src/Pure/library.ML
author skalberg
Thu Mar 03 12:43:01 2005 +0100 (2005-03-03)
changeset 15570 8d8c70b41bab
parent 15531 08c8dad8e399
child 15670 963cd3f7976c
permissions -rw-r--r--
Move towards standard functions.
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(*  Title:      Pure/library.ML
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    ID:         $Id$
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    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
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    Author:     Markus Wenzel, TU Munich
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Basic library: functions, options, pairs, booleans, lists, integers,
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rational numbers, strings, lists as sets, association lists, generic
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tables, balanced trees, orders, current directory, misc.
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*)
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infix |> |>> |>>> ~~ \ \\ ins ins_string ins_int orf andf prefix upto downto
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  mem mem_int mem_string union union_int union_string inter inter_int
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  inter_string subset subset_int subset_string;
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infix 3 oo ooo oooo;
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signature LIBRARY =
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sig
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  (*functions*)
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  val curry: ('a * 'b -> 'c) -> 'a -> 'b -> 'c
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  val uncurry: ('a -> 'b -> 'c) -> 'a * 'b -> 'c
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  val I: 'a -> 'a
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  val K: 'a -> 'b -> 'a
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  val |> : 'a * ('a -> 'b) -> 'b
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  val |>> : ('a * 'b) * ('a -> 'c) -> 'c * 'b
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  val |>>> : ('a * 'b) * ('a -> 'c * 'd) -> 'c * ('b * 'd)
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  val apl: 'a * ('a * 'b -> 'c) -> 'b -> 'c
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  val apr: ('a * 'b -> 'c) * 'b -> 'a -> 'c
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  val funpow: int -> ('a -> 'a) -> 'a -> 'a
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  val oo: ('a -> 'b) * ('c -> 'd -> 'a) -> 'c -> 'd -> 'b
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  val ooo: ('a -> 'b) * ('c -> 'd -> 'e -> 'a) -> 'c -> 'd -> 'e -> 'b
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  val oooo: ('a -> 'b) * ('c -> 'd -> 'e -> 'f -> 'a) -> 'c -> 'd -> 'e -> 'f -> 'b
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  (*stamps*)
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  type stamp
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  val stamp: unit -> stamp
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  (*options*)
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  val is_none: 'a option -> bool
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  exception ERROR
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  val try: ('a -> 'b) -> 'a -> 'b option
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  val can: ('a -> 'b) -> 'a -> bool
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  datatype 'a result = Result of 'a | Exn of exn
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  val capture: ('a -> 'b) -> 'a -> 'b result
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  val release: 'a result -> 'a
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  val get_result: 'a result -> 'a option
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  val get_exn: 'a result -> exn option
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  (*pairs*)
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  val pair: 'a -> 'b -> 'a * 'b
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  val rpair: 'a -> 'b -> 'b * 'a
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  val fst: 'a * 'b -> 'a
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  val snd: 'a * 'b -> 'b
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  val eq_fst: (''a * 'b) * (''a * 'c) -> bool
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  val eq_snd: ('a * ''b) * ('c * ''b) -> bool
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  val swap: 'a * 'b -> 'b * 'a
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  val apfst: ('a -> 'b) -> 'a * 'c -> 'b * 'c
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  val apsnd: ('a -> 'b) -> 'c * 'a -> 'c * 'b
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  val pairself: ('a -> 'b) -> 'a * 'a -> 'b * 'b
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  (*booleans*)
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  val equal: ''a -> ''a -> bool
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  val not_equal: ''a -> ''a -> bool
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  val orf: ('a -> bool) * ('a -> bool) -> 'a -> bool
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  val andf: ('a -> bool) * ('a -> bool) -> 'a -> bool
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  val exists: ('a -> bool) -> 'a list -> bool
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  val forall: ('a -> bool) -> 'a list -> bool
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  val set: bool ref -> bool
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  val reset: bool ref -> bool
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  val toggle: bool ref -> bool
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  val change: 'a ref -> ('a -> 'a) -> unit
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  val setmp: 'a ref -> 'a -> ('b -> 'c) -> 'b -> 'c
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  val conditional: bool -> (unit -> unit) -> unit
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  (*lists*)
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  exception UnequalLengths
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  val cons: 'a -> 'a list -> 'a list
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  val single: 'a -> 'a list
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  val append: 'a list -> 'a list -> 'a list
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  val apply: ('a -> 'a) list -> 'a -> 'a
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  val foldr1: ('a * 'a -> 'a) -> 'a list -> 'a
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  val fold: ('a -> 'b -> 'b) -> 'a list -> 'b -> 'b
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  val fold_rev: ('a -> 'b -> 'b) -> 'a list -> 'b -> 'b
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  val foldl_map: ('a * 'b -> 'a * 'c) -> 'a * 'b list -> 'a * 'c list
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  val foldln: ('a * int -> 'b -> 'b) -> 'a list -> 'b -> 'b
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  val unflat: 'a list list -> 'b list -> 'b list list
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  val splitAt: int * 'a list -> 'a list * 'a list
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  val dropwhile: ('a -> bool) -> 'a list -> 'a list
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  val map_nth_elem: int -> ('a -> 'a) -> 'a list -> 'a list
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  val split_last: 'a list -> 'a list * 'a
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  val nth_update: 'a -> int * 'a list -> 'a list
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  val find_index: ('a -> bool) -> 'a list -> int
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  val find_index_eq: ''a -> ''a list -> int
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  val find_first: ('a -> bool) -> 'a list -> 'a option
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  val get_first: ('a -> 'b option) -> 'a list -> 'b option
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  val separate: 'a -> 'a list -> 'a list
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  val replicate: int -> 'a -> 'a list
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  val multiply: 'a list * 'a list list -> 'a list list
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  val product: 'a list -> 'b list -> ('a * 'b) list
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  val filter_out: ('a -> bool) -> 'a list -> 'a list
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  val map2: ('a * 'b -> 'c) -> 'a list * 'b list -> 'c list
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  val exists2: ('a * 'b -> bool) -> 'a list * 'b list -> bool
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  val forall2: ('a * 'b -> bool) -> 'a list * 'b list -> bool
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  val seq2: ('a * 'b -> unit) -> 'a list * 'b list -> unit
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  val ~~ : 'a list * 'b list -> ('a * 'b) list
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  val split_list: ('a * 'b) list -> 'a list * 'b list
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  val equal_lists: ('a * 'b -> bool) -> 'a list * 'b list -> bool
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  val prefix: ''a list * ''a list -> bool
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  val take_prefix: ('a -> bool) -> 'a list -> 'a list * 'a list
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  val take_suffix: ('a -> bool) -> 'a list -> 'a list * 'a list
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  val prefixes1: 'a list -> 'a list list
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  val suffixes1: 'a list -> 'a list list
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  (*integers*)
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  val gcd: int * int -> int
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  val lcm: int * int -> int
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  val inc: int ref -> int
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  val dec: int ref -> int
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  val upto: int * int -> int list
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  val downto: int * int -> int list
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  val downto0: int list * int -> bool
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  val radixpand: int * int -> int list
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  val radixstring: int * string * int -> string
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  val string_of_int: int -> string
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  val string_of_indexname: string * int -> string
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  val read_radixint: int * string list -> int * string list
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  val read_int: string list -> int * string list
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  val oct_char: string -> string
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  (*rational numbers*)
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  type rat
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  exception RAT of string
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  val rep_rat: rat -> int * int
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  val ratadd: rat * rat -> rat
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  val ratmul: rat * rat -> rat
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  val ratinv: rat -> rat
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  val int_ratdiv: int * int -> rat
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  val ratneg: rat -> rat
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  val rat_of_int: int -> rat
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  (*strings*)
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  val nth_elem_string: int * string -> string
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  val foldl_string: ('a * string -> 'a) -> 'a * string -> 'a
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  val exists_string: (string -> bool) -> string -> bool
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  val enclose: string -> string -> string -> string
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  val unenclose: string -> string
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  val quote: string -> string
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  val space_implode: string -> string list -> string
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  val commas: string list -> string
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  val commas_quote: string list -> string
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  val cat_lines: string list -> string
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  val space_explode: string -> string -> string list
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  val split_lines: string -> string list
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  val prefix_lines: string -> string -> string
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  val untabify: string list -> string list
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  val suffix: string -> string -> string
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  val unsuffix: string -> string -> string
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  val unprefix: string -> string -> string
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  val replicate_string: int -> string -> string
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  val translate_string: (string -> string) -> string -> string
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  (*lists as sets*)
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  val mem: ''a * ''a list -> bool
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  val mem_int: int * int list -> bool
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  val mem_string: string * string list -> bool
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  val gen_mem: ('a * 'b -> bool) -> 'a * 'b list -> bool
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  val ins: ''a * ''a list -> ''a list
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  val ins_int: int * int list -> int list
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  val ins_string: string * string list -> string list
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  val gen_ins: ('a * 'a -> bool) -> 'a * 'a list -> 'a list
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  val union: ''a list * ''a list -> ''a list
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  val union_int: int list * int list -> int list
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  val union_string: string list * string list -> string list
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  val gen_union: ('a * 'a -> bool) -> 'a list * 'a list -> 'a list
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  val gen_inter: ('a * 'b -> bool) -> 'a list * 'b list -> 'a list
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  val inter: ''a list * ''a list -> ''a list
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  val inter_int: int list * int list -> int list
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  val inter_string: string list * string list -> string list
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  val subset: ''a list * ''a list -> bool
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  val subset_int: int list * int list -> bool
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  val subset_string: string list * string list -> bool
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  val eq_set: ''a list * ''a list -> bool
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  val eq_set_string: string list * string list -> bool
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  val gen_subset: ('a * 'b -> bool) -> 'a list * 'b list -> bool
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  val \ : ''a list * ''a -> ''a list
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  val \\ : ''a list * ''a list -> ''a list
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  val gen_rem: ('a * 'b -> bool) -> 'a list * 'b -> 'a list
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  val gen_rems: ('a * 'b -> bool) -> 'a list * 'b list -> 'a list
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  val gen_distinct: ('a * 'a -> bool) -> 'a list -> 'a list
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  val distinct: ''a list -> ''a list
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  val findrep: ''a list -> ''a list
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  val gen_duplicates: ('a * 'a -> bool) -> 'a list -> 'a list
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  val duplicates: ''a list -> ''a list
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  (*association lists*)
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  val assoc: (''a * 'b) list * ''a -> 'b option
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  val assoc_int: (int * 'a) list * int -> 'a option
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  val assoc_string: (string * 'a) list * string -> 'a option
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  val assoc_string_int: ((string * int) * 'a) list * (string * int) -> 'a option
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  val assocs: (''a * 'b list) list -> ''a -> 'b list
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  val assoc2: (''a * (''b * 'c) list) list * (''a * ''b) -> 'c option
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  val gen_assoc: ('a * 'b -> bool) -> ('b * 'c) list * 'a -> 'c option
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  val overwrite: (''a * 'b) list * (''a * 'b) -> (''a * 'b) list
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  val gen_overwrite: ('a * 'a -> bool) -> ('a * 'b) list * ('a * 'b) -> ('a * 'b) list
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  (*lists as tables*)
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  val gen_merge_lists: ('a * 'a -> bool) -> 'a list -> 'a list -> 'a list
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  val gen_merge_lists': ('a * 'a -> bool) -> 'a list -> 'a list -> 'a list
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  val merge_lists: ''a list -> ''a list -> ''a list
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  val merge_lists': ''a list -> ''a list -> ''a list
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  val merge_alists: (''a * 'b) list -> (''a * 'b) list -> (''a * 'b) list
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  val merge_alists': (''a * 'b) list -> (''a * 'b) list -> (''a * 'b) list
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  (*balanced trees*)
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  exception Balance
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  val fold_bal: ('a * 'a -> 'a) -> 'a list -> 'a
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  val access_bal: ('a -> 'a) * ('a -> 'a) * 'a -> int -> int -> 'a
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  val accesses_bal: ('a -> 'a) * ('a -> 'a) * 'a -> int -> 'a list
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  (*orders*)
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  val rev_order: order -> order
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  val make_ord: ('a * 'a -> bool) -> 'a * 'a -> order
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  val int_ord: int * int -> order
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  val string_ord: string * string -> order
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  val prod_ord: ('a * 'b -> order) -> ('c * 'd -> order) -> ('a * 'c) * ('b * 'd) -> order
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  val dict_ord: ('a * 'b -> order) -> 'a list * 'b list -> order
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  val list_ord: ('a * 'b -> order) -> 'a list * 'b list -> order
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  val sort: ('a * 'a -> order) -> 'a list -> 'a list
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  val sort_strings: string list -> string list
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  val sort_wrt: ('a -> string) -> 'a list -> 'a list
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  val unique_strings: string list -> string list
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  (*random numbers*)
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  exception RANDOM
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  val random: unit -> real
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  val random_range: int -> int -> int
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  val one_of: 'a list -> 'a
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  val frequency: (int * 'a) list -> 'a
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  (*current directory*)
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  val cd: string -> unit
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  val pwd: unit -> string
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  (*misc*)
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  val make_keylist: ('a -> 'b) -> 'a list -> ('a * 'b) list
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  val keyfilter: ('a * ''b) list -> ''b -> 'a list
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  val partition_eq: ('a * 'a -> bool) -> 'a list -> 'a list list
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  val partition_list: (int -> 'a -> bool) -> int -> int -> 'a list -> 'a list list
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  val gensym: string -> string
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  val scanwords: (string -> bool) -> string list -> string list
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end;
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signature LIBRARY_CLOSED =
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sig
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  include LIBRARY
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  val the: 'a option -> 'a
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  val if_none: 'a option -> 'a -> 'a
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  val is_some: 'a option -> bool
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  val apsome: ('a -> 'b) -> 'a option -> 'b option
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  val rev_append: 'a list -> 'a list -> 'a list
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  val foldl: ('a * 'b -> 'a) -> 'a * 'b list -> 'a
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  val foldr: ('a * 'b -> 'b) -> 'a list * 'b -> 'b
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  val take: int * 'a list -> 'a list
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  val drop: int * 'a list -> 'a list
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  val nth_elem: int * 'a list -> 'a
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  val last_elem: 'a list -> 'a
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  val flat: 'a list list -> 'a list
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  val seq: ('a -> unit) -> 'a list -> unit
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  val partition: ('a -> bool) -> 'a list -> 'a list * 'a list
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  val filter: ('a -> bool) -> 'a list -> 'a list
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  val mapfilter: ('a -> 'b option) -> 'a list -> 'b list
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end;
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structure Library: LIBRARY_CLOSED =
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struct
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(** functions **)
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(*handy combinators*)
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fun curry f x y = f (x, y);
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fun uncurry f (x, y) = f x y;
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fun I x = x;
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fun K x y = x;
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(*reverse apply*)
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fun (x |> f) = f x;
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fun ((x, y) |>> f) = (f x, y);
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fun ((x, y) |>>> f) = let val (x', z) = f x in (x', (y, z)) end;
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(*application of (infix) operator to its left or right argument*)
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fun apl (x, f) y = f (x, y);
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   295
fun apr (f, y) x = f (x, y);
clasohm@0
   296
wenzelm@233
   297
(*function exponentiation: f(...(f x)...) with n applications of f*)
wenzelm@233
   298
fun funpow n f x =
wenzelm@233
   299
  let fun rep (0, x) = x
wenzelm@233
   300
        | rep (n, x) = rep (n - 1, f x)
wenzelm@233
   301
  in rep (n, x) end;
wenzelm@160
   302
wenzelm@5893
   303
(*concatenation: 2 and 3 args*)
wenzelm@5893
   304
fun (f oo g) x y = f (g x y);
wenzelm@5893
   305
fun (f ooo g) x y z = f (g x y z);
wenzelm@6510
   306
fun (f oooo g) x y z w = f (g x y z w);
wenzelm@6510
   307
wenzelm@160
   308
wenzelm@160
   309
wenzelm@2471
   310
(** stamps **)
wenzelm@2471
   311
wenzelm@2471
   312
type stamp = unit ref;
wenzelm@2471
   313
val stamp: unit -> stamp = ref;
wenzelm@2471
   314
wenzelm@2471
   315
wenzelm@2471
   316
wenzelm@233
   317
(** options **)
clasohm@0
   318
skalberg@15570
   319
val the = valOf;
clasohm@0
   320
wenzelm@4212
   321
(*strict!*)
skalberg@15531
   322
fun if_none opt a = getOpt(opt,a);
wenzelm@255
   323
skalberg@15570
   324
val is_some = isSome;
clasohm@0
   325
skalberg@15570
   326
fun is_none opt = not (isSome opt);
clasohm@0
   327
skalberg@15570
   328
val apsome = Option.map;
clasohm@0
   329
wenzelm@6959
   330
wenzelm@6959
   331
(* exception handling *)
wenzelm@6959
   332
wenzelm@6959
   333
exception ERROR;
wenzelm@6959
   334
skalberg@15531
   335
fun try f x = SOME (f x)
skalberg@15531
   336
  handle Interrupt => raise Interrupt | ERROR => raise ERROR | _ => NONE;
wenzelm@6959
   337
wenzelm@6959
   338
fun can f x = is_some (try f x);
wenzelm@4139
   339
wenzelm@4139
   340
wenzelm@14868
   341
datatype 'a result =
wenzelm@14868
   342
  Result of 'a |
wenzelm@14868
   343
  Exn of exn;
wenzelm@14868
   344
wenzelm@14868
   345
fun capture f x = Result (f x) handle e => Exn e;
wenzelm@14868
   346
wenzelm@14868
   347
fun release (Result y) = y
wenzelm@14868
   348
  | release (Exn e) = raise e;
wenzelm@14868
   349
skalberg@15531
   350
fun get_result (Result x) = SOME x
skalberg@15531
   351
  | get_result _ = NONE;
wenzelm@14868
   352
skalberg@15531
   353
fun get_exn (Exn exn) = SOME exn
skalberg@15531
   354
  | get_exn _ = NONE;
wenzelm@14868
   355
wenzelm@14868
   356
wenzelm@4139
   357
wenzelm@233
   358
(** pairs **)
wenzelm@233
   359
wenzelm@233
   360
fun pair x y = (x, y);
wenzelm@233
   361
fun rpair x y = (y, x);
wenzelm@233
   362
wenzelm@233
   363
fun fst (x, y) = x;
wenzelm@233
   364
fun snd (x, y) = y;
wenzelm@233
   365
wenzelm@233
   366
fun eq_fst ((x1, _), (x2, _)) = x1 = x2;
wenzelm@233
   367
fun eq_snd ((_, y1), (_, y2)) = y1 = y2;
wenzelm@233
   368
wenzelm@233
   369
fun swap (x, y) = (y, x);
wenzelm@233
   370
wenzelm@4212
   371
(*apply function to components*)
wenzelm@233
   372
fun apfst f (x, y) = (f x, y);
wenzelm@233
   373
fun apsnd f (x, y) = (x, f y);
wenzelm@4212
   374
fun pairself f (x, y) = (f x, f y);
wenzelm@233
   375
wenzelm@233
   376
wenzelm@233
   377
wenzelm@233
   378
(** booleans **)
wenzelm@233
   379
wenzelm@233
   380
(* equality *)
wenzelm@233
   381
wenzelm@233
   382
fun equal x y = x = y;
wenzelm@233
   383
fun not_equal x y = x <> y;
wenzelm@233
   384
wenzelm@233
   385
wenzelm@233
   386
(* operators for combining predicates *)
wenzelm@233
   387
paulson@2175
   388
fun (p orf q) = fn x => p x orelse q x;
paulson@2175
   389
fun (p andf q) = fn x => p x andalso q x;
wenzelm@233
   390
wenzelm@233
   391
wenzelm@233
   392
(* predicates on lists *)
wenzelm@233
   393
wenzelm@233
   394
(*exists pred [x1, ..., xn] ===> pred x1 orelse ... orelse pred xn*)
wenzelm@233
   395
fun exists (pred: 'a -> bool) : 'a list -> bool =
wenzelm@233
   396
  let fun boolf [] = false
wenzelm@233
   397
        | boolf (x :: xs) = pred x orelse boolf xs
wenzelm@233
   398
  in boolf end;
wenzelm@233
   399
wenzelm@233
   400
(*forall pred [x1, ..., xn] ===> pred x1 andalso ... andalso pred xn*)
wenzelm@233
   401
fun forall (pred: 'a -> bool) : 'a list -> bool =
wenzelm@233
   402
  let fun boolf [] = true
wenzelm@233
   403
        | boolf (x :: xs) = pred x andalso boolf xs
wenzelm@233
   404
  in boolf end;
clasohm@0
   405
wenzelm@233
   406
wenzelm@380
   407
(* flags *)
wenzelm@380
   408
wenzelm@380
   409
fun set flag = (flag := true; true);
wenzelm@380
   410
fun reset flag = (flag := false; false);
wenzelm@380
   411
fun toggle flag = (flag := not (! flag); ! flag);
wenzelm@380
   412
wenzelm@9118
   413
fun change r f = r := f (! r);
wenzelm@9118
   414
wenzelm@14826
   415
(*temporarily set flag, handling exceptions*)
wenzelm@2978
   416
fun setmp flag value f x =
wenzelm@2958
   417
  let
wenzelm@2958
   418
    val orig_value = ! flag;
wenzelm@2958
   419
    fun return y = (flag := orig_value; y);
wenzelm@2958
   420
  in
wenzelm@2958
   421
    flag := value;
wenzelm@2958
   422
    return (f x handle exn => (return (); raise exn))
wenzelm@2958
   423
  end;
wenzelm@2958
   424
wenzelm@380
   425
wenzelm@11853
   426
(* conditional execution *)
wenzelm@11853
   427
wenzelm@11853
   428
fun conditional b f = if b then f () else ();
wenzelm@11853
   429
wenzelm@11853
   430
wenzelm@233
   431
wenzelm@233
   432
(** lists **)
wenzelm@233
   433
skalberg@15570
   434
exception UnequalLengths;
wenzelm@233
   435
wenzelm@233
   436
fun cons x xs = x :: xs;
wenzelm@5285
   437
fun single x = [x];
wenzelm@233
   438
wenzelm@4629
   439
fun append xs ys = xs @ ys;
wenzelm@4629
   440
berghofe@13794
   441
(* tail recursive version *)
skalberg@15531
   442
fun rev_append xs ys = List.revAppend(xs,ys);
berghofe@13794
   443
wenzelm@5904
   444
fun apply [] x = x
wenzelm@5904
   445
  | apply (f :: fs) x = apply fs (f x);
wenzelm@5904
   446
wenzelm@233
   447
wenzelm@233
   448
(* fold *)
wenzelm@233
   449
wenzelm@233
   450
(*the following versions of fold are designed to fit nicely with infixes*)
clasohm@0
   451
wenzelm@233
   452
(*  (op @) (e, [x1, ..., xn])  ===>  ((e @ x1) @ x2) ... @ xn
wenzelm@233
   453
    for operators that associate to the left (TAIL RECURSIVE)*)
wenzelm@233
   454
fun foldl (f: 'a * 'b -> 'a) : 'a * 'b list -> 'a =
wenzelm@233
   455
  let fun itl (e, [])  = e
wenzelm@233
   456
        | itl (e, a::l) = itl (f(e, a), l)
wenzelm@233
   457
  in  itl end;
wenzelm@233
   458
wenzelm@233
   459
(*  (op @) ([x1, ..., xn], e)  ===>   x1 @ (x2 ... @ (xn @ e))
wenzelm@233
   460
    for operators that associate to the right (not tail recursive)*)
wenzelm@233
   461
fun foldr f (l, e) =
wenzelm@233
   462
  let fun itr [] = e
wenzelm@233
   463
        | itr (a::l) = f(a, itr l)
wenzelm@233
   464
  in  itr l  end;
wenzelm@233
   465
wenzelm@233
   466
(*  (op @) [x1, ..., xn]  ===>   x1 @ (x2 ... @ (x[n-1] @ xn))
wenzelm@233
   467
    for n > 0, operators that associate to the right (not tail recursive)*)
wenzelm@233
   468
fun foldr1 f l =
wenzelm@4181
   469
  let fun itr [x] = x
wenzelm@233
   470
        | itr (x::l) = f(x, itr l)
wenzelm@233
   471
  in  itr l  end;
wenzelm@233
   472
wenzelm@14792
   473
fun fold f xs y = foldl (fn (y', x) => f x y') (y, xs);
wenzelm@15035
   474
fun fold_rev f xs y = foldr (fn (x, y') => f x y') (xs, y);
wenzelm@14792
   475
wenzelm@4956
   476
fun foldl_map _ (x, []) = (x, [])
wenzelm@4956
   477
  | foldl_map f (x, y :: ys) =
wenzelm@4956
   478
      let
wenzelm@4956
   479
        val (x', y') = f (x, y);
wenzelm@4956
   480
        val (x'', ys') = foldl_map f (x', ys);
wenzelm@4956
   481
      in (x'', y' :: ys') end;
wenzelm@4956
   482
oheimb@11002
   483
fun foldln f xs e = fst (foldl (fn ((e,i), x) => (f (x,i) e, i+1)) ((e,1),xs));
wenzelm@233
   484
wenzelm@233
   485
(* basic list functions *)
wenzelm@233
   486
wenzelm@233
   487
(*take the first n elements from a list*)
wenzelm@233
   488
fun take (n, []) = []
wenzelm@233
   489
  | take (n, x :: xs) =
wenzelm@233
   490
      if n > 0 then x :: take (n - 1, xs) else [];
wenzelm@233
   491
wenzelm@233
   492
(*drop the first n elements from a list*)
wenzelm@233
   493
fun drop (n, []) = []
wenzelm@233
   494
  | drop (n, x :: xs) =
wenzelm@233
   495
      if n > 0 then drop (n - 1, xs) else x :: xs;
clasohm@0
   496
nipkow@13629
   497
fun splitAt(n,[]) = ([],[])
nipkow@13629
   498
  | splitAt(n,xs as x::ys) =
nipkow@13629
   499
      if n>0 then let val (ps,qs) = splitAt(n-1,ys) in (x::ps,qs) end
nipkow@13629
   500
      else ([],xs)
nipkow@13629
   501
nipkow@4713
   502
fun dropwhile P [] = []
nipkow@4713
   503
  | dropwhile P (ys as x::xs) = if P x then dropwhile P xs else ys;
nipkow@4713
   504
wenzelm@233
   505
(*return nth element of a list, where 0 designates the first element;
wenzelm@233
   506
  raise EXCEPTION if list too short*)
skalberg@15570
   507
fun nth_elem (i,xs) = List.nth(xs,i);
wenzelm@233
   508
wenzelm@11773
   509
fun map_nth_elem 0 f (x :: xs) = f x :: xs
wenzelm@11773
   510
  | map_nth_elem n f (x :: xs) = x :: map_nth_elem (n - 1) f xs
skalberg@15570
   511
  | map_nth_elem _ _ [] = raise Subscript;
wenzelm@11773
   512
wenzelm@233
   513
(*last element of a list*)
skalberg@15570
   514
val last_elem = List.last;
wenzelm@233
   515
wenzelm@3762
   516
(*rear decomposition*)
skalberg@15570
   517
fun split_last [] = raise Empty
wenzelm@3762
   518
  | split_last [x] = ([], x)
wenzelm@3762
   519
  | split_last (x :: xs) = apfst (cons x) (split_last xs);
wenzelm@3762
   520
wenzelm@4893
   521
(*update nth element*)
nipkow@13629
   522
fun nth_update x n_xs =
nipkow@13629
   523
    (case splitAt n_xs of
skalberg@15570
   524
      (_,[]) => raise Subscript
nipkow@13629
   525
    | (prfx, _ :: sffx') => prfx @ (x :: sffx'))
wenzelm@4893
   526
wenzelm@4212
   527
(*find the position of an element in a list*)
wenzelm@4212
   528
fun find_index pred =
wenzelm@4212
   529
  let fun find _ [] = ~1
wenzelm@4212
   530
        | find n (x :: xs) = if pred x then n else find (n + 1) xs;
wenzelm@4212
   531
  in find 0 end;
wenzelm@3762
   532
wenzelm@4224
   533
fun find_index_eq x = find_index (equal x);
wenzelm@4212
   534
wenzelm@4212
   535
(*find first element satisfying predicate*)
skalberg@15531
   536
fun find_first _ [] = NONE
wenzelm@4212
   537
  | find_first pred (x :: xs) =
skalberg@15531
   538
      if pred x then SOME x else find_first pred xs;
wenzelm@233
   539
wenzelm@4916
   540
(*get first element by lookup function*)
skalberg@15531
   541
fun get_first _ [] = NONE
wenzelm@4916
   542
  | get_first f (x :: xs) =
wenzelm@4916
   543
      (case f x of
skalberg@15531
   544
        NONE => get_first f xs
wenzelm@4916
   545
      | some => some);
wenzelm@4916
   546
wenzelm@233
   547
(*flatten a list of lists to a list*)
skalberg@15531
   548
val flat = List.concat;
wenzelm@233
   549
wenzelm@12136
   550
fun unflat (xs :: xss) ys =
nipkow@13629
   551
      let val (ps,qs) = splitAt(length xs,ys)
nipkow@13629
   552
      in ps :: unflat xss qs end
wenzelm@12136
   553
  | unflat [] [] = []
skalberg@15570
   554
  | unflat _ _ = raise UnequalLengths;
wenzelm@12136
   555
wenzelm@233
   556
(*like Lisp's MAPC -- seq proc [x1, ..., xn] evaluates
wenzelm@233
   557
  (proc x1; ...; proc xn) for side effects*)
skalberg@15570
   558
val seq = List.app;
wenzelm@233
   559
wenzelm@233
   560
(*separate s [x1, x2, ..., xn]  ===>  [x1, s, x2, s, ..., s, xn]*)
wenzelm@233
   561
fun separate s (x :: (xs as _ :: _)) = x :: s :: separate s xs
wenzelm@233
   562
  | separate _ xs = xs;
wenzelm@233
   563
wenzelm@233
   564
(*make the list [x, x, ..., x] of length n*)
wenzelm@233
   565
fun replicate n (x: 'a) : 'a list =
wenzelm@233
   566
  let fun rep (0, xs) = xs
wenzelm@233
   567
        | rep (n, xs) = rep (n - 1, x :: xs)
wenzelm@233
   568
  in
skalberg@15570
   569
    if n < 0 then raise Subscript
wenzelm@233
   570
    else rep (n, [])
wenzelm@233
   571
  end;
wenzelm@233
   572
wenzelm@14926
   573
fun translate_string f = String.translate (f o String.str);
wenzelm@14926
   574
wenzelm@4248
   575
(*multiply [a, b, c, ...] * [xs, ys, zs, ...]*)
wenzelm@4248
   576
fun multiply ([], _) = []
wenzelm@4248
   577
  | multiply (x :: xs, yss) = map (cons x) yss @ multiply (xs, yss);
wenzelm@4248
   578
wenzelm@14792
   579
(*direct product*)
wenzelm@14792
   580
fun product _ [] = []
wenzelm@14792
   581
  | product [] _ = []
wenzelm@14792
   582
  | product (x :: xs) ys = map (pair x) ys @ product xs ys;
wenzelm@14792
   583
wenzelm@233
   584
wenzelm@233
   585
(* filter *)
wenzelm@233
   586
wenzelm@233
   587
(*copy the list preserving elements that satisfy the predicate*)
skalberg@15531
   588
val filter = List.filter;
clasohm@0
   589
clasohm@0
   590
fun filter_out f = filter (not o f);
clasohm@0
   591
skalberg@15570
   592
val mapfilter = List.mapPartial;
wenzelm@233
   593
wenzelm@233
   594
wenzelm@233
   595
(* lists of pairs *)
wenzelm@233
   596
skalberg@15570
   597
exception UnequalLengths;
skalberg@15570
   598
wenzelm@380
   599
fun map2 _ ([], []) = []
wenzelm@380
   600
  | map2 f (x :: xs, y :: ys) = (f (x, y) :: map2 f (xs, ys))
skalberg@15570
   601
  | map2 _ _ = raise UnequalLengths;
wenzelm@380
   602
wenzelm@380
   603
fun exists2 _ ([], []) = false
wenzelm@380
   604
  | exists2 pred (x :: xs, y :: ys) = pred (x, y) orelse exists2 pred (xs, ys)
skalberg@15570
   605
  | exists2 _ _ = raise UnequalLengths;
wenzelm@380
   606
wenzelm@380
   607
fun forall2 _ ([], []) = true
wenzelm@380
   608
  | forall2 pred (x :: xs, y :: ys) = pred (x, y) andalso forall2 pred (xs, ys)
skalberg@15570
   609
  | forall2 _ _ = raise UnequalLengths;
wenzelm@380
   610
wenzelm@4956
   611
fun seq2 _ ([], []) = ()
wenzelm@4956
   612
  | seq2 f (x :: xs, y :: ys) = (f (x, y); seq2 f (xs, ys))
skalberg@15570
   613
  | seq2 _ _ = raise UnequalLengths;
wenzelm@4956
   614
wenzelm@233
   615
(*combine two lists forming a list of pairs:
wenzelm@233
   616
  [x1, ..., xn] ~~ [y1, ..., yn]  ===>  [(x1, y1), ..., (xn, yn)]*)
wenzelm@233
   617
fun [] ~~ [] = []
wenzelm@233
   618
  | (x :: xs) ~~ (y :: ys) = (x, y) :: (xs ~~ ys)
skalberg@15570
   619
  | _ ~~ _ = raise UnequalLengths;
wenzelm@233
   620
wenzelm@233
   621
(*inverse of ~~; the old 'split':
wenzelm@233
   622
  [(x1, y1), ..., (xn, yn)]  ===>  ([x1, ..., xn], [y1, ..., yn])*)
skalberg@15570
   623
val split_list = ListPair.unzip;
wenzelm@233
   624
wenzelm@7468
   625
fun equal_lists eq (xs, ys) = length xs = length ys andalso forall2 eq (xs, ys);
wenzelm@7468
   626
wenzelm@233
   627
wenzelm@233
   628
(* prefixes, suffixes *)
wenzelm@233
   629
wenzelm@233
   630
fun [] prefix _ = true
wenzelm@233
   631
  | (x :: xs) prefix (y :: ys) = x = y andalso (xs prefix ys)
wenzelm@233
   632
  | _ prefix _ = false;
wenzelm@233
   633
wenzelm@233
   634
(* [x1, ..., xi, ..., xn]  --->  ([x1, ..., x(i-1)], [xi, ..., xn])
wenzelm@233
   635
   where xi is the first element that does not satisfy the predicate*)
wenzelm@233
   636
fun take_prefix (pred : 'a -> bool)  (xs: 'a list) : 'a list * 'a list =
wenzelm@233
   637
  let fun take (rxs, []) = (rev rxs, [])
wenzelm@255
   638
        | take (rxs, x :: xs) =
wenzelm@255
   639
            if  pred x  then  take(x :: rxs, xs)  else  (rev rxs, x :: xs)
wenzelm@233
   640
  in  take([], xs)  end;
wenzelm@233
   641
wenzelm@233
   642
(* [x1, ..., xi, ..., xn]  --->  ([x1, ..., xi], [x(i+1), ..., xn])
wenzelm@233
   643
   where xi is the last element that does not satisfy the predicate*)
wenzelm@233
   644
fun take_suffix _ [] = ([], [])
wenzelm@233
   645
  | take_suffix pred (x :: xs) =
wenzelm@233
   646
      (case take_suffix pred xs of
wenzelm@233
   647
        ([], sffx) => if pred x then ([], x :: sffx) else ([x], sffx)
wenzelm@233
   648
      | (prfx, sffx) => (x :: prfx, sffx));
wenzelm@233
   649
wenzelm@12249
   650
fun prefixes1 [] = []
wenzelm@12249
   651
  | prefixes1 (x :: xs) = map (cons x) ([] :: prefixes1 xs);
wenzelm@12249
   652
wenzelm@12249
   653
fun suffixes1 xs = map rev (prefixes1 (rev xs));
wenzelm@12249
   654
wenzelm@233
   655
wenzelm@233
   656
wenzelm@233
   657
(** integers **)
wenzelm@233
   658
nipkow@10692
   659
fun gcd(x,y) =
nipkow@10692
   660
  let fun gxd x y =
nipkow@10692
   661
    if y = 0 then x else gxd y (x mod y)
nipkow@10692
   662
  in if x < y then gxd y x else gxd x y end;
nipkow@10692
   663
nipkow@10692
   664
fun lcm(x,y) = (x * y) div gcd(x,y);
nipkow@10692
   665
wenzelm@2958
   666
fun inc i = (i := ! i + 1; ! i);
wenzelm@2958
   667
fun dec i = (i := ! i - 1; ! i);
wenzelm@233
   668
wenzelm@233
   669
wenzelm@233
   670
(* lists of integers *)
wenzelm@233
   671
wenzelm@233
   672
(*make the list [from, from + 1, ..., to]*)
paulson@2175
   673
fun (from upto to) =
wenzelm@233
   674
  if from > to then [] else from :: ((from + 1) upto to);
wenzelm@233
   675
wenzelm@233
   676
(*make the list [from, from - 1, ..., to]*)
paulson@2175
   677
fun (from downto to) =
wenzelm@233
   678
  if from < to then [] else from :: ((from - 1) downto to);
wenzelm@233
   679
wenzelm@233
   680
(*predicate: downto0 (is, n) <=> is = [n, n - 1, ..., 0]*)
wenzelm@233
   681
fun downto0 (i :: is, n) = i = n andalso downto0 (is, n - 1)
wenzelm@233
   682
  | downto0 ([], n) = n = ~1;
wenzelm@233
   683
wenzelm@233
   684
wenzelm@233
   685
(* convert integers to strings *)
wenzelm@233
   686
wenzelm@233
   687
(*expand the number in the given base;
wenzelm@233
   688
  example: radixpand (2, 8) gives [1, 0, 0, 0]*)
wenzelm@233
   689
fun radixpand (base, num) : int list =
wenzelm@233
   690
  let
wenzelm@233
   691
    fun radix (n, tail) =
wenzelm@233
   692
      if n < base then n :: tail
wenzelm@233
   693
      else radix (n div base, (n mod base) :: tail)
wenzelm@233
   694
  in radix (num, []) end;
wenzelm@233
   695
wenzelm@233
   696
(*expands a number into a string of characters starting from "zerochar";
wenzelm@233
   697
  example: radixstring (2, "0", 8) gives "1000"*)
wenzelm@233
   698
fun radixstring (base, zerochar, num) =
wenzelm@233
   699
  let val offset = ord zerochar;
wenzelm@233
   700
      fun chrof n = chr (offset + n)
wenzelm@233
   701
  in implode (map chrof (radixpand (base, num))) end;
wenzelm@233
   702
wenzelm@233
   703
paulson@3407
   704
val string_of_int = Int.toString;
wenzelm@233
   705
paulson@3407
   706
fun string_of_indexname (a,0) = a
paulson@3407
   707
  | string_of_indexname (a,i) = a ^ "_" ^ Int.toString i;
wenzelm@233
   708
wenzelm@233
   709
wenzelm@14826
   710
(* read integers *)
wenzelm@14826
   711
wenzelm@14826
   712
fun read_radixint (radix: int, cs) : int * string list =
wenzelm@14826
   713
  let val zero = ord"0"
wenzelm@14826
   714
      val limit = zero+radix
wenzelm@14826
   715
      fun scan (num,[]) = (num,[])
wenzelm@14826
   716
        | scan (num, c::cs) =
wenzelm@14826
   717
              if  zero <= ord c  andalso  ord c < limit
wenzelm@14826
   718
              then scan(radix*num + ord c - zero, cs)
wenzelm@14826
   719
              else (num, c::cs)
wenzelm@14826
   720
  in  scan(0,cs)  end;
wenzelm@14826
   721
wenzelm@14826
   722
fun read_int cs = read_radixint (10, cs);
wenzelm@14826
   723
wenzelm@14826
   724
fun oct_char s = chr (#1 (read_radixint (8, explode s)));
wenzelm@14826
   725
wenzelm@14826
   726
wenzelm@14826
   727
wenzelm@233
   728
(** strings **)
wenzelm@233
   729
wenzelm@6312
   730
(*functions tuned for strings, avoiding explode*)
wenzelm@6312
   731
wenzelm@6312
   732
fun nth_elem_string (i, str) =
wenzelm@6959
   733
  (case try String.substring (str, i, 1) of
skalberg@15531
   734
    SOME s => s
skalberg@15570
   735
  | NONE => raise Subscript);
wenzelm@6312
   736
wenzelm@6282
   737
fun foldl_string f (x0, str) =
wenzelm@6282
   738
  let
wenzelm@6282
   739
    val n = size str;
wenzelm@14968
   740
    fun fold (x, i) =
wenzelm@14968
   741
      if i < n then fold (f (x, String.substring (str, i, 1)), i + 1) else x;
wenzelm@6282
   742
  in fold (x0, 0) end;
wenzelm@6282
   743
wenzelm@14968
   744
fun exists_string pred str =
wenzelm@14968
   745
  let
wenzelm@14968
   746
    val n = size str;
wenzelm@14968
   747
    fun ex i = i < n andalso (pred (String.substring (str, i, 1)) orelse ex (i + 1));
wenzelm@14968
   748
  in ex 0 end;
wenzelm@6312
   749
lcp@512
   750
(*enclose in brackets*)
lcp@512
   751
fun enclose lpar rpar str = lpar ^ str ^ rpar;
wenzelm@6642
   752
fun unenclose str = String.substring (str, 1, size str - 2);
wenzelm@255
   753
wenzelm@233
   754
(*simple quoting (does not escape special chars)*)
lcp@512
   755
val quote = enclose "\"" "\"";
wenzelm@233
   756
wenzelm@4212
   757
(*space_implode "..." (explode "hello") = "h...e...l...l...o"*)
wenzelm@233
   758
fun space_implode a bs = implode (separate a bs);
wenzelm@233
   759
wenzelm@255
   760
val commas = space_implode ", ";
wenzelm@380
   761
val commas_quote = commas o map quote;
wenzelm@255
   762
wenzelm@233
   763
(*concatenate messages, one per line, into a string*)
wenzelm@255
   764
val cat_lines = space_implode "\n";
wenzelm@233
   765
wenzelm@4212
   766
(*space_explode "." "h.e..l.lo" = ["h", "e", "", "l", "lo"]*)
wenzelm@3832
   767
fun space_explode _ "" = []
wenzelm@3832
   768
  | space_explode sep str =
wenzelm@3832
   769
      let
wenzelm@3832
   770
        fun expl chs =
wenzelm@3832
   771
          (case take_prefix (not_equal sep) chs of
wenzelm@3832
   772
            (cs, []) => [implode cs]
wenzelm@3832
   773
          | (cs, _ :: cs') => implode cs :: expl cs');
wenzelm@3832
   774
      in expl (explode str) end;
wenzelm@3832
   775
wenzelm@3832
   776
val split_lines = space_explode "\n";
wenzelm@3832
   777
wenzelm@14826
   778
fun prefix_lines "" txt = txt
wenzelm@14826
   779
  | prefix_lines prfx txt = txt |> split_lines |> map (fn s => prfx ^ s) |> cat_lines;
wenzelm@14826
   780
wenzelm@7712
   781
(*untabify*)
wenzelm@7712
   782
fun untabify chs =
wenzelm@7712
   783
  let
wenzelm@7712
   784
    val tab_width = 8;
wenzelm@7712
   785
wenzelm@7712
   786
    fun untab (_, "\n") = (0, ["\n"])
wenzelm@9118
   787
      | untab (pos, "\t") =
wenzelm@9118
   788
          let val d = tab_width - (pos mod tab_width) in (pos + d, replicate d " ") end
wenzelm@7712
   789
      | untab (pos, c) = (pos + 1, [c]);
wenzelm@7712
   790
  in
wenzelm@7712
   791
    if not (exists (equal "\t") chs) then chs
wenzelm@7712
   792
    else flat (#2 (foldl_map untab (0, chs)))
wenzelm@7712
   793
  end;
wenzelm@7712
   794
wenzelm@5285
   795
(*append suffix*)
wenzelm@5285
   796
fun suffix sfx s = s ^ sfx;
wenzelm@5285
   797
wenzelm@5285
   798
(*remove suffix*)
wenzelm@5285
   799
fun unsuffix sfx s =
wenzelm@5285
   800
  let
wenzelm@5285
   801
    val cs = explode s;
wenzelm@5285
   802
    val prfx_len = size s - size sfx;
wenzelm@5285
   803
  in
wenzelm@5285
   804
    if prfx_len >= 0 andalso implode (drop (prfx_len, cs)) = sfx then
wenzelm@5285
   805
      implode (take (prfx_len, cs))
skalberg@15570
   806
    else raise Fail "unsuffix"
wenzelm@5285
   807
  end;
wenzelm@5285
   808
berghofe@15060
   809
(*remove prefix*)
berghofe@15060
   810
fun unprefix prfx s =
berghofe@15060
   811
  let val (prfx', sfx) = splitAt (size prfx, explode s)
berghofe@15060
   812
  in
berghofe@15060
   813
    if implode prfx' = prfx then implode sfx
skalberg@15570
   814
    else raise Fail "unprefix"
berghofe@15060
   815
  end;
berghofe@15060
   816
wenzelm@10951
   817
fun replicate_string 0 _ = ""
wenzelm@10951
   818
  | replicate_string 1 a = a
wenzelm@10951
   819
  | replicate_string k a =
wenzelm@10951
   820
      if k mod 2 = 0 then replicate_string (k div 2) (a ^ a)
wenzelm@10951
   821
      else replicate_string (k div 2) (a ^ a) ^ a;
wenzelm@10951
   822
wenzelm@3832
   823
wenzelm@233
   824
wenzelm@233
   825
(** lists as sets **)
wenzelm@233
   826
wenzelm@233
   827
(*membership in a list*)
wenzelm@233
   828
fun x mem [] = false
wenzelm@233
   829
  | x mem (y :: ys) = x = y orelse x mem ys;
clasohm@0
   830
paulson@2175
   831
(*membership in a list, optimized version for ints*)
berghofe@1576
   832
fun (x:int) mem_int [] = false
berghofe@1576
   833
  | x mem_int (y :: ys) = x = y orelse x mem_int ys;
berghofe@1576
   834
paulson@2175
   835
(*membership in a list, optimized version for strings*)
berghofe@1576
   836
fun (x:string) mem_string [] = false
berghofe@1576
   837
  | x mem_string (y :: ys) = x = y orelse x mem_string ys;
berghofe@1576
   838
clasohm@0
   839
(*generalized membership test*)
wenzelm@233
   840
fun gen_mem eq (x, []) = false
wenzelm@233
   841
  | gen_mem eq (x, y :: ys) = eq (x, y) orelse gen_mem eq (x, ys);
wenzelm@233
   842
wenzelm@233
   843
wenzelm@233
   844
(*insertion into list if not already there*)
paulson@2175
   845
fun (x ins xs) = if x mem xs then xs else x :: xs;
clasohm@0
   846
paulson@2175
   847
(*insertion into list, optimized version for ints*)
paulson@2175
   848
fun (x ins_int xs) = if x mem_int xs then xs else x :: xs;
berghofe@1576
   849
paulson@2175
   850
(*insertion into list, optimized version for strings*)
paulson@2175
   851
fun (x ins_string xs) = if x mem_string xs then xs else x :: xs;
berghofe@1576
   852
clasohm@0
   853
(*generalized insertion*)
wenzelm@233
   854
fun gen_ins eq (x, xs) = if gen_mem eq (x, xs) then xs else x :: xs;
wenzelm@233
   855
wenzelm@233
   856
wenzelm@233
   857
(*union of sets represented as lists: no repetitions*)
wenzelm@233
   858
fun xs union [] = xs
wenzelm@233
   859
  | [] union ys = ys
wenzelm@233
   860
  | (x :: xs) union ys = xs union (x ins ys);
clasohm@0
   861
paulson@2175
   862
(*union of sets, optimized version for ints*)
berghofe@1576
   863
fun (xs:int list) union_int [] = xs
berghofe@1576
   864
  | [] union_int ys = ys
berghofe@1576
   865
  | (x :: xs) union_int ys = xs union_int (x ins_int ys);
berghofe@1576
   866
paulson@2175
   867
(*union of sets, optimized version for strings*)
berghofe@1576
   868
fun (xs:string list) union_string [] = xs
berghofe@1576
   869
  | [] union_string ys = ys
berghofe@1576
   870
  | (x :: xs) union_string ys = xs union_string (x ins_string ys);
berghofe@1576
   871
clasohm@0
   872
(*generalized union*)
wenzelm@233
   873
fun gen_union eq (xs, []) = xs
wenzelm@233
   874
  | gen_union eq ([], ys) = ys
wenzelm@233
   875
  | gen_union eq (x :: xs, ys) = gen_union eq (xs, gen_ins eq (x, ys));
wenzelm@233
   876
wenzelm@233
   877
wenzelm@233
   878
(*intersection*)
wenzelm@233
   879
fun [] inter ys = []
wenzelm@233
   880
  | (x :: xs) inter ys =
wenzelm@233
   881
      if x mem ys then x :: (xs inter ys) else xs inter ys;
wenzelm@233
   882
paulson@2175
   883
(*intersection, optimized version for ints*)
berghofe@1576
   884
fun ([]:int list) inter_int ys = []
berghofe@1576
   885
  | (x :: xs) inter_int ys =
berghofe@1576
   886
      if x mem_int ys then x :: (xs inter_int ys) else xs inter_int ys;
berghofe@1576
   887
paulson@2175
   888
(*intersection, optimized version for strings *)
berghofe@1576
   889
fun ([]:string list) inter_string ys = []
berghofe@1576
   890
  | (x :: xs) inter_string ys =
berghofe@1576
   891
      if x mem_string ys then x :: (xs inter_string ys) else xs inter_string ys;
berghofe@1576
   892
paulson@7090
   893
(*generalized intersection*)
paulson@7090
   894
fun gen_inter eq ([], ys) = []
wenzelm@12284
   895
  | gen_inter eq (x::xs, ys) =
paulson@7090
   896
      if gen_mem eq (x,ys) then x :: gen_inter eq (xs, ys)
wenzelm@12284
   897
                           else      gen_inter eq (xs, ys);
paulson@7090
   898
wenzelm@233
   899
wenzelm@233
   900
(*subset*)
wenzelm@233
   901
fun [] subset ys = true
wenzelm@233
   902
  | (x :: xs) subset ys = x mem ys andalso xs subset ys;
wenzelm@233
   903
paulson@2175
   904
(*subset, optimized version for ints*)
berghofe@1576
   905
fun ([]:int list) subset_int ys = true
berghofe@1576
   906
  | (x :: xs) subset_int ys = x mem_int ys andalso xs subset_int ys;
berghofe@1576
   907
paulson@2175
   908
(*subset, optimized version for strings*)
berghofe@1576
   909
fun ([]:string list) subset_string ys = true
berghofe@1576
   910
  | (x :: xs) subset_string ys = x mem_string ys andalso xs subset_string ys;
berghofe@1576
   911
wenzelm@4363
   912
(*set equality*)
wenzelm@4363
   913
fun eq_set (xs, ys) =
wenzelm@4363
   914
  xs = ys orelse (xs subset ys andalso ys subset xs);
wenzelm@4363
   915
paulson@2182
   916
(*set equality for strings*)
berghofe@1576
   917
fun eq_set_string ((xs:string list), ys) =
berghofe@1576
   918
  xs = ys orelse (xs subset_string ys andalso ys subset_string xs);
berghofe@1576
   919
paulson@2182
   920
fun gen_subset eq (xs, ys) = forall (fn x => gen_mem eq (x, ys)) xs;
paulson@2182
   921
wenzelm@265
   922
wenzelm@233
   923
(*removing an element from a list WITHOUT duplicates*)
wenzelm@233
   924
fun (y :: ys) \ x = if x = y then ys else y :: (ys \ x)
wenzelm@233
   925
  | [] \ x = [];
wenzelm@233
   926
paulson@2243
   927
fun ys \\ xs = foldl (op \) (ys,xs);
clasohm@0
   928
wenzelm@233
   929
(*removing an element from a list -- possibly WITH duplicates*)
wenzelm@233
   930
fun gen_rem eq (xs, y) = filter_out (fn x => eq (x, y)) xs;
wenzelm@12295
   931
fun gen_rems eq (xs, ys) = filter_out (fn x => gen_mem eq (x, ys)) xs;
wenzelm@233
   932
wenzelm@233
   933
wenzelm@233
   934
(*makes a list of the distinct members of the input; preserves order, takes
wenzelm@233
   935
  first of equal elements*)
wenzelm@233
   936
fun gen_distinct eq lst =
wenzelm@233
   937
  let
wenzelm@233
   938
    val memb = gen_mem eq;
clasohm@0
   939
wenzelm@233
   940
    fun dist (rev_seen, []) = rev rev_seen
wenzelm@233
   941
      | dist (rev_seen, x :: xs) =
wenzelm@233
   942
          if memb (x, rev_seen) then dist (rev_seen, xs)
wenzelm@233
   943
          else dist (x :: rev_seen, xs);
wenzelm@233
   944
  in
wenzelm@233
   945
    dist ([], lst)
wenzelm@233
   946
  end;
wenzelm@233
   947
paulson@2243
   948
fun distinct l = gen_distinct (op =) l;
wenzelm@233
   949
wenzelm@233
   950
wenzelm@233
   951
(*returns the tail beginning with the first repeated element, or []*)
wenzelm@233
   952
fun findrep [] = []
wenzelm@233
   953
  | findrep (x :: xs) = if x mem xs then x :: xs else findrep xs;
wenzelm@233
   954
wenzelm@233
   955
wenzelm@255
   956
(*returns a list containing all repeated elements exactly once; preserves
wenzelm@255
   957
  order, takes first of equal elements*)
wenzelm@255
   958
fun gen_duplicates eq lst =
wenzelm@255
   959
  let
wenzelm@255
   960
    val memb = gen_mem eq;
wenzelm@255
   961
wenzelm@255
   962
    fun dups (rev_dups, []) = rev rev_dups
wenzelm@255
   963
      | dups (rev_dups, x :: xs) =
wenzelm@255
   964
          if memb (x, rev_dups) orelse not (memb (x, xs)) then
wenzelm@255
   965
            dups (rev_dups, xs)
wenzelm@255
   966
          else dups (x :: rev_dups, xs);
wenzelm@255
   967
  in
wenzelm@255
   968
    dups ([], lst)
wenzelm@255
   969
  end;
wenzelm@255
   970
paulson@2243
   971
fun duplicates l = gen_duplicates (op =) l;
wenzelm@255
   972
wenzelm@255
   973
wenzelm@233
   974
wenzelm@233
   975
(** association lists **)
clasohm@0
   976
wenzelm@233
   977
(*association list lookup*)
skalberg@15531
   978
fun assoc ([], key) = NONE
wenzelm@233
   979
  | assoc ((keyi, xi) :: pairs, key) =
skalberg@15531
   980
      if key = keyi then SOME xi else assoc (pairs, key);
wenzelm@233
   981
paulson@2175
   982
(*association list lookup, optimized version for ints*)
skalberg@15531
   983
fun assoc_int ([], (key:int)) = NONE
berghofe@1576
   984
  | assoc_int ((keyi, xi) :: pairs, key) =
skalberg@15531
   985
      if key = keyi then SOME xi else assoc_int (pairs, key);
berghofe@1576
   986
paulson@2175
   987
(*association list lookup, optimized version for strings*)
skalberg@15531
   988
fun assoc_string ([], (key:string)) = NONE
berghofe@1576
   989
  | assoc_string ((keyi, xi) :: pairs, key) =
skalberg@15531
   990
      if key = keyi then SOME xi else assoc_string (pairs, key);
berghofe@1576
   991
paulson@2175
   992
(*association list lookup, optimized version for string*ints*)
skalberg@15531
   993
fun assoc_string_int ([], (key:string*int)) = NONE
berghofe@1576
   994
  | assoc_string_int ((keyi, xi) :: pairs, key) =
skalberg@15531
   995
      if key = keyi then SOME xi else assoc_string_int (pairs, key);
berghofe@1576
   996
wenzelm@233
   997
fun assocs ps x =
wenzelm@233
   998
  (case assoc (ps, x) of
skalberg@15531
   999
    NONE => []
skalberg@15531
  1000
  | SOME ys => ys);
wenzelm@233
  1001
wenzelm@255
  1002
(*two-fold association list lookup*)
wenzelm@255
  1003
fun assoc2 (aal, (key1, key2)) =
wenzelm@255
  1004
  (case assoc (aal, key1) of
skalberg@15531
  1005
    SOME al => assoc (al, key2)
skalberg@15531
  1006
  | NONE => NONE);
wenzelm@255
  1007
wenzelm@233
  1008
(*generalized association list lookup*)
skalberg@15531
  1009
fun gen_assoc eq ([], key) = NONE
wenzelm@233
  1010
  | gen_assoc eq ((keyi, xi) :: pairs, key) =
skalberg@15531
  1011
      if eq (key, keyi) then SOME xi else gen_assoc eq (pairs, key);
wenzelm@233
  1012
wenzelm@233
  1013
(*association list update*)
wenzelm@233
  1014
fun overwrite (al, p as (key, _)) =
wenzelm@233
  1015
  let fun over ((q as (keyi, _)) :: pairs) =
wenzelm@233
  1016
            if keyi = key then p :: pairs else q :: (over pairs)
wenzelm@233
  1017
        | over [] = [p]
wenzelm@233
  1018
  in over al end;
wenzelm@233
  1019
wenzelm@2522
  1020
fun gen_overwrite eq (al, p as (key, _)) =
wenzelm@2522
  1021
  let fun over ((q as (keyi, _)) :: pairs) =
wenzelm@2522
  1022
            if eq (keyi, key) then p :: pairs else q :: (over pairs)
wenzelm@2522
  1023
        | over [] = [p]
wenzelm@2522
  1024
  in over al end;
wenzelm@2522
  1025
wenzelm@233
  1026
wenzelm@12284
  1027
(* lists as tables *)
wenzelm@233
  1028
wenzelm@12284
  1029
fun gen_merge_lists _ xs [] = xs
wenzelm@12284
  1030
  | gen_merge_lists _ [] ys = ys
wenzelm@12284
  1031
  | gen_merge_lists eq xs ys = xs @ gen_rems eq (ys, xs);
clasohm@0
  1032
wenzelm@12284
  1033
fun gen_merge_lists' _ xs [] = xs
wenzelm@12284
  1034
  | gen_merge_lists' _ [] ys = ys
wenzelm@12295
  1035
  | gen_merge_lists' eq xs ys = gen_rems eq (ys, xs) @ xs;
clasohm@0
  1036
wenzelm@12284
  1037
fun merge_lists xs ys = gen_merge_lists (op =) xs ys;
wenzelm@12284
  1038
fun merge_lists' xs ys = gen_merge_lists' (op =) xs ys;
wenzelm@12284
  1039
fun merge_alists al = gen_merge_lists eq_fst al;
berghofe@15263
  1040
fun merge_alists' al = gen_merge_lists' eq_fst al;
wenzelm@380
  1041
clasohm@0
  1042
clasohm@0
  1043
wenzelm@233
  1044
(** balanced trees **)
wenzelm@233
  1045
wenzelm@233
  1046
exception Balance;      (*indicates non-positive argument to balancing fun*)
wenzelm@233
  1047
wenzelm@233
  1048
(*balanced folding; avoids deep nesting*)
wenzelm@233
  1049
fun fold_bal f [x] = x
wenzelm@233
  1050
  | fold_bal f [] = raise Balance
wenzelm@233
  1051
  | fold_bal f xs =
nipkow@13629
  1052
      let val (ps,qs) = splitAt(length xs div 2, xs)
nipkow@13629
  1053
      in  f (fold_bal f ps, fold_bal f qs)  end;
wenzelm@233
  1054
wenzelm@233
  1055
(*construct something of the form f(...g(...(x)...)) for balanced access*)
wenzelm@233
  1056
fun access_bal (f, g, x) n i =
wenzelm@233
  1057
  let fun acc n i =     (*1<=i<=n*)
wenzelm@233
  1058
          if n=1 then x else
wenzelm@233
  1059
          let val n2 = n div 2
wenzelm@233
  1060
          in  if i<=n2 then f (acc n2 i)
wenzelm@233
  1061
                       else g (acc (n-n2) (i-n2))
wenzelm@233
  1062
          end
wenzelm@233
  1063
  in  if 1<=i andalso i<=n then acc n i else raise Balance  end;
wenzelm@233
  1064
wenzelm@233
  1065
(*construct ALL such accesses; could try harder to share recursive calls!*)
wenzelm@233
  1066
fun accesses_bal (f, g, x) n =
wenzelm@233
  1067
  let fun acc n =
wenzelm@233
  1068
          if n=1 then [x] else
wenzelm@233
  1069
          let val n2 = n div 2
wenzelm@233
  1070
              val acc2 = acc n2
wenzelm@233
  1071
          in  if n-n2=n2 then map f acc2 @ map g acc2
wenzelm@233
  1072
                         else map f acc2 @ map g (acc (n-n2)) end
wenzelm@233
  1073
  in  if 1<=n then acc n else raise Balance  end;
wenzelm@233
  1074
wenzelm@233
  1075
wenzelm@233
  1076
wenzelm@2506
  1077
(** orders **)
wenzelm@2506
  1078
wenzelm@4445
  1079
fun rev_order LESS = GREATER
wenzelm@4445
  1080
  | rev_order EQUAL = EQUAL
wenzelm@4445
  1081
  | rev_order GREATER = LESS;
wenzelm@4445
  1082
wenzelm@4479
  1083
(*assume rel is a linear strict order*)
wenzelm@4445
  1084
fun make_ord rel (x, y) =
wenzelm@4445
  1085
  if rel (x, y) then LESS
wenzelm@4445
  1086
  else if rel (y, x) then GREATER
wenzelm@4445
  1087
  else EQUAL;
wenzelm@4445
  1088
wenzelm@15051
  1089
val int_ord = Int.compare;
wenzelm@15051
  1090
val string_ord = String.compare;
wenzelm@2506
  1091
wenzelm@4343
  1092
(*lexicographic product*)
wenzelm@4343
  1093
fun prod_ord a_ord b_ord ((x, y), (x', y')) =
wenzelm@4343
  1094
  (case a_ord (x, x') of EQUAL => b_ord (y, y') | ord => ord);
wenzelm@4343
  1095
wenzelm@4343
  1096
(*dictionary order -- in general NOT well-founded!*)
wenzelm@4343
  1097
fun dict_ord _ ([], []) = EQUAL
wenzelm@4343
  1098
  | dict_ord _ ([], _ :: _) = LESS
wenzelm@4343
  1099
  | dict_ord _ (_ :: _, []) = GREATER
wenzelm@4343
  1100
  | dict_ord elem_ord (x :: xs, y :: ys) =
wenzelm@4343
  1101
      (case elem_ord (x, y) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord);
wenzelm@4343
  1102
wenzelm@4343
  1103
(*lexicographic product of lists*)
wenzelm@4343
  1104
fun list_ord elem_ord (xs, ys) =
wenzelm@4343
  1105
  prod_ord int_ord (dict_ord elem_ord) ((length xs, xs), (length ys, ys));
wenzelm@4343
  1106
wenzelm@2506
  1107
wenzelm@4621
  1108
(* sorting *)
wenzelm@4621
  1109
wenzelm@4621
  1110
(*quicksort (stable, i.e. does not reorder equal elements)*)
wenzelm@4621
  1111
fun sort ord =
wenzelm@4621
  1112
  let
wenzelm@4621
  1113
    fun qsort xs =
wenzelm@4621
  1114
      let val len = length xs in
wenzelm@4621
  1115
        if len <= 1 then xs
wenzelm@4621
  1116
        else
wenzelm@4621
  1117
          let val (lts, eqs, gts) = part (nth_elem (len div 2, xs)) xs in
wenzelm@4621
  1118
            qsort lts @ eqs @ qsort gts
wenzelm@4621
  1119
          end
wenzelm@4621
  1120
      end
wenzelm@4621
  1121
    and part _ [] = ([], [], [])
wenzelm@4621
  1122
      | part pivot (x :: xs) = add (ord (x, pivot)) x (part pivot xs)
wenzelm@4621
  1123
    and add LESS x (lts, eqs, gts) = (x :: lts, eqs, gts)
wenzelm@4621
  1124
      | add EQUAL x (lts, eqs, gts) = (lts, x :: eqs, gts)
wenzelm@4621
  1125
      | add GREATER x (lts, eqs, gts) = (lts, eqs, x :: gts);
wenzelm@4621
  1126
  in qsort end;
wenzelm@4621
  1127
wenzelm@4621
  1128
(*sort strings*)
wenzelm@4621
  1129
val sort_strings = sort string_ord;
wenzelm@4621
  1130
fun sort_wrt sel xs = sort (string_ord o pairself sel) xs;
wenzelm@4621
  1131
berghofe@11514
  1132
fun unique_strings ([]: string list) = []
berghofe@11514
  1133
  | unique_strings [x] = [x]
berghofe@11514
  1134
  | unique_strings (x :: y :: ys) =
berghofe@11514
  1135
      if x = y then unique_strings (y :: ys)
berghofe@11514
  1136
      else x :: unique_strings (y :: ys);
wenzelm@4621
  1137
wenzelm@2506
  1138
berghofe@14106
  1139
(** random numbers **)
berghofe@14106
  1140
berghofe@14106
  1141
exception RANDOM;
berghofe@14106
  1142
berghofe@14618
  1143
fun rmod x y = x - y * Real.realFloor (x / y);
berghofe@14106
  1144
berghofe@14106
  1145
local
berghofe@14106
  1146
  val a = 16807.0;
berghofe@14106
  1147
  val m = 2147483647.0;
berghofe@14106
  1148
  val random_seed = ref 1.0;
berghofe@14106
  1149
in
berghofe@14106
  1150
berghofe@14106
  1151
fun random () =
berghofe@14106
  1152
  let val r = rmod (a * !random_seed) m
berghofe@14106
  1153
  in (random_seed := r; r) end;
berghofe@14106
  1154
berghofe@14106
  1155
end;
berghofe@14106
  1156
berghofe@14106
  1157
fun random_range l h =
berghofe@14106
  1158
  if h < l orelse l < 0 then raise RANDOM
berghofe@14106
  1159
  else l + Real.floor (rmod (random ()) (real (h - l + 1)));
berghofe@14106
  1160
berghofe@14106
  1161
fun one_of xs = nth_elem (random_range 0 (length xs - 1), xs);
berghofe@14106
  1162
berghofe@14106
  1163
fun frequency xs =
berghofe@14106
  1164
  let
berghofe@14106
  1165
    val sum = foldl op + (0, map fst xs);
berghofe@14106
  1166
    fun pick n ((k, x) :: xs) =
berghofe@14106
  1167
      if n <= k then x else pick (n - k) xs
berghofe@14106
  1168
  in pick (random_range 1 sum) xs end;
berghofe@14106
  1169
berghofe@14106
  1170
wenzelm@14826
  1171
(** current directory **)
wenzelm@233
  1172
paulson@2243
  1173
val cd = OS.FileSys.chDir;
wenzelm@2317
  1174
val pwd = OS.FileSys.getDir;
paulson@2243
  1175
berghofe@3606
  1176
wenzelm@233
  1177
nipkow@10692
  1178
(** rational numbers **)
nipkow@10692
  1179
nipkow@10692
  1180
datatype rat = Rat of bool * int * int
nipkow@10692
  1181
wenzelm@14826
  1182
exception RAT of string;
wenzelm@14826
  1183
nipkow@10692
  1184
fun rep_rat(Rat(a,p,q)) = (if a then p else ~p,q)
nipkow@10692
  1185
nipkow@10692
  1186
fun ratnorm(a,p,q) = if p=0 then Rat(a,0,1) else
nipkow@10692
  1187
  let val absp = abs p
nipkow@10692
  1188
      val m = gcd(absp,q)
nipkow@10692
  1189
  in Rat(a = (0 <= p), absp div m, q div m) end;
nipkow@10692
  1190
nipkow@10692
  1191
fun ratadd(Rat(a,p,q),Rat(b,r,s)) =
nipkow@10692
  1192
  let val den = lcm(q,s)
nipkow@10692
  1193
      val p = p*(den div q) and r = r*(den div s)
nipkow@10692
  1194
      val num = (if a then p else ~p) + (if b then r else ~r)
nipkow@10692
  1195
  in ratnorm(true,num,den) end;
nipkow@10692
  1196
nipkow@10692
  1197
fun ratmul(Rat(a,p,q),Rat(b,r,s)) = ratnorm(a=b,p*r,q*s)
nipkow@10692
  1198
wenzelm@14826
  1199
fun ratinv(Rat(a,p,q)) = if p=0 then raise RAT "ratinv" else Rat(a,q,p)
nipkow@10692
  1200
nipkow@10692
  1201
fun int_ratdiv(p,q) =
wenzelm@14826
  1202
  if q=0 then raise RAT "int_ratdiv" else ratnorm(0<=q, p, abs q)
nipkow@10692
  1203
nipkow@10692
  1204
fun ratneg(Rat(b,p,q)) = Rat(not b,p,q);
nipkow@10692
  1205
nipkow@10692
  1206
fun rat_of_int i = if i < 0 then Rat(false,abs i,1) else Rat(true,i,1);
nipkow@10692
  1207
nipkow@10692
  1208
wenzelm@4621
  1209
(** misc **)
wenzelm@233
  1210
wenzelm@233
  1211
(*use the keyfun to make a list of (x, key) pairs*)
clasohm@0
  1212
fun make_keylist (keyfun: 'a->'b) : 'a list -> ('a * 'b) list =
wenzelm@233
  1213
  let fun keypair x = (x, keyfun x)
wenzelm@233
  1214
  in map keypair end;
clasohm@0
  1215
wenzelm@233
  1216
(*given a list of (x, key) pairs and a searchkey
clasohm@0
  1217
  return the list of xs from each pair whose key equals searchkey*)
clasohm@0
  1218
fun keyfilter [] searchkey = []
wenzelm@233
  1219
  | keyfilter ((x, key) :: pairs) searchkey =
wenzelm@233
  1220
      if key = searchkey then x :: keyfilter pairs searchkey
wenzelm@233
  1221
      else keyfilter pairs searchkey;
clasohm@0
  1222
clasohm@0
  1223
clasohm@0
  1224
(*Partition list into elements that satisfy predicate and those that don't.
wenzelm@233
  1225
  Preserves order of elements in both lists.*)
skalberg@15570
  1226
val partition = List.partition;
clasohm@0
  1227
clasohm@0
  1228
clasohm@0
  1229
fun partition_eq (eq:'a * 'a -> bool) =
clasohm@0
  1230
    let fun part [] = []
wenzelm@233
  1231
          | part (x::ys) = let val (xs, xs') = partition (apl(x, eq)) ys
wenzelm@233
  1232
                           in (x::xs)::(part xs') end
clasohm@0
  1233
    in part end;
clasohm@0
  1234
clasohm@0
  1235
wenzelm@233
  1236
(*Partition a list into buckets  [ bi, b(i+1), ..., bj ]
clasohm@0
  1237
   putting x in bk if p(k)(x) holds.  Preserve order of elements if possible.*)
clasohm@0
  1238
fun partition_list p i j =
wenzelm@233
  1239
  let fun part k xs =
wenzelm@233
  1240
            if k>j then
clasohm@0
  1241
              (case xs of [] => []
skalberg@15570
  1242
                         | _ => raise Fail "partition_list")
clasohm@0
  1243
            else
wenzelm@233
  1244
            let val (ns, rest) = partition (p k) xs;
wenzelm@233
  1245
            in  ns :: part(k+1)rest  end
clasohm@0
  1246
  in  part i end;
clasohm@0
  1247
clasohm@0
  1248
wenzelm@233
  1249
(* generating identifiers *)
clasohm@0
  1250
paulson@4063
  1251
(** Freshly generated identifiers; supplied prefix MUST start with a letter **)
clasohm@0
  1252
local
paulson@4063
  1253
(*Maps 0-63 to A-Z, a-z, 0-9 or _ or ' for generating random identifiers*)
paulson@4063
  1254
fun char i =      if i<26 then chr (ord "A" + i)
wenzelm@5904
  1255
             else if i<52 then chr (ord "a" + i - 26)
wenzelm@5904
  1256
             else if i<62 then chr (ord"0" + i - 52)
wenzelm@5904
  1257
             else if i=62 then "_"
wenzelm@5904
  1258
             else  (*i=63*)    "'";
paulson@4063
  1259
paulson@4063
  1260
val charVec = Vector.tabulate (64, char);
paulson@4063
  1261
wenzelm@5904
  1262
fun newid n =
wenzelm@5904
  1263
  let
wenzelm@4284
  1264
  in  implode (map (fn i => Vector.sub(charVec,i)) (radixpand (64,n)))  end;
paulson@2003
  1265
wenzelm@4284
  1266
val seedr = ref 0;
clasohm@0
  1267
paulson@4063
  1268
in
wenzelm@4284
  1269
wenzelm@12346
  1270
fun gensym pre = pre ^ (#1(newid (!seedr), inc seedr));
paulson@2003
  1271
paulson@4063
  1272
end;
paulson@4063
  1273
paulson@4063
  1274
wenzelm@233
  1275
(* lexical scanning *)
clasohm@0
  1276
wenzelm@233
  1277
(*scan a list of characters into "words" composed of "letters" (recognized by
wenzelm@233
  1278
  is_let) and separated by any number of non-"letters"*)
wenzelm@233
  1279
fun scanwords is_let cs =
clasohm@0
  1280
  let fun scan1 [] = []
wenzelm@233
  1281
        | scan1 cs =
wenzelm@233
  1282
            let val (lets, rest) = take_prefix is_let cs
wenzelm@233
  1283
            in implode lets :: scanwords is_let rest end;
wenzelm@233
  1284
  in scan1 (#2 (take_prefix (not o is_let) cs)) end;
clasohm@24
  1285
wenzelm@4212
  1286
clasohm@1364
  1287
end;
clasohm@1364
  1288
skalberg@15570
  1289
structure OpenLibrary: LIBRARY = Library;
skalberg@15570
  1290
open OpenLibrary;