src/Pure/library.ML
author wenzelm
Tue, 20 Nov 2001 20:56:13 +0100
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child 12260 4898247d0102
permissions -rw-r--r--
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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 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 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 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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  (*generic tables*)
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  val generic_extend: ('a * 'a -> bool)
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    -> ('b -> 'a list) -> ('a list -> 'b) -> 'b -> 'a list -> 'b
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  val generic_merge: ('a * 'a -> bool) -> ('b -> 'a list) -> ('a list -> 'b) -> 'b -> 'b -> 'b
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  val extend_list: ''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_rev_lists: ''a list -> ''a list -> ''a 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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  (*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 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 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 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
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  val transitive_closure: (string * string list) list -> (string * string list) list
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  val init_gensym: unit -> unit    (* FIXME !!??! *)
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  val gensym: string -> string
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  val bump_int_list: string list -> string list
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  val bump_list: string list * string -> string list
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  val bump_string: string -> string
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  val scanwords: (string -> bool) -> string list -> string list
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  datatype 'a mtree = Join of 'a * 'a mtree list
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end;
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structure Library: LIBRARY =
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struct
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905cd6f73429 removed type object (see object.ML);
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233
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(** functions **)
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233
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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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380
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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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233
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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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fun apr (f, y) x = f (x, y);
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(*function exponentiation: f(...(f x)...) with n applications of f*)
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fun funpow n f x =
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  let fun rep (0, x) = x
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        | rep (n, x) = rep (n - 1, f x)
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  in rep (n, x) end;
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(*concatenation: 2 and 3 args*)
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fun (f oo g) x y = f (g x y);
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fun (f ooo g) x y z = f (g x y z);
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fun (f oooo g) x y z w = f (g x y z w);
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160
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(** stamps **)
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type stamp = unit ref;
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val stamp: unit -> stamp = ref;
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09634c9cbf3c added stamp util;
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09634c9cbf3c added stamp util;
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233
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   331
(** options **)
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datatype 'a option = None | Some of 'a;
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exception OPTION;
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fun the (Some x) = x
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  | the None = raise OPTION;
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(*strict!*)
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fun if_none None y = y
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  | if_none (Some x) _ = x;
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fun is_some (Some _) = true
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  | is_some None = false;
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fun is_none (Some _) = false
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   348
  | is_none None = true;
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fun apsome f (Some x) = Some (f x)
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  | apsome _ None = None;
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6959
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   353
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   354
(* exception handling *)
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   355
d33b1629eaf9 try/can: pass Interrupt and ERROR;
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   356
exception ERROR;
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   357
d33b1629eaf9 try/can: pass Interrupt and ERROR;
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   358
fun try f x = Some (f x)
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   359
  handle Interrupt => raise Interrupt | ERROR => raise ERROR | _ => None;
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d33b1629eaf9 try/can: pass Interrupt and ERROR;
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   361
fun can f x = is_some (try f x);
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   362
e1659fd7a221 fixed exception OPTION;
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   363
e1659fd7a221 fixed exception OPTION;
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   364
233
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   365
(** pairs **)
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   366
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   367
fun pair x y = (x, y);
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   368
fun rpair x y = (y, x);
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   369
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   370
fun fst (x, y) = x;
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   371
fun snd (x, y) = y;
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   372
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   373
fun eq_fst ((x1, _), (x2, _)) = x1 = x2;
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   374
fun eq_snd ((_, y1), (_, y2)) = y1 = y2;
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   375
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   376
fun swap (x, y) = (y, x);
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   377
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   378
(*apply function to components*)
233
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   379
fun apfst f (x, y) = (f x, y);
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   380
fun apsnd f (x, y) = (x, f y);
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   381
fun pairself f (x, y) = (f x, f y);
233
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   382
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   383
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   384
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diff changeset
   385
(** booleans **)
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   386
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   387
(* equality *)
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   388
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   389
fun equal x y = x = y;
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   390
fun not_equal x y = x <> y;
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   391
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diff changeset
   392
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   393
(* operators for combining predicates *)
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   394
2175
21fde76bc742 Updated syntax; shortened comments; put in monomorphic versions of ins
paulson
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   395
fun (p orf q) = fn x => p x orelse q x;
21fde76bc742 Updated syntax; shortened comments; put in monomorphic versions of ins
paulson
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diff changeset
   396
fun (p andf q) = fn x => p x andalso q x;
233
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   397
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   398
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diff changeset
   399
(* predicates on lists *)
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   400
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   401
(*exists pred [x1, ..., xn] ===> pred x1 orelse ... orelse pred xn*)
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   402
fun exists (pred: 'a -> bool) : 'a list -> bool =
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   403
  let fun boolf [] = false
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diff changeset
   404
        | boolf (x :: xs) = pred x orelse boolf xs
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diff changeset
   405
  in boolf end;
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   406
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diff changeset
   407
(*forall pred [x1, ..., xn] ===> pred x1 andalso ... andalso pred xn*)
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   408
fun forall (pred: 'a -> bool) : 'a list -> bool =
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   409
  let fun boolf [] = true
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diff changeset
   410
        | boolf (x :: xs) = pred x andalso boolf xs
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   411
  in boolf end;
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   412
233
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diff changeset
   413
380
daca5b594fb3 added infix op also: 'a * ('a -> 'b) -> 'b;
wenzelm
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diff changeset
   414
(* flags *)
daca5b594fb3 added infix op also: 'a * ('a -> 'b) -> 'b;
wenzelm
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diff changeset
   415
daca5b594fb3 added infix op also: 'a * ('a -> 'b) -> 'b;
wenzelm
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diff changeset
   416
fun set flag = (flag := true; true);
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wenzelm
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diff changeset
   417
fun reset flag = (flag := false; false);
daca5b594fb3 added infix op also: 'a * ('a -> 'b) -> 'b;
wenzelm
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diff changeset
   418
fun toggle flag = (flag := not (! flag); ! flag);
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wenzelm
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diff changeset
   419
9118
62367f8fef02 added change: 'a ref -> ('a -> 'a) -> unit;
wenzelm
parents: 8999
diff changeset
   420
fun change r f = r := f (! r);
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diff changeset
   421
4212
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   422
(*temporarily set flag, handling errors*)
2978
83a4c4f79dcd renamed set_ap to setmp;
wenzelm
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diff changeset
   423
fun setmp flag value f x =
2958
7837471d2f27 improved inc, dec;
wenzelm
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diff changeset
   424
  let
7837471d2f27 improved inc, dec;
wenzelm
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diff changeset
   425
    val orig_value = ! flag;
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wenzelm
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diff changeset
   426
    fun return y = (flag := orig_value; y);
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wenzelm
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diff changeset
   427
  in
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diff changeset
   428
    flag := value;
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wenzelm
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diff changeset
   429
    return (f x handle exn => (return (); raise exn))
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wenzelm
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diff changeset
   430
  end;
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wenzelm
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diff changeset
   431
380
daca5b594fb3 added infix op also: 'a * ('a -> 'b) -> 'b;
wenzelm
parents: 265
diff changeset
   432
11853
651650b717e1 conditional: bool -> (unit -> unit) -> unit;
wenzelm
parents: 11773
diff changeset
   433
(* conditional execution *)
651650b717e1 conditional: bool -> (unit -> unit) -> unit;
wenzelm
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diff changeset
   434
651650b717e1 conditional: bool -> (unit -> unit) -> unit;
wenzelm
parents: 11773
diff changeset
   435
fun conditional b f = if b then f () else ();
651650b717e1 conditional: bool -> (unit -> unit) -> unit;
wenzelm
parents: 11773
diff changeset
   436
651650b717e1 conditional: bool -> (unit -> unit) -> unit;
wenzelm
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diff changeset
   437
233
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diff changeset
   438
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diff changeset
   439
(** lists **)
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diff changeset
   440
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diff changeset
   441
exception LIST of string;
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diff changeset
   442
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diff changeset
   443
fun null [] = true
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diff changeset
   444
  | null (_ :: _) = false;
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diff changeset
   445
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diff changeset
   446
fun hd [] = raise LIST "hd"
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diff changeset
   447
  | hd (x :: _) = x;
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diff changeset
   448
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diff changeset
   449
fun tl [] = raise LIST "tl"
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diff changeset
   450
  | tl (_ :: xs) = xs;
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diff changeset
   451
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diff changeset
   452
fun cons x xs = x :: xs;
5285
2d1425492fb3 val single: 'a -> 'a list;
wenzelm
parents: 5112
diff changeset
   453
fun single x = [x];
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   454
4629
401dd9b1b548 added append (curried);
wenzelm
parents: 4621
diff changeset
   455
fun append xs ys = xs @ ys;
401dd9b1b548 added append (curried);
wenzelm
parents: 4621
diff changeset
   456
5904
e077a0e66563 val apply: ('a -> 'a) list -> 'a -> 'a;
wenzelm
parents: 5893
diff changeset
   457
fun apply [] x = x
e077a0e66563 val apply: ('a -> 'a) list -> 'a -> 'a;
wenzelm
parents: 5893
diff changeset
   458
  | apply (f :: fs) x = apply fs (f x);
e077a0e66563 val apply: ('a -> 'a) list -> 'a -> 'a;
wenzelm
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diff changeset
   459
233
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diff changeset
   460
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diff changeset
   461
(* fold *)
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diff changeset
   462
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
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diff changeset
   463
(*the following versions of fold are designed to fit nicely with infixes*)
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a5a9c433f639 Initial revision
clasohm
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diff changeset
   464
233
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diff changeset
   465
(*  (op @) (e, [x1, ..., xn])  ===>  ((e @ x1) @ x2) ... @ xn
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diff changeset
   466
    for operators that associate to the left (TAIL RECURSIVE)*)
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diff changeset
   467
fun foldl (f: 'a * 'b -> 'a) : 'a * 'b list -> 'a =
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wenzelm
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diff changeset
   468
  let fun itl (e, [])  = e
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diff changeset
   469
        | itl (e, a::l) = itl (f(e, a), l)
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diff changeset
   470
  in  itl end;
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wenzelm
parents: 205
diff changeset
   471
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wenzelm
parents: 205
diff changeset
   472
(*  (op @) ([x1, ..., xn], e)  ===>   x1 @ (x2 ... @ (xn @ e))
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wenzelm
parents: 205
diff changeset
   473
    for operators that associate to the right (not tail recursive)*)
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parents: 205
diff changeset
   474
fun foldr f (l, e) =
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diff changeset
   475
  let fun itr [] = e
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diff changeset
   476
        | itr (a::l) = f(a, itr l)
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diff changeset
   477
  in  itr l  end;
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parents: 205
diff changeset
   478
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diff changeset
   479
(*  (op @) [x1, ..., xn]  ===>   x1 @ (x2 ... @ (x[n-1] @ xn))
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wenzelm
parents: 205
diff changeset
   480
    for n > 0, operators that associate to the right (not tail recursive)*)
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wenzelm
parents: 205
diff changeset
   481
fun foldr1 f l =
4181
wenzelm
parents: 4139
diff changeset
   482
  let fun itr [x] = x
233
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parents: 205
diff changeset
   483
        | itr (x::l) = f(x, itr l)
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wenzelm
parents: 205
diff changeset
   484
  in  itr l  end;
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wenzelm
parents: 205
diff changeset
   485
4956
a7538e43896e added foldl_map: ('a * 'b -> 'a * 'c) -> 'a * 'b list -> 'a * 'c list;
wenzelm
parents: 4945
diff changeset
   486
fun foldl_map _ (x, []) = (x, [])
a7538e43896e added foldl_map: ('a * 'b -> 'a * 'c) -> 'a * 'b list -> 'a * 'c list;
wenzelm
parents: 4945
diff changeset
   487
  | foldl_map f (x, y :: ys) =
a7538e43896e added foldl_map: ('a * 'b -> 'a * 'c) -> 'a * 'b list -> 'a * 'c list;
wenzelm
parents: 4945
diff changeset
   488
      let
a7538e43896e added foldl_map: ('a * 'b -> 'a * 'c) -> 'a * 'b list -> 'a * 'c list;
wenzelm
parents: 4945
diff changeset
   489
        val (x', y') = f (x, y);
a7538e43896e added foldl_map: ('a * 'b -> 'a * 'c) -> 'a * 'b list -> 'a * 'c list;
wenzelm
parents: 4945
diff changeset
   490
        val (x'', ys') = foldl_map f (x', ys);
a7538e43896e added foldl_map: ('a * 'b -> 'a * 'c) -> 'a * 'b list -> 'a * 'c list;
wenzelm
parents: 4945
diff changeset
   491
      in (x'', y' :: ys') end;
a7538e43896e added foldl_map: ('a * 'b -> 'a * 'c) -> 'a * 'b list -> 'a * 'c list;
wenzelm
parents: 4945
diff changeset
   492
11002
e33dfe9bde39 added foldln
oheimb
parents: 10951
diff changeset
   493
fun foldln f xs e = fst (foldl (fn ((e,i), x) => (f (x,i) e, i+1)) ((e,1),xs));
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   494
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   495
(* basic list functions *)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   496
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   497
(*length of a list, should unquestionably be a standard function*)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   498
local fun length1 (n, [])  = n   (*TAIL RECURSIVE*)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   499
        | length1 (n, x :: xs) = length1 (n + 1, xs)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   500
in  fun length l = length1 (0, l) end;
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   501
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   502
(*take the first n elements from a list*)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   503
fun take (n, []) = []
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   504
  | take (n, x :: xs) =
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   505
      if n > 0 then x :: take (n - 1, xs) else [];
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   506
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   507
(*drop the first n elements from a list*)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   508
fun drop (n, []) = []
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   509
  | drop (n, x :: xs) =
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   510
      if n > 0 then drop (n - 1, xs) else x :: xs;
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   511
4713
bea2ab2e360b New simplifier flag for mutual simplification.
nipkow
parents: 4692
diff changeset
   512
fun dropwhile P [] = []
bea2ab2e360b New simplifier flag for mutual simplification.
nipkow
parents: 4692
diff changeset
   513
  | dropwhile P (ys as x::xs) = if P x then dropwhile P xs else ys;
bea2ab2e360b New simplifier flag for mutual simplification.
nipkow
parents: 4692
diff changeset
   514
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   515
(*return nth element of a list, where 0 designates the first element;
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   516
  raise EXCEPTION if list too short*)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   517
fun nth_elem NL =
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   518
  (case drop NL of
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   519
    [] => raise LIST "nth_elem"
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   520
  | x :: _ => x);
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   521
11773
983d2db52062 map_nth_elem;
wenzelm
parents: 11514
diff changeset
   522
fun map_nth_elem 0 f (x :: xs) = f x :: xs
983d2db52062 map_nth_elem;
wenzelm
parents: 11514
diff changeset
   523
  | map_nth_elem n f (x :: xs) = x :: map_nth_elem (n - 1) f xs
983d2db52062 map_nth_elem;
wenzelm
parents: 11514
diff changeset
   524
  | map_nth_elem _ _ [] = raise LIST "map_nth_elem";
983d2db52062 map_nth_elem;
wenzelm
parents: 11514
diff changeset
   525
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   526
(*last element of a list*)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   527
fun last_elem [] = raise LIST "last_elem"
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   528
  | last_elem [x] = x
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   529
  | last_elem (_ :: xs) = last_elem xs;
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   530
3762
f20b071a429a added split_last;
wenzelm
parents: 3699
diff changeset
   531
(*rear decomposition*)
f20b071a429a added split_last;
wenzelm
parents: 3699
diff changeset
   532
fun split_last [] = raise LIST "split_last"
f20b071a429a added split_last;
wenzelm
parents: 3699
diff changeset
   533
  | split_last [x] = ([], x)
f20b071a429a added split_last;
wenzelm
parents: 3699
diff changeset
   534
  | split_last (x :: xs) = apfst (cons x) (split_last xs);
f20b071a429a added split_last;
wenzelm
parents: 3699
diff changeset
   535
4893
df9d6eef16d5 added nth_update: 'a -> int * 'a list -> 'a list;
wenzelm
parents: 4849
diff changeset
   536
(*update nth element*)
df9d6eef16d5 added nth_update: 'a -> int * 'a list -> 'a list;
wenzelm
parents: 4849
diff changeset
   537
fun nth_update x (n, xs) =
df9d6eef16d5 added nth_update: 'a -> int * 'a list -> 'a list;
wenzelm
parents: 4849
diff changeset
   538
  let
df9d6eef16d5 added nth_update: 'a -> int * 'a list -> 'a list;
wenzelm
parents: 4849
diff changeset
   539
    val prfx = take (n, xs);
df9d6eef16d5 added nth_update: 'a -> int * 'a list -> 'a list;
wenzelm
parents: 4849
diff changeset
   540
    val sffx = drop (n, xs);
df9d6eef16d5 added nth_update: 'a -> int * 'a list -> 'a list;
wenzelm
parents: 4849
diff changeset
   541
  in
df9d6eef16d5 added nth_update: 'a -> int * 'a list -> 'a list;
wenzelm
parents: 4849
diff changeset
   542
    (case sffx of
df9d6eef16d5 added nth_update: 'a -> int * 'a list -> 'a list;
wenzelm
parents: 4849
diff changeset
   543
      [] => raise LIST "nth_update"
df9d6eef16d5 added nth_update: 'a -> int * 'a list -> 'a list;
wenzelm
parents: 4849
diff changeset
   544
    | _ :: sffx' => prfx @ (x :: sffx'))
df9d6eef16d5 added nth_update: 'a -> int * 'a list -> 'a list;
wenzelm
parents: 4849
diff changeset
   545
  end;
df9d6eef16d5 added nth_update: 'a -> int * 'a list -> 'a list;
wenzelm
parents: 4849
diff changeset
   546
4212
68c7b37f8721 major cleanup;
wenzelm
parents: 4194
diff changeset
   547
(*find the position of an element in a list*)
68c7b37f8721 major cleanup;
wenzelm
parents: 4194
diff changeset
   548
fun find_index pred =
68c7b37f8721 major cleanup;
wenzelm
parents: 4194
diff changeset
   549
  let fun find _ [] = ~1
68c7b37f8721 major cleanup;
wenzelm
parents: 4194
diff changeset
   550
        | find n (x :: xs) = if pred x then n else find (n + 1) xs;
68c7b37f8721 major cleanup;
wenzelm
parents: 4194
diff changeset
   551
  in find 0 end;
3762
f20b071a429a added split_last;
wenzelm
parents: 3699
diff changeset
   552
4224
79e205c3a82c made SML/NJ happy;
wenzelm
parents: 4212
diff changeset
   553
fun find_index_eq x = find_index (equal x);
4212
68c7b37f8721 major cleanup;
wenzelm
parents: 4194
diff changeset
   554
68c7b37f8721 major cleanup;
wenzelm
parents: 4194
diff changeset
   555
(*find first element satisfying predicate*)
68c7b37f8721 major cleanup;
wenzelm
parents: 4194
diff changeset
   556
fun find_first _ [] = None
68c7b37f8721 major cleanup;
wenzelm
parents: 4194
diff changeset
   557
  | find_first pred (x :: xs) =
68c7b37f8721 major cleanup;
wenzelm
parents: 4194
diff changeset
   558
      if pred x then Some x else find_first pred xs;
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   559
4916
fe8b0c82691b get_first: ('a -> 'b option) -> 'a list -> 'b option;
wenzelm
parents: 4893
diff changeset
   560
(*get first element by lookup function*)
fe8b0c82691b get_first: ('a -> 'b option) -> 'a list -> 'b option;
wenzelm
parents: 4893
diff changeset
   561
fun get_first _ [] = None
fe8b0c82691b get_first: ('a -> 'b option) -> 'a list -> 'b option;
wenzelm
parents: 4893
diff changeset
   562
  | get_first f (x :: xs) =
fe8b0c82691b get_first: ('a -> 'b option) -> 'a list -> 'b option;
wenzelm
parents: 4893
diff changeset
   563
      (case f x of
fe8b0c82691b get_first: ('a -> 'b option) -> 'a list -> 'b option;
wenzelm
parents: 4893
diff changeset
   564
        None => get_first f xs
fe8b0c82691b get_first: ('a -> 'b option) -> 'a list -> 'b option;
wenzelm
parents: 4893
diff changeset
   565
      | some => some);
fe8b0c82691b get_first: ('a -> 'b option) -> 'a list -> 'b option;
wenzelm
parents: 4893
diff changeset
   566
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   567
(*flatten a list of lists to a list*)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   568
fun flat (ls: 'c list list) : 'c list = foldr (op @) (ls, []);
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   569
12136
74156e7bb22e added unflat;
wenzelm
parents: 11853
diff changeset
   570
fun unflat (xs :: xss) ys =
74156e7bb22e added unflat;
wenzelm
parents: 11853
diff changeset
   571
      let val n = length xs in take (n, ys) :: unflat xss (drop (n, ys)) end
74156e7bb22e added unflat;
wenzelm
parents: 11853
diff changeset
   572
  | unflat [] [] = []
74156e7bb22e added unflat;
wenzelm
parents: 11853
diff changeset
   573
  | unflat _ _ = raise LIST "unflat";
74156e7bb22e added unflat;
wenzelm
parents: 11853
diff changeset
   574
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   575
(*like Lisp's MAPC -- seq proc [x1, ..., xn] evaluates
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   576
  (proc x1; ...; proc xn) for side effects*)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   577
fun seq (proc: 'a -> unit) : 'a list -> unit =
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   578
  let fun seqf [] = ()
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   579
        | seqf (x :: xs) = (proc x; seqf xs)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   580
  in seqf end;
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   581
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   582
(*separate s [x1, x2, ..., xn]  ===>  [x1, s, x2, s, ..., s, xn]*)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   583
fun separate s (x :: (xs as _ :: _)) = x :: s :: separate s xs
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   584
  | separate _ xs = xs;
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   585
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   586
(*make the list [x, x, ..., x] of length n*)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   587
fun replicate n (x: 'a) : 'a list =
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   588
  let fun rep (0, xs) = xs
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   589
        | rep (n, xs) = rep (n - 1, x :: xs)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   590
  in
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   591
    if n < 0 then raise LIST "replicate"
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   592
    else rep (n, [])
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   593
  end;
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   594
4248
5e8a31c41d44 added get_error: 'a error -> string option, get_ok: 'a error -> 'a option;
wenzelm
parents: 4224
diff changeset
   595
(*multiply [a, b, c, ...] * [xs, ys, zs, ...]*)
5e8a31c41d44 added get_error: 'a error -> string option, get_ok: 'a error -> 'a option;
wenzelm
parents: 4224
diff changeset
   596
fun multiply ([], _) = []
5e8a31c41d44 added get_error: 'a error -> string option, get_ok: 'a error -> 'a option;
wenzelm
parents: 4224
diff changeset
   597
  | multiply (x :: xs, yss) = map (cons x) yss @ multiply (xs, yss);
5e8a31c41d44 added get_error: 'a error -> string option, get_ok: 'a error -> 'a option;
wenzelm
parents: 4224
diff changeset
   598
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   599
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   600
(* filter *)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   601
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   602
(*copy the list preserving elements that satisfy the predicate*)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   603
fun filter (pred: 'a->bool) : 'a list -> 'a list =
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   604
  let fun filt [] = []
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   605
        | filt (x :: xs) = if pred x then x :: filt xs else filt xs
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   606
  in filt end;
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   607
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   608
fun filter_out f = filter (not o f);
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   609
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   610
fun mapfilter (f: 'a -> 'b option) ([]: 'a list) = [] : 'b list
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   611
  | mapfilter f (x :: xs) =
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   612
      (case f x of
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   613
        None => mapfilter f xs
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   614
      | Some y => y :: mapfilter f xs);
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   615
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   616
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   617
(* lists of pairs *)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   618
380
daca5b594fb3 added infix op also: 'a * ('a -> 'b) -> 'b;
wenzelm
parents: 265
diff changeset
   619
fun map2 _ ([], []) = []
daca5b594fb3 added infix op also: 'a * ('a -> 'b) -> 'b;
wenzelm
parents: 265
diff changeset
   620
  | map2 f (x :: xs, y :: ys) = (f (x, y) :: map2 f (xs, ys))
daca5b594fb3 added infix op also: 'a * ('a -> 'b) -> 'b;
wenzelm
parents: 265
diff changeset
   621
  | map2 _ _ = raise LIST "map2";
daca5b594fb3 added infix op also: 'a * ('a -> 'b) -> 'b;
wenzelm
parents: 265
diff changeset
   622
daca5b594fb3 added infix op also: 'a * ('a -> 'b) -> 'b;
wenzelm
parents: 265
diff changeset
   623
fun exists2 _ ([], []) = false
daca5b594fb3 added infix op also: 'a * ('a -> 'b) -> 'b;
wenzelm
parents: 265
diff changeset
   624
  | exists2 pred (x :: xs, y :: ys) = pred (x, y) orelse exists2 pred (xs, ys)
daca5b594fb3 added infix op also: 'a * ('a -> 'b) -> 'b;
wenzelm
parents: 265
diff changeset
   625
  | exists2 _ _ = raise LIST "exists2";
daca5b594fb3 added infix op also: 'a * ('a -> 'b) -> 'b;
wenzelm
parents: 265
diff changeset
   626
daca5b594fb3 added infix op also: 'a * ('a -> 'b) -> 'b;
wenzelm
parents: 265
diff changeset
   627
fun forall2 _ ([], []) = true
daca5b594fb3 added infix op also: 'a * ('a -> 'b) -> 'b;
wenzelm
parents: 265
diff changeset
   628
  | forall2 pred (x :: xs, y :: ys) = pred (x, y) andalso forall2 pred (xs, ys)
daca5b594fb3 added infix op also: 'a * ('a -> 'b) -> 'b;
wenzelm
parents: 265
diff changeset
   629
  | forall2 _ _ = raise LIST "forall2";
daca5b594fb3 added infix op also: 'a * ('a -> 'b) -> 'b;
wenzelm
parents: 265
diff changeset
   630
4956
a7538e43896e added foldl_map: ('a * 'b -> 'a * 'c) -> 'a * 'b list -> 'a * 'c list;
wenzelm
parents: 4945
diff changeset
   631
fun seq2 _ ([], []) = ()
a7538e43896e added foldl_map: ('a * 'b -> 'a * 'c) -> 'a * 'b list -> 'a * 'c list;
wenzelm
parents: 4945
diff changeset
   632
  | seq2 f (x :: xs, y :: ys) = (f (x, y); seq2 f (xs, ys))
a7538e43896e added foldl_map: ('a * 'b -> 'a * 'c) -> 'a * 'b list -> 'a * 'c list;
wenzelm
parents: 4945
diff changeset
   633
  | seq2 _ _ = raise LIST "seq2";
a7538e43896e added foldl_map: ('a * 'b -> 'a * 'c) -> 'a * 'b list -> 'a * 'c list;
wenzelm
parents: 4945
diff changeset
   634
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   635
(*combine two lists forming a list of pairs:
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   636
  [x1, ..., xn] ~~ [y1, ..., yn]  ===>  [(x1, y1), ..., (xn, yn)]*)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   637
fun [] ~~ [] = []
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   638
  | (x :: xs) ~~ (y :: ys) = (x, y) :: (xs ~~ ys)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   639
  | _ ~~ _ = raise LIST "~~";
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   640
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   641
(*inverse of ~~; the old 'split':
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   642
  [(x1, y1), ..., (xn, yn)]  ===>  ([x1, ..., xn], [y1, ..., yn])*)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   643
fun split_list (l: ('a * 'b) list) = (map #1 l, map #2 l);
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   644
7468
6ce03d2f7d91 equal_lists: ('a * 'b -> bool) -> 'a list * 'b list -> bool;
wenzelm
parents: 7090
diff changeset
   645
fun equal_lists eq (xs, ys) = length xs = length ys andalso forall2 eq (xs, ys);
6ce03d2f7d91 equal_lists: ('a * 'b -> bool) -> 'a list * 'b list -> bool;
wenzelm
parents: 7090
diff changeset
   646
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   647
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   648
(* prefixes, suffixes *)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   649
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   650
fun [] prefix _ = true
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   651
  | (x :: xs) prefix (y :: ys) = x = y andalso (xs prefix ys)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   652
  | _ prefix _ = false;
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   653
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   654
(* [x1, ..., xi, ..., xn]  --->  ([x1, ..., x(i-1)], [xi, ..., xn])
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   655
   where xi is the first element that does not satisfy the predicate*)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   656
fun take_prefix (pred : 'a -> bool)  (xs: 'a list) : 'a list * 'a list =
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   657
  let fun take (rxs, []) = (rev rxs, [])
255
ee132db91681 added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents: 245
diff changeset
   658
        | take (rxs, x :: xs) =
ee132db91681 added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents: 245
diff changeset
   659
            if  pred x  then  take(x :: rxs, xs)  else  (rev rxs, x :: xs)
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   660
  in  take([], xs)  end;
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   661
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   662
(* [x1, ..., xi, ..., xn]  --->  ([x1, ..., xi], [x(i+1), ..., xn])
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   663
   where xi is the last element that does not satisfy the predicate*)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   664
fun take_suffix _ [] = ([], [])
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   665
  | take_suffix pred (x :: xs) =
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   666
      (case take_suffix pred xs of
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   667
        ([], sffx) => if pred x then ([], x :: sffx) else ([x], sffx)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   668
      | (prfx, sffx) => (x :: prfx, sffx));
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   669
12249
dd9a51255855 added prefixes1, suffixes1;
wenzelm
parents: 12136
diff changeset
   670
fun prefixes1 [] = []
dd9a51255855 added prefixes1, suffixes1;
wenzelm
parents: 12136
diff changeset
   671
  | prefixes1 (x :: xs) = map (cons x) ([] :: prefixes1 xs);
dd9a51255855 added prefixes1, suffixes1;
wenzelm
parents: 12136
diff changeset
   672
dd9a51255855 added prefixes1, suffixes1;
wenzelm
parents: 12136
diff changeset
   673
fun suffixes1 xs = map rev (prefixes1 (rev xs));
dd9a51255855 added prefixes1, suffixes1;
wenzelm
parents: 12136
diff changeset
   674
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   675
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   676
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   677
(** integers **)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   678
10692
6077fd933575 added rational arithmetic
nipkow
parents: 9830
diff changeset
   679
fun gcd(x,y) =
6077fd933575 added rational arithmetic
nipkow
parents: 9830
diff changeset
   680
  let fun gxd x y =
6077fd933575 added rational arithmetic
nipkow
parents: 9830
diff changeset
   681
    if y = 0 then x else gxd y (x mod y)
6077fd933575 added rational arithmetic
nipkow
parents: 9830
diff changeset
   682
  in if x < y then gxd y x else gxd x y end;
6077fd933575 added rational arithmetic
nipkow
parents: 9830
diff changeset
   683
6077fd933575 added rational arithmetic
nipkow
parents: 9830
diff changeset
   684
fun lcm(x,y) = (x * y) div gcd(x,y);
6077fd933575 added rational arithmetic
nipkow
parents: 9830
diff changeset
   685
2958
7837471d2f27 improved inc, dec;
wenzelm
parents: 2806
diff changeset
   686
fun inc i = (i := ! i + 1; ! i);
7837471d2f27 improved inc, dec;
wenzelm
parents: 2806
diff changeset
   687
fun dec i = (i := ! i - 1; ! i);
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   688
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   689
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   690
(* lists of integers *)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   691
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   692
(*make the list [from, from + 1, ..., to]*)
2175
21fde76bc742 Updated syntax; shortened comments; put in monomorphic versions of ins
paulson
parents: 2157
diff changeset
   693
fun (from upto to) =
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   694
  if from > to then [] else from :: ((from + 1) upto to);
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   695
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   696
(*make the list [from, from - 1, ..., to]*)
2175
21fde76bc742 Updated syntax; shortened comments; put in monomorphic versions of ins
paulson
parents: 2157
diff changeset
   697
fun (from downto to) =
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   698
  if from < to then [] else from :: ((from - 1) downto to);
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   699
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   700
(*predicate: downto0 (is, n) <=> is = [n, n - 1, ..., 0]*)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   701
fun downto0 (i :: is, n) = i = n andalso downto0 (is, n - 1)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   702
  | downto0 ([], n) = n = ~1;
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   703
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   704
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   705
(* convert integers to strings *)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   706
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   707
(*expand the number in the given base;
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   708
  example: radixpand (2, 8) gives [1, 0, 0, 0]*)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   709
fun radixpand (base, num) : int list =
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   710
  let
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   711
    fun radix (n, tail) =
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   712
      if n < base then n :: tail
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   713
      else radix (n div base, (n mod base) :: tail)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   714
  in radix (num, []) end;
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   715
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   716
(*expands a number into a string of characters starting from "zerochar";
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   717
  example: radixstring (2, "0", 8) gives "1000"*)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   718
fun radixstring (base, zerochar, num) =
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   719
  let val offset = ord zerochar;
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   720
      fun chrof n = chr (offset + n)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   721
  in implode (map chrof (radixpand (base, num))) end;
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   722
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   723
3407
afd288caf573 Removal of radixstring from string_of_int; addition of string_of_indexname
paulson
parents: 3393
diff changeset
   724
val string_of_int = Int.toString;
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   725
3407
afd288caf573 Removal of radixstring from string_of_int; addition of string_of_indexname
paulson
parents: 3393
diff changeset
   726
fun string_of_indexname (a,0) = a
afd288caf573 Removal of radixstring from string_of_int; addition of string_of_indexname
paulson
parents: 3393
diff changeset
   727
  | string_of_indexname (a,i) = a ^ "_" ^ Int.toString i;
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   728
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   729
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   730
(** strings **)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   731
6312
d361b0a99e31 added nth_elem_string, exists_string;
wenzelm
parents: 6282
diff changeset
   732
(*functions tuned for strings, avoiding explode*)
d361b0a99e31 added nth_elem_string, exists_string;
wenzelm
parents: 6282
diff changeset
   733
d361b0a99e31 added nth_elem_string, exists_string;
wenzelm
parents: 6282
diff changeset
   734
fun nth_elem_string (i, str) =
6959
d33b1629eaf9 try/can: pass Interrupt and ERROR;
wenzelm
parents: 6642
diff changeset
   735
  (case try String.substring (str, i, 1) of
d33b1629eaf9 try/can: pass Interrupt and ERROR;
wenzelm
parents: 6642
diff changeset
   736
    Some s => s
d33b1629eaf9 try/can: pass Interrupt and ERROR;
wenzelm
parents: 6642
diff changeset
   737
  | None => raise LIST "nth_elem_string");
6312
d361b0a99e31 added nth_elem_string, exists_string;
wenzelm
parents: 6282
diff changeset
   738
6282
589671bebbb3 foldl_string;
wenzelm
parents: 5966
diff changeset
   739
fun foldl_string f (x0, str) =
589671bebbb3 foldl_string;
wenzelm
parents: 5966
diff changeset
   740
  let
589671bebbb3 foldl_string;
wenzelm
parents: 5966
diff changeset
   741
    val n = size str;
589671bebbb3 foldl_string;
wenzelm
parents: 5966
diff changeset
   742
    fun fold (x, i) = if i < n then fold (f (x, String.substring (str, i, 1)), i + 1) else x
589671bebbb3 foldl_string;
wenzelm
parents: 5966
diff changeset
   743
  in fold (x0, 0) end;
589671bebbb3 foldl_string;
wenzelm
parents: 5966
diff changeset
   744
6312
d361b0a99e31 added nth_elem_string, exists_string;
wenzelm
parents: 6282
diff changeset
   745
fun exists_string pred str = foldl_string (fn (b, s) => b orelse pred s) (false, str);
d361b0a99e31 added nth_elem_string, exists_string;
wenzelm
parents: 6282
diff changeset
   746
512
55755ed9fab9 Pure/library/enclose, Pure/Syntax/pretty/enclose: renamed from parents
lcp
parents: 410
diff changeset
   747
(*enclose in brackets*)
55755ed9fab9 Pure/library/enclose, Pure/Syntax/pretty/enclose: renamed from parents
lcp
parents: 410
diff changeset
   748
fun enclose lpar rpar str = lpar ^ str ^ rpar;
6642
732af87c0650 strip_quotes replaced by unenclose;
wenzelm
parents: 6510
diff changeset
   749
fun unenclose str = String.substring (str, 1, size str - 2);
255
ee132db91681 added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents: 245
diff changeset
   750
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   751
(*simple quoting (does not escape special chars)*)
512
55755ed9fab9 Pure/library/enclose, Pure/Syntax/pretty/enclose: renamed from parents
lcp
parents: 410
diff changeset
   752
val quote = enclose "\"" "\"";
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   753
4212
68c7b37f8721 major cleanup;
wenzelm
parents: 4194
diff changeset
   754
(*space_implode "..." (explode "hello") = "h...e...l...l...o"*)
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   755
fun space_implode a bs = implode (separate a bs);
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   756
255
ee132db91681 added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents: 245
diff changeset
   757
val commas = space_implode ", ";
380
daca5b594fb3 added infix op also: 'a * ('a -> 'b) -> 'b;
wenzelm
parents: 265
diff changeset
   758
val commas_quote = commas o map quote;
255
ee132db91681 added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents: 245
diff changeset
   759
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   760
(*concatenate messages, one per line, into a string*)
255
ee132db91681 added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents: 245
diff changeset
   761
val cat_lines = space_implode "\n";
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   762
4212
68c7b37f8721 major cleanup;
wenzelm
parents: 4194
diff changeset
   763
(*space_explode "." "h.e..l.lo" = ["h", "e", "", "l", "lo"]*)
3832
17a20a2af8f5 fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents: 3762
diff changeset
   764
fun space_explode _ "" = []
17a20a2af8f5 fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents: 3762
diff changeset
   765
  | space_explode sep str =
17a20a2af8f5 fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents: 3762
diff changeset
   766
      let
17a20a2af8f5 fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents: 3762
diff changeset
   767
        fun expl chs =
17a20a2af8f5 fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents: 3762
diff changeset
   768
          (case take_prefix (not_equal sep) chs of
17a20a2af8f5 fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents: 3762
diff changeset
   769
            (cs, []) => [implode cs]
17a20a2af8f5 fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents: 3762
diff changeset
   770
          | (cs, _ :: cs') => implode cs :: expl cs');
17a20a2af8f5 fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents: 3762
diff changeset
   771
      in expl (explode str) end;
17a20a2af8f5 fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents: 3762
diff changeset
   772
17a20a2af8f5 fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents: 3762
diff changeset
   773
val split_lines = space_explode "\n";
17a20a2af8f5 fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents: 3762
diff changeset
   774
7712
c522ec2adc37 added untabify;
wenzelm
parents: 7468
diff changeset
   775
(*untabify*)
c522ec2adc37 added untabify;
wenzelm
parents: 7468
diff changeset
   776
fun untabify chs =
c522ec2adc37 added untabify;
wenzelm
parents: 7468
diff changeset
   777
  let
c522ec2adc37 added untabify;
wenzelm
parents: 7468
diff changeset
   778
    val tab_width = 8;
c522ec2adc37 added untabify;
wenzelm
parents: 7468
diff changeset
   779
c522ec2adc37 added untabify;
wenzelm
parents: 7468
diff changeset
   780
    fun untab (_, "\n") = (0, ["\n"])
9118
62367f8fef02 added change: 'a ref -> ('a -> 'a) -> unit;
wenzelm
parents: 8999
diff changeset
   781
      | untab (pos, "\t") =
62367f8fef02 added change: 'a ref -> ('a -> 'a) -> unit;
wenzelm
parents: 8999
diff changeset
   782
          let val d = tab_width - (pos mod tab_width) in (pos + d, replicate d " ") end
7712
c522ec2adc37 added untabify;
wenzelm
parents: 7468
diff changeset
   783
      | untab (pos, c) = (pos + 1, [c]);
c522ec2adc37 added untabify;
wenzelm
parents: 7468
diff changeset
   784
  in
c522ec2adc37 added untabify;
wenzelm
parents: 7468
diff changeset
   785
    if not (exists (equal "\t") chs) then chs
c522ec2adc37 added untabify;
wenzelm
parents: 7468
diff changeset
   786
    else flat (#2 (foldl_map untab (0, chs)))
c522ec2adc37 added untabify;
wenzelm
parents: 7468
diff changeset
   787
  end;
c522ec2adc37 added untabify;
wenzelm
parents: 7468
diff changeset
   788
5285
2d1425492fb3 val single: 'a -> 'a list;
wenzelm
parents: 5112
diff changeset
   789
(*append suffix*)
2d1425492fb3 val single: 'a -> 'a list;
wenzelm
parents: 5112
diff changeset
   790
fun suffix sfx s = s ^ sfx;
2d1425492fb3 val single: 'a -> 'a list;
wenzelm
parents: 5112
diff changeset
   791
2d1425492fb3 val single: 'a -> 'a list;
wenzelm
parents: 5112
diff changeset
   792
(*remove suffix*)
2d1425492fb3 val single: 'a -> 'a list;
wenzelm
parents: 5112
diff changeset
   793
fun unsuffix sfx s =
2d1425492fb3 val single: 'a -> 'a list;
wenzelm
parents: 5112
diff changeset
   794
  let
2d1425492fb3 val single: 'a -> 'a list;
wenzelm
parents: 5112
diff changeset
   795
    val cs = explode s;
2d1425492fb3 val single: 'a -> 'a list;
wenzelm
parents: 5112
diff changeset
   796
    val prfx_len = size s - size sfx;
2d1425492fb3 val single: 'a -> 'a list;
wenzelm
parents: 5112
diff changeset
   797
  in
2d1425492fb3 val single: 'a -> 'a list;
wenzelm
parents: 5112
diff changeset
   798
    if prfx_len >= 0 andalso implode (drop (prfx_len, cs)) = sfx then
2d1425492fb3 val single: 'a -> 'a list;
wenzelm
parents: 5112
diff changeset
   799
      implode (take (prfx_len, cs))
2d1425492fb3 val single: 'a -> 'a list;
wenzelm
parents: 5112
diff changeset
   800
    else raise LIST "unsuffix"
2d1425492fb3 val single: 'a -> 'a list;
wenzelm
parents: 5112
diff changeset
   801
  end;
2d1425492fb3 val single: 'a -> 'a list;
wenzelm
parents: 5112
diff changeset
   802
10951
ddb9b820d8a5 added replicate_string;
wenzelm
parents: 10692
diff changeset
   803
fun replicate_string 0 _ = ""
ddb9b820d8a5 added replicate_string;
wenzelm
parents: 10692
diff changeset
   804
  | replicate_string 1 a = a
ddb9b820d8a5 added replicate_string;
wenzelm
parents: 10692
diff changeset
   805
  | replicate_string k a =
ddb9b820d8a5 added replicate_string;
wenzelm
parents: 10692
diff changeset
   806
      if k mod 2 = 0 then replicate_string (k div 2) (a ^ a)
ddb9b820d8a5 added replicate_string;
wenzelm
parents: 10692
diff changeset
   807
      else replicate_string (k div 2) (a ^ a) ^ a;
ddb9b820d8a5 added replicate_string;
wenzelm
parents: 10692
diff changeset
   808
3832
17a20a2af8f5 fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents: 3762
diff changeset
   809
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   810
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   811
(** lists as sets **)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   812
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   813
(*membership in a list*)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   814
fun x mem [] = false
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   815
  | x mem (y :: ys) = x = y orelse x mem ys;
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   816
2175
21fde76bc742 Updated syntax; shortened comments; put in monomorphic versions of ins
paulson
parents: 2157
diff changeset
   817
(*membership in a list, optimized version for ints*)
1576
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   818
fun (x:int) mem_int [] = false
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   819
  | x mem_int (y :: ys) = x = y orelse x mem_int ys;
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   820
2175
21fde76bc742 Updated syntax; shortened comments; put in monomorphic versions of ins
paulson
parents: 2157
diff changeset
   821
(*membership in a list, optimized version for strings*)
1576
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   822
fun (x:string) mem_string [] = false
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   823
  | x mem_string (y :: ys) = x = y orelse x mem_string ys;
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   824
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   825
(*generalized membership test*)
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   826
fun gen_mem eq (x, []) = false
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   827
  | gen_mem eq (x, y :: ys) = eq (x, y) orelse gen_mem eq (x, ys);
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   828
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   829
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   830
(*insertion into list if not already there*)
2175
21fde76bc742 Updated syntax; shortened comments; put in monomorphic versions of ins
paulson
parents: 2157
diff changeset
   831
fun (x ins xs) = if x mem xs then xs else x :: xs;
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   832
2175
21fde76bc742 Updated syntax; shortened comments; put in monomorphic versions of ins
paulson
parents: 2157
diff changeset
   833
(*insertion into list, optimized version for ints*)
21fde76bc742 Updated syntax; shortened comments; put in monomorphic versions of ins
paulson
parents: 2157
diff changeset
   834
fun (x ins_int xs) = if x mem_int xs then xs else x :: xs;
1576
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   835
2175
21fde76bc742 Updated syntax; shortened comments; put in monomorphic versions of ins
paulson
parents: 2157
diff changeset
   836
(*insertion into list, optimized version for strings*)
21fde76bc742 Updated syntax; shortened comments; put in monomorphic versions of ins
paulson
parents: 2157
diff changeset
   837
fun (x ins_string xs) = if x mem_string xs then xs else x :: xs;
1576
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   838
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   839
(*generalized insertion*)
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   840
fun gen_ins eq (x, xs) = if gen_mem eq (x, xs) then xs else x :: xs;
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   841
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   842
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   843
(*union of sets represented as lists: no repetitions*)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   844
fun xs union [] = xs
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   845
  | [] union ys = ys
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   846
  | (x :: xs) union ys = xs union (x ins ys);
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   847
2175
21fde76bc742 Updated syntax; shortened comments; put in monomorphic versions of ins
paulson
parents: 2157
diff changeset
   848
(*union of sets, optimized version for ints*)
1576
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   849
fun (xs:int list) union_int [] = xs
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   850
  | [] union_int ys = ys
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   851
  | (x :: xs) union_int ys = xs union_int (x ins_int ys);
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   852
2175
21fde76bc742 Updated syntax; shortened comments; put in monomorphic versions of ins
paulson
parents: 2157
diff changeset
   853
(*union of sets, optimized version for strings*)
1576
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   854
fun (xs:string list) union_string [] = xs
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   855
  | [] union_string ys = ys
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   856
  | (x :: xs) union_string ys = xs union_string (x ins_string ys);
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   857
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   858
(*generalized union*)
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   859
fun gen_union eq (xs, []) = xs
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   860
  | gen_union eq ([], ys) = ys
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   861
  | gen_union eq (x :: xs, ys) = gen_union eq (xs, gen_ins eq (x, ys));
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   862
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   863
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   864
(*intersection*)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   865
fun [] inter ys = []
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   866
  | (x :: xs) inter ys =
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   867
      if x mem ys then x :: (xs inter ys) else xs inter ys;
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   868
2175
21fde76bc742 Updated syntax; shortened comments; put in monomorphic versions of ins
paulson
parents: 2157
diff changeset
   869
(*intersection, optimized version for ints*)
1576
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   870
fun ([]:int list) inter_int ys = []
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   871
  | (x :: xs) inter_int ys =
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   872
      if x mem_int ys then x :: (xs inter_int ys) else xs inter_int ys;
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   873
2175
21fde76bc742 Updated syntax; shortened comments; put in monomorphic versions of ins
paulson
parents: 2157
diff changeset
   874
(*intersection, optimized version for strings *)
1576
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   875
fun ([]:string list) inter_string ys = []
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   876
  | (x :: xs) inter_string ys =
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   877
      if x mem_string ys then x :: (xs inter_string ys) else xs inter_string ys;
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   878
7090
dd30a72880c7 added gen_inter
paulson
parents: 6959
diff changeset
   879
(*generalized intersection*)
dd30a72880c7 added gen_inter
paulson
parents: 6959
diff changeset
   880
fun gen_inter eq ([], ys) = []
dd30a72880c7 added gen_inter
paulson
parents: 6959
diff changeset
   881
  | gen_inter eq (x::xs, ys) = 
dd30a72880c7 added gen_inter
paulson
parents: 6959
diff changeset
   882
      if gen_mem eq (x,ys) then x :: gen_inter eq (xs, ys)
dd30a72880c7 added gen_inter
paulson
parents: 6959
diff changeset
   883
	                   else      gen_inter eq (xs, ys);
dd30a72880c7 added gen_inter
paulson
parents: 6959
diff changeset
   884
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   885
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   886
(*subset*)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   887
fun [] subset ys = true
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   888
  | (x :: xs) subset ys = x mem ys andalso xs subset ys;
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   889
2175
21fde76bc742 Updated syntax; shortened comments; put in monomorphic versions of ins
paulson
parents: 2157
diff changeset
   890
(*subset, optimized version for ints*)
1576
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   891
fun ([]:int list) subset_int ys = true
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   892
  | (x :: xs) subset_int ys = x mem_int ys andalso xs subset_int ys;
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   893
2175
21fde76bc742 Updated syntax; shortened comments; put in monomorphic versions of ins
paulson
parents: 2157
diff changeset
   894
(*subset, optimized version for strings*)
1576
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   895
fun ([]:string list) subset_string ys = true
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   896
  | (x :: xs) subset_string ys = x mem_string ys andalso xs subset_string ys;
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   897
4363
b449831f03f4 added eq_set;
wenzelm
parents: 4343
diff changeset
   898
(*set equality*)
b449831f03f4 added eq_set;
wenzelm
parents: 4343
diff changeset
   899
fun eq_set (xs, ys) =
b449831f03f4 added eq_set;
wenzelm
parents: 4343
diff changeset
   900
  xs = ys orelse (xs subset ys andalso ys subset xs);
b449831f03f4 added eq_set;
wenzelm
parents: 4343
diff changeset
   901
2182
29e56f003599 Removal of polymorphic equality via mem, subset, eq_set, etc
paulson
parents: 2175
diff changeset
   902
(*set equality for strings*)
1576
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   903
fun eq_set_string ((xs:string list), ys) =
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   904
  xs = ys orelse (xs subset_string ys andalso ys subset_string xs);
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   905
2182
29e56f003599 Removal of polymorphic equality via mem, subset, eq_set, etc
paulson
parents: 2175
diff changeset
   906
fun gen_subset eq (xs, ys) = forall (fn x => gen_mem eq (x, ys)) xs;
29e56f003599 Removal of polymorphic equality via mem, subset, eq_set, etc
paulson
parents: 2175
diff changeset
   907
265
443dc2c37583 added eq_set;
wenzelm
parents: 255
diff changeset
   908
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   909
(*removing an element from a list WITHOUT duplicates*)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   910
fun (y :: ys) \ x = if x = y then ys else y :: (ys \ x)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   911
  | [] \ x = [];
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   912
2243
3ebeaaacfbd1 Eta-expanded some declarations that are illegal under value polymorphism
paulson
parents: 2196
diff changeset
   913
fun ys \\ xs = foldl (op \) (ys,xs);
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   914
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   915
(*removing an element from a list -- possibly WITH duplicates*)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   916
fun gen_rem eq (xs, y) = filter_out (fn x => eq (x, y)) xs;
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   917
2243
3ebeaaacfbd1 Eta-expanded some declarations that are illegal under value polymorphism
paulson
parents: 2196
diff changeset
   918
fun gen_rems eq = foldl (gen_rem eq);
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   919
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   920
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   921
(*makes a list of the distinct members of the input; preserves order, takes
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   922
  first of equal elements*)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   923
fun gen_distinct eq lst =
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   924
  let
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   925
    val memb = gen_mem eq;
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   926
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   927
    fun dist (rev_seen, []) = rev rev_seen
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   928
      | dist (rev_seen, x :: xs) =
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   929
          if memb (x, rev_seen) then dist (rev_seen, xs)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   930
          else dist (x :: rev_seen, xs);
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   931
  in
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   932
    dist ([], lst)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   933
  end;
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   934
2243
3ebeaaacfbd1 Eta-expanded some declarations that are illegal under value polymorphism
paulson
parents: 2196
diff changeset
   935
fun distinct l = gen_distinct (op =) l;
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   936
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   937
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   938
(*returns the tail beginning with the first repeated element, or []*)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   939
fun findrep [] = []
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   940
  | findrep (x :: xs) = if x mem xs then x :: xs else findrep xs;
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   941
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   942
255
ee132db91681 added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents: 245
diff changeset
   943
(*returns a list containing all repeated elements exactly once; preserves
ee132db91681 added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents: 245
diff changeset
   944
  order, takes first of equal elements*)
ee132db91681 added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents: 245
diff changeset
   945
fun gen_duplicates eq lst =
ee132db91681 added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents: 245
diff changeset
   946
  let
ee132db91681 added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents: 245
diff changeset
   947
    val memb = gen_mem eq;
ee132db91681 added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents: 245
diff changeset
   948
ee132db91681 added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents: 245
diff changeset
   949
    fun dups (rev_dups, []) = rev rev_dups
ee132db91681 added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents: 245
diff changeset
   950
      | dups (rev_dups, x :: xs) =
ee132db91681 added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents: 245
diff changeset
   951
          if memb (x, rev_dups) orelse not (memb (x, xs)) then
ee132db91681 added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents: 245
diff changeset
   952
            dups (rev_dups, xs)
ee132db91681 added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents: 245
diff changeset
   953
          else dups (x :: rev_dups, xs);
ee132db91681 added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents: 245
diff changeset
   954
  in
ee132db91681 added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents: 245
diff changeset
   955
    dups ([], lst)
ee132db91681 added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents: 245
diff changeset
   956
  end;
ee132db91681 added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents: 245
diff changeset
   957
2243
3ebeaaacfbd1 Eta-expanded some declarations that are illegal under value polymorphism
paulson
parents: 2196
diff changeset
   958
fun duplicates l = gen_duplicates (op =) l;
255
ee132db91681 added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents: 245
diff changeset
   959
ee132db91681 added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents: 245
diff changeset
   960
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   961
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   962
(** association lists **)
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   963
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   964
(*association list lookup*)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   965
fun assoc ([], key) = None
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   966
  | assoc ((keyi, xi) :: pairs, key) =
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   967
      if key = keyi then Some xi else assoc (pairs, key);
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   968
2175
21fde76bc742 Updated syntax; shortened comments; put in monomorphic versions of ins
paulson
parents: 2157
diff changeset
   969
(*association list lookup, optimized version for ints*)
1576
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   970
fun assoc_int ([], (key:int)) = None
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   971
  | assoc_int ((keyi, xi) :: pairs, key) =
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   972
      if key = keyi then Some xi else assoc_int (pairs, key);
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   973
2175
21fde76bc742 Updated syntax; shortened comments; put in monomorphic versions of ins
paulson
parents: 2157
diff changeset
   974
(*association list lookup, optimized version for strings*)
1576
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   975
fun assoc_string ([], (key:string)) = None
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   976
  | assoc_string ((keyi, xi) :: pairs, key) =
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   977
      if key = keyi then Some xi else assoc_string (pairs, key);
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   978
2175
21fde76bc742 Updated syntax; shortened comments; put in monomorphic versions of ins
paulson
parents: 2157
diff changeset
   979
(*association list lookup, optimized version for string*ints*)
1576
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   980
fun assoc_string_int ([], (key:string*int)) = None
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   981
  | assoc_string_int ((keyi, xi) :: pairs, key) =
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   982
      if key = keyi then Some xi else assoc_string_int (pairs, key);
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   983
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   984
fun assocs ps x =
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   985
  (case assoc (ps, x) of
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   986
    None => []
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   987
  | Some ys => ys);
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   988
255
ee132db91681 added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents: 245
diff changeset
   989
(*two-fold association list lookup*)
ee132db91681 added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents: 245
diff changeset
   990
fun assoc2 (aal, (key1, key2)) =
ee132db91681 added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents: 245
diff changeset
   991
  (case assoc (aal, key1) of
ee132db91681 added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents: 245
diff changeset
   992
    Some al => assoc (al, key2)
ee132db91681 added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents: 245
diff changeset
   993
  | None => None);
ee132db91681 added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents: 245
diff changeset
   994
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   995
(*generalized association list lookup*)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   996
fun gen_assoc eq ([], key) = None
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   997
  | gen_assoc eq ((keyi, xi) :: pairs, key) =
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   998
      if eq (key, keyi) then Some xi else gen_assoc eq (pairs, key);
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   999
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1000
(*association list update*)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1001
fun overwrite (al, p as (key, _)) =
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1002
  let fun over ((q as (keyi, _)) :: pairs) =
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1003
            if keyi = key then p :: pairs else q :: (over pairs)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1004
        | over [] = [p]
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1005
  in over al end;
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1006
2522
a1a18530c4ac added gen_overwrite;
wenzelm
parents: 2506
diff changeset
  1007
fun gen_overwrite eq (al, p as (key, _)) =
a1a18530c4ac added gen_overwrite;
wenzelm
parents: 2506
diff changeset
  1008
  let fun over ((q as (keyi, _)) :: pairs) =
a1a18530c4ac added gen_overwrite;
wenzelm
parents: 2506
diff changeset
  1009
            if eq (keyi, key) then p :: pairs else q :: (over pairs)
a1a18530c4ac added gen_overwrite;
wenzelm
parents: 2506
diff changeset
  1010
        | over [] = [p]
a1a18530c4ac added gen_overwrite;
wenzelm
parents: 2506
diff changeset
  1011
  in over al end;
a1a18530c4ac added gen_overwrite;
wenzelm
parents: 2506
diff changeset
  1012
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1013
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1014
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1015
(** generic tables **)
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
  1016
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1017
(*Tables are supposed to be 'efficient' encodings of lists of elements distinct
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1018
  wrt. an equality "eq". The extend and merge operations below are optimized
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1019
  for long-term space efficiency.*)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1020
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1021
(*append (new) elements to a table*)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1022
fun generic_extend _ _ _ tab [] = tab
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1023
  | generic_extend eq dest_tab mk_tab tab1 lst2 =
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1024
      let
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1025
        val lst1 = dest_tab tab1;
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1026
        val new_lst2 = gen_rems eq (lst2, lst1);
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1027
      in
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1028
        if null new_lst2 then tab1
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1029
        else mk_tab (lst1 @ new_lst2)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1030
      end;
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
  1031
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1032
(*append (new) elements of 2nd table to 1st table*)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1033
fun generic_merge eq dest_tab mk_tab tab1 tab2 =
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1034
  let
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1035
    val lst1 = dest_tab tab1;
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1036
    val lst2 = dest_tab tab2;
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1037
    val new_lst2 = gen_rems eq (lst2, lst1);
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1038
  in
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1039
    if null new_lst2 then tab1
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1040
    else if gen_subset eq (lst1, lst2) then tab2
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1041
    else mk_tab (lst1 @ new_lst2)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1042
  end;
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
  1043
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1044
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1045
(*lists as tables*)
2243
3ebeaaacfbd1 Eta-expanded some declarations that are illegal under value polymorphism
paulson
parents: 2196
diff changeset
  1046
fun extend_list tab = generic_extend (op =) I I tab;
3ebeaaacfbd1 Eta-expanded some declarations that are illegal under value polymorphism
paulson
parents: 2196
diff changeset
  1047
fun merge_lists tab = generic_merge (op =) I I tab;
4692
748f4e365d14 added merge_alists;
wenzelm
parents: 4630
diff changeset
  1048
fun merge_alists tab = generic_merge eq_fst I I tab;
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1049
380
daca5b594fb3 added infix op also: 'a * ('a -> 'b) -> 'b;
wenzelm
parents: 265
diff changeset
  1050
fun merge_rev_lists xs [] = xs
daca5b594fb3 added infix op also: 'a * ('a -> 'b) -> 'b;
wenzelm
parents: 265
diff changeset
  1051
  | merge_rev_lists [] ys = ys
daca5b594fb3 added infix op also: 'a * ('a -> 'b) -> 'b;
wenzelm
parents: 265
diff changeset
  1052
  | merge_rev_lists xs (y :: ys) =
daca5b594fb3 added infix op also: 'a * ('a -> 'b) -> 'b;
wenzelm
parents: 265
diff changeset
  1053
      (if y mem xs then I else cons y) (merge_rev_lists xs ys);
daca5b594fb3 added infix op also: 'a * ('a -> 'b) -> 'b;
wenzelm
parents: 265
diff changeset
  1054
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
  1055
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
  1056
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1057
(** balanced trees **)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1058
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1059
exception Balance;      (*indicates non-positive argument to balancing fun*)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1060
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1061
(*balanced folding; avoids deep nesting*)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1062
fun fold_bal f [x] = x
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1063
  | fold_bal f [] = raise Balance
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1064
  | fold_bal f xs =
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1065
      let val k = length xs div 2
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1066
      in  f (fold_bal f (take(k, xs)),
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1067
             fold_bal f (drop(k, xs)))
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1068
      end;
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1069
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1070
(*construct something of the form f(...g(...(x)...)) for balanced access*)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1071
fun access_bal (f, g, x) n i =
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1072
  let fun acc n i =     (*1<=i<=n*)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1073
          if n=1 then x else
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1074
          let val n2 = n div 2
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1075
          in  if i<=n2 then f (acc n2 i)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1076
                       else g (acc (n-n2) (i-n2))
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1077
          end
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1078
  in  if 1<=i andalso i<=n then acc n i else raise Balance  end;
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1079
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1080
(*construct ALL such accesses; could try harder to share recursive calls!*)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1081
fun accesses_bal (f, g, x) n =
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1082
  let fun acc n =
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1083
          if n=1 then [x] else
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1084
          let val n2 = n div 2
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1085
              val acc2 = acc n2
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1086
          in  if n-n2=n2 then map f acc2 @ map g acc2
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1087
                         else map f acc2 @ map g (acc (n-n2)) end
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1088
  in  if 1<=n then acc n else raise Balance  end;
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1089
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1090
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1091
2506
965127966331 added datatype order;
wenzelm
parents: 2471
diff changeset
  1092
(** orders **)
965127966331 added datatype order;
wenzelm
parents: 2471
diff changeset
  1093
965127966331 added datatype order;
wenzelm
parents: 2471
diff changeset
  1094
datatype order = LESS | EQUAL | GREATER;
965127966331 added datatype order;
wenzelm
parents: 2471
diff changeset
  1095
4445
de74b549f976 added rev_order, make_ord;
wenzelm
parents: 4363
diff changeset
  1096
fun rev_order LESS = GREATER
de74b549f976 added rev_order, make_ord;
wenzelm
parents: 4363
diff changeset
  1097
  | rev_order EQUAL = EQUAL
de74b549f976 added rev_order, make_ord;
wenzelm
parents: 4363
diff changeset
  1098
  | rev_order GREATER = LESS;
de74b549f976 added rev_order, make_ord;
wenzelm
parents: 4363
diff changeset
  1099
4479
708d7c26db5b improved comment;
wenzelm
parents: 4445
diff changeset
  1100
(*assume rel is a linear strict order*)
4445
de74b549f976 added rev_order, make_ord;
wenzelm
parents: 4363
diff changeset
  1101
fun make_ord rel (x, y) =
de74b549f976 added rev_order, make_ord;
wenzelm
parents: 4363
diff changeset
  1102
  if rel (x, y) then LESS
de74b549f976 added rev_order, make_ord;
wenzelm
parents: 4363
diff changeset
  1103
  else if rel (y, x) then GREATER
de74b549f976 added rev_order, make_ord;
wenzelm
parents: 4363
diff changeset
  1104
  else EQUAL;
de74b549f976 added rev_order, make_ord;
wenzelm
parents: 4363
diff changeset
  1105
4343
9849fb57c395 added prod_ord, dict_ord, list_ord;
wenzelm
parents: 4326
diff changeset
  1106
fun int_ord (i, j: int) =
2506
965127966331 added datatype order;
wenzelm
parents: 2471
diff changeset
  1107
  if i < j then LESS
965127966331 added datatype order;
wenzelm
parents: 2471
diff changeset
  1108
  else if i = j then EQUAL
965127966331 added datatype order;
wenzelm
parents: 2471
diff changeset
  1109
  else GREATER;
965127966331 added datatype order;
wenzelm
parents: 2471
diff changeset
  1110
4343
9849fb57c395 added prod_ord, dict_ord, list_ord;
wenzelm
parents: 4326
diff changeset
  1111
fun string_ord (a, b: string) =
2506
965127966331 added datatype order;
wenzelm
parents: 2471
diff changeset
  1112
  if a < b then LESS
965127966331 added datatype order;
wenzelm
parents: 2471
diff changeset
  1113
  else if a = b then EQUAL
965127966331 added datatype order;
wenzelm
parents: 2471
diff changeset
  1114
  else GREATER;
965127966331 added datatype order;
wenzelm
parents: 2471
diff changeset
  1115
4343
9849fb57c395 added prod_ord, dict_ord, list_ord;
wenzelm
parents: 4326
diff changeset
  1116
(*lexicographic product*)
9849fb57c395 added prod_ord, dict_ord, list_ord;
wenzelm
parents: 4326
diff changeset
  1117
fun prod_ord a_ord b_ord ((x, y), (x', y')) =
9849fb57c395 added prod_ord, dict_ord, list_ord;
wenzelm
parents: 4326
diff changeset
  1118
  (case a_ord (x, x') of EQUAL => b_ord (y, y') | ord => ord);
9849fb57c395 added prod_ord, dict_ord, list_ord;
wenzelm
parents: 4326
diff changeset
  1119
9849fb57c395 added prod_ord, dict_ord, list_ord;
wenzelm
parents: 4326
diff changeset
  1120
(*dictionary order -- in general NOT well-founded!*)
9849fb57c395 added prod_ord, dict_ord, list_ord;
wenzelm
parents: 4326
diff changeset
  1121
fun dict_ord _ ([], []) = EQUAL
9849fb57c395 added prod_ord, dict_ord, list_ord;
wenzelm
parents: 4326
diff changeset
  1122
  | dict_ord _ ([], _ :: _) = LESS
9849fb57c395 added prod_ord, dict_ord, list_ord;
wenzelm
parents: 4326
diff changeset
  1123
  | dict_ord _ (_ :: _, []) = GREATER
9849fb57c395 added prod_ord, dict_ord, list_ord;
wenzelm
parents: 4326
diff changeset
  1124
  | dict_ord elem_ord (x :: xs, y :: ys) =
9849fb57c395 added prod_ord, dict_ord, list_ord;
wenzelm
parents: 4326
diff changeset
  1125
      (case elem_ord (x, y) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord);
9849fb57c395 added prod_ord, dict_ord, list_ord;
wenzelm
parents: 4326
diff changeset
  1126
9849fb57c395 added prod_ord, dict_ord, list_ord;
wenzelm
parents: 4326
diff changeset
  1127
(*lexicographic product of lists*)
9849fb57c395 added prod_ord, dict_ord, list_ord;
wenzelm
parents: 4326
diff changeset
  1128
fun list_ord elem_ord (xs, ys) =
9849fb57c395 added prod_ord, dict_ord, list_ord;
wenzelm
parents: 4326
diff changeset
  1129
  prod_ord int_ord (dict_ord elem_ord) ((length xs, xs), (length ys, ys));
9849fb57c395 added prod_ord, dict_ord, list_ord;
wenzelm
parents: 4326
diff changeset
  1130
2506
965127966331 added datatype order;
wenzelm
parents: 2471
diff changeset
  1131
4621
79e6a11ba8a9 added explicit signature;
wenzelm
parents: 4616
diff changeset
  1132
(* sorting *)
79e6a11ba8a9 added explicit signature;
wenzelm
parents: 4616
diff changeset
  1133
79e6a11ba8a9 added explicit signature;
wenzelm
parents: 4616
diff changeset
  1134
(*quicksort (stable, i.e. does not reorder equal elements)*)
79e6a11ba8a9 added explicit signature;
wenzelm
parents: 4616
diff changeset
  1135
fun sort ord =
79e6a11ba8a9 added explicit signature;
wenzelm
parents: 4616
diff changeset
  1136
  let
79e6a11ba8a9 added explicit signature;
wenzelm
parents: 4616
diff changeset
  1137
    fun qsort xs =
79e6a11ba8a9 added explicit signature;
wenzelm
parents: 4616
diff changeset
  1138
      let val len = length xs in
79e6a11ba8a9 added explicit signature;
wenzelm
parents: 4616
diff changeset
  1139
        if len <= 1 then xs
79e6a11ba8a9 added explicit signature;
wenzelm
parents: 4616
diff changeset
  1140
        else
79e6a11ba8a9 added explicit signature;
wenzelm
parents: 4616
diff changeset
  1141
          let val (lts, eqs, gts) = part (nth_elem (len div 2, xs)) xs in
79e6a11ba8a9 added explicit signature;
wenzelm
parents: 4616
diff changeset
  1142
            qsort lts @ eqs @ qsort gts
79e6a11ba8a9 added explicit signature;
wenzelm
parents: 4616
diff changeset
  1143
          end
79e6a11ba8a9 added explicit signature;
wenzelm
parents: 4616
diff changeset
  1144
      end
79e6a11ba8a9 added explicit signature;
wenzelm
parents: 4616
diff changeset
  1145
    and part _ [] = ([], [], [])
79e6a11ba8a9 added explicit signature;
wenzelm
parents: 4616
diff changeset
  1146
      | part pivot (x :: xs) = add (ord (x, pivot)) x (part pivot xs)
79e6a11ba8a9 added explicit signature;
wenzelm
parents: 4616
diff changeset
  1147
    and add LESS x (lts, eqs, gts) = (x :: lts, eqs, gts)
79e6a11ba8a9 added explicit signature;
wenzelm
parents: 4616
diff changeset
  1148
      | add EQUAL x (lts, eqs, gts) = (lts, x :: eqs, gts)
79e6a11ba8a9 added explicit signature;
wenzelm
parents: 4616
diff changeset
  1149
      | add GREATER x (lts, eqs, gts) = (lts, eqs, x :: gts);
79e6a11ba8a9 added explicit signature;
wenzelm
parents: 4616
diff changeset
  1150
  in qsort end;
79e6a11ba8a9 added explicit signature;
wenzelm
parents: 4616
diff changeset
  1151
79e6a11ba8a9 added explicit signature;
wenzelm
parents: 4616
diff changeset
  1152
(*sort strings*)
79e6a11ba8a9 added explicit signature;
wenzelm
parents: 4616
diff changeset
  1153
val sort_strings = sort string_ord;
79e6a11ba8a9 added explicit signature;
wenzelm
parents: 4616
diff changeset
  1154
fun sort_wrt sel xs = sort (string_ord o pairself sel) xs;
79e6a11ba8a9 added explicit signature;
wenzelm
parents: 4616
diff changeset
  1155
11514
a12def3d1847 Added function unique_strings.
berghofe
parents: 11021
diff changeset
  1156
fun unique_strings ([]: string list) = []
a12def3d1847 Added function unique_strings.
berghofe
parents: 11021
diff changeset
  1157
  | unique_strings [x] = [x]
a12def3d1847 Added function unique_strings.
berghofe
parents: 11021
diff changeset
  1158
  | unique_strings (x :: y :: ys) =
a12def3d1847 Added function unique_strings.
berghofe
parents: 11021
diff changeset
  1159
      if x = y then unique_strings (y :: ys)
a12def3d1847 Added function unique_strings.
berghofe
parents: 11021
diff changeset
  1160
      else x :: unique_strings (y :: ys);
4621
79e6a11ba8a9 added explicit signature;
wenzelm
parents: 4616
diff changeset
  1161
2506
965127966331 added datatype order;
wenzelm
parents: 2471
diff changeset
  1162
3525
88edd3450460 improved output channels: normal, warning, error;
wenzelm
parents: 3407
diff changeset
  1163
(** input / output and diagnostics **)
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1164
2243
3ebeaaacfbd1 Eta-expanded some declarations that are illegal under value polymorphism
paulson
parents: 2196
diff changeset
  1165
val cd = OS.FileSys.chDir;
2317
672015b535d7 added pwd;
wenzelm
parents: 2303
diff changeset
  1166
val pwd = OS.FileSys.getDir;
2243
3ebeaaacfbd1 Eta-expanded some declarations that are illegal under value polymorphism
paulson
parents: 2196
diff changeset
  1167
11853
651650b717e1 conditional: bool -> (unit -> unit) -> unit;
wenzelm
parents: 11773
diff changeset
  1168
fun std_output s = (TextIO.output (TextIO.stdOut, s); TextIO.flushOut TextIO.stdOut);
651650b717e1 conditional: bool -> (unit -> unit) -> unit;
wenzelm
parents: 11773
diff changeset
  1169
fun std_error s = (TextIO.output (TextIO.stdErr, s); TextIO.flushOut TextIO.stdErr);
3525
88edd3450460 improved output channels: normal, warning, error;
wenzelm
parents: 3407
diff changeset
  1170
5942
9a7bf515fde1 std_output, prefix_lines;
wenzelm
parents: 5904
diff changeset
  1171
fun prefix_lines prfx txt =
5949
1e1d997e5c10 fixed prefix_lines: *separate* by \n;
wenzelm
parents: 5942
diff changeset
  1172
  txt |> split_lines |> map (fn s => prfx ^ s) |> cat_lines;
3525
88edd3450460 improved output channels: normal, warning, error;
wenzelm
parents: 3407
diff changeset
  1173
88edd3450460 improved output channels: normal, warning, error;
wenzelm
parents: 3407
diff changeset
  1174
(*hooks for output channels: normal, warning, error*)
5966
60f80b2a2777 removed prs / prs_fn (broken, because it did not include \n in its
wenzelm
parents: 5949
diff changeset
  1175
val writeln_fn = ref (std_output o suffix "\n");
9774
e745a418e6a5 added priority, priority_fn;
wenzelm
parents: 9721
diff changeset
  1176
val priority_fn = ref (fn s => ! writeln_fn s);
5949
1e1d997e5c10 fixed prefix_lines: *separate* by \n;
wenzelm
parents: 5942
diff changeset
  1177
val warning_fn = ref (std_output o suffix "\n" o prefix_lines "### ");
1e1d997e5c10 fixed prefix_lines: *separate* by \n;
wenzelm
parents: 5942
diff changeset
  1178
val error_fn = ref (std_output o suffix "\n" o prefix_lines "*** ");
1580
e3fd931e6095 Added some functions which allow redirection of Isabelle's output
berghofe
parents: 1576
diff changeset
  1179
5966
60f80b2a2777 removed prs / prs_fn (broken, because it did not include \n in its
wenzelm
parents: 5949
diff changeset
  1180
fun writeln s = ! writeln_fn s;
9774
e745a418e6a5 added priority, priority_fn;
wenzelm
parents: 9721
diff changeset
  1181
fun priority s = ! priority_fn s;
5942
9a7bf515fde1 std_output, prefix_lines;
wenzelm
parents: 5904
diff changeset
  1182
fun warning s = ! warning_fn s;
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1183
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1184
(*print error message and abort to top level*)
6959
d33b1629eaf9 try/can: pass Interrupt and ERROR;
wenzelm
parents: 6642
diff changeset
  1185
5949
1e1d997e5c10 fixed prefix_lines: *separate* by \n;
wenzelm
parents: 5942
diff changeset
  1186
fun error_msg s = ! error_fn s;
3553
a148c7e7152e added error_msg;
wenzelm
parents: 3525
diff changeset
  1187
fun error s = (error_msg s; raise ERROR);
4849
a9d5b8f8e40f tuned error msgs;
wenzelm
parents: 4792
diff changeset
  1188
fun sys_error msg = error ("## SYSTEM ERROR ##\n" ^ msg);
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1189
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1190
fun assert p msg = if p then () else error msg;
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1191
fun deny p msg = if p then error msg else ();
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1192
544
c53386a5bcf1 Pure/library/assert_all: new, moved from ZF/ind_syntax.ML
lcp
parents: 512
diff changeset
  1193
(*Assert pred for every member of l, generating a message if pred fails*)
4212
68c7b37f8721 major cleanup;
wenzelm
parents: 4194
diff changeset
  1194
fun assert_all pred l msg_fn =
544
c53386a5bcf1 Pure/library/assert_all: new, moved from ZF/ind_syntax.ML
lcp
parents: 512
diff changeset
  1195
  let fun asl [] = ()
4212
68c7b37f8721 major cleanup;
wenzelm
parents: 4194
diff changeset
  1196
        | asl (x::xs) = if pred x then asl xs else error (msg_fn x)
68c7b37f8721 major cleanup;
wenzelm
parents: 4194
diff changeset
  1197
  in asl l end;
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1198
3624
36e19fce289e added read_file, write_file;
wenzelm
parents: 3606
diff changeset
  1199
4212
68c7b37f8721 major cleanup;
wenzelm
parents: 4194
diff changeset
  1200
(* handle errors capturing messages *)
3699
7c30ab9e25d1 added handle_error: ('a -> 'b) -> 'a -> 'b error;
wenzelm
parents: 3645
diff changeset
  1201
7c30ab9e25d1 added handle_error: ('a -> 'b) -> 'a -> 'b error;
wenzelm
parents: 3645
diff changeset
  1202
datatype 'a error =
7c30ab9e25d1 added handle_error: ('a -> 'b) -> 'a -> 'b error;
wenzelm
parents: 3645
diff changeset
  1203
  Error of string |
7c30ab9e25d1 added handle_error: ('a -> 'b) -> 'a -> 'b error;
wenzelm
parents: 3645
diff changeset
  1204
  OK of 'a;
7c30ab9e25d1 added handle_error: ('a -> 'b) -> 'a -> 'b error;
wenzelm
parents: 3645
diff changeset
  1205
4248
5e8a31c41d44 added get_error: 'a error -> string option, get_ok: 'a error -> 'a option;
wenzelm
parents: 4224
diff changeset
  1206
fun get_error (Error msg) = Some msg
5e8a31c41d44 added get_error: 'a error -> string option, get_ok: 'a error -> 'a option;
wenzelm
parents: 4224
diff changeset
  1207
  | get_error _ = None;
5e8a31c41d44 added get_error: 'a error -> string option, get_ok: 'a error -> 'a option;
wenzelm
parents: 4224
diff changeset
  1208
5e8a31c41d44 added get_error: 'a error -> string option, get_ok: 'a error -> 'a option;
wenzelm
parents: 4224
diff changeset
  1209
fun get_ok (OK x) = Some x
5e8a31c41d44 added get_error: 'a error -> string option, get_ok: 'a error -> 'a option;
wenzelm
parents: 4224
diff changeset
  1210
  | get_ok _ = None;
5e8a31c41d44 added get_error: 'a error -> string option, get_ok: 'a error -> 'a option;
wenzelm
parents: 4224
diff changeset
  1211
5037
224887671646 handle_error: capture error msgs, even if no exception raised;
wenzelm
parents: 4995
diff changeset
  1212
datatype 'a result =
224887671646 handle_error: capture error msgs, even if no exception raised;
wenzelm
parents: 4995
diff changeset
  1213
  Result of 'a |
224887671646 handle_error: capture error msgs, even if no exception raised;
wenzelm
parents: 4995
diff changeset
  1214
  Exn of exn;
224887671646 handle_error: capture error msgs, even if no exception raised;
wenzelm
parents: 4995
diff changeset
  1215
3699
7c30ab9e25d1 added handle_error: ('a -> 'b) -> 'a -> 'b error;
wenzelm
parents: 3645
diff changeset
  1216
fun handle_error f x =
7c30ab9e25d1 added handle_error: ('a -> 'b) -> 'a -> 'b error;
wenzelm
parents: 3645
diff changeset
  1217
  let
4945
d8c809afafb8 fixed handle_error: cat_lines;
wenzelm
parents: 4923
diff changeset
  1218
    val buffer = ref ([]: string list);
d8c809afafb8 fixed handle_error: cat_lines;
wenzelm
parents: 4923
diff changeset
  1219
    fun capture s = buffer := ! buffer @ [s];
5037
224887671646 handle_error: capture error msgs, even if no exception raised;
wenzelm
parents: 4995
diff changeset
  1220
    fun err_msg () = if not (null (! buffer)) then error_msg (cat_lines (! buffer)) else ();
3699
7c30ab9e25d1 added handle_error: ('a -> 'b) -> 'a -> 'b error;
wenzelm
parents: 3645
diff changeset
  1221
  in
5037
224887671646 handle_error: capture error msgs, even if no exception raised;
wenzelm
parents: 4995
diff changeset
  1222
    (case Result (setmp error_fn capture f x) handle exn => Exn exn of
224887671646 handle_error: capture error msgs, even if no exception raised;
wenzelm
parents: 4995
diff changeset
  1223
      Result y => (err_msg (); OK y)
224887671646 handle_error: capture error msgs, even if no exception raised;
wenzelm
parents: 4995
diff changeset
  1224
    | Exn ERROR => Error (cat_lines (! buffer))
224887671646 handle_error: capture error msgs, even if no exception raised;
wenzelm
parents: 4995
diff changeset
  1225
    | Exn exn => (err_msg (); raise exn))
3624
36e19fce289e added read_file, write_file;
wenzelm
parents: 3606
diff changeset
  1226
  end;
36e19fce289e added read_file, write_file;
wenzelm
parents: 3606
diff changeset
  1227
36e19fce289e added read_file, write_file;
wenzelm
parents: 3606
diff changeset
  1228
5037
224887671646 handle_error: capture error msgs, even if no exception raised;
wenzelm
parents: 4995
diff changeset
  1229
(* transform ERROR into ERROR_MESSAGE *)
4923
ec71c480e600 added transform_error, exception ERROR_MESSAGE;
wenzelm
parents: 4916
diff changeset
  1230
ec71c480e600 added transform_error, exception ERROR_MESSAGE;
wenzelm
parents: 4916
diff changeset
  1231
exception ERROR_MESSAGE of string;
ec71c480e600 added transform_error, exception ERROR_MESSAGE;
wenzelm
parents: 4916
diff changeset
  1232
ec71c480e600 added transform_error, exception ERROR_MESSAGE;
wenzelm
parents: 4916
diff changeset
  1233
fun transform_error f x =
ec71c480e600 added transform_error, exception ERROR_MESSAGE;
wenzelm
parents: 4916
diff changeset
  1234
  (case handle_error f x of
ec71c480e600 added transform_error, exception ERROR_MESSAGE;
wenzelm
parents: 4916
diff changeset
  1235
    OK y => y
ec71c480e600 added transform_error, exception ERROR_MESSAGE;
wenzelm
parents: 4916
diff changeset
  1236
  | Error msg => raise ERROR_MESSAGE msg);
ec71c480e600 added transform_error, exception ERROR_MESSAGE;
wenzelm
parents: 4916
diff changeset
  1237
ec71c480e600 added transform_error, exception ERROR_MESSAGE;
wenzelm
parents: 4916
diff changeset
  1238
5904
e077a0e66563 val apply: ('a -> 'a) list -> 'a -> 'a;
wenzelm
parents: 5893
diff changeset
  1239
(* transform any exception, including ERROR *)
e077a0e66563 val apply: ('a -> 'a) list -> 'a -> 'a;
wenzelm
parents: 5893
diff changeset
  1240
e077a0e66563 val apply: ('a -> 'a) list -> 'a -> 'a;
wenzelm
parents: 5893
diff changeset
  1241
fun transform_failure exn f x =
e077a0e66563 val apply: ('a -> 'a) list -> 'a -> 'a;
wenzelm
parents: 5893
diff changeset
  1242
  transform_error f x handle e => raise exn e;
e077a0e66563 val apply: ('a -> 'a) list -> 'a -> 'a;
wenzelm
parents: 5893
diff changeset
  1243
e077a0e66563 val apply: ('a -> 'a) list -> 'a -> 'a;
wenzelm
parents: 5893
diff changeset
  1244
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1245
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1246
(** timing **)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1247
4326
7211ea5f29e2 New timing functions startTiming and endTiming
paulson
parents: 4284
diff changeset
  1248
(*a conditional timing function: applies f to () and, if the flag is true,
8999
ad8260dc6e4a global timing flag;
wenzelm
parents: 8806
diff changeset
  1249
  prints its runtime on warning channel*)
4326
7211ea5f29e2 New timing functions startTiming and endTiming
paulson
parents: 4284
diff changeset
  1250
fun cond_timeit flag f =
7211ea5f29e2 New timing functions startTiming and endTiming
paulson
parents: 4284
diff changeset
  1251
  if flag then
7211ea5f29e2 New timing functions startTiming and endTiming
paulson
parents: 4284
diff changeset
  1252
    let val start = startTiming()
7211ea5f29e2 New timing functions startTiming and endTiming
paulson
parents: 4284
diff changeset
  1253
        val result = f ()
8999
ad8260dc6e4a global timing flag;
wenzelm
parents: 8806
diff changeset
  1254
    in warning (endTiming start);  result end
4326
7211ea5f29e2 New timing functions startTiming and endTiming
paulson
parents: 4284
diff changeset
  1255
  else f ();
7211ea5f29e2 New timing functions startTiming and endTiming
paulson
parents: 4284
diff changeset
  1256
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1257
(*unconditional timing function*)
2243
3ebeaaacfbd1 Eta-expanded some declarations that are illegal under value polymorphism
paulson
parents: 2196
diff changeset
  1258
fun timeit x = cond_timeit true x;
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1259
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1260
(*timed application function*)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1261
fun timeap f x = timeit (fn () => f x);
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1262
8999
ad8260dc6e4a global timing flag;
wenzelm
parents: 8806
diff changeset
  1263
(*global timing mode*)
ad8260dc6e4a global timing flag;
wenzelm
parents: 8806
diff changeset
  1264
val timing = ref false;
ad8260dc6e4a global timing flag;
wenzelm
parents: 8806
diff changeset
  1265
3606
5d7073700fbc Added function "file_exists".
berghofe
parents: 3553
diff changeset
  1266
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1267
10692
6077fd933575 added rational arithmetic
nipkow
parents: 9830
diff changeset
  1268
(** rational numbers **)
6077fd933575 added rational arithmetic
nipkow
parents: 9830
diff changeset
  1269
6077fd933575 added rational arithmetic
nipkow
parents: 9830
diff changeset
  1270
datatype rat = Rat of bool * int * int
6077fd933575 added rational arithmetic
nipkow
parents: 9830
diff changeset
  1271
6077fd933575 added rational arithmetic
nipkow
parents: 9830
diff changeset
  1272
fun rep_rat(Rat(a,p,q)) = (if a then p else ~p,q)
6077fd933575 added rational arithmetic
nipkow
parents: 9830
diff changeset
  1273
6077fd933575 added rational arithmetic
nipkow
parents: 9830
diff changeset
  1274
fun ratnorm(a,p,q) = if p=0 then Rat(a,0,1) else
6077fd933575 added rational arithmetic
nipkow
parents: 9830
diff changeset
  1275
  let val absp = abs p
6077fd933575 added rational arithmetic
nipkow
parents: 9830
diff changeset
  1276
      val m = gcd(absp,q)
6077fd933575 added rational arithmetic
nipkow
parents: 9830
diff changeset
  1277
  in Rat(a = (0 <= p), absp div m, q div m) end;
6077fd933575 added rational arithmetic
nipkow
parents: 9830
diff changeset
  1278
6077fd933575 added rational arithmetic
nipkow
parents: 9830
diff changeset
  1279
fun ratadd(Rat(a,p,q),Rat(b,r,s)) =
6077fd933575 added rational arithmetic
nipkow
parents: 9830
diff changeset
  1280
  let val den = lcm(q,s)
6077fd933575 added rational arithmetic
nipkow
parents: 9830
diff changeset
  1281
      val p = p*(den div q) and r = r*(den div s)
6077fd933575 added rational arithmetic
nipkow
parents: 9830
diff changeset
  1282
      val num = (if a then p else ~p) + (if b then r else ~r)
6077fd933575 added rational arithmetic
nipkow
parents: 9830
diff changeset
  1283
  in ratnorm(true,num,den) end;
6077fd933575 added rational arithmetic
nipkow
parents: 9830
diff changeset
  1284
6077fd933575 added rational arithmetic
nipkow
parents: 9830
diff changeset
  1285
fun ratmul(Rat(a,p,q),Rat(b,r,s)) = ratnorm(a=b,p*r,q*s)
6077fd933575 added rational arithmetic
nipkow
parents: 9830
diff changeset
  1286
6077fd933575 added rational arithmetic
nipkow
parents: 9830
diff changeset
  1287
fun ratinv(Rat(a,p,q)) = if p=0 then error("ratinv") else Rat(a,q,p)
6077fd933575 added rational arithmetic
nipkow
parents: 9830
diff changeset
  1288
6077fd933575 added rational arithmetic
nipkow
parents: 9830
diff changeset
  1289
fun int_ratdiv(p,q) =
6077fd933575 added rational arithmetic
nipkow
parents: 9830
diff changeset
  1290
  if q=0 then error("int_ratdiv") else ratnorm(0<=q, p, abs q)
6077fd933575 added rational arithmetic
nipkow
parents: 9830
diff changeset
  1291
6077fd933575 added rational arithmetic
nipkow
parents: 9830
diff changeset
  1292
fun ratneg(Rat(b,p,q)) = Rat(not b,p,q);
6077fd933575 added rational arithmetic
nipkow
parents: 9830
diff changeset
  1293
6077fd933575 added rational arithmetic
nipkow
parents: 9830
diff changeset
  1294
fun rat_of_int i = if i < 0 then Rat(false,abs i,1) else Rat(true,i,1);
6077fd933575 added rational arithmetic
nipkow
parents: 9830
diff changeset
  1295
6077fd933575 added rational arithmetic
nipkow
parents: 9830
diff changeset
  1296
4621
79e6a11ba8a9 added explicit signature;
wenzelm
parents: 4616
diff changeset
  1297
(** misc **)
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1298
9830
wenzelm
parents: 9774
diff changeset
  1299
fun overwrite_warn (args as (alist, (a, _))) msg =
wenzelm
parents: 9774
diff changeset
  1300
 (if is_none (assoc (alist, a)) then () else warning msg;
wenzelm
parents: 9774
diff changeset
  1301
  overwrite args);
9721
7e51c9f3d5a0 *** empty log message ***
nipkow
parents: 9118
diff changeset
  1302
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1303
(*use the keyfun to make a list of (x, key) pairs*)
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
  1304
fun make_keylist (keyfun: 'a->'b) : 'a list -> ('a * 'b) list =
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1305
  let fun keypair x = (x, keyfun x)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1306
  in map keypair end;
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
  1307
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1308
(*given a list of (x, key) pairs and a searchkey
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
  1309
  return the list of xs from each pair whose key equals searchkey*)
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
  1310
fun keyfilter [] searchkey = []
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1311
  | keyfilter ((x, key) :: pairs) searchkey =
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1312
      if key = searchkey then x :: keyfilter pairs searchkey
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1313
      else keyfilter pairs searchkey;
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
  1314
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
  1315
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
  1316
(*Partition list into elements that satisfy predicate and those that don't.
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1317
  Preserves order of elements in both lists.*)
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
  1318
fun partition (pred: 'a->bool) (ys: 'a list) : ('a list * 'a list) =
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
  1319
    let fun part ([], answer) = answer
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1320
          | part (x::xs, (ys, ns)) = if pred(x)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1321
            then  part (xs, (x::ys, ns))
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1322
            else  part (xs, (ys, x::ns))
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1323
    in  part (rev ys, ([], []))  end;
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
  1324
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
  1325
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
  1326
fun partition_eq (eq:'a * 'a -> bool) =
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
  1327
    let fun part [] = []
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1328
          | part (x::ys) = let val (xs, xs') = partition (apl(x, eq)) ys
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1329
                           in (x::xs)::(part xs') end
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
  1330
    in part end;
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
  1331
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
  1332
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1333
(*Partition a list into buckets  [ bi, b(i+1), ..., bj ]
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
  1334
   putting x in bk if p(k)(x) holds.  Preserve order of elements if possible.*)
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
  1335
fun partition_list p i j =
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1336
  let fun part k xs =
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1337
            if k>j then
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
  1338
              (case xs of [] => []
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
  1339
                         | _ => raise LIST "partition_list")
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
  1340
            else
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1341
            let val (ns, rest) = partition (p k) xs;
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1342
            in  ns :: part(k+1)rest  end
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
  1343
  in  part i end;
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
  1344
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
  1345
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1346
(* transitive closure (not Warshall's algorithm) *)
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
  1347
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1348
fun transitive_closure [] = []
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1349
  | transitive_closure ((x, ys)::ps) =
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1350
      let val qs = transitive_closure ps
2182
29e56f003599 Removal of polymorphic equality via mem, subset, eq_set, etc
paulson
parents: 2175
diff changeset
  1351
          val zs = foldl (fn (zs, y) => assocs qs y union_string zs) (ys, ys)
5904
e077a0e66563 val apply: ('a -> 'a) list -> 'a -> 'a;
wenzelm
parents: 5893
diff changeset
  1352
          fun step(u, us) = (u, if x mem_string us then zs union_string us
2243
3ebeaaacfbd1 Eta-expanded some declarations that are illegal under value polymorphism
paulson
parents: 2196
diff changeset
  1353
                                else us)
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1354
      in (x, zs) :: map step qs end;
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
  1355
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
  1356
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1357
(* generating identifiers *)
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
  1358