src/Pure/library.ML
author berghofe
Fri Jul 11 14:59:50 2003 +0200 (2003-07-11 ago)
changeset 14106 bbf708a7e27f
parent 13794 332eb2e69a65
child 14472 cba7c0a3ffb3
permissions -rw-r--r--
Added several functions for producing random numbers.
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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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    License:    GPL (GNU GENERAL PUBLIC LICENSE)
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Basic library: functions, options, pairs, booleans, lists, integers,
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strings, lists as sets, association lists, generic tables, balanced
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trees, orders, I/O and diagnostics, timing, 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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  datatype 'a option = None | Some of 'a
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  exception OPTION
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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 is_none: 'a option -> bool
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  val apsome: ('a -> 'b) -> 'a option -> 'b option
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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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  (*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 LIST of string
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  val null: 'a list -> bool
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  val hd: 'a list -> 'a
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  val tl: 'a list -> 'a list
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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 rev_append: 'a list -> 'a list -> 'a list
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  val apply: ('a -> 'a) list -> 'a -> 'a
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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 foldr1: ('a * 'a -> 'a) -> 'a list -> 'a
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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 length: 'a list -> int
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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 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 nth_elem: int * 'a list -> 'a
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  val map_nth_elem: int -> ('a -> 'a) -> 'a list -> 'a list
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  val last_elem: 'a list -> 'a
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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 flat: 'a list list -> 'a list
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  val unflat: 'a list list -> 'b list -> 'b list list
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  val seq: ('a -> unit) -> 'a list -> unit
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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 filter: ('a -> bool) -> 'a list -> 'a list
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  val filter_out: ('a -> bool) -> 'a list -> 'a list
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  val mapfilter: ('a -> 'b option) -> 'a list -> 'b 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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  (*rational numbers*)
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  type rat
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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 std_output: string -> unit
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  val std_error: string -> unit
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  val writeln_default: string -> unit
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  val prefix_lines: string -> string -> string
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  val split_lines: string -> string list
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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 replicate_string: int -> 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 overwrite_warn: (''a * 'b) list * (''a * 'b) -> string -> (''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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  (*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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  datatype order = LESS | EQUAL | GREATER
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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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  (*I/O and diagnostics*)
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  val cd: string -> unit
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  val pwd: unit -> string
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  val writeln_fn: (string -> unit) ref
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  val priority_fn: (string -> unit) ref
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  val tracing_fn: (string -> unit) ref
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  val warning_fn: (string -> unit) ref
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  val error_fn: (string -> unit) ref
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  val writeln: string -> unit
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  val priority: string -> unit
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  val tracing: string -> unit
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  val warning: string -> unit
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  exception ERROR
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  val error_msg: string -> unit
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  val error: string -> 'a
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  val sys_error: string -> 'a
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  val assert: bool -> string -> unit
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  val deny: bool -> string -> unit
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  val assert_all: ('a -> bool) -> 'a list -> ('a -> string) -> unit
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  datatype 'a error = Error of string | OK of 'a
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  val get_error: 'a error -> string option
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  val get_ok: 'a error -> 'a option
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  val handle_error: ('a -> 'b) -> 'a -> 'b error
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  exception ERROR_MESSAGE of string
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  val transform_error: ('a -> 'b) -> 'a -> 'b
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  val transform_failure: (exn -> exn) -> ('a -> 'b) -> 'a -> 'b
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  (*timing*)
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  val cond_timeit: bool -> (unit -> 'a) -> 'a
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  val timeit: (unit -> 'a) -> 'a
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  val timeap: ('a -> 'b) -> 'a -> 'b
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  val timeap_msg: string -> ('a -> 'b) -> 'a -> 'b
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  val timing: bool ref
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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: ('a -> bool) -> 'a list -> 'a list * '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
wenzelm@4621
   291
  val transitive_closure: (string * string list) list -> (string * string list) list
wenzelm@4621
   292
  val gensym: string -> string
wenzelm@4621
   293
  val scanwords: (string -> bool) -> string list -> string list
wenzelm@4621
   294
  datatype 'a mtree = Join of 'a * 'a mtree list
wenzelm@4621
   295
end;
wenzelm@4621
   296
wenzelm@4621
   297
structure Library: LIBRARY =
clasohm@1364
   298
struct
clasohm@0
   299
wenzelm@4995
   300
wenzelm@233
   301
(** functions **)
clasohm@0
   302
wenzelm@233
   303
(*handy combinators*)
wenzelm@233
   304
fun curry f x y = f (x, y);
wenzelm@233
   305
fun uncurry f (x, y) = f x y;
wenzelm@233
   306
fun I x = x;
wenzelm@233
   307
fun K x y = x;
clasohm@0
   308
wenzelm@380
   309
(*reverse apply*)
wenzelm@410
   310
fun (x |> f) = f x;
wenzelm@8418
   311
fun ((x, y) |>> f) = (f x, y);
wenzelm@8418
   312
fun ((x, y) |>>> f) = let val (x', z) = f x in (x', (y, z)) end;
wenzelm@380
   313
wenzelm@233
   314
(*application of (infix) operator to its left or right argument*)
wenzelm@233
   315
fun apl (x, f) y = f (x, y);
wenzelm@233
   316
fun apr (f, y) x = f (x, y);
clasohm@0
   317
wenzelm@233
   318
(*function exponentiation: f(...(f x)...) with n applications of f*)
wenzelm@233
   319
fun funpow n f x =
wenzelm@233
   320
  let fun rep (0, x) = x
wenzelm@233
   321
        | rep (n, x) = rep (n - 1, f x)
wenzelm@233
   322
  in rep (n, x) end;
wenzelm@160
   323
wenzelm@5893
   324
(*concatenation: 2 and 3 args*)
wenzelm@5893
   325
fun (f oo g) x y = f (g x y);
wenzelm@5893
   326
fun (f ooo g) x y z = f (g x y z);
wenzelm@6510
   327
fun (f oooo g) x y z w = f (g x y z w);
wenzelm@6510
   328
wenzelm@160
   329
wenzelm@160
   330
wenzelm@2471
   331
(** stamps **)
wenzelm@2471
   332
wenzelm@2471
   333
type stamp = unit ref;
wenzelm@2471
   334
val stamp: unit -> stamp = ref;
wenzelm@2471
   335
wenzelm@2471
   336
wenzelm@2471
   337
wenzelm@233
   338
(** options **)
clasohm@0
   339
clasohm@0
   340
datatype 'a option = None | Some of 'a;
clasohm@0
   341
wenzelm@4139
   342
exception OPTION;
clasohm@0
   343
clasohm@0
   344
fun the (Some x) = x
wenzelm@4139
   345
  | the None = raise OPTION;
clasohm@0
   346
wenzelm@4212
   347
(*strict!*)
wenzelm@255
   348
fun if_none None y = y
wenzelm@255
   349
  | if_none (Some x) _ = x;
wenzelm@255
   350
clasohm@0
   351
fun is_some (Some _) = true
clasohm@0
   352
  | is_some None = false;
clasohm@0
   353
clasohm@0
   354
fun is_none (Some _) = false
clasohm@0
   355
  | is_none None = true;
clasohm@0
   356
wenzelm@233
   357
fun apsome f (Some x) = Some (f x)
wenzelm@233
   358
  | apsome _ None = None;
clasohm@0
   359
wenzelm@6959
   360
wenzelm@6959
   361
(* exception handling *)
wenzelm@6959
   362
wenzelm@6959
   363
exception ERROR;
wenzelm@6959
   364
wenzelm@6959
   365
fun try f x = Some (f x)
wenzelm@6959
   366
  handle Interrupt => raise Interrupt | ERROR => raise ERROR | _ => None;
wenzelm@6959
   367
wenzelm@6959
   368
fun can f x = is_some (try f x);
wenzelm@4139
   369
wenzelm@4139
   370
wenzelm@4139
   371
wenzelm@233
   372
(** pairs **)
wenzelm@233
   373
wenzelm@233
   374
fun pair x y = (x, y);
wenzelm@233
   375
fun rpair x y = (y, x);
wenzelm@233
   376
wenzelm@233
   377
fun fst (x, y) = x;
wenzelm@233
   378
fun snd (x, y) = y;
wenzelm@233
   379
wenzelm@233
   380
fun eq_fst ((x1, _), (x2, _)) = x1 = x2;
wenzelm@233
   381
fun eq_snd ((_, y1), (_, y2)) = y1 = y2;
wenzelm@233
   382
wenzelm@233
   383
fun swap (x, y) = (y, x);
wenzelm@233
   384
wenzelm@4212
   385
(*apply function to components*)
wenzelm@233
   386
fun apfst f (x, y) = (f x, y);
wenzelm@233
   387
fun apsnd f (x, y) = (x, f y);
wenzelm@4212
   388
fun pairself f (x, y) = (f x, f y);
wenzelm@233
   389
wenzelm@233
   390
wenzelm@233
   391
wenzelm@233
   392
(** booleans **)
wenzelm@233
   393
wenzelm@233
   394
(* equality *)
wenzelm@233
   395
wenzelm@233
   396
fun equal x y = x = y;
wenzelm@233
   397
fun not_equal x y = x <> y;
wenzelm@233
   398
wenzelm@233
   399
wenzelm@233
   400
(* operators for combining predicates *)
wenzelm@233
   401
paulson@2175
   402
fun (p orf q) = fn x => p x orelse q x;
paulson@2175
   403
fun (p andf q) = fn x => p x andalso q x;
wenzelm@233
   404
wenzelm@233
   405
wenzelm@233
   406
(* predicates on lists *)
wenzelm@233
   407
wenzelm@233
   408
(*exists pred [x1, ..., xn] ===> pred x1 orelse ... orelse pred xn*)
wenzelm@233
   409
fun exists (pred: 'a -> bool) : 'a list -> bool =
wenzelm@233
   410
  let fun boolf [] = false
wenzelm@233
   411
        | boolf (x :: xs) = pred x orelse boolf xs
wenzelm@233
   412
  in boolf end;
wenzelm@233
   413
wenzelm@233
   414
(*forall pred [x1, ..., xn] ===> pred x1 andalso ... andalso pred xn*)
wenzelm@233
   415
fun forall (pred: 'a -> bool) : 'a list -> bool =
wenzelm@233
   416
  let fun boolf [] = true
wenzelm@233
   417
        | boolf (x :: xs) = pred x andalso boolf xs
wenzelm@233
   418
  in boolf end;
clasohm@0
   419
wenzelm@233
   420
wenzelm@380
   421
(* flags *)
wenzelm@380
   422
wenzelm@380
   423
fun set flag = (flag := true; true);
wenzelm@380
   424
fun reset flag = (flag := false; false);
wenzelm@380
   425
fun toggle flag = (flag := not (! flag); ! flag);
wenzelm@380
   426
wenzelm@9118
   427
fun change r f = r := f (! r);
wenzelm@9118
   428
wenzelm@4212
   429
(*temporarily set flag, handling errors*)
wenzelm@2978
   430
fun setmp flag value f x =
wenzelm@2958
   431
  let
wenzelm@2958
   432
    val orig_value = ! flag;
wenzelm@2958
   433
    fun return y = (flag := orig_value; y);
wenzelm@2958
   434
  in
wenzelm@2958
   435
    flag := value;
wenzelm@2958
   436
    return (f x handle exn => (return (); raise exn))
wenzelm@2958
   437
  end;
wenzelm@2958
   438
wenzelm@380
   439
wenzelm@11853
   440
(* conditional execution *)
wenzelm@11853
   441
wenzelm@11853
   442
fun conditional b f = if b then f () else ();
wenzelm@11853
   443
wenzelm@11853
   444
wenzelm@233
   445
wenzelm@233
   446
(** lists **)
wenzelm@233
   447
wenzelm@233
   448
exception LIST of string;
wenzelm@233
   449
wenzelm@233
   450
fun null [] = true
wenzelm@233
   451
  | null (_ :: _) = false;
wenzelm@233
   452
wenzelm@233
   453
fun hd [] = raise LIST "hd"
wenzelm@233
   454
  | hd (x :: _) = x;
wenzelm@233
   455
wenzelm@233
   456
fun tl [] = raise LIST "tl"
wenzelm@233
   457
  | tl (_ :: xs) = xs;
wenzelm@233
   458
wenzelm@233
   459
fun cons x xs = x :: xs;
wenzelm@5285
   460
fun single x = [x];
wenzelm@233
   461
wenzelm@4629
   462
fun append xs ys = xs @ ys;
wenzelm@4629
   463
berghofe@13794
   464
(* tail recursive version *)
berghofe@13794
   465
fun rev_append [] ys = ys
berghofe@13794
   466
  | rev_append (x :: xs) ys = rev_append xs (x :: ys);
berghofe@13794
   467
wenzelm@5904
   468
fun apply [] x = x
wenzelm@5904
   469
  | apply (f :: fs) x = apply fs (f x);
wenzelm@5904
   470
wenzelm@233
   471
wenzelm@233
   472
(* fold *)
wenzelm@233
   473
wenzelm@233
   474
(*the following versions of fold are designed to fit nicely with infixes*)
clasohm@0
   475
wenzelm@233
   476
(*  (op @) (e, [x1, ..., xn])  ===>  ((e @ x1) @ x2) ... @ xn
wenzelm@233
   477
    for operators that associate to the left (TAIL RECURSIVE)*)
wenzelm@233
   478
fun foldl (f: 'a * 'b -> 'a) : 'a * 'b list -> 'a =
wenzelm@233
   479
  let fun itl (e, [])  = e
wenzelm@233
   480
        | itl (e, a::l) = itl (f(e, a), l)
wenzelm@233
   481
  in  itl end;
wenzelm@233
   482
wenzelm@233
   483
(*  (op @) ([x1, ..., xn], e)  ===>   x1 @ (x2 ... @ (xn @ e))
wenzelm@233
   484
    for operators that associate to the right (not tail recursive)*)
wenzelm@233
   485
fun foldr f (l, e) =
wenzelm@233
   486
  let fun itr [] = e
wenzelm@233
   487
        | itr (a::l) = f(a, itr l)
wenzelm@233
   488
  in  itr l  end;
wenzelm@233
   489
wenzelm@233
   490
(*  (op @) [x1, ..., xn]  ===>   x1 @ (x2 ... @ (x[n-1] @ xn))
wenzelm@233
   491
    for n > 0, operators that associate to the right (not tail recursive)*)
wenzelm@233
   492
fun foldr1 f l =
wenzelm@4181
   493
  let fun itr [x] = x
wenzelm@233
   494
        | itr (x::l) = f(x, itr l)
wenzelm@233
   495
  in  itr l  end;
wenzelm@233
   496
wenzelm@4956
   497
fun foldl_map _ (x, []) = (x, [])
wenzelm@4956
   498
  | foldl_map f (x, y :: ys) =
wenzelm@4956
   499
      let
wenzelm@4956
   500
        val (x', y') = f (x, y);
wenzelm@4956
   501
        val (x'', ys') = foldl_map f (x', ys);
wenzelm@4956
   502
      in (x'', y' :: ys') end;
wenzelm@4956
   503
oheimb@11002
   504
fun foldln f xs e = fst (foldl (fn ((e,i), x) => (f (x,i) e, i+1)) ((e,1),xs));
wenzelm@233
   505
wenzelm@233
   506
(* basic list functions *)
wenzelm@233
   507
wenzelm@233
   508
(*length of a list, should unquestionably be a standard function*)
wenzelm@233
   509
local fun length1 (n, [])  = n   (*TAIL RECURSIVE*)
wenzelm@233
   510
        | length1 (n, x :: xs) = length1 (n + 1, xs)
wenzelm@233
   511
in  fun length l = length1 (0, l) end;
wenzelm@233
   512
wenzelm@233
   513
(*take the first n elements from a list*)
wenzelm@233
   514
fun take (n, []) = []
wenzelm@233
   515
  | take (n, x :: xs) =
wenzelm@233
   516
      if n > 0 then x :: take (n - 1, xs) else [];
wenzelm@233
   517
wenzelm@233
   518
(*drop the first n elements from a list*)
wenzelm@233
   519
fun drop (n, []) = []
wenzelm@233
   520
  | drop (n, x :: xs) =
wenzelm@233
   521
      if n > 0 then drop (n - 1, xs) else x :: xs;
clasohm@0
   522
nipkow@13629
   523
fun splitAt(n,[]) = ([],[])
nipkow@13629
   524
  | splitAt(n,xs as x::ys) =
nipkow@13629
   525
      if n>0 then let val (ps,qs) = splitAt(n-1,ys) in (x::ps,qs) end
nipkow@13629
   526
      else ([],xs)
nipkow@13629
   527
nipkow@4713
   528
fun dropwhile P [] = []
nipkow@4713
   529
  | dropwhile P (ys as x::xs) = if P x then dropwhile P xs else ys;
nipkow@4713
   530
wenzelm@233
   531
(*return nth element of a list, where 0 designates the first element;
wenzelm@233
   532
  raise EXCEPTION if list too short*)
wenzelm@233
   533
fun nth_elem NL =
wenzelm@233
   534
  (case drop NL of
wenzelm@233
   535
    [] => raise LIST "nth_elem"
wenzelm@233
   536
  | x :: _ => x);
wenzelm@233
   537
wenzelm@11773
   538
fun map_nth_elem 0 f (x :: xs) = f x :: xs
wenzelm@11773
   539
  | map_nth_elem n f (x :: xs) = x :: map_nth_elem (n - 1) f xs
wenzelm@11773
   540
  | map_nth_elem _ _ [] = raise LIST "map_nth_elem";
wenzelm@11773
   541
wenzelm@233
   542
(*last element of a list*)
wenzelm@233
   543
fun last_elem [] = raise LIST "last_elem"
wenzelm@233
   544
  | last_elem [x] = x
wenzelm@233
   545
  | last_elem (_ :: xs) = last_elem xs;
wenzelm@233
   546
wenzelm@3762
   547
(*rear decomposition*)
wenzelm@3762
   548
fun split_last [] = raise LIST "split_last"
wenzelm@3762
   549
  | split_last [x] = ([], x)
wenzelm@3762
   550
  | split_last (x :: xs) = apfst (cons x) (split_last xs);
wenzelm@3762
   551
wenzelm@4893
   552
(*update nth element*)
nipkow@13629
   553
fun nth_update x n_xs =
nipkow@13629
   554
    (case splitAt n_xs of
nipkow@13629
   555
      (_,[]) => raise LIST "nth_update"
nipkow@13629
   556
    | (prfx, _ :: sffx') => prfx @ (x :: sffx'))
wenzelm@4893
   557
wenzelm@4212
   558
(*find the position of an element in a list*)
wenzelm@4212
   559
fun find_index pred =
wenzelm@4212
   560
  let fun find _ [] = ~1
wenzelm@4212
   561
        | find n (x :: xs) = if pred x then n else find (n + 1) xs;
wenzelm@4212
   562
  in find 0 end;
wenzelm@3762
   563
wenzelm@4224
   564
fun find_index_eq x = find_index (equal x);
wenzelm@4212
   565
wenzelm@4212
   566
(*find first element satisfying predicate*)
wenzelm@4212
   567
fun find_first _ [] = None
wenzelm@4212
   568
  | find_first pred (x :: xs) =
wenzelm@4212
   569
      if pred x then Some x else find_first pred xs;
wenzelm@233
   570
wenzelm@4916
   571
(*get first element by lookup function*)
wenzelm@4916
   572
fun get_first _ [] = None
wenzelm@4916
   573
  | get_first f (x :: xs) =
wenzelm@4916
   574
      (case f x of
wenzelm@4916
   575
        None => get_first f xs
wenzelm@4916
   576
      | some => some);
wenzelm@4916
   577
wenzelm@233
   578
(*flatten a list of lists to a list*)
wenzelm@233
   579
fun flat (ls: 'c list list) : 'c list = foldr (op @) (ls, []);
wenzelm@233
   580
wenzelm@12136
   581
fun unflat (xs :: xss) ys =
nipkow@13629
   582
      let val (ps,qs) = splitAt(length xs,ys)
nipkow@13629
   583
      in ps :: unflat xss qs end
wenzelm@12136
   584
  | unflat [] [] = []
wenzelm@12136
   585
  | unflat _ _ = raise LIST "unflat";
wenzelm@12136
   586
wenzelm@233
   587
(*like Lisp's MAPC -- seq proc [x1, ..., xn] evaluates
wenzelm@233
   588
  (proc x1; ...; proc xn) for side effects*)
wenzelm@233
   589
fun seq (proc: 'a -> unit) : 'a list -> unit =
wenzelm@233
   590
  let fun seqf [] = ()
wenzelm@233
   591
        | seqf (x :: xs) = (proc x; seqf xs)
wenzelm@233
   592
  in seqf end;
wenzelm@233
   593
wenzelm@233
   594
(*separate s [x1, x2, ..., xn]  ===>  [x1, s, x2, s, ..., s, xn]*)
wenzelm@233
   595
fun separate s (x :: (xs as _ :: _)) = x :: s :: separate s xs
wenzelm@233
   596
  | separate _ xs = xs;
wenzelm@233
   597
wenzelm@233
   598
(*make the list [x, x, ..., x] of length n*)
wenzelm@233
   599
fun replicate n (x: 'a) : 'a list =
wenzelm@233
   600
  let fun rep (0, xs) = xs
wenzelm@233
   601
        | rep (n, xs) = rep (n - 1, x :: xs)
wenzelm@233
   602
  in
wenzelm@233
   603
    if n < 0 then raise LIST "replicate"
wenzelm@233
   604
    else rep (n, [])
wenzelm@233
   605
  end;
wenzelm@233
   606
wenzelm@4248
   607
(*multiply [a, b, c, ...] * [xs, ys, zs, ...]*)
wenzelm@4248
   608
fun multiply ([], _) = []
wenzelm@4248
   609
  | multiply (x :: xs, yss) = map (cons x) yss @ multiply (xs, yss);
wenzelm@4248
   610
wenzelm@233
   611
wenzelm@233
   612
(* filter *)
wenzelm@233
   613
wenzelm@233
   614
(*copy the list preserving elements that satisfy the predicate*)
wenzelm@233
   615
fun filter (pred: 'a->bool) : 'a list -> 'a list =
clasohm@0
   616
  let fun filt [] = []
wenzelm@233
   617
        | filt (x :: xs) = if pred x then x :: filt xs else filt xs
wenzelm@233
   618
  in filt end;
clasohm@0
   619
clasohm@0
   620
fun filter_out f = filter (not o f);
clasohm@0
   621
wenzelm@233
   622
fun mapfilter (f: 'a -> 'b option) ([]: 'a list) = [] : 'b list
wenzelm@233
   623
  | mapfilter f (x :: xs) =
wenzelm@233
   624
      (case f x of
wenzelm@233
   625
        None => mapfilter f xs
wenzelm@233
   626
      | Some y => y :: mapfilter f xs);
wenzelm@233
   627
wenzelm@233
   628
wenzelm@233
   629
(* lists of pairs *)
wenzelm@233
   630
wenzelm@380
   631
fun map2 _ ([], []) = []
wenzelm@380
   632
  | map2 f (x :: xs, y :: ys) = (f (x, y) :: map2 f (xs, ys))
wenzelm@380
   633
  | map2 _ _ = raise LIST "map2";
wenzelm@380
   634
wenzelm@380
   635
fun exists2 _ ([], []) = false
wenzelm@380
   636
  | exists2 pred (x :: xs, y :: ys) = pred (x, y) orelse exists2 pred (xs, ys)
wenzelm@380
   637
  | exists2 _ _ = raise LIST "exists2";
wenzelm@380
   638
wenzelm@380
   639
fun forall2 _ ([], []) = true
wenzelm@380
   640
  | forall2 pred (x :: xs, y :: ys) = pred (x, y) andalso forall2 pred (xs, ys)
wenzelm@380
   641
  | forall2 _ _ = raise LIST "forall2";
wenzelm@380
   642
wenzelm@4956
   643
fun seq2 _ ([], []) = ()
wenzelm@4956
   644
  | seq2 f (x :: xs, y :: ys) = (f (x, y); seq2 f (xs, ys))
wenzelm@4956
   645
  | seq2 _ _ = raise LIST "seq2";
wenzelm@4956
   646
wenzelm@233
   647
(*combine two lists forming a list of pairs:
wenzelm@233
   648
  [x1, ..., xn] ~~ [y1, ..., yn]  ===>  [(x1, y1), ..., (xn, yn)]*)
wenzelm@233
   649
fun [] ~~ [] = []
wenzelm@233
   650
  | (x :: xs) ~~ (y :: ys) = (x, y) :: (xs ~~ ys)
wenzelm@233
   651
  | _ ~~ _ = raise LIST "~~";
wenzelm@233
   652
wenzelm@233
   653
(*inverse of ~~; the old 'split':
wenzelm@233
   654
  [(x1, y1), ..., (xn, yn)]  ===>  ([x1, ..., xn], [y1, ..., yn])*)
wenzelm@233
   655
fun split_list (l: ('a * 'b) list) = (map #1 l, map #2 l);
wenzelm@233
   656
wenzelm@7468
   657
fun equal_lists eq (xs, ys) = length xs = length ys andalso forall2 eq (xs, ys);
wenzelm@7468
   658
wenzelm@233
   659
wenzelm@233
   660
(* prefixes, suffixes *)
wenzelm@233
   661
wenzelm@233
   662
fun [] prefix _ = true
wenzelm@233
   663
  | (x :: xs) prefix (y :: ys) = x = y andalso (xs prefix ys)
wenzelm@233
   664
  | _ prefix _ = false;
wenzelm@233
   665
wenzelm@233
   666
(* [x1, ..., xi, ..., xn]  --->  ([x1, ..., x(i-1)], [xi, ..., xn])
wenzelm@233
   667
   where xi is the first element that does not satisfy the predicate*)
wenzelm@233
   668
fun take_prefix (pred : 'a -> bool)  (xs: 'a list) : 'a list * 'a list =
wenzelm@233
   669
  let fun take (rxs, []) = (rev rxs, [])
wenzelm@255
   670
        | take (rxs, x :: xs) =
wenzelm@255
   671
            if  pred x  then  take(x :: rxs, xs)  else  (rev rxs, x :: xs)
wenzelm@233
   672
  in  take([], xs)  end;
wenzelm@233
   673
wenzelm@233
   674
(* [x1, ..., xi, ..., xn]  --->  ([x1, ..., xi], [x(i+1), ..., xn])
wenzelm@233
   675
   where xi is the last element that does not satisfy the predicate*)
wenzelm@233
   676
fun take_suffix _ [] = ([], [])
wenzelm@233
   677
  | take_suffix pred (x :: xs) =
wenzelm@233
   678
      (case take_suffix pred xs of
wenzelm@233
   679
        ([], sffx) => if pred x then ([], x :: sffx) else ([x], sffx)
wenzelm@233
   680
      | (prfx, sffx) => (x :: prfx, sffx));
wenzelm@233
   681
wenzelm@12249
   682
fun prefixes1 [] = []
wenzelm@12249
   683
  | prefixes1 (x :: xs) = map (cons x) ([] :: prefixes1 xs);
wenzelm@12249
   684
wenzelm@12249
   685
fun suffixes1 xs = map rev (prefixes1 (rev xs));
wenzelm@12249
   686
wenzelm@233
   687
wenzelm@233
   688
wenzelm@233
   689
(** integers **)
wenzelm@233
   690
nipkow@10692
   691
fun gcd(x,y) =
nipkow@10692
   692
  let fun gxd x y =
nipkow@10692
   693
    if y = 0 then x else gxd y (x mod y)
nipkow@10692
   694
  in if x < y then gxd y x else gxd x y end;
nipkow@10692
   695
nipkow@10692
   696
fun lcm(x,y) = (x * y) div gcd(x,y);
nipkow@10692
   697
wenzelm@2958
   698
fun inc i = (i := ! i + 1; ! i);
wenzelm@2958
   699
fun dec i = (i := ! i - 1; ! i);
wenzelm@233
   700
wenzelm@233
   701
wenzelm@233
   702
(* lists of integers *)
wenzelm@233
   703
wenzelm@233
   704
(*make the list [from, from + 1, ..., to]*)
paulson@2175
   705
fun (from upto to) =
wenzelm@233
   706
  if from > to then [] else from :: ((from + 1) upto to);
wenzelm@233
   707
wenzelm@233
   708
(*make the list [from, from - 1, ..., to]*)
paulson@2175
   709
fun (from downto to) =
wenzelm@233
   710
  if from < to then [] else from :: ((from - 1) downto to);
wenzelm@233
   711
wenzelm@233
   712
(*predicate: downto0 (is, n) <=> is = [n, n - 1, ..., 0]*)
wenzelm@233
   713
fun downto0 (i :: is, n) = i = n andalso downto0 (is, n - 1)
wenzelm@233
   714
  | downto0 ([], n) = n = ~1;
wenzelm@233
   715
wenzelm@233
   716
wenzelm@233
   717
(* convert integers to strings *)
wenzelm@233
   718
wenzelm@233
   719
(*expand the number in the given base;
wenzelm@233
   720
  example: radixpand (2, 8) gives [1, 0, 0, 0]*)
wenzelm@233
   721
fun radixpand (base, num) : int list =
wenzelm@233
   722
  let
wenzelm@233
   723
    fun radix (n, tail) =
wenzelm@233
   724
      if n < base then n :: tail
wenzelm@233
   725
      else radix (n div base, (n mod base) :: tail)
wenzelm@233
   726
  in radix (num, []) end;
wenzelm@233
   727
wenzelm@233
   728
(*expands a number into a string of characters starting from "zerochar";
wenzelm@233
   729
  example: radixstring (2, "0", 8) gives "1000"*)
wenzelm@233
   730
fun radixstring (base, zerochar, num) =
wenzelm@233
   731
  let val offset = ord zerochar;
wenzelm@233
   732
      fun chrof n = chr (offset + n)
wenzelm@233
   733
  in implode (map chrof (radixpand (base, num))) end;
wenzelm@233
   734
wenzelm@233
   735
paulson@3407
   736
val string_of_int = Int.toString;
wenzelm@233
   737
paulson@3407
   738
fun string_of_indexname (a,0) = a
paulson@3407
   739
  | string_of_indexname (a,i) = a ^ "_" ^ Int.toString i;
wenzelm@233
   740
wenzelm@233
   741
wenzelm@233
   742
(** strings **)
wenzelm@233
   743
wenzelm@6312
   744
(*functions tuned for strings, avoiding explode*)
wenzelm@6312
   745
wenzelm@6312
   746
fun nth_elem_string (i, str) =
wenzelm@6959
   747
  (case try String.substring (str, i, 1) of
wenzelm@6959
   748
    Some s => s
wenzelm@6959
   749
  | None => raise LIST "nth_elem_string");
wenzelm@6312
   750
wenzelm@6282
   751
fun foldl_string f (x0, str) =
wenzelm@6282
   752
  let
wenzelm@6282
   753
    val n = size str;
wenzelm@6282
   754
    fun fold (x, i) = if i < n then fold (f (x, String.substring (str, i, 1)), i + 1) else x
wenzelm@6282
   755
  in fold (x0, 0) end;
wenzelm@6282
   756
wenzelm@6312
   757
fun exists_string pred str = foldl_string (fn (b, s) => b orelse pred s) (false, str);
wenzelm@6312
   758
lcp@512
   759
(*enclose in brackets*)
lcp@512
   760
fun enclose lpar rpar str = lpar ^ str ^ rpar;
wenzelm@6642
   761
fun unenclose str = String.substring (str, 1, size str - 2);
wenzelm@255
   762
wenzelm@233
   763
(*simple quoting (does not escape special chars)*)
lcp@512
   764
val quote = enclose "\"" "\"";
wenzelm@233
   765
wenzelm@4212
   766
(*space_implode "..." (explode "hello") = "h...e...l...l...o"*)
wenzelm@233
   767
fun space_implode a bs = implode (separate a bs);
wenzelm@233
   768
wenzelm@255
   769
val commas = space_implode ", ";
wenzelm@380
   770
val commas_quote = commas o map quote;
wenzelm@255
   771
wenzelm@233
   772
(*concatenate messages, one per line, into a string*)
wenzelm@255
   773
val cat_lines = space_implode "\n";
wenzelm@233
   774
wenzelm@4212
   775
(*space_explode "." "h.e..l.lo" = ["h", "e", "", "l", "lo"]*)
wenzelm@3832
   776
fun space_explode _ "" = []
wenzelm@3832
   777
  | space_explode sep str =
wenzelm@3832
   778
      let
wenzelm@3832
   779
        fun expl chs =
wenzelm@3832
   780
          (case take_prefix (not_equal sep) chs of
wenzelm@3832
   781
            (cs, []) => [implode cs]
wenzelm@3832
   782
          | (cs, _ :: cs') => implode cs :: expl cs');
wenzelm@3832
   783
      in expl (explode str) end;
wenzelm@3832
   784
wenzelm@3832
   785
val split_lines = space_explode "\n";
wenzelm@3832
   786
wenzelm@7712
   787
(*untabify*)
wenzelm@7712
   788
fun untabify chs =
wenzelm@7712
   789
  let
wenzelm@7712
   790
    val tab_width = 8;
wenzelm@7712
   791
wenzelm@7712
   792
    fun untab (_, "\n") = (0, ["\n"])
wenzelm@9118
   793
      | untab (pos, "\t") =
wenzelm@9118
   794
          let val d = tab_width - (pos mod tab_width) in (pos + d, replicate d " ") end
wenzelm@7712
   795
      | untab (pos, c) = (pos + 1, [c]);
wenzelm@7712
   796
  in
wenzelm@7712
   797
    if not (exists (equal "\t") chs) then chs
wenzelm@7712
   798
    else flat (#2 (foldl_map untab (0, chs)))
wenzelm@7712
   799
  end;
wenzelm@7712
   800
wenzelm@5285
   801
(*append suffix*)
wenzelm@5285
   802
fun suffix sfx s = s ^ sfx;
wenzelm@5285
   803
wenzelm@5285
   804
(*remove suffix*)
wenzelm@5285
   805
fun unsuffix sfx s =
wenzelm@5285
   806
  let
wenzelm@5285
   807
    val cs = explode s;
wenzelm@5285
   808
    val prfx_len = size s - size sfx;
wenzelm@5285
   809
  in
wenzelm@5285
   810
    if prfx_len >= 0 andalso implode (drop (prfx_len, cs)) = sfx then
wenzelm@5285
   811
      implode (take (prfx_len, cs))
wenzelm@5285
   812
    else raise LIST "unsuffix"
wenzelm@5285
   813
  end;
wenzelm@5285
   814
wenzelm@10951
   815
fun replicate_string 0 _ = ""
wenzelm@10951
   816
  | replicate_string 1 a = a
wenzelm@10951
   817
  | replicate_string k a =
wenzelm@10951
   818
      if k mod 2 = 0 then replicate_string (k div 2) (a ^ a)
wenzelm@10951
   819
      else replicate_string (k div 2) (a ^ a) ^ a;
wenzelm@10951
   820
wenzelm@3832
   821
wenzelm@233
   822
wenzelm@233
   823
(** lists as sets **)
wenzelm@233
   824
wenzelm@233
   825
(*membership in a list*)
wenzelm@233
   826
fun x mem [] = false
wenzelm@233
   827
  | x mem (y :: ys) = x = y orelse x mem ys;
clasohm@0
   828
paulson@2175
   829
(*membership in a list, optimized version for ints*)
berghofe@1576
   830
fun (x:int) mem_int [] = false
berghofe@1576
   831
  | x mem_int (y :: ys) = x = y orelse x mem_int ys;
berghofe@1576
   832
paulson@2175
   833
(*membership in a list, optimized version for strings*)
berghofe@1576
   834
fun (x:string) mem_string [] = false
berghofe@1576
   835
  | x mem_string (y :: ys) = x = y orelse x mem_string ys;
berghofe@1576
   836
clasohm@0
   837
(*generalized membership test*)
wenzelm@233
   838
fun gen_mem eq (x, []) = false
wenzelm@233
   839
  | gen_mem eq (x, y :: ys) = eq (x, y) orelse gen_mem eq (x, ys);
wenzelm@233
   840
wenzelm@233
   841
wenzelm@233
   842
(*insertion into list if not already there*)
paulson@2175
   843
fun (x ins xs) = if x mem xs then xs else x :: xs;
clasohm@0
   844
paulson@2175
   845
(*insertion into list, optimized version for ints*)
paulson@2175
   846
fun (x ins_int xs) = if x mem_int xs then xs else x :: xs;
berghofe@1576
   847
paulson@2175
   848
(*insertion into list, optimized version for strings*)
paulson@2175
   849
fun (x ins_string xs) = if x mem_string xs then xs else x :: xs;
berghofe@1576
   850
clasohm@0
   851
(*generalized insertion*)
wenzelm@233
   852
fun gen_ins eq (x, xs) = if gen_mem eq (x, xs) then xs else x :: xs;
wenzelm@233
   853
wenzelm@233
   854
wenzelm@233
   855
(*union of sets represented as lists: no repetitions*)
wenzelm@233
   856
fun xs union [] = xs
wenzelm@233
   857
  | [] union ys = ys
wenzelm@233
   858
  | (x :: xs) union ys = xs union (x ins ys);
clasohm@0
   859
paulson@2175
   860
(*union of sets, optimized version for ints*)
berghofe@1576
   861
fun (xs:int list) union_int [] = xs
berghofe@1576
   862
  | [] union_int ys = ys
berghofe@1576
   863
  | (x :: xs) union_int ys = xs union_int (x ins_int ys);
berghofe@1576
   864
paulson@2175
   865
(*union of sets, optimized version for strings*)
berghofe@1576
   866
fun (xs:string list) union_string [] = xs
berghofe@1576
   867
  | [] union_string ys = ys
berghofe@1576
   868
  | (x :: xs) union_string ys = xs union_string (x ins_string ys);
berghofe@1576
   869
clasohm@0
   870
(*generalized union*)
wenzelm@233
   871
fun gen_union eq (xs, []) = xs
wenzelm@233
   872
  | gen_union eq ([], ys) = ys
wenzelm@233
   873
  | gen_union eq (x :: xs, ys) = gen_union eq (xs, gen_ins eq (x, ys));
wenzelm@233
   874
wenzelm@233
   875
wenzelm@233
   876
(*intersection*)
wenzelm@233
   877
fun [] inter ys = []
wenzelm@233
   878
  | (x :: xs) inter ys =
wenzelm@233
   879
      if x mem ys then x :: (xs inter ys) else xs inter ys;
wenzelm@233
   880
paulson@2175
   881
(*intersection, optimized version for ints*)
berghofe@1576
   882
fun ([]:int list) inter_int ys = []
berghofe@1576
   883
  | (x :: xs) inter_int ys =
berghofe@1576
   884
      if x mem_int ys then x :: (xs inter_int ys) else xs inter_int ys;
berghofe@1576
   885
paulson@2175
   886
(*intersection, optimized version for strings *)
berghofe@1576
   887
fun ([]:string list) inter_string ys = []
berghofe@1576
   888
  | (x :: xs) inter_string ys =
berghofe@1576
   889
      if x mem_string ys then x :: (xs inter_string ys) else xs inter_string ys;
berghofe@1576
   890
paulson@7090
   891
(*generalized intersection*)
paulson@7090
   892
fun gen_inter eq ([], ys) = []
wenzelm@12284
   893
  | gen_inter eq (x::xs, ys) =
paulson@7090
   894
      if gen_mem eq (x,ys) then x :: gen_inter eq (xs, ys)
wenzelm@12284
   895
                           else      gen_inter eq (xs, ys);
paulson@7090
   896
wenzelm@233
   897
wenzelm@233
   898
(*subset*)
wenzelm@233
   899
fun [] subset ys = true
wenzelm@233
   900
  | (x :: xs) subset ys = x mem ys andalso xs subset ys;
wenzelm@233
   901
paulson@2175
   902
(*subset, optimized version for ints*)
berghofe@1576
   903
fun ([]:int list) subset_int ys = true
berghofe@1576
   904
  | (x :: xs) subset_int ys = x mem_int ys andalso xs subset_int ys;
berghofe@1576
   905
paulson@2175
   906
(*subset, optimized version for strings*)
berghofe@1576
   907
fun ([]:string list) subset_string ys = true
berghofe@1576
   908
  | (x :: xs) subset_string ys = x mem_string ys andalso xs subset_string ys;
berghofe@1576
   909
wenzelm@4363
   910
(*set equality*)
wenzelm@4363
   911
fun eq_set (xs, ys) =
wenzelm@4363
   912
  xs = ys orelse (xs subset ys andalso ys subset xs);
wenzelm@4363
   913
paulson@2182
   914
(*set equality for strings*)
berghofe@1576
   915
fun eq_set_string ((xs:string list), ys) =
berghofe@1576
   916
  xs = ys orelse (xs subset_string ys andalso ys subset_string xs);
berghofe@1576
   917
paulson@2182
   918
fun gen_subset eq (xs, ys) = forall (fn x => gen_mem eq (x, ys)) xs;
paulson@2182
   919
wenzelm@265
   920
wenzelm@233
   921
(*removing an element from a list WITHOUT duplicates*)
wenzelm@233
   922
fun (y :: ys) \ x = if x = y then ys else y :: (ys \ x)
wenzelm@233
   923
  | [] \ x = [];
wenzelm@233
   924
paulson@2243
   925
fun ys \\ xs = foldl (op \) (ys,xs);
clasohm@0
   926
wenzelm@233
   927
(*removing an element from a list -- possibly WITH duplicates*)
wenzelm@233
   928
fun gen_rem eq (xs, y) = filter_out (fn x => eq (x, y)) xs;
wenzelm@12295
   929
fun gen_rems eq (xs, ys) = filter_out (fn x => gen_mem eq (x, ys)) xs;
wenzelm@233
   930
wenzelm@233
   931
wenzelm@233
   932
(*makes a list of the distinct members of the input; preserves order, takes
wenzelm@233
   933
  first of equal elements*)
wenzelm@233
   934
fun gen_distinct eq lst =
wenzelm@233
   935
  let
wenzelm@233
   936
    val memb = gen_mem eq;
clasohm@0
   937
wenzelm@233
   938
    fun dist (rev_seen, []) = rev rev_seen
wenzelm@233
   939
      | dist (rev_seen, x :: xs) =
wenzelm@233
   940
          if memb (x, rev_seen) then dist (rev_seen, xs)
wenzelm@233
   941
          else dist (x :: rev_seen, xs);
wenzelm@233
   942
  in
wenzelm@233
   943
    dist ([], lst)
wenzelm@233
   944
  end;
wenzelm@233
   945
paulson@2243
   946
fun distinct l = gen_distinct (op =) l;
wenzelm@233
   947
wenzelm@233
   948
wenzelm@233
   949
(*returns the tail beginning with the first repeated element, or []*)
wenzelm@233
   950
fun findrep [] = []
wenzelm@233
   951
  | findrep (x :: xs) = if x mem xs then x :: xs else findrep xs;
wenzelm@233
   952
wenzelm@233
   953
wenzelm@255
   954
(*returns a list containing all repeated elements exactly once; preserves
wenzelm@255
   955
  order, takes first of equal elements*)
wenzelm@255
   956
fun gen_duplicates eq lst =
wenzelm@255
   957
  let
wenzelm@255
   958
    val memb = gen_mem eq;
wenzelm@255
   959
wenzelm@255
   960
    fun dups (rev_dups, []) = rev rev_dups
wenzelm@255
   961
      | dups (rev_dups, x :: xs) =
wenzelm@255
   962
          if memb (x, rev_dups) orelse not (memb (x, xs)) then
wenzelm@255
   963
            dups (rev_dups, xs)
wenzelm@255
   964
          else dups (x :: rev_dups, xs);
wenzelm@255
   965
  in
wenzelm@255
   966
    dups ([], lst)
wenzelm@255
   967
  end;
wenzelm@255
   968
paulson@2243
   969
fun duplicates l = gen_duplicates (op =) l;
wenzelm@255
   970
wenzelm@255
   971
wenzelm@233
   972
wenzelm@233
   973
(** association lists **)
clasohm@0
   974
wenzelm@233
   975
(*association list lookup*)
wenzelm@233
   976
fun assoc ([], key) = None
wenzelm@233
   977
  | assoc ((keyi, xi) :: pairs, key) =
wenzelm@233
   978
      if key = keyi then Some xi else assoc (pairs, key);
wenzelm@233
   979
paulson@2175
   980
(*association list lookup, optimized version for ints*)
berghofe@1576
   981
fun assoc_int ([], (key:int)) = None
berghofe@1576
   982
  | assoc_int ((keyi, xi) :: pairs, key) =
berghofe@1576
   983
      if key = keyi then Some xi else assoc_int (pairs, key);
berghofe@1576
   984
paulson@2175
   985
(*association list lookup, optimized version for strings*)
berghofe@1576
   986
fun assoc_string ([], (key:string)) = None
berghofe@1576
   987
  | assoc_string ((keyi, xi) :: pairs, key) =
berghofe@1576
   988
      if key = keyi then Some xi else assoc_string (pairs, key);
berghofe@1576
   989
paulson@2175
   990
(*association list lookup, optimized version for string*ints*)
berghofe@1576
   991
fun assoc_string_int ([], (key:string*int)) = None
berghofe@1576
   992
  | assoc_string_int ((keyi, xi) :: pairs, key) =
berghofe@1576
   993
      if key = keyi then Some xi else assoc_string_int (pairs, key);
berghofe@1576
   994
wenzelm@233
   995
fun assocs ps x =
wenzelm@233
   996
  (case assoc (ps, x) of
wenzelm@233
   997
    None => []
wenzelm@233
   998
  | Some ys => ys);
wenzelm@233
   999
wenzelm@255
  1000
(*two-fold association list lookup*)
wenzelm@255
  1001
fun assoc2 (aal, (key1, key2)) =
wenzelm@255
  1002
  (case assoc (aal, key1) of
wenzelm@255
  1003
    Some al => assoc (al, key2)
wenzelm@255
  1004
  | None => None);
wenzelm@255
  1005
wenzelm@233
  1006
(*generalized association list lookup*)
wenzelm@233
  1007
fun gen_assoc eq ([], key) = None
wenzelm@233
  1008
  | gen_assoc eq ((keyi, xi) :: pairs, key) =
wenzelm@233
  1009
      if eq (key, keyi) then Some xi else gen_assoc eq (pairs, key);
wenzelm@233
  1010
wenzelm@233
  1011
(*association list update*)
wenzelm@233
  1012
fun overwrite (al, p as (key, _)) =
wenzelm@233
  1013
  let fun over ((q as (keyi, _)) :: pairs) =
wenzelm@233
  1014
            if keyi = key then p :: pairs else q :: (over pairs)
wenzelm@233
  1015
        | over [] = [p]
wenzelm@233
  1016
  in over al end;
wenzelm@233
  1017
wenzelm@2522
  1018
fun gen_overwrite eq (al, p as (key, _)) =
wenzelm@2522
  1019
  let fun over ((q as (keyi, _)) :: pairs) =
wenzelm@2522
  1020
            if eq (keyi, key) then p :: pairs else q :: (over pairs)
wenzelm@2522
  1021
        | over [] = [p]
wenzelm@2522
  1022
  in over al end;
wenzelm@2522
  1023
wenzelm@233
  1024
wenzelm@12284
  1025
(* lists as tables *)
wenzelm@233
  1026
wenzelm@12284
  1027
fun gen_merge_lists _ xs [] = xs
wenzelm@12284
  1028
  | gen_merge_lists _ [] ys = ys
wenzelm@12284
  1029
  | gen_merge_lists eq xs ys = xs @ gen_rems eq (ys, xs);
clasohm@0
  1030
wenzelm@12284
  1031
fun gen_merge_lists' _ xs [] = xs
wenzelm@12284
  1032
  | gen_merge_lists' _ [] ys = ys
wenzelm@12295
  1033
  | gen_merge_lists' eq xs ys = gen_rems eq (ys, xs) @ xs;
clasohm@0
  1034
wenzelm@12284
  1035
fun merge_lists xs ys = gen_merge_lists (op =) xs ys;
wenzelm@12284
  1036
fun merge_lists' xs ys = gen_merge_lists' (op =) xs ys;
wenzelm@12284
  1037
fun merge_alists al = gen_merge_lists eq_fst al;
wenzelm@380
  1038
clasohm@0
  1039
clasohm@0
  1040
wenzelm@233
  1041
(** balanced trees **)
wenzelm@233
  1042
wenzelm@233
  1043
exception Balance;      (*indicates non-positive argument to balancing fun*)
wenzelm@233
  1044
wenzelm@233
  1045
(*balanced folding; avoids deep nesting*)
wenzelm@233
  1046
fun fold_bal f [x] = x
wenzelm@233
  1047
  | fold_bal f [] = raise Balance
wenzelm@233
  1048
  | fold_bal f xs =
nipkow@13629
  1049
      let val (ps,qs) = splitAt(length xs div 2, xs)
nipkow@13629
  1050
      in  f (fold_bal f ps, fold_bal f qs)  end;
wenzelm@233
  1051
wenzelm@233
  1052
(*construct something of the form f(...g(...(x)...)) for balanced access*)
wenzelm@233
  1053
fun access_bal (f, g, x) n i =
wenzelm@233
  1054
  let fun acc n i =     (*1<=i<=n*)
wenzelm@233
  1055
          if n=1 then x else
wenzelm@233
  1056
          let val n2 = n div 2
wenzelm@233
  1057
          in  if i<=n2 then f (acc n2 i)
wenzelm@233
  1058
                       else g (acc (n-n2) (i-n2))
wenzelm@233
  1059
          end
wenzelm@233
  1060
  in  if 1<=i andalso i<=n then acc n i else raise Balance  end;
wenzelm@233
  1061
wenzelm@233
  1062
(*construct ALL such accesses; could try harder to share recursive calls!*)
wenzelm@233
  1063
fun accesses_bal (f, g, x) n =
wenzelm@233
  1064
  let fun acc n =
wenzelm@233
  1065
          if n=1 then [x] else
wenzelm@233
  1066
          let val n2 = n div 2
wenzelm@233
  1067
              val acc2 = acc n2
wenzelm@233
  1068
          in  if n-n2=n2 then map f acc2 @ map g acc2
wenzelm@233
  1069
                         else map f acc2 @ map g (acc (n-n2)) end
wenzelm@233
  1070
  in  if 1<=n then acc n else raise Balance  end;
wenzelm@233
  1071
wenzelm@233
  1072
wenzelm@233
  1073
wenzelm@2506
  1074
(** orders **)
wenzelm@2506
  1075
wenzelm@2506
  1076
datatype order = LESS | EQUAL | GREATER;
wenzelm@2506
  1077
wenzelm@4445
  1078
fun rev_order LESS = GREATER
wenzelm@4445
  1079
  | rev_order EQUAL = EQUAL
wenzelm@4445
  1080
  | rev_order GREATER = LESS;
wenzelm@4445
  1081
wenzelm@4479
  1082
(*assume rel is a linear strict order*)
wenzelm@4445
  1083
fun make_ord rel (x, y) =
wenzelm@4445
  1084
  if rel (x, y) then LESS
wenzelm@4445
  1085
  else if rel (y, x) then GREATER
wenzelm@4445
  1086
  else EQUAL;
wenzelm@4445
  1087
wenzelm@4343
  1088
fun int_ord (i, j: int) =
wenzelm@2506
  1089
  if i < j then LESS
wenzelm@2506
  1090
  else if i = j then EQUAL
wenzelm@2506
  1091
  else GREATER;
wenzelm@2506
  1092
wenzelm@4343
  1093
fun string_ord (a, b: string) =
wenzelm@2506
  1094
  if a < b then LESS
wenzelm@2506
  1095
  else if a = b then EQUAL
wenzelm@2506
  1096
  else GREATER;
wenzelm@2506
  1097
wenzelm@4343
  1098
(*lexicographic product*)
wenzelm@4343
  1099
fun prod_ord a_ord b_ord ((x, y), (x', y')) =
wenzelm@4343
  1100
  (case a_ord (x, x') of EQUAL => b_ord (y, y') | ord => ord);
wenzelm@4343
  1101
wenzelm@4343
  1102
(*dictionary order -- in general NOT well-founded!*)
wenzelm@4343
  1103
fun dict_ord _ ([], []) = EQUAL
wenzelm@4343
  1104
  | dict_ord _ ([], _ :: _) = LESS
wenzelm@4343
  1105
  | dict_ord _ (_ :: _, []) = GREATER
wenzelm@4343
  1106
  | dict_ord elem_ord (x :: xs, y :: ys) =
wenzelm@4343
  1107
      (case elem_ord (x, y) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord);
wenzelm@4343
  1108
wenzelm@4343
  1109
(*lexicographic product of lists*)
wenzelm@4343
  1110
fun list_ord elem_ord (xs, ys) =
wenzelm@4343
  1111
  prod_ord int_ord (dict_ord elem_ord) ((length xs, xs), (length ys, ys));
wenzelm@4343
  1112
wenzelm@2506
  1113
wenzelm@4621
  1114
(* sorting *)
wenzelm@4621
  1115
wenzelm@4621
  1116
(*quicksort (stable, i.e. does not reorder equal elements)*)
wenzelm@4621
  1117
fun sort ord =
wenzelm@4621
  1118
  let
wenzelm@4621
  1119
    fun qsort xs =
wenzelm@4621
  1120
      let val len = length xs in
wenzelm@4621
  1121
        if len <= 1 then xs
wenzelm@4621
  1122
        else
wenzelm@4621
  1123
          let val (lts, eqs, gts) = part (nth_elem (len div 2, xs)) xs in
wenzelm@4621
  1124
            qsort lts @ eqs @ qsort gts
wenzelm@4621
  1125
          end
wenzelm@4621
  1126
      end
wenzelm@4621
  1127
    and part _ [] = ([], [], [])
wenzelm@4621
  1128
      | part pivot (x :: xs) = add (ord (x, pivot)) x (part pivot xs)
wenzelm@4621
  1129
    and add LESS x (lts, eqs, gts) = (x :: lts, eqs, gts)
wenzelm@4621
  1130
      | add EQUAL x (lts, eqs, gts) = (lts, x :: eqs, gts)
wenzelm@4621
  1131
      | add GREATER x (lts, eqs, gts) = (lts, eqs, x :: gts);
wenzelm@4621
  1132
  in qsort end;
wenzelm@4621
  1133
wenzelm@4621
  1134
(*sort strings*)
wenzelm@4621
  1135
val sort_strings = sort string_ord;
wenzelm@4621
  1136
fun sort_wrt sel xs = sort (string_ord o pairself sel) xs;
wenzelm@4621
  1137
berghofe@11514
  1138
fun unique_strings ([]: string list) = []
berghofe@11514
  1139
  | unique_strings [x] = [x]
berghofe@11514
  1140
  | unique_strings (x :: y :: ys) =
berghofe@11514
  1141
      if x = y then unique_strings (y :: ys)
berghofe@11514
  1142
      else x :: unique_strings (y :: ys);
wenzelm@4621
  1143
wenzelm@2506
  1144
berghofe@14106
  1145
(** random numbers **)
berghofe@14106
  1146
berghofe@14106
  1147
exception RANDOM;
berghofe@14106
  1148
berghofe@14106
  1149
fun rmod x y = x - y * real (Real.floor (x / y));
berghofe@14106
  1150
berghofe@14106
  1151
local
berghofe@14106
  1152
  val a = 16807.0;
berghofe@14106
  1153
  val m = 2147483647.0;
berghofe@14106
  1154
  val random_seed = ref 1.0;
berghofe@14106
  1155
in
berghofe@14106
  1156
berghofe@14106
  1157
fun random () =
berghofe@14106
  1158
  let val r = rmod (a * !random_seed) m
berghofe@14106
  1159
  in (random_seed := r; r) end;
berghofe@14106
  1160
berghofe@14106
  1161
end;
berghofe@14106
  1162
berghofe@14106
  1163
fun random_range l h =
berghofe@14106
  1164
  if h < l orelse l < 0 then raise RANDOM
berghofe@14106
  1165
  else l + Real.floor (rmod (random ()) (real (h - l + 1)));
berghofe@14106
  1166
berghofe@14106
  1167
fun one_of xs = nth_elem (random_range 0 (length xs - 1), xs);
berghofe@14106
  1168
berghofe@14106
  1169
fun frequency xs =
berghofe@14106
  1170
  let
berghofe@14106
  1171
    val sum = foldl op + (0, map fst xs);
berghofe@14106
  1172
    fun pick n ((k, x) :: xs) =
berghofe@14106
  1173
      if n <= k then x else pick (n - k) xs
berghofe@14106
  1174
  in pick (random_range 1 sum) xs end;
berghofe@14106
  1175
berghofe@14106
  1176
wenzelm@3525
  1177
(** input / output and diagnostics **)
wenzelm@233
  1178
paulson@2243
  1179
val cd = OS.FileSys.chDir;
wenzelm@2317
  1180
val pwd = OS.FileSys.getDir;
paulson@2243
  1181
wenzelm@11853
  1182
fun std_output s = (TextIO.output (TextIO.stdOut, s); TextIO.flushOut TextIO.stdOut);
wenzelm@11853
  1183
fun std_error s = (TextIO.output (TextIO.stdErr, s); TextIO.flushOut TextIO.stdErr);
wenzelm@3525
  1184
wenzelm@12419
  1185
fun prefix_lines "" txt = txt
wenzelm@12419
  1186
  | prefix_lines prfx txt = txt |> split_lines |> map (fn s => prfx ^ s) |> cat_lines;
wenzelm@3525
  1187
wenzelm@12419
  1188
val writeln_default = std_output o suffix "\n";
wenzelm@12419
  1189
wenzelm@12419
  1190
(*hooks for various output channels*)
wenzelm@12419
  1191
val writeln_fn = ref writeln_default;
wenzelm@9774
  1192
val priority_fn = ref (fn s => ! writeln_fn s);
wenzelm@12260
  1193
val tracing_fn = ref (fn s => ! writeln_fn s);
wenzelm@5949
  1194
val warning_fn = ref (std_output o suffix "\n" o prefix_lines "### ");
wenzelm@5949
  1195
val error_fn = ref (std_output o suffix "\n" o prefix_lines "*** ");
berghofe@1580
  1196
wenzelm@5966
  1197
fun writeln s = ! writeln_fn s;
wenzelm@9774
  1198
fun priority s = ! priority_fn s;
wenzelm@12260
  1199
fun tracing s = ! tracing_fn s;
wenzelm@5942
  1200
fun warning s = ! warning_fn s;
wenzelm@233
  1201
wenzelm@233
  1202
(*print error message and abort to top level*)
wenzelm@6959
  1203
wenzelm@5949
  1204
fun error_msg s = ! error_fn s;
wenzelm@3553
  1205
fun error s = (error_msg s; raise ERROR);
wenzelm@4849
  1206
fun sys_error msg = error ("## SYSTEM ERROR ##\n" ^ msg);
wenzelm@233
  1207
wenzelm@233
  1208
fun assert p msg = if p then () else error msg;
wenzelm@233
  1209
fun deny p msg = if p then error msg else ();
wenzelm@233
  1210
lcp@544
  1211
(*Assert pred for every member of l, generating a message if pred fails*)
wenzelm@4212
  1212
fun assert_all pred l msg_fn =
lcp@544
  1213
  let fun asl [] = ()
wenzelm@4212
  1214
        | asl (x::xs) = if pred x then asl xs else error (msg_fn x)
wenzelm@4212
  1215
  in asl l end;
wenzelm@233
  1216
wenzelm@3624
  1217
wenzelm@4212
  1218
(* handle errors capturing messages *)
wenzelm@3699
  1219
wenzelm@3699
  1220
datatype 'a error =
wenzelm@3699
  1221
  Error of string |
wenzelm@3699
  1222
  OK of 'a;
wenzelm@3699
  1223
wenzelm@4248
  1224
fun get_error (Error msg) = Some msg
wenzelm@4248
  1225
  | get_error _ = None;
wenzelm@4248
  1226
wenzelm@4248
  1227
fun get_ok (OK x) = Some x
wenzelm@4248
  1228
  | get_ok _ = None;
wenzelm@4248
  1229
wenzelm@5037
  1230
datatype 'a result =
wenzelm@5037
  1231
  Result of 'a |
wenzelm@5037
  1232
  Exn of exn;
wenzelm@5037
  1233
wenzelm@3699
  1234
fun handle_error f x =
wenzelm@3699
  1235
  let
wenzelm@4945
  1236
    val buffer = ref ([]: string list);
wenzelm@4945
  1237
    fun capture s = buffer := ! buffer @ [s];
wenzelm@5037
  1238
    fun err_msg () = if not (null (! buffer)) then error_msg (cat_lines (! buffer)) else ();
wenzelm@3699
  1239
  in
wenzelm@5037
  1240
    (case Result (setmp error_fn capture f x) handle exn => Exn exn of
wenzelm@5037
  1241
      Result y => (err_msg (); OK y)
wenzelm@5037
  1242
    | Exn ERROR => Error (cat_lines (! buffer))
wenzelm@5037
  1243
    | Exn exn => (err_msg (); raise exn))
wenzelm@3624
  1244
  end;
wenzelm@3624
  1245
wenzelm@3624
  1246
wenzelm@5037
  1247
(* transform ERROR into ERROR_MESSAGE *)
wenzelm@4923
  1248
wenzelm@4923
  1249
exception ERROR_MESSAGE of string;
wenzelm@4923
  1250
wenzelm@4923
  1251
fun transform_error f x =
wenzelm@4923
  1252
  (case handle_error f x of
wenzelm@4923
  1253
    OK y => y
wenzelm@4923
  1254
  | Error msg => raise ERROR_MESSAGE msg);
wenzelm@4923
  1255
wenzelm@4923
  1256
wenzelm@5904
  1257
(* transform any exception, including ERROR *)
wenzelm@5904
  1258
wenzelm@5904
  1259
fun transform_failure exn f x =
wenzelm@13488
  1260
  transform_error f x handle Interrupt => raise Interrupt | e => raise exn e;
wenzelm@5904
  1261
wenzelm@5904
  1262
wenzelm@233
  1263
wenzelm@233
  1264
(** timing **)
wenzelm@233
  1265
paulson@4326
  1266
(*a conditional timing function: applies f to () and, if the flag is true,
wenzelm@8999
  1267
  prints its runtime on warning channel*)
paulson@4326
  1268
fun cond_timeit flag f =
paulson@4326
  1269
  if flag then
paulson@4326
  1270
    let val start = startTiming()
paulson@4326
  1271
        val result = f ()
wenzelm@8999
  1272
    in warning (endTiming start);  result end
paulson@4326
  1273
  else f ();
paulson@4326
  1274
wenzelm@233
  1275
(*unconditional timing function*)
paulson@2243
  1276
fun timeit x = cond_timeit true x;
wenzelm@233
  1277
wenzelm@233
  1278
(*timed application function*)
wenzelm@233
  1279
fun timeap f x = timeit (fn () => f x);
wenzelm@12795
  1280
fun timeap_msg s f x = (warning s; timeap f x);
wenzelm@233
  1281
wenzelm@8999
  1282
(*global timing mode*)
wenzelm@8999
  1283
val timing = ref false;
wenzelm@8999
  1284
berghofe@3606
  1285
wenzelm@233
  1286
nipkow@10692
  1287
(** rational numbers **)
nipkow@10692
  1288
nipkow@10692
  1289
datatype rat = Rat of bool * int * int
nipkow@10692
  1290
nipkow@10692
  1291
fun rep_rat(Rat(a,p,q)) = (if a then p else ~p,q)
nipkow@10692
  1292
nipkow@10692
  1293
fun ratnorm(a,p,q) = if p=0 then Rat(a,0,1) else
nipkow@10692
  1294
  let val absp = abs p
nipkow@10692
  1295
      val m = gcd(absp,q)
nipkow@10692
  1296
  in Rat(a = (0 <= p), absp div m, q div m) end;
nipkow@10692
  1297
nipkow@10692
  1298
fun ratadd(Rat(a,p,q),Rat(b,r,s)) =
nipkow@10692
  1299
  let val den = lcm(q,s)
nipkow@10692
  1300
      val p = p*(den div q) and r = r*(den div s)
nipkow@10692
  1301
      val num = (if a then p else ~p) + (if b then r else ~r)
nipkow@10692
  1302
  in ratnorm(true,num,den) end;
nipkow@10692
  1303
nipkow@10692
  1304
fun ratmul(Rat(a,p,q),Rat(b,r,s)) = ratnorm(a=b,p*r,q*s)
nipkow@10692
  1305
nipkow@10692
  1306
fun ratinv(Rat(a,p,q)) = if p=0 then error("ratinv") else Rat(a,q,p)
nipkow@10692
  1307
nipkow@10692
  1308
fun int_ratdiv(p,q) =
nipkow@10692
  1309
  if q=0 then error("int_ratdiv") else ratnorm(0<=q, p, abs q)
nipkow@10692
  1310
nipkow@10692
  1311
fun ratneg(Rat(b,p,q)) = Rat(not b,p,q);
nipkow@10692
  1312
nipkow@10692
  1313
fun rat_of_int i = if i < 0 then Rat(false,abs i,1) else Rat(true,i,1);
nipkow@10692
  1314
nipkow@10692
  1315
wenzelm@4621
  1316
(** misc **)
wenzelm@233
  1317
wenzelm@9830
  1318
fun overwrite_warn (args as (alist, (a, _))) msg =
wenzelm@9830
  1319
 (if is_none (assoc (alist, a)) then () else warning msg;
wenzelm@9830
  1320
  overwrite args);
nipkow@9721
  1321
wenzelm@233
  1322
(*use the keyfun to make a list of (x, key) pairs*)
clasohm@0
  1323
fun make_keylist (keyfun: 'a->'b) : 'a list -> ('a * 'b) list =
wenzelm@233
  1324
  let fun keypair x = (x, keyfun x)
wenzelm@233
  1325
  in map keypair end;
clasohm@0
  1326
wenzelm@233
  1327
(*given a list of (x, key) pairs and a searchkey
clasohm@0
  1328
  return the list of xs from each pair whose key equals searchkey*)
clasohm@0
  1329
fun keyfilter [] searchkey = []
wenzelm@233
  1330
  | keyfilter ((x, key) :: pairs) searchkey =
wenzelm@233
  1331
      if key = searchkey then x :: keyfilter pairs searchkey
wenzelm@233
  1332
      else keyfilter pairs searchkey;
clasohm@0
  1333
clasohm@0
  1334
clasohm@0
  1335
(*Partition list into elements that satisfy predicate and those that don't.
wenzelm@233
  1336
  Preserves order of elements in both lists.*)
clasohm@0
  1337
fun partition (pred: 'a->bool) (ys: 'a list) : ('a list * 'a list) =
clasohm@0
  1338
    let fun part ([], answer) = answer
wenzelm@233
  1339
          | part (x::xs, (ys, ns)) = if pred(x)
wenzelm@233
  1340
            then  part (xs, (x::ys, ns))
wenzelm@233
  1341
            else  part (xs, (ys, x::ns))
wenzelm@233
  1342
    in  part (rev ys, ([], []))  end;
clasohm@0
  1343
clasohm@0
  1344
clasohm@0
  1345
fun partition_eq (eq:'a * 'a -> bool) =
clasohm@0
  1346
    let fun part [] = []
wenzelm@233
  1347
          | part (x::ys) = let val (xs, xs') = partition (apl(x, eq)) ys
wenzelm@233
  1348
                           in (x::xs)::(part xs') end
clasohm@0
  1349
    in part end;
clasohm@0
  1350
clasohm@0
  1351
wenzelm@233
  1352
(*Partition a list into buckets  [ bi, b(i+1), ..., bj ]
clasohm@0
  1353
   putting x in bk if p(k)(x) holds.  Preserve order of elements if possible.*)
clasohm@0
  1354
fun partition_list p i j =
wenzelm@233
  1355
  let fun part k xs =
wenzelm@233
  1356
            if k>j then
clasohm@0
  1357
              (case xs of [] => []
clasohm@0
  1358
                         | _ => raise LIST "partition_list")
clasohm@0
  1359
            else
wenzelm@233
  1360
            let val (ns, rest) = partition (p k) xs;
wenzelm@233
  1361
            in  ns :: part(k+1)rest  end
clasohm@0
  1362
  in  part i end;
clasohm@0
  1363
clasohm@0
  1364
wenzelm@233
  1365
(* transitive closure (not Warshall's algorithm) *)
clasohm@0
  1366
wenzelm@233
  1367
fun transitive_closure [] = []
wenzelm@233
  1368
  | transitive_closure ((x, ys)::ps) =
wenzelm@233
  1369
      let val qs = transitive_closure ps
paulson@2182
  1370
          val zs = foldl (fn (zs, y) => assocs qs y union_string zs) (ys, ys)
wenzelm@5904
  1371
          fun step(u, us) = (u, if x mem_string us then zs union_string us
paulson@2243
  1372
                                else us)
wenzelm@233
  1373
      in (x, zs) :: map step qs end;
clasohm@0
  1374
clasohm@0
  1375
wenzelm@233
  1376
(* generating identifiers *)
clasohm@0
  1377
paulson@4063
  1378
(** Freshly generated identifiers; supplied prefix MUST start with a letter **)
clasohm@0
  1379
local
paulson@4063
  1380
(*Maps 0-63 to A-Z, a-z, 0-9 or _ or ' for generating random identifiers*)
paulson@4063
  1381
fun char i =      if i<26 then chr (ord "A" + i)
wenzelm@5904
  1382
             else if i<52 then chr (ord "a" + i - 26)
wenzelm@5904
  1383
             else if i<62 then chr (ord"0" + i - 52)
wenzelm@5904
  1384
             else if i=62 then "_"
wenzelm@5904
  1385
             else  (*i=63*)    "'";
paulson@4063
  1386
paulson@4063
  1387
val charVec = Vector.tabulate (64, char);
paulson@4063
  1388
wenzelm@5904
  1389
fun newid n =
wenzelm@5904
  1390
  let
wenzelm@4284
  1391
  in  implode (map (fn i => Vector.sub(charVec,i)) (radixpand (64,n)))  end;
paulson@2003
  1392
wenzelm@4284
  1393
val seedr = ref 0;
clasohm@0
  1394
paulson@4063
  1395
in
wenzelm@4284
  1396
wenzelm@12346
  1397
fun gensym pre = pre ^ (#1(newid (!seedr), inc seedr));
paulson@2003
  1398
paulson@4063
  1399
end;
paulson@4063
  1400
paulson@4063
  1401
wenzelm@233
  1402
(* lexical scanning *)
clasohm@0
  1403
wenzelm@233
  1404
(*scan a list of characters into "words" composed of "letters" (recognized by
wenzelm@233
  1405
  is_let) and separated by any number of non-"letters"*)
wenzelm@233
  1406
fun scanwords is_let cs =
clasohm@0
  1407
  let fun scan1 [] = []
wenzelm@233
  1408
        | scan1 cs =
wenzelm@233
  1409
            let val (lets, rest) = take_prefix is_let cs
wenzelm@233
  1410
            in implode lets :: scanwords is_let rest end;
wenzelm@233
  1411
  in scan1 (#2 (take_prefix (not o is_let) cs)) end;
clasohm@24
  1412
wenzelm@4212
  1413
wenzelm@4212
  1414
wenzelm@4212
  1415
(* Variable-branching trees: for proof terms etc. *)
wenzelm@4212
  1416
datatype 'a mtree = Join of 'a * 'a mtree list;
wenzelm@4212
  1417
wenzelm@4212
  1418
clasohm@1364
  1419
end;
clasohm@1364
  1420
clasohm@1364
  1421
open Library;