm@16678
   817
                NONE => Var (xi, typ_subst_TVars instT T)
wenzelm@16678
   818
              | SOME t => t)
wenzelm@16678
   819
          | subst (t as Bound _) = t
wenzelm@16678
   820
          | subst (Abs (a, T, t)) = Abs (a, typ_subst_TVars instT T, subst t)
wenzelm@16678
   821
          | subst (t $ u) = subst t $ subst u;
wenzelm@16678
   822
      in subst tm end;
clasohm@0
   823
wenzelm@25050
   824
fun close_schematic_term t =
wenzelm@25050
   825
  let
wenzelm@56243
   826
    val extra_types = map (fn v => Const ("Pure.type", itselfT (TVar v))) (hidden_polymorphism t);
wenzelm@30285
   827
    val extra_terms = map Var (add_vars t []);
wenzelm@30285
   828
  in fold lambda (extra_terms @ extra_types) t end;
wenzelm@25050
   829
wenzelm@25050
   830
clasohm@0
   831
paulson@15573
   832
(** Identifying first-order terms **)
paulson@15573
   833
wenzelm@20199
   834
(*Differs from proofterm/is_fun in its treatment of TVar*)
wenzelm@29256
   835
fun is_funtype (Type ("fun", [_, _])) = true
wenzelm@20199
   836
  | is_funtype _ = false;
wenzelm@20199
   837
paulson@15573
   838
(*Argument Ts is a reverse list of binder types, needed if term t contains Bound vars*)
wenzelm@29256
   839
fun has_not_funtype Ts t = not (is_funtype (fastype_of1 (Ts, t)));
paulson@15573
   840
wenzelm@16537
   841
(*First order means in all terms of the form f(t1,...,tn) no argument has a
paulson@16589
   842
  function type. The supplied quantifiers are excluded: their argument always
paulson@16589
   843
  has a function type through a recursive call into its body.*)
wenzelm@16667
   844
fun is_first_order quants =
paulson@16589
   845
  let fun first_order1 Ts (Abs (_,T,body)) = first_order1 (T::Ts) body
wenzelm@16667
   846
        | first_order1 Ts (Const(q,_) $ Abs(a,T,body)) =
wenzelm@20664
   847
            member (op =) quants q  andalso   (*it is a known quantifier*)
paulson@16589
   848
            not (is_funtype T)   andalso first_order1 (T::Ts) body
wenzelm@16667
   849
        | first_order1 Ts t =
wenzelm@16667
   850
            case strip_comb t of
wenzelm@16667
   851
                 (Var _, ts) => forall (first_order1 Ts andf has_not_funtype Ts) ts
wenzelm@16667
   852
               | (Free _, ts) => forall (first_order1 Ts andf has_not_funtype Ts) ts
wenzelm@16667
   853
               | (Const _, ts) => forall (first_order1 Ts andf has_not_funtype Ts) ts
wenzelm@16667
   854
               | (Bound _, ts) => forall (first_order1 Ts andf has_not_funtype Ts) ts
wenzelm@16667
   855
               | (Abs _, ts) => false (*not in beta-normal form*)
wenzelm@16667
   856
               | _ => error "first_order: unexpected case"
paulson@16589
   857
    in  first_order1 []  end;
paulson@15573
   858
wenzelm@16710
   859
wenzelm@16990
   860
(* maximum index of typs and terms *)
clasohm@0
   861
wenzelm@16710
   862
fun maxidx_typ (TVar ((_, j), _)) i = Int.max (i, j)
wenzelm@16710
   863
  | maxidx_typ (Type (_, Ts)) i = maxidx_typs Ts i
wenzelm@16710
   864
  | maxidx_typ (TFree _) i = i
wenzelm@16710
   865
and maxidx_typs [] i = i
wenzelm@16710
   866
  | maxidx_typs (T :: Ts) i = maxidx_typs Ts (maxidx_typ T i);
clasohm@0
   867
wenzelm@16710
   868
fun maxidx_term (Var ((_, j), T)) i = maxidx_typ T (Int.max (i, j))
wenzelm@16710
   869
  | maxidx_term (Const (_, T)) i = maxidx_typ T i
wenzelm@16710
   870
  | maxidx_term (Free (_, T)) i = maxidx_typ T i
wenzelm@16710
   871
  | maxidx_term (Bound _) i = i
wenzelm@16710
   872
  | maxidx_term (Abs (_, T, t)) i = maxidx_term t (maxidx_typ T i)
wenzelm@16710
   873
  | maxidx_term (t $ u) i = maxidx_term u (maxidx_term t i);
clasohm@0
   874
wenzelm@16710
   875
fun maxidx_of_typ T = maxidx_typ T ~1;
wenzelm@16710
   876
fun maxidx_of_typs Ts = maxidx_typs Ts ~1;
wenzelm@16710
   877
fun maxidx_of_term t = maxidx_term t ~1;
berghofe@13665
   878
clasohm@0
   879
clasohm@0
   880
wenzelm@29270
   881
(** misc syntax operations **)
clasohm@0
   882
wenzelm@19909
   883
(* substructure *)
wenzelm@4017
   884
wenzelm@61248
   885
fun fold_subtypes f =
wenzelm@61248
   886
  let
wenzelm@61248
   887
    fun iter ty =
wenzelm@61248
   888
      (case ty of Type (_, Ts) => f ty #> fold iter Ts | _ => f ty);
wenzelm@61248
   889
  in iter end;
wenzelm@61248
   890
wenzelm@19909
   891
fun exists_subtype P =
wenzelm@19909
   892
  let
wenzelm@19909
   893
    fun ex ty = P ty orelse
wenzelm@19909
   894
      (case ty of Type (_, Ts) => exists ex Ts | _ => false);
wenzelm@19909
   895
  in ex end;
nipkow@13646
   896
wenzelm@20531
   897
fun exists_type P =
wenzelm@20531
   898
  let
wenzelm@20531
   899
    fun ex (Const (_, T)) = P T
wenzelm@20531
   900
      | ex (Free (_, T)) = P T
wenzelm@20531
   901
      | ex (Var (_, T)) = P T
wenzelm@20531
   902
      | ex (Bound _) = false
wenzelm@20531
   903
      | ex (Abs (_, T, t)) = P T orelse ex t
wenzelm@20531
   904
      | ex (t $ u) = ex t orelse ex u;
wenzelm@20531
   905
  in ex end;
wenzelm@20531
   906
wenzelm@16943
   907
fun exists_subterm P =
wenzelm@16943
   908
  let
wenzelm@16943
   909
    fun ex tm = P tm orelse
wenzelm@16943
   910
      (case tm of
wenzelm@16943
   911
        t $ u => ex t orelse ex u
wenzelm@16943
   912
      | Abs (_, _, t) => ex t
wenzelm@16943
   913
      | _ => false);
wenzelm@16943
   914
  in ex end;
obua@16108
   915
wenzelm@29270
   916
fun exists_Const P = exists_subterm (fn Const c => P c | _ => false);
wenzelm@29270
   917
wenzelm@63619
   918
wenzelm@63619
   919
(* contraction *)
wenzelm@63619
   920
wenzelm@63619
   921
fun could_beta_contract (Abs _ $ _) = true
wenzelm@63619
   922
  | could_beta_contract (t $ u) = could_beta_contract t orelse could_beta_contract u
wenzelm@63619
   923
  | could_beta_contract (Abs (_, _, b)) = could_beta_contract b
wenzelm@63619
   924
  | could_beta_contract _ = false;
wenzelm@63619
   925
wenzelm@63619
   926
fun could_eta_contract (Abs (_, _, _ $ Bound 0)) = true
wenzelm@63619
   927
  | could_eta_contract (Abs (_, _, b)) = could_eta_contract b
wenzelm@63619
   928
  | could_eta_contract (t $ u) = could_eta_contract t orelse could_eta_contract u
wenzelm@63619
   929
  | could_eta_contract _ = false;
wenzelm@63619
   930
wenzelm@63619
   931
fun could_beta_eta_contract (Abs _ $ _) = true
wenzelm@63619
   932
  | could_beta_eta_contract (Abs (_, _, _ $ Bound 0)) = true
wenzelm@63619
   933
  | could_beta_eta_contract (Abs (_, _, b)) = could_beta_eta_contract b
wenzelm@63619
   934
  | could_beta_eta_contract (t $ u) = could_beta_eta_contract t orelse could_beta_eta_contract u
wenzelm@63619
   935
  | could_beta_eta_contract _ = false;
wenzelm@24671
   936
wenzelm@24671
   937
wenzelm@20199
   938
(* dest abstraction *)
clasohm@0
   939
wenzelm@16678
   940
fun dest_abs (x, T, body) =
wenzelm@16678
   941
  let
wenzelm@16678
   942
    fun name_clash (Free (y, _)) = (x = y)
wenzelm@16678
   943
      | name_clash (t $ u) = name_clash t orelse name_clash u
wenzelm@16678
   944
      | name_clash (Abs (_, _, t)) = name_clash t
wenzelm@16678
   945
      | name_clash _ = false;
wenzelm@16678
   946
  in
wenzelm@43324
   947
    if name_clash body then
wenzelm@43324
   948
      dest_abs (singleton (Name.variant_list [x]) x, T, body)    (*potentially slow*)
wenzelm@16678
   949
    else (x, subst_bound (Free (x, T), body))
wenzelm@16678
   950
  end;
wenzelm@16678
   951
wenzelm@20160
   952
wenzelm@9536
   953
(* dummy patterns *)
wenzelm@9536
   954
wenzelm@56241
   955
fun dummy_pattern T = Const ("Pure.dummy_pattern", T);
wenzelm@45156
   956
val dummy = dummy_pattern dummyT;
wenzelm@45156
   957
val dummy_prop = dummy_pattern propT;
wenzelm@18253
   958
wenzelm@56241
   959
fun is_dummy_pattern (Const ("Pure.dummy_pattern", _)) = true
wenzelm@9536
   960
  | is_dummy_pattern _ = false;
wenzelm@9536
   961
wenzelm@9536
   962
fun no_dummy_patterns tm =
haftmann@16787
   963
  if not (fold_aterms (fn t => fn b => b orelse is_dummy_pattern t) tm false) then tm
wenzelm@9536
   964
  else raise TERM ("Illegal occurrence of '_' dummy pattern", [tm]);
wenzelm@9536
   965
wenzelm@56241
   966
fun free_dummy_patterns (Const ("Pure.dummy_pattern", T)) used =
wenzelm@43329
   967
      let val [x] = Name.invent used Name.uu 1
wenzelm@24733
   968
      in (Free (Name.internal x, T), Name.declare x used) end
wenzelm@24733
   969
  | free_dummy_patterns (Abs (x, T, b)) used =
wenzelm@24733
   970
      let val (b', used') = free_dummy_patterns b used
wenzelm@24733
   971
      in (Abs (x, T, b'), used') end
wenzelm@24733
   972
  | free_dummy_patterns (t $ u) used =
wenzelm@24733
   973
      let
wenzelm@24733
   974
        val (t', used') = free_dummy_patterns t used;
wenzelm@24733
   975
        val (u', used'') = free_dummy_patterns u used';
wenzelm@24733
   976
      in (t' $ u', used'') end
wenzelm@24733
   977
  | free_dummy_patterns a used = (a, used);
wenzelm@24733
   978
wenzelm@56241
   979
fun replace_dummy Ts (Const ("Pure.dummy_pattern", T)) i =
haftmann@33063
   980
      (list_comb (Var (("_dummy_", i), Ts ---> T), map_range Bound (length Ts)), i + 1)
wenzelm@24762
   981
  | replace_dummy Ts (Abs (x, T, t)) i =
wenzelm@24762
   982
      let val (t', i') = replace_dummy (T :: Ts) t i
wenzelm@24762
   983
      in (Abs (x, T, t'), i') end
wenzelm@24762
   984
  | replace_dummy Ts (t $ u) i =
wenzelm@24762
   985
      let
wenzelm@24762
   986
        val (t', i') = replace_dummy Ts t i;
wenzelm@24762
   987
        val (u', i'') = replace_dummy Ts u i';
wenzelm@24762
   988
      in (t' $ u', i'') end
wenzelm@24762
   989
  | replace_dummy _ a i = (a, i);
wenzelm@11903
   990
wenzelm@11903
   991
val replace_dummy_patterns = replace_dummy [];
wenzelm@9536
   992
wenzelm@45156
   993
fun show_dummy_patterns (Var (("_dummy_", _), T)) = dummy_pattern T
wenzelm@16035
   994
  | show_dummy_patterns (t $ u) = show_dummy_patterns t $ show_dummy_patterns u
wenzelm@16035
   995
  | show_dummy_patterns (Abs (x, T, t)) = Abs (x, T, show_dummy_patterns t)
wenzelm@16035
   996
  | show_dummy_patterns a = a;
wenzelm@16035
   997
wenzelm@13484
   998
wenzelm@20100
   999
(* display variables *)
wenzelm@20100
  1000
wenzelm@14786
  1001
fun string_of_vname (x, i) =
wenzelm@14786
  1002
  let
wenzelm@15986
  1003
    val idx = string_of_int i;
wenzelm@15986
  1004
    val dot =
wenzelm@15986
  1005
      (case rev (Symbol.explode x) of
wenzelm@62529
  1006
        _ :: "\<^sub>" :: _ => false
wenzelm@15986
  1007
      | c :: _ => Symbol.is_digit c
wenzelm@15986
  1008
      | _ => true);
wenzelm@14786
  1009
  in
wenzelm@38980
  1010
    if dot then "?" ^ x ^ "." ^ idx
wenzelm@38980
  1011
    else if i <> 0 then "?" ^ x ^ idx
wenzelm@38980
  1012
    else "?" ^ x
wenzelm@14786
  1013
  end;
wenzelm@14786
  1014
wenzelm@14786
  1015
fun string_of_vname' (x, ~1) = x
wenzelm@14786
  1016
  | string_of_vname' xi = string_of_vname xi;
wenzelm@14786
  1017
clasohm@1364
  1018
end;
clasohm@1364
  1019
wenzelm@40841
  1020
structure Basic_Term: BASIC_TERM = Term;
wenzelm@40841
  1021
open Basic_Term;