src/Pure/thm.ML
author nipkow
Sun May 29 15:14:28 1994 +0200 (1994-05-29)
changeset 405 c97514f63633
parent 399 86cc2b98f9e0
child 421 95e1d4faa863
permissions -rw-r--r--
Internale optimization of the simplifier: in case a subterm stays unchanged,
None is returned. Speeds things up a little bit and is going to be useful
later on.
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(*  Title:      Pure/thm.ML
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    ID:         $Id$
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    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
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    Copyright   1994  University of Cambridge
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The abstract types "theory" and "thm".
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Also "cterm" / "ctyp" (certified terms / typs under a signature).
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*)
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signature THM =
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sig
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  structure Envir : ENVIR
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  structure Sequence : SEQUENCE
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  structure Sign : SIGN
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  type ctyp
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  type cterm
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  type thm
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  type theory
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  type meta_simpset
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  exception THM of string * int * thm list
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  exception THEORY of string * theory list
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  exception SIMPLIFIER of string * thm
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  (*certified terms/types; previously in sign.ML*)
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  val cterm_of: Sign.sg -> term -> cterm
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  val ctyp_of: Sign.sg -> typ -> ctyp
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  val read_ctyp: Sign.sg -> string -> ctyp
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  val read_cterm: Sign.sg -> string * typ -> cterm
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  val rep_cterm: cterm -> {T: typ, t: term, sign: Sign.sg, maxidx: int}
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  val rep_ctyp: ctyp -> {T: typ, sign: Sign.sg}
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  val term_of: cterm -> term
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  val typ_of: ctyp -> typ
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  val cterm_fun: (term -> term) -> (cterm -> cterm)
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  (*end of cterm/ctyp functions*)
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  (* FIXME *)
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  local open Sign.Syntax Sign.Syntax.Mixfix in  (* FIXME remove ...Mixfix *)
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    val add_classes: (class list * class * class list) list -> theory -> theory
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    val add_defsort: sort -> theory -> theory
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    val add_types: (string * int * mixfix) list -> theory -> theory
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    val add_tyabbrs: (string * string list * string * mixfix) list
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      -> theory -> theory
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    val add_tyabbrs_i: (string * string list * typ * mixfix) list
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      -> theory -> theory
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    val add_arities: (string * sort list * sort) list -> theory -> theory
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    val add_consts: (string * string * mixfix) list -> theory -> theory
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    val add_consts_i: (string * typ * mixfix) list -> theory -> theory
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    val add_syntax: (string * string * mixfix) list -> theory -> theory
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    val add_syntax_i: (string * typ * mixfix) list -> theory -> theory
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    val add_trfuns:
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      (string * (ast list -> ast)) list *
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      (string * (term list -> term)) list *
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      (string * (term list -> term)) list *
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      (string * (ast list -> ast)) list -> theory -> theory
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    val add_trrules: xrule list -> theory -> theory
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    val add_axioms: (string * string) list -> theory -> theory
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    val add_axioms_i: (string * term) list -> theory -> theory
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    val add_thyname: string -> theory -> theory
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  end
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  val cert_axm: Sign.sg -> string * term -> string * term
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  val read_axm: Sign.sg -> string * string -> string * term
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  val abstract_rule: string -> cterm -> thm -> thm
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  val add_congs: meta_simpset * thm list -> meta_simpset
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  val add_prems: meta_simpset * thm list -> meta_simpset
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  val add_simps: meta_simpset * thm list -> meta_simpset
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  val assume: cterm -> thm
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  val assumption: int -> thm -> thm Sequence.seq
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  val axioms_of: theory -> (string * term) list
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  val beta_conversion: cterm -> thm
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  val bicompose: bool -> bool * thm * int -> int -> thm -> thm Sequence.seq
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  val biresolution: bool -> (bool*thm)list -> int -> thm -> thm Sequence.seq
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  val combination: thm -> thm -> thm
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  val concl_of: thm -> term
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  val cprop_of: thm -> cterm
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  val del_simps: meta_simpset * thm list -> meta_simpset
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  val dest_cimplies: cterm -> cterm*cterm
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  val dest_state: thm * int -> (term*term)list * term list * term * term
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  val empty_mss: meta_simpset
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  val eq_assumption: int -> thm -> thm
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  val equal_intr: thm -> thm -> thm
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  val equal_elim: thm -> thm -> thm
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  val extend_theory: theory -> string
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        -> (class * class list) list * sort
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           * (string list * int)list
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           * (string * string list * string) list
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           * (string list * (sort list * class))list
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           * (string list * string)list * Sign.Syntax.sext option
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        -> (string*string)list -> theory
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  val extensional: thm -> thm
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  val flexflex_rule: thm -> thm Sequence.seq
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  val flexpair_def: thm
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  val forall_elim: cterm -> thm -> thm
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  val forall_intr: cterm -> thm -> thm
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  val freezeT: thm -> thm
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  val get_axiom: theory -> string -> thm
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  val implies_elim: thm -> thm -> thm
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  val implies_intr: cterm -> thm -> thm
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  val implies_intr_hyps: thm -> thm
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  val instantiate: (indexname*ctyp)list * (cterm*cterm)list
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                   -> thm -> thm
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  val lift_rule: (thm * int) -> thm -> thm
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  val merge_theories: theory * theory -> theory
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  val merge_thy_list: bool -> theory list -> theory
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  val mk_rews_of_mss: meta_simpset -> thm -> thm list
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  val mss_of: thm list -> meta_simpset
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  val nprems_of: thm -> int
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  val parents_of: theory -> theory list
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  val prems_of: thm -> term list
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  val prems_of_mss: meta_simpset -> thm list
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  val pure_thy: theory
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  val read_def_cterm :
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         Sign.sg * (indexname -> typ option) * (indexname -> sort option) ->
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         string * typ -> cterm * (indexname * typ) list
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   val reflexive: cterm -> thm
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  val rename_params_rule: string list * int -> thm -> thm
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  val rep_thm: thm -> {prop: term, hyps: term list, maxidx: int, sign: Sign.sg}
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  val rewrite_cterm:
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         bool*bool -> meta_simpset -> (meta_simpset -> thm -> thm option)
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           -> cterm -> thm
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  val set_mk_rews: meta_simpset * (thm -> thm list) -> meta_simpset
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  val rep_theory: theory -> {sign: Sign.sg, new_axioms: term Sign.Symtab.table, 
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    parents: theory list}
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  val subthy: theory * theory -> bool
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  val eq_thy: theory * theory -> bool
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  val sign_of: theory -> Sign.sg
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  val syn_of: theory -> Sign.Syntax.syntax
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  val stamps_of_thm: thm -> string ref list
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  val stamps_of_thy: theory -> string ref list
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  val symmetric: thm -> thm
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  val tpairs_of: thm -> (term*term)list
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  val trace_simp: bool ref
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  val transitive: thm -> thm -> thm
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  val trivial: cterm -> thm
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  val class_triv: theory -> class -> thm
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  val varifyT: thm -> thm
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end;
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functor ThmFun (structure Logic: LOGIC and Unify: UNIFY and Pattern: PATTERN
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  and Net:NET sharing type Pattern.type_sig = Unify.Sign.Type.type_sig): THM =
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struct
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structure Sequence = Unify.Sequence;
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structure Envir = Unify.Envir;
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structure Sign = Unify.Sign;
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structure Type = Sign.Type;
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structure Syntax = Sign.Syntax;
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structure Symtab = Sign.Symtab;
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(*** Certified terms and types ***)
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(** certified types **)
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(*certified typs under a signature*)
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datatype ctyp = Ctyp of {sign: Sign.sg, T: typ};
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fun rep_ctyp (Ctyp args) = args;
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fun typ_of (Ctyp {T, ...}) = T;
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fun ctyp_of sign T =
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  Ctyp {sign = sign, T = Sign.certify_typ sign T};
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fun read_ctyp sign s =
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  Ctyp {sign = sign, T = Sign.read_typ (sign, K None) s};
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(** certified terms **)
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(*certified terms under a signature, with checked typ and maxidx of Vars*)
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datatype cterm = Cterm of {sign: Sign.sg, t: term, T: typ, maxidx: int};
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fun rep_cterm (Cterm args) = args;
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fun term_of (Cterm {t, ...}) = t;
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(*create a cterm by checking a "raw" term with respect to a signature*)
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fun cterm_of sign tm =
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  let val (t, T, maxidx) = Sign.certify_term sign tm
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  in Cterm {sign = sign, t = t, T = T, maxidx = maxidx}
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  end handle TYPE (msg, _, _)
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    => raise TERM ("Term not in signature\n" ^ msg, [tm]);
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fun cterm_fun f (Cterm {sign, t, ...}) = cterm_of sign (f t);
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(*dest_implies for cterms. Note T=prop below*)
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fun dest_cimplies (Cterm{sign, T, maxidx, t=Const("==>", _) $ A $ B}) =
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       (Cterm{sign=sign, T=T, maxidx=maxidx, t=A},
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        Cterm{sign=sign, T=T, maxidx=maxidx, t=B})
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  | dest_cimplies ct = raise TERM ("dest_cimplies", [term_of ct]);
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(** read cterms **)
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(*read term, infer types, certify term*)
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fun read_def_cterm (sign, types, sorts) (a, T) =
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  let
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    val {tsig, const_tab, syn, ...} = Sign.rep_sg sign;
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    val showtyp = Sign.string_of_typ sign;
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    val showterm = Sign.string_of_term sign;
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    fun termerr [] = ""
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      | termerr [t] = "\nInvolving this term:\n" ^ showterm t
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      | termerr ts = "\nInvolving these terms:\n" ^ cat_lines (map showterm ts);
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    val T' = Sign.certify_typ sign T
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      handle TYPE (msg, _, _) => error msg;
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    val t = Syntax.read syn T' a;
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    val (t', tye) = Type.infer_types (tsig, const_tab, types, sorts, T', t)
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      handle TYPE (msg, Ts, ts) => error ("Type checking error: " ^ msg ^ "\n"
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        ^ cat_lines (map showtyp Ts) ^ termerr ts);
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    val ct = cterm_of sign t' handle TERM (msg, _) => error msg;
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  in (ct, tye) end;
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fun read_cterm sign = #1 o read_def_cterm (sign, K None, K None);
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(*** Meta theorems ***)
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datatype thm = Thm of
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  {sign: Sign.sg, maxidx: int, hyps: term list, prop: term};
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fun rep_thm (Thm args) = args;
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(*errors involving theorems*)
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exception THM of string * int * thm list;
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val sign_of_thm = #sign o rep_thm;
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val stamps_of_thm = #stamps o Sign.rep_sg o sign_of_thm;
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(*merge signatures of two theorems; raise exception if incompatible*)
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fun merge_thm_sgs (th1, th2) =
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  Sign.merge (pairself sign_of_thm (th1, th2))
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    handle TERM _ => raise THM ("incompatible signatures", 0, [th1, th2]);
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(*maps object-rule to tpairs*)
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fun tpairs_of (Thm {prop, ...}) = #1 (Logic.strip_flexpairs prop);
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(*maps object-rule to premises*)
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fun prems_of (Thm {prop, ...}) =
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  Logic.strip_imp_prems (Logic.skip_flexpairs prop);
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(*counts premises in a rule*)
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fun nprems_of (Thm {prop, ...}) =
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  Logic.count_prems (Logic.skip_flexpairs prop, 0);
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(*maps object-rule to conclusion*)
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fun concl_of (Thm {prop, ...}) = Logic.strip_imp_concl prop;
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(*the statement of any thm is a cterm*)
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fun cprop_of (Thm {sign, maxidx, hyps, prop}) =
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  Cterm {sign = sign, maxidx = maxidx, T = propT, t = prop};
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(*** Theories ***)
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datatype theory =
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  Theory of {
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    sign: Sign.sg,
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    new_axioms: term Symtab.table,
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    parents: theory list};
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fun rep_theory (Theory args) = args;
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(*errors involving theories*)
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exception THEORY of string * theory list;
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val sign_of = #sign o rep_theory;
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val syn_of = #syn o Sign.rep_sg o sign_of;
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(*stamps associated with a theory*)
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val stamps_of_thy = #stamps o Sign.rep_sg o sign_of;
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(*return additional axioms of this theory node*)
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val axioms_of = Symtab.dest o #new_axioms o rep_theory;
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(*return the immediate ancestors*)
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val parents_of = #parents o rep_theory;
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(*compare theories*)
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val subthy = Sign.subsig o pairself sign_of;
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val eq_thy = Sign.eq_sg o pairself sign_of;
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(*look up the named axiom in the theory*)
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fun get_axiom theory name =
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  let
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    fun get_ax [] = raise Match
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      | get_ax (Theory {sign, new_axioms, parents} :: thys) =
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          (case Symtab.lookup (new_axioms, name) of
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            Some t =>
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              Thm {sign = sign, maxidx = maxidx_of_term t, hyps = [], prop = t}
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          | None => get_ax parents handle Match => get_ax thys);
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  in
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    get_ax [theory] handle Match
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      => raise THEORY ("get_axiom: no axiom " ^ quote name, [theory])
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  end;
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(* the Pure theory *)
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val pure_thy =
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  Theory {sign = Sign.pure, new_axioms = Symtab.null, parents = []};
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(** extend theory **)
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fun err_dup_axms names =
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  error ("Duplicate axiom name(s) " ^ commas_quote names);
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fun ext_thy (thy as Theory {sign, new_axioms, parents}) sign1 new_axms =
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  let
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    val draft = Sign.is_draft sign;
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    val new_axioms1 =
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      Symtab.extend_new (if draft then new_axioms else Symtab.null, new_axms)
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        handle Symtab.DUPS names => err_dup_axms names;
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    val parents1 = if draft then parents else [thy];
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  in
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    Theory {sign = sign1, new_axioms = new_axioms1, parents = parents1}
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  end;
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(* extend signature of a theory *)
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fun ext_sg extfun decls (thy as Theory {sign, ...}) =
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  ext_thy thy (extfun decls sign) [];
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val add_classes   = ext_sg Sign.add_classes;
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val add_defsort   = ext_sg Sign.add_defsort;
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val add_types     = ext_sg Sign.add_types;
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val add_tyabbrs   = ext_sg Sign.add_tyabbrs;
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   342
val add_tyabbrs_i = ext_sg Sign.add_tyabbrs_i;
wenzelm@387
   343
val add_arities   = ext_sg Sign.add_arities;
wenzelm@387
   344
val add_consts    = ext_sg Sign.add_consts;
wenzelm@387
   345
val add_consts_i  = ext_sg Sign.add_consts_i;
wenzelm@387
   346
val add_syntax    = ext_sg Sign.add_syntax;
wenzelm@387
   347
val add_syntax_i  = ext_sg Sign.add_syntax_i;
wenzelm@387
   348
val add_trfuns    = ext_sg Sign.add_trfuns;
wenzelm@387
   349
val add_trrules   = ext_sg Sign.add_trrules;
wenzelm@387
   350
val add_thyname   = ext_sg Sign.add_name;
clasohm@0
   351
clasohm@0
   352
wenzelm@387
   353
(* prepare axioms *)
wenzelm@387
   354
wenzelm@387
   355
fun err_in_axm name =
wenzelm@387
   356
  error ("The error(s) above occurred in axiom " ^ quote name);
wenzelm@387
   357
wenzelm@387
   358
fun no_vars tm =
wenzelm@387
   359
  if null (term_vars tm) andalso null (term_tvars tm) then tm
wenzelm@387
   360
  else error "Illegal schematic variable(s) in term";
wenzelm@387
   361
wenzelm@387
   362
fun cert_axm sg (name, raw_tm) =
wenzelm@387
   363
  let
wenzelm@387
   364
    val Cterm {t, T, ...} = cterm_of sg raw_tm
wenzelm@387
   365
      handle TERM (msg, _) => error msg;
wenzelm@387
   366
  in
wenzelm@387
   367
    assert (T = propT) "Term not of type prop";
wenzelm@387
   368
    (name, no_vars t)
wenzelm@387
   369
  end
wenzelm@387
   370
  handle ERROR => err_in_axm name;
wenzelm@387
   371
wenzelm@387
   372
fun read_axm sg (name, str) =
wenzelm@387
   373
  (name, no_vars (term_of (read_cterm sg (str, propT))))
wenzelm@387
   374
    handle ERROR => err_in_axm name;
wenzelm@387
   375
wenzelm@387
   376
wenzelm@387
   377
(* extend axioms of a theory *)
wenzelm@387
   378
wenzelm@387
   379
fun ext_axms prep_axm axms (thy as Theory {sign, ...}) =
wenzelm@387
   380
  let
wenzelm@387
   381
    val sign1 = Sign.make_draft sign;
wenzelm@399
   382
    val axioms = map (apsnd Logic.varify o prep_axm sign) axms;
wenzelm@387
   383
  in
wenzelm@399
   384
    ext_thy thy sign1 axioms
wenzelm@387
   385
  end;
wenzelm@387
   386
wenzelm@387
   387
val add_axioms = ext_axms read_axm;
wenzelm@387
   388
val add_axioms_i = ext_axms cert_axm;
wenzelm@387
   389
wenzelm@387
   390
wenzelm@387
   391
(* extend theory (old) *)   (* FIXME remove *)
clasohm@0
   392
wenzelm@387
   393
(*converts Frees to Vars: axioms can be written without question marks*)
wenzelm@387
   394
fun prepare_axiom sign sP =
wenzelm@387
   395
  Logic.varify (term_of (read_cterm sign (sP, propT)));
wenzelm@387
   396
wenzelm@387
   397
(*read an axiom for a new theory*)
wenzelm@387
   398
fun read_ax sign (a, sP) =
wenzelm@387
   399
  (a, prepare_axiom sign sP) handle ERROR => err_in_axm a;
wenzelm@387
   400
wenzelm@387
   401
(*extension of a theory with given classes, types, constants and syntax;
wenzelm@387
   402
  reads the axioms from strings: axpairs have the form (axname, axiom)*)
wenzelm@387
   403
fun extend_theory thy thyname ext axpairs =
wenzelm@387
   404
  let
wenzelm@387
   405
    val Theory {sign, ...} = thy;
wenzelm@387
   406
wenzelm@387
   407
    val sign1 = Sign.extend sign thyname ext;
wenzelm@399
   408
    val axioms = map (read_ax sign1) axpairs;
wenzelm@387
   409
  in
wenzelm@387
   410
    writeln "WARNING: called obsolete function \"extend_theory\"";
wenzelm@399
   411
    ext_thy thy sign1 axioms
wenzelm@387
   412
  end;
wenzelm@387
   413
wenzelm@387
   414
wenzelm@387
   415
wenzelm@387
   416
(** merge theories **)
wenzelm@387
   417
wenzelm@387
   418
fun merge_thy_list mk_draft thys =
wenzelm@387
   419
  let
wenzelm@387
   420
    fun is_union thy = forall (fn t => subthy (t, thy)) thys;
wenzelm@387
   421
    val is_draft = Sign.is_draft o sign_of;
wenzelm@387
   422
wenzelm@387
   423
    fun add_sign (sg, Theory {sign, ...}) =
wenzelm@387
   424
      Sign.merge (sg, sign) handle TERM (msg, _) => error msg;
wenzelm@387
   425
  in
wenzelm@387
   426
    (case (find_first is_union thys, exists is_draft thys) of
wenzelm@387
   427
      (Some thy, _) => thy
wenzelm@387
   428
    | (None, true) => raise THEORY ("Illegal merge of draft theories", thys)
wenzelm@387
   429
    | (None, false) => Theory {
wenzelm@387
   430
        sign =
wenzelm@387
   431
          (if mk_draft then Sign.make_draft else I)
wenzelm@387
   432
          (foldl add_sign (Sign.pure, thys)),
wenzelm@399
   433
        new_axioms = Symtab.null,
wenzelm@387
   434
        parents = thys})
wenzelm@387
   435
  end;
wenzelm@387
   436
wenzelm@387
   437
fun merge_theories (thy1, thy2) = merge_thy_list false [thy1, thy2];
wenzelm@387
   438
clasohm@0
   439
clasohm@0
   440
clasohm@0
   441
(**** Primitive rules ****)
clasohm@0
   442
clasohm@0
   443
(* discharge all assumptions t from ts *)
clasohm@0
   444
val disch = gen_rem (op aconv);
clasohm@0
   445
clasohm@0
   446
(*The assumption rule A|-A in a theory  *)
wenzelm@250
   447
fun assume ct : thm =
lcp@229
   448
  let val {sign, t=prop, T, maxidx} = rep_cterm ct
wenzelm@250
   449
  in  if T<>propT then
wenzelm@250
   450
        raise THM("assume: assumptions must have type prop", 0, [])
clasohm@0
   451
      else if maxidx <> ~1 then
wenzelm@250
   452
        raise THM("assume: assumptions may not contain scheme variables",
wenzelm@250
   453
                  maxidx, [])
clasohm@0
   454
      else Thm{sign = sign, maxidx = ~1, hyps = [prop], prop = prop}
clasohm@0
   455
  end;
clasohm@0
   456
wenzelm@250
   457
(* Implication introduction
wenzelm@250
   458
              A |- B
wenzelm@250
   459
              -------
wenzelm@250
   460
              A ==> B    *)
clasohm@0
   461
fun implies_intr cA (thB as Thm{sign,maxidx,hyps,prop}) : thm =
lcp@229
   462
  let val {sign=signA, t=A, T, maxidx=maxidxA} = rep_cterm cA
clasohm@0
   463
  in  if T<>propT then
wenzelm@250
   464
        raise THM("implies_intr: assumptions must have type prop", 0, [thB])
wenzelm@250
   465
      else Thm{sign= Sign.merge (sign,signA),  maxidx= max[maxidxA, maxidx],
wenzelm@250
   466
             hyps= disch(hyps,A),  prop= implies$A$prop}
clasohm@0
   467
      handle TERM _ =>
clasohm@0
   468
        raise THM("implies_intr: incompatible signatures", 0, [thB])
clasohm@0
   469
  end;
clasohm@0
   470
clasohm@0
   471
(* Implication elimination
wenzelm@250
   472
        A ==> B       A
wenzelm@250
   473
        ---------------
wenzelm@250
   474
                B      *)
clasohm@0
   475
fun implies_elim thAB thA : thm =
clasohm@0
   476
    let val Thm{maxidx=maxA, hyps=hypsA, prop=propA,...} = thA
wenzelm@250
   477
        and Thm{sign, maxidx, hyps, prop,...} = thAB;
wenzelm@250
   478
        fun err(a) = raise THM("implies_elim: "^a, 0, [thAB,thA])
clasohm@0
   479
    in  case prop of
wenzelm@250
   480
            imp$A$B =>
wenzelm@250
   481
                if imp=implies andalso  A aconv propA
wenzelm@387
   482
                then  Thm{sign= merge_thm_sgs(thAB,thA),
wenzelm@250
   483
                          maxidx= max[maxA,maxidx],
wenzelm@250
   484
                          hyps= hypsA union hyps,  (*dups suppressed*)
wenzelm@250
   485
                          prop= B}
wenzelm@250
   486
                else err("major premise")
wenzelm@250
   487
          | _ => err("major premise")
clasohm@0
   488
    end;
wenzelm@250
   489
clasohm@0
   490
(* Forall introduction.  The Free or Var x must not be free in the hypotheses.
clasohm@0
   491
     A
clasohm@0
   492
   ------
clasohm@0
   493
   !!x.A       *)
clasohm@0
   494
fun forall_intr cx (th as Thm{sign,maxidx,hyps,prop}) =
lcp@229
   495
  let val x = term_of cx;
clasohm@0
   496
      fun result(a,T) = Thm{sign= sign, maxidx= maxidx, hyps= hyps,
wenzelm@250
   497
                            prop= all(T) $ Abs(a, T, abstract_over (x,prop))}
clasohm@0
   498
  in  case x of
wenzelm@250
   499
        Free(a,T) =>
wenzelm@250
   500
          if exists (apl(x, Logic.occs)) hyps
wenzelm@250
   501
          then  raise THM("forall_intr: variable free in assumptions", 0, [th])
wenzelm@250
   502
          else  result(a,T)
clasohm@0
   503
      | Var((a,_),T) => result(a,T)
clasohm@0
   504
      | _ => raise THM("forall_intr: not a variable", 0, [th])
clasohm@0
   505
  end;
clasohm@0
   506
clasohm@0
   507
(* Forall elimination
wenzelm@250
   508
              !!x.A
wenzelm@250
   509
             --------
wenzelm@250
   510
              A[t/x]     *)
clasohm@0
   511
fun forall_elim ct (th as Thm{sign,maxidx,hyps,prop}) : thm =
lcp@229
   512
  let val {sign=signt, t, T, maxidx=maxt} = rep_cterm ct
clasohm@0
   513
  in  case prop of
wenzelm@250
   514
          Const("all",Type("fun",[Type("fun",[qary,_]),_])) $ A =>
wenzelm@250
   515
            if T<>qary then
wenzelm@250
   516
                raise THM("forall_elim: type mismatch", 0, [th])
wenzelm@250
   517
            else Thm{sign= Sign.merge(sign,signt),
wenzelm@250
   518
                     maxidx= max[maxidx, maxt],
wenzelm@250
   519
                     hyps= hyps,  prop= betapply(A,t)}
wenzelm@250
   520
        | _ => raise THM("forall_elim: not quantified", 0, [th])
clasohm@0
   521
  end
clasohm@0
   522
  handle TERM _ =>
wenzelm@250
   523
         raise THM("forall_elim: incompatible signatures", 0, [th]);
clasohm@0
   524
clasohm@0
   525
clasohm@0
   526
(*** Equality ***)
clasohm@0
   527
clasohm@0
   528
(*Definition of the relation =?= *)
clasohm@0
   529
val flexpair_def =
wenzelm@250
   530
  Thm{sign= Sign.pure, hyps= [], maxidx= 0,
wenzelm@250
   531
      prop= term_of
wenzelm@250
   532
              (read_cterm Sign.pure
wenzelm@250
   533
                 ("(?t =?= ?u) == (?t == ?u::?'a::{})", propT))};
clasohm@0
   534
clasohm@0
   535
(*The reflexivity rule: maps  t   to the theorem   t==t   *)
wenzelm@250
   536
fun reflexive ct =
lcp@229
   537
  let val {sign, t, T, maxidx} = rep_cterm ct
clasohm@0
   538
  in  Thm{sign= sign, hyps= [], maxidx= maxidx, prop= Logic.mk_equals(t,t)}
clasohm@0
   539
  end;
clasohm@0
   540
clasohm@0
   541
(*The symmetry rule
clasohm@0
   542
    t==u
clasohm@0
   543
    ----
clasohm@0
   544
    u==t         *)
clasohm@0
   545
fun symmetric (th as Thm{sign,hyps,prop,maxidx}) =
clasohm@0
   546
  case prop of
clasohm@0
   547
      (eq as Const("==",_)) $ t $ u =>
wenzelm@250
   548
          Thm{sign=sign, hyps=hyps, maxidx=maxidx, prop= eq$u$t}
clasohm@0
   549
    | _ => raise THM("symmetric", 0, [th]);
clasohm@0
   550
clasohm@0
   551
(*The transitive rule
clasohm@0
   552
    t1==u    u==t2
clasohm@0
   553
    ------------
clasohm@0
   554
        t1==t2      *)
clasohm@0
   555
fun transitive th1 th2 =
clasohm@0
   556
  let val Thm{maxidx=max1, hyps=hyps1, prop=prop1,...} = th1
clasohm@0
   557
      and Thm{maxidx=max2, hyps=hyps2, prop=prop2,...} = th2;
clasohm@0
   558
      fun err(msg) = raise THM("transitive: "^msg, 0, [th1,th2])
clasohm@0
   559
  in case (prop1,prop2) of
clasohm@0
   560
       ((eq as Const("==",_)) $ t1 $ u, Const("==",_) $ u' $ t2) =>
wenzelm@250
   561
          if not (u aconv u') then err"middle term"  else
wenzelm@387
   562
              Thm{sign= merge_thm_sgs(th1,th2), hyps= hyps1 union hyps2,
wenzelm@250
   563
                  maxidx= max[max1,max2], prop= eq$t1$t2}
clasohm@0
   564
     | _ =>  err"premises"
clasohm@0
   565
  end;
clasohm@0
   566
clasohm@0
   567
(*Beta-conversion: maps (%(x)t)(u) to the theorem  (%(x)t)(u) == t[u/x]   *)
wenzelm@250
   568
fun beta_conversion ct =
lcp@229
   569
  let val {sign, t, T, maxidx} = rep_cterm ct
clasohm@0
   570
  in  case t of
wenzelm@250
   571
          Abs(_,_,bodt) $ u =>
wenzelm@250
   572
            Thm{sign= sign,  hyps= [],
wenzelm@250
   573
                maxidx= maxidx_of_term t,
wenzelm@250
   574
                prop= Logic.mk_equals(t, subst_bounds([u],bodt))}
wenzelm@250
   575
        | _ =>  raise THM("beta_conversion: not a redex", 0, [])
clasohm@0
   576
  end;
clasohm@0
   577
clasohm@0
   578
(*The extensionality rule   (proviso: x not free in f, g, or hypotheses)
clasohm@0
   579
    f(x) == g(x)
clasohm@0
   580
    ------------
clasohm@0
   581
       f == g    *)
clasohm@0
   582
fun extensional (th as Thm{sign,maxidx,hyps,prop}) =
clasohm@0
   583
  case prop of
clasohm@0
   584
    (Const("==",_)) $ (f$x) $ (g$y) =>
wenzelm@250
   585
      let fun err(msg) = raise THM("extensional: "^msg, 0, [th])
clasohm@0
   586
      in (if x<>y then err"different variables" else
clasohm@0
   587
          case y of
wenzelm@250
   588
                Free _ =>
wenzelm@250
   589
                  if exists (apl(y, Logic.occs)) (f::g::hyps)
wenzelm@250
   590
                  then err"variable free in hyps or functions"    else  ()
wenzelm@250
   591
              | Var _ =>
wenzelm@250
   592
                  if Logic.occs(y,f)  orelse  Logic.occs(y,g)
wenzelm@250
   593
                  then err"variable free in functions"   else  ()
wenzelm@250
   594
              | _ => err"not a variable");
wenzelm@250
   595
          Thm{sign=sign, hyps=hyps, maxidx=maxidx,
wenzelm@250
   596
              prop= Logic.mk_equals(f,g)}
clasohm@0
   597
      end
clasohm@0
   598
 | _ =>  raise THM("extensional: premise", 0, [th]);
clasohm@0
   599
clasohm@0
   600
(*The abstraction rule.  The Free or Var x must not be free in the hypotheses.
clasohm@0
   601
  The bound variable will be named "a" (since x will be something like x320)
clasohm@0
   602
          t == u
clasohm@0
   603
    ----------------
clasohm@0
   604
      %(x)t == %(x)u     *)
clasohm@0
   605
fun abstract_rule a cx (th as Thm{sign,maxidx,hyps,prop}) =
lcp@229
   606
  let val x = term_of cx;
wenzelm@250
   607
      val (t,u) = Logic.dest_equals prop
wenzelm@250
   608
            handle TERM _ =>
wenzelm@250
   609
                raise THM("abstract_rule: premise not an equality", 0, [th])
clasohm@0
   610
      fun result T =
clasohm@0
   611
            Thm{sign= sign, maxidx= maxidx, hyps= hyps,
wenzelm@250
   612
                prop= Logic.mk_equals(Abs(a, T, abstract_over (x,t)),
wenzelm@250
   613
                                      Abs(a, T, abstract_over (x,u)))}
clasohm@0
   614
  in  case x of
wenzelm@250
   615
        Free(_,T) =>
wenzelm@250
   616
         if exists (apl(x, Logic.occs)) hyps
wenzelm@250
   617
         then raise THM("abstract_rule: variable free in assumptions", 0, [th])
wenzelm@250
   618
         else result T
clasohm@0
   619
      | Var(_,T) => result T
clasohm@0
   620
      | _ => raise THM("abstract_rule: not a variable", 0, [th])
clasohm@0
   621
  end;
clasohm@0
   622
clasohm@0
   623
(*The combination rule
clasohm@0
   624
    f==g    t==u
clasohm@0
   625
    ------------
clasohm@0
   626
     f(t)==g(u)      *)
clasohm@0
   627
fun combination th1 th2 =
clasohm@0
   628
  let val Thm{maxidx=max1, hyps=hyps1, prop=prop1,...} = th1
clasohm@0
   629
      and Thm{maxidx=max2, hyps=hyps2, prop=prop2,...} = th2
clasohm@0
   630
  in  case (prop1,prop2)  of
clasohm@0
   631
       (Const("==",_) $ f $ g, Const("==",_) $ t $ u) =>
wenzelm@387
   632
              Thm{sign= merge_thm_sgs(th1,th2), hyps= hyps1 union hyps2,
wenzelm@250
   633
                  maxidx= max[max1,max2], prop= Logic.mk_equals(f$t, g$u)}
clasohm@0
   634
     | _ =>  raise THM("combination: premises", 0, [th1,th2])
clasohm@0
   635
  end;
clasohm@0
   636
clasohm@0
   637
clasohm@0
   638
(*The equal propositions rule
clasohm@0
   639
    A==B    A
clasohm@0
   640
    ---------
clasohm@0
   641
        B          *)
clasohm@0
   642
fun equal_elim th1 th2 =
clasohm@0
   643
  let val Thm{maxidx=max1, hyps=hyps1, prop=prop1,...} = th1
clasohm@0
   644
      and Thm{maxidx=max2, hyps=hyps2, prop=prop2,...} = th2;
clasohm@0
   645
      fun err(msg) = raise THM("equal_elim: "^msg, 0, [th1,th2])
clasohm@0
   646
  in  case prop1  of
clasohm@0
   647
       Const("==",_) $ A $ B =>
wenzelm@250
   648
          if not (prop2 aconv A) then err"not equal"  else
wenzelm@387
   649
              Thm{sign= merge_thm_sgs(th1,th2), hyps= hyps1 union hyps2,
wenzelm@250
   650
                  maxidx= max[max1,max2], prop= B}
clasohm@0
   651
     | _ =>  err"major premise"
clasohm@0
   652
  end;
clasohm@0
   653
clasohm@0
   654
clasohm@0
   655
(* Equality introduction
clasohm@0
   656
    A==>B    B==>A
clasohm@0
   657
    -------------
clasohm@0
   658
         A==B            *)
clasohm@0
   659
fun equal_intr th1 th2 =
clasohm@0
   660
let val Thm{maxidx=max1, hyps=hyps1, prop=prop1,...} = th1
clasohm@0
   661
    and Thm{maxidx=max2, hyps=hyps2, prop=prop2,...} = th2;
clasohm@0
   662
    fun err(msg) = raise THM("equal_intr: "^msg, 0, [th1,th2])
clasohm@0
   663
in case (prop1,prop2) of
clasohm@0
   664
     (Const("==>",_) $ A $ B, Const("==>",_) $ B' $ A')  =>
wenzelm@250
   665
        if A aconv A' andalso B aconv B'
wenzelm@387
   666
        then Thm{sign= merge_thm_sgs(th1,th2), hyps= hyps1 union hyps2,
wenzelm@250
   667
                 maxidx= max[max1,max2], prop= Logic.mk_equals(A,B)}
wenzelm@250
   668
        else err"not equal"
clasohm@0
   669
   | _ =>  err"premises"
clasohm@0
   670
end;
clasohm@0
   671
clasohm@0
   672
(**** Derived rules ****)
clasohm@0
   673
clasohm@0
   674
(*Discharge all hypotheses (need not verify cterms)
clasohm@0
   675
  Repeated hypotheses are discharged only once;  fold cannot do this*)
clasohm@0
   676
fun implies_intr_hyps (Thm{sign, maxidx, hyps=A::As, prop}) =
clasohm@0
   677
      implies_intr_hyps
wenzelm@250
   678
            (Thm{sign=sign,  maxidx=maxidx,
wenzelm@250
   679
                 hyps= disch(As,A),  prop= implies$A$prop})
clasohm@0
   680
  | implies_intr_hyps th = th;
clasohm@0
   681
clasohm@0
   682
(*Smash" unifies the list of term pairs leaving no flex-flex pairs.
wenzelm@250
   683
  Instantiates the theorem and deletes trivial tpairs.
clasohm@0
   684
  Resulting sequence may contain multiple elements if the tpairs are
clasohm@0
   685
    not all flex-flex. *)
clasohm@0
   686
fun flexflex_rule (Thm{sign,maxidx,hyps,prop}) =
wenzelm@250
   687
  let fun newthm env =
wenzelm@250
   688
          let val (tpairs,horn) =
wenzelm@250
   689
                        Logic.strip_flexpairs (Envir.norm_term env prop)
wenzelm@250
   690
                (*Remove trivial tpairs, of the form t=t*)
wenzelm@250
   691
              val distpairs = filter (not o op aconv) tpairs
wenzelm@250
   692
              val newprop = Logic.list_flexpairs(distpairs, horn)
wenzelm@250
   693
          in  Thm{sign= sign, hyps= hyps,
wenzelm@250
   694
                  maxidx= maxidx_of_term newprop, prop= newprop}
wenzelm@250
   695
          end;
clasohm@0
   696
      val (tpairs,_) = Logic.strip_flexpairs prop
clasohm@0
   697
  in Sequence.maps newthm
wenzelm@250
   698
            (Unify.smash_unifiers(sign, Envir.empty maxidx, tpairs))
clasohm@0
   699
  end;
clasohm@0
   700
clasohm@0
   701
(*Instantiation of Vars
wenzelm@250
   702
                      A
wenzelm@250
   703
             --------------------
wenzelm@250
   704
              A[t1/v1,....,tn/vn]     *)
clasohm@0
   705
clasohm@0
   706
(*Check that all the terms are Vars and are distinct*)
clasohm@0
   707
fun instl_ok ts = forall is_Var ts andalso null(findrep ts);
clasohm@0
   708
clasohm@0
   709
(*For instantiate: process pair of cterms, merge theories*)
clasohm@0
   710
fun add_ctpair ((ct,cu), (sign,tpairs)) =
lcp@229
   711
  let val {sign=signt, t=t, T= T, ...} = rep_cterm ct
lcp@229
   712
      and {sign=signu, t=u, T= U, ...} = rep_cterm cu
clasohm@0
   713
  in  if T=U  then (Sign.merge(sign, Sign.merge(signt, signu)), (t,u)::tpairs)
clasohm@0
   714
      else raise TYPE("add_ctpair", [T,U], [t,u])
clasohm@0
   715
  end;
clasohm@0
   716
clasohm@0
   717
fun add_ctyp ((v,ctyp), (sign',vTs)) =
lcp@229
   718
  let val {T,sign} = rep_ctyp ctyp
clasohm@0
   719
  in (Sign.merge(sign,sign'), (v,T)::vTs) end;
clasohm@0
   720
clasohm@0
   721
(*Left-to-right replacements: ctpairs = [...,(vi,ti),...].
clasohm@0
   722
  Instantiates distinct Vars by terms of same type.
clasohm@0
   723
  Normalizes the new theorem! *)
wenzelm@250
   724
fun instantiate (vcTs,ctpairs)  (th as Thm{sign,maxidx,hyps,prop}) =
clasohm@0
   725
  let val (newsign,tpairs) = foldr add_ctpair (ctpairs, (sign,[]));
clasohm@0
   726
      val (newsign,vTs) = foldr add_ctyp (vcTs, (newsign,[]));
wenzelm@250
   727
      val newprop =
wenzelm@250
   728
            Envir.norm_term (Envir.empty 0)
wenzelm@250
   729
              (subst_atomic tpairs
wenzelm@250
   730
               (Type.inst_term_tvars(#tsig(Sign.rep_sg newsign),vTs) prop))
clasohm@0
   731
      val newth = Thm{sign= newsign, hyps= hyps,
wenzelm@250
   732
                      maxidx= maxidx_of_term newprop, prop= newprop}
wenzelm@250
   733
  in  if not(instl_ok(map #1 tpairs))
nipkow@193
   734
      then raise THM("instantiate: variables not distinct", 0, [th])
nipkow@193
   735
      else if not(null(findrep(map #1 vTs)))
nipkow@193
   736
      then raise THM("instantiate: type variables not distinct", 0, [th])
nipkow@193
   737
      else (*Check types of Vars for agreement*)
nipkow@193
   738
      case findrep (map (#1 o dest_Var) (term_vars newprop)) of
wenzelm@250
   739
          ix::_ => raise THM("instantiate: conflicting types for variable " ^
wenzelm@250
   740
                             Syntax.string_of_vname ix ^ "\n", 0, [newth])
wenzelm@250
   741
        | [] =>
wenzelm@250
   742
             case findrep (map #1 (term_tvars newprop)) of
wenzelm@250
   743
             ix::_ => raise THM
wenzelm@250
   744
                    ("instantiate: conflicting sorts for type variable " ^
wenzelm@250
   745
                     Syntax.string_of_vname ix ^ "\n", 0, [newth])
nipkow@193
   746
        | [] => newth
clasohm@0
   747
  end
wenzelm@250
   748
  handle TERM _ =>
clasohm@0
   749
           raise THM("instantiate: incompatible signatures",0,[th])
nipkow@193
   750
       | TYPE _ => raise THM("instantiate: type conflict", 0, [th]);
clasohm@0
   751
clasohm@0
   752
(*The trivial implication A==>A, justified by assume and forall rules.
clasohm@0
   753
  A can contain Vars, not so for assume!   *)
wenzelm@250
   754
fun trivial ct : thm =
lcp@229
   755
  let val {sign, t=A, T, maxidx} = rep_cterm ct
wenzelm@250
   756
  in  if T<>propT then
wenzelm@250
   757
            raise THM("trivial: the term must have type prop", 0, [])
clasohm@0
   758
      else Thm{sign= sign, maxidx= maxidx, hyps= [], prop= implies$A$A}
clasohm@0
   759
  end;
clasohm@0
   760
wenzelm@399
   761
(*Axiom-scheme reflecting signature contents: "(| ?'a::c : c_class |)".
wenzelm@399
   762
  Is weaker than some definition of c_class, e.g. "c_class == %x.T";
wenzelm@399
   763
  may be interpreted as an instance of A==>A.*)
wenzelm@399
   764
fun class_triv thy c =
wenzelm@399
   765
  let
wenzelm@399
   766
    val sign = sign_of thy;
wenzelm@399
   767
    val Cterm {t, maxidx, ...} =
wenzelm@399
   768
      cterm_of sign (Logic.mk_inclass (TVar (("'a", 0), [c]), c))
wenzelm@399
   769
        handle TERM (msg, _) => raise THM ("class_triv: " ^ msg, 0, []);
wenzelm@399
   770
  in
wenzelm@399
   771
    Thm {sign = sign, maxidx = maxidx, hyps = [], prop = t}
wenzelm@399
   772
  end;
wenzelm@399
   773
wenzelm@399
   774
clasohm@0
   775
(* Replace all TFrees not in the hyps by new TVars *)
clasohm@0
   776
fun varifyT(Thm{sign,maxidx,hyps,prop}) =
clasohm@0
   777
  let val tfrees = foldr add_term_tfree_names (hyps,[])
clasohm@0
   778
  in Thm{sign=sign, maxidx=max[0,maxidx], hyps=hyps,
wenzelm@250
   779
         prop= Type.varify(prop,tfrees)}
clasohm@0
   780
  end;
clasohm@0
   781
clasohm@0
   782
(* Replace all TVars by new TFrees *)
clasohm@0
   783
fun freezeT(Thm{sign,maxidx,hyps,prop}) =
clasohm@0
   784
  let val prop' = Type.freeze (K true) prop
clasohm@0
   785
  in Thm{sign=sign, maxidx=maxidx_of_term prop', hyps=hyps, prop=prop'} end;
clasohm@0
   786
clasohm@0
   787
clasohm@0
   788
(*** Inference rules for tactics ***)
clasohm@0
   789
clasohm@0
   790
(*Destruct proof state into constraints, other goals, goal(i), rest *)
clasohm@0
   791
fun dest_state (state as Thm{prop,...}, i) =
clasohm@0
   792
  let val (tpairs,horn) = Logic.strip_flexpairs prop
clasohm@0
   793
  in  case  Logic.strip_prems(i, [], horn) of
clasohm@0
   794
          (B::rBs, C) => (tpairs, rev rBs, B, C)
clasohm@0
   795
        | _ => raise THM("dest_state", i, [state])
clasohm@0
   796
  end
clasohm@0
   797
  handle TERM _ => raise THM("dest_state", i, [state]);
clasohm@0
   798
lcp@309
   799
(*Increment variables and parameters of orule as required for
clasohm@0
   800
  resolution with goal i of state. *)
clasohm@0
   801
fun lift_rule (state, i) orule =
clasohm@0
   802
  let val Thm{prop=sprop,maxidx=smax,...} = state;
clasohm@0
   803
      val (Bi::_, _) = Logic.strip_prems(i, [], Logic.skip_flexpairs sprop)
wenzelm@250
   804
        handle TERM _ => raise THM("lift_rule", i, [orule,state]);
clasohm@0
   805
      val (lift_abs,lift_all) = Logic.lift_fns(Bi,smax+1);
clasohm@0
   806
      val (Thm{sign,maxidx,hyps,prop}) = orule
clasohm@0
   807
      val (tpairs,As,B) = Logic.strip_horn prop
wenzelm@387
   808
  in  Thm{hyps=hyps, sign= merge_thm_sgs(state,orule),
wenzelm@250
   809
          maxidx= maxidx+smax+1,
wenzelm@250
   810
          prop= Logic.rule_of(map (pairself lift_abs) tpairs,
wenzelm@250
   811
                              map lift_all As,    lift_all B)}
clasohm@0
   812
  end;
clasohm@0
   813
clasohm@0
   814
(*Solve subgoal Bi of proof state B1...Bn/C by assumption. *)
clasohm@0
   815
fun assumption i state =
clasohm@0
   816
  let val Thm{sign,maxidx,hyps,prop} = state;
clasohm@0
   817
      val (tpairs, Bs, Bi, C) = dest_state(state,i)
wenzelm@250
   818
      fun newth (env as Envir.Envir{maxidx, ...}, tpairs) =
wenzelm@250
   819
          Thm{sign=sign, hyps=hyps, maxidx=maxidx, prop=
wenzelm@250
   820
            if Envir.is_empty env then (*avoid wasted normalizations*)
wenzelm@250
   821
              Logic.rule_of (tpairs, Bs, C)
wenzelm@250
   822
            else (*normalize the new rule fully*)
wenzelm@250
   823
              Envir.norm_term env (Logic.rule_of (tpairs, Bs, C))};
clasohm@0
   824
      fun addprfs [] = Sequence.null
clasohm@0
   825
        | addprfs ((t,u)::apairs) = Sequence.seqof (fn()=> Sequence.pull
clasohm@0
   826
             (Sequence.mapp newth
wenzelm@250
   827
                (Unify.unifiers(sign,Envir.empty maxidx, (t,u)::tpairs))
wenzelm@250
   828
                (addprfs apairs)))
clasohm@0
   829
  in  addprfs (Logic.assum_pairs Bi)  end;
clasohm@0
   830
wenzelm@250
   831
(*Solve subgoal Bi of proof state B1...Bn/C by assumption.
clasohm@0
   832
  Checks if Bi's conclusion is alpha-convertible to one of its assumptions*)
clasohm@0
   833
fun eq_assumption i state =
clasohm@0
   834
  let val Thm{sign,maxidx,hyps,prop} = state;
clasohm@0
   835
      val (tpairs, Bs, Bi, C) = dest_state(state,i)
clasohm@0
   836
  in  if exists (op aconv) (Logic.assum_pairs Bi)
wenzelm@250
   837
      then Thm{sign=sign, hyps=hyps, maxidx=maxidx,
wenzelm@250
   838
               prop=Logic.rule_of(tpairs, Bs, C)}
clasohm@0
   839
      else  raise THM("eq_assumption", 0, [state])
clasohm@0
   840
  end;
clasohm@0
   841
clasohm@0
   842
clasohm@0
   843
(** User renaming of parameters in a subgoal **)
clasohm@0
   844
clasohm@0
   845
(*Calls error rather than raising an exception because it is intended
clasohm@0
   846
  for top-level use -- exception handling would not make sense here.
clasohm@0
   847
  The names in cs, if distinct, are used for the innermost parameters;
clasohm@0
   848
   preceding parameters may be renamed to make all params distinct.*)
clasohm@0
   849
fun rename_params_rule (cs, i) state =
clasohm@0
   850
  let val Thm{sign,maxidx,hyps,prop} = state
clasohm@0
   851
      val (tpairs, Bs, Bi, C) = dest_state(state,i)
clasohm@0
   852
      val iparams = map #1 (Logic.strip_params Bi)
clasohm@0
   853
      val short = length iparams - length cs
wenzelm@250
   854
      val newnames =
wenzelm@250
   855
            if short<0 then error"More names than abstractions!"
wenzelm@250
   856
            else variantlist(take (short,iparams), cs) @ cs
clasohm@0
   857
      val freenames = map (#1 o dest_Free) (term_frees prop)
clasohm@0
   858
      val newBi = Logic.list_rename_params (newnames, Bi)
wenzelm@250
   859
  in
clasohm@0
   860
  case findrep cs of
clasohm@0
   861
     c::_ => error ("Bound variables not distinct: " ^ c)
clasohm@0
   862
   | [] => (case cs inter freenames of
clasohm@0
   863
       a::_ => error ("Bound/Free variable clash: " ^ a)
clasohm@0
   864
     | [] => Thm{sign=sign, hyps=hyps, maxidx=maxidx, prop=
wenzelm@250
   865
                    Logic.rule_of(tpairs, Bs@[newBi], C)})
clasohm@0
   866
  end;
clasohm@0
   867
clasohm@0
   868
(*** Preservation of bound variable names ***)
clasohm@0
   869
wenzelm@250
   870
(*Scan a pair of terms; while they are similar,
clasohm@0
   871
  accumulate corresponding bound vars in "al"*)
clasohm@0
   872
fun match_bvs(Abs(x,_,s),Abs(y,_,t), al) = match_bvs(s,t,(x,y)::al)
clasohm@0
   873
  | match_bvs(f$s, g$t, al) = match_bvs(f,g,match_bvs(s,t,al))
clasohm@0
   874
  | match_bvs(_,_,al) = al;
clasohm@0
   875
clasohm@0
   876
(* strip abstractions created by parameters *)
clasohm@0
   877
fun match_bvars((s,t),al) = match_bvs(strip_abs_body s, strip_abs_body t, al);
clasohm@0
   878
clasohm@0
   879
wenzelm@250
   880
(* strip_apply f A(,B) strips off all assumptions/parameters from A
clasohm@0
   881
   introduced by lifting over B, and applies f to remaining part of A*)
clasohm@0
   882
fun strip_apply f =
clasohm@0
   883
  let fun strip(Const("==>",_)$ A1 $ B1,
wenzelm@250
   884
                Const("==>",_)$ _  $ B2) = implies $ A1 $ strip(B1,B2)
wenzelm@250
   885
        | strip((c as Const("all",_)) $ Abs(a,T,t1),
wenzelm@250
   886
                      Const("all",_)  $ Abs(_,_,t2)) = c$Abs(a,T,strip(t1,t2))
wenzelm@250
   887
        | strip(A,_) = f A
clasohm@0
   888
  in strip end;
clasohm@0
   889
clasohm@0
   890
(*Use the alist to rename all bound variables and some unknowns in a term
clasohm@0
   891
  dpairs = current disagreement pairs;  tpairs = permanent ones (flexflex);
clasohm@0
   892
  Preserves unknowns in tpairs and on lhs of dpairs. *)
clasohm@0
   893
fun rename_bvs([],_,_,_) = I
clasohm@0
   894
  | rename_bvs(al,dpairs,tpairs,B) =
wenzelm@250
   895
    let val vars = foldr add_term_vars
wenzelm@250
   896
                        (map fst dpairs @ map fst tpairs @ map snd tpairs, [])
wenzelm@250
   897
        (*unknowns appearing elsewhere be preserved!*)
wenzelm@250
   898
        val vids = map (#1 o #1 o dest_Var) vars;
wenzelm@250
   899
        fun rename(t as Var((x,i),T)) =
wenzelm@250
   900
                (case assoc(al,x) of
wenzelm@250
   901
                   Some(y) => if x mem vids orelse y mem vids then t
wenzelm@250
   902
                              else Var((y,i),T)
wenzelm@250
   903
                 | None=> t)
clasohm@0
   904
          | rename(Abs(x,T,t)) =
wenzelm@250
   905
              Abs(case assoc(al,x) of Some(y) => y | None => x,
wenzelm@250
   906
                  T, rename t)
clasohm@0
   907
          | rename(f$t) = rename f $ rename t
clasohm@0
   908
          | rename(t) = t;
wenzelm@250
   909
        fun strip_ren Ai = strip_apply rename (Ai,B)
clasohm@0
   910
    in strip_ren end;
clasohm@0
   911
clasohm@0
   912
(*Function to rename bounds/unknowns in the argument, lifted over B*)
clasohm@0
   913
fun rename_bvars(dpairs, tpairs, B) =
wenzelm@250
   914
        rename_bvs(foldr match_bvars (dpairs,[]), dpairs, tpairs, B);
clasohm@0
   915
clasohm@0
   916
clasohm@0
   917
(*** RESOLUTION ***)
clasohm@0
   918
clasohm@0
   919
(*strip off pairs of assumptions/parameters in parallel -- they are
clasohm@0
   920
  identical because of lifting*)
wenzelm@250
   921
fun strip_assums2 (Const("==>", _) $ _ $ B1,
wenzelm@250
   922
                   Const("==>", _) $ _ $ B2) = strip_assums2 (B1,B2)
clasohm@0
   923
  | strip_assums2 (Const("all",_)$Abs(a,T,t1),
wenzelm@250
   924
                   Const("all",_)$Abs(_,_,t2)) =
clasohm@0
   925
      let val (B1,B2) = strip_assums2 (t1,t2)
clasohm@0
   926
      in  (Abs(a,T,B1), Abs(a,T,B2))  end
clasohm@0
   927
  | strip_assums2 BB = BB;
clasohm@0
   928
clasohm@0
   929
clasohm@0
   930
(*Composition of object rule r=(A1...Am/B) with proof state s=(B1...Bn/C)
wenzelm@250
   931
  Unifies B with Bi, replacing subgoal i    (1 <= i <= n)
clasohm@0
   932
  If match then forbid instantiations in proof state
clasohm@0
   933
  If lifted then shorten the dpair using strip_assums2.
clasohm@0
   934
  If eres_flg then simultaneously proves A1 by assumption.
wenzelm@250
   935
  nsubgoal is the number of new subgoals (written m above).
clasohm@0
   936
  Curried so that resolution calls dest_state only once.
clasohm@0
   937
*)
clasohm@0
   938
local open Sequence; exception Bicompose
clasohm@0
   939
in
wenzelm@250
   940
fun bicompose_aux match (state, (stpairs, Bs, Bi, C), lifted)
clasohm@0
   941
                        (eres_flg, orule, nsubgoal) =
clasohm@0
   942
 let val Thm{maxidx=smax, hyps=shyps, ...} = state
clasohm@0
   943
     and Thm{maxidx=rmax, hyps=rhyps, prop=rprop,...} = orule;
wenzelm@387
   944
     val sign = merge_thm_sgs(state,orule);
clasohm@0
   945
     (** Add new theorem with prop = '[| Bs; As |] ==> C' to thq **)
wenzelm@250
   946
     fun addth As ((env as Envir.Envir {maxidx, ...}, tpairs), thq) =
wenzelm@250
   947
       let val normt = Envir.norm_term env;
wenzelm@250
   948
           (*perform minimal copying here by examining env*)
wenzelm@250
   949
           val normp =
wenzelm@250
   950
             if Envir.is_empty env then (tpairs, Bs @ As, C)
wenzelm@250
   951
             else
wenzelm@250
   952
             let val ntps = map (pairself normt) tpairs
wenzelm@250
   953
             in if the (Envir.minidx env) > smax then (*no assignments in state*)
wenzelm@250
   954
                  (ntps, Bs @ map normt As, C)
wenzelm@250
   955
                else if match then raise Bicompose
wenzelm@250
   956
                else (*normalize the new rule fully*)
wenzelm@250
   957
                  (ntps, map normt (Bs @ As), normt C)
wenzelm@250
   958
             end
wenzelm@250
   959
           val th = Thm{sign=sign, hyps=rhyps union shyps, maxidx=maxidx,
wenzelm@250
   960
                        prop= Logic.rule_of normp}
clasohm@0
   961
        in  cons(th, thq)  end  handle Bicompose => thq
clasohm@0
   962
     val (rtpairs,rhorn) = Logic.strip_flexpairs(rprop);
clasohm@0
   963
     val (rAs,B) = Logic.strip_prems(nsubgoal, [], rhorn)
clasohm@0
   964
       handle TERM _ => raise THM("bicompose: rule", 0, [orule,state]);
clasohm@0
   965
     (*Modify assumptions, deleting n-th if n>0 for e-resolution*)
clasohm@0
   966
     fun newAs(As0, n, dpairs, tpairs) =
clasohm@0
   967
       let val As1 = if !Logic.auto_rename orelse not lifted then As0
wenzelm@250
   968
                     else map (rename_bvars(dpairs,tpairs,B)) As0
clasohm@0
   969
       in (map (Logic.flatten_params n) As1)
wenzelm@250
   970
          handle TERM _ =>
wenzelm@250
   971
          raise THM("bicompose: 1st premise", 0, [orule])
clasohm@0
   972
       end;
clasohm@0
   973
     val env = Envir.empty(max[rmax,smax]);
clasohm@0
   974
     val BBi = if lifted then strip_assums2(B,Bi) else (B,Bi);
clasohm@0
   975
     val dpairs = BBi :: (rtpairs@stpairs);
clasohm@0
   976
     (*elim-resolution: try each assumption in turn.  Initially n=1*)
clasohm@0
   977
     fun tryasms (_, _, []) = null
clasohm@0
   978
       | tryasms (As, n, (t,u)::apairs) =
wenzelm@250
   979
          (case pull(Unify.unifiers(sign, env, (t,u)::dpairs))  of
wenzelm@250
   980
               None                   => tryasms (As, n+1, apairs)
wenzelm@250
   981
             | cell as Some((_,tpairs),_) =>
wenzelm@250
   982
                   its_right (addth (newAs(As, n, [BBi,(u,t)], tpairs)))
wenzelm@250
   983
                       (seqof (fn()=> cell),
wenzelm@250
   984
                        seqof (fn()=> pull (tryasms (As, n+1, apairs)))));
clasohm@0
   985
     fun eres [] = raise THM("bicompose: no premises", 0, [orule,state])
clasohm@0
   986
       | eres (A1::As) = tryasms (As, 1, Logic.assum_pairs A1);
clasohm@0
   987
     (*ordinary resolution*)
clasohm@0
   988
     fun res(None) = null
wenzelm@250
   989
       | res(cell as Some((_,tpairs),_)) =
wenzelm@250
   990
             its_right (addth(newAs(rev rAs, 0, [BBi], tpairs)))
wenzelm@250
   991
                       (seqof (fn()=> cell), null)
clasohm@0
   992
 in  if eres_flg then eres(rev rAs)
clasohm@0
   993
     else res(pull(Unify.unifiers(sign, env, dpairs)))
clasohm@0
   994
 end;
clasohm@0
   995
end;  (*open Sequence*)
clasohm@0
   996
clasohm@0
   997
clasohm@0
   998
fun bicompose match arg i state =
clasohm@0
   999
    bicompose_aux match (state, dest_state(state,i), false) arg;
clasohm@0
  1000
clasohm@0
  1001
(*Quick test whether rule is resolvable with the subgoal with hyps Hs
clasohm@0
  1002
  and conclusion B.  If eres_flg then checks 1st premise of rule also*)
clasohm@0
  1003
fun could_bires (Hs, B, eres_flg, rule) =
clasohm@0
  1004
    let fun could_reshyp (A1::_) = exists (apl(A1,could_unify)) Hs
wenzelm@250
  1005
          | could_reshyp [] = false;  (*no premise -- illegal*)
wenzelm@250
  1006
    in  could_unify(concl_of rule, B) andalso
wenzelm@250
  1007
        (not eres_flg  orelse  could_reshyp (prems_of rule))
clasohm@0
  1008
    end;
clasohm@0
  1009
clasohm@0
  1010
(*Bi-resolution of a state with a list of (flag,rule) pairs.
clasohm@0
  1011
  Puts the rule above:  rule/state.  Renames vars in the rules. *)
wenzelm@250
  1012
fun biresolution match brules i state =
clasohm@0
  1013
    let val lift = lift_rule(state, i);
wenzelm@250
  1014
        val (stpairs, Bs, Bi, C) = dest_state(state,i)
wenzelm@250
  1015
        val B = Logic.strip_assums_concl Bi;
wenzelm@250
  1016
        val Hs = Logic.strip_assums_hyp Bi;
wenzelm@250
  1017
        val comp = bicompose_aux match (state, (stpairs, Bs, Bi, C), true);
wenzelm@250
  1018
        fun res [] = Sequence.null
wenzelm@250
  1019
          | res ((eres_flg, rule)::brules) =
wenzelm@250
  1020
              if could_bires (Hs, B, eres_flg, rule)
wenzelm@250
  1021
              then Sequence.seqof (*delay processing remainder til needed*)
wenzelm@250
  1022
                  (fn()=> Some(comp (eres_flg, lift rule, nprems_of rule),
wenzelm@250
  1023
                               res brules))
wenzelm@250
  1024
              else res brules
clasohm@0
  1025
    in  Sequence.flats (res brules)  end;
clasohm@0
  1026
clasohm@0
  1027
clasohm@0
  1028
clasohm@0
  1029
(*** Meta simp sets ***)
clasohm@0
  1030
nipkow@288
  1031
type rrule = {thm:thm, lhs:term, perm:bool};
nipkow@288
  1032
type cong = {thm:thm, lhs:term};
clasohm@0
  1033
datatype meta_simpset =
nipkow@405
  1034
  Mss of {net:rrule Net.net, congs:(string * cong)list, bounds:string list,
clasohm@0
  1035
          prems: thm list, mk_rews: thm -> thm list};
clasohm@0
  1036
clasohm@0
  1037
(*A "mss" contains data needed during conversion:
clasohm@0
  1038
  net: discrimination net of rewrite rules
clasohm@0
  1039
  congs: association list of congruence rules
nipkow@405
  1040
  bounds: names of bound variables already used;
nipkow@405
  1041
          for generating new names when rewriting under lambda abstractions
clasohm@0
  1042
  mk_rews: used when local assumptions are added
clasohm@0
  1043
*)
clasohm@0
  1044
nipkow@405
  1045
val empty_mss = Mss{net= Net.empty, congs= [], bounds=[], prems= [],
clasohm@0
  1046
                    mk_rews = K[]};
clasohm@0
  1047
clasohm@0
  1048
exception SIMPLIFIER of string * thm;
clasohm@0
  1049
lcp@229
  1050
fun prtm a sign t = (writeln a; writeln(Sign.string_of_term sign t));
clasohm@0
  1051
nipkow@209
  1052
val trace_simp = ref false;
nipkow@209
  1053
lcp@229
  1054
fun trace_term a sign t = if !trace_simp then prtm a sign t else ();
nipkow@209
  1055
nipkow@209
  1056
fun trace_thm a (Thm{sign,prop,...}) = trace_term a sign prop;
nipkow@209
  1057
nipkow@288
  1058
fun var_perm(Var _, Var _) = true
nipkow@288
  1059
  | var_perm(Abs(_,_,s), Abs(_,_,t)) = var_perm(s,t)
nipkow@288
  1060
  | var_perm(t1$t2, u1$u2) = var_perm(t1,u1) andalso var_perm(t2,u2)
nipkow@288
  1061
  | var_perm(t,u) = (t=u);
nipkow@288
  1062
nipkow@288
  1063
clasohm@0
  1064
(*simple test for looping rewrite*)
clasohm@0
  1065
fun loops sign prems (lhs,rhs) =
clasohm@0
  1066
  null(prems) andalso
clasohm@0
  1067
  Pattern.eta_matches (#tsig(Sign.rep_sg sign)) (lhs,rhs);
clasohm@0
  1068
clasohm@0
  1069
fun mk_rrule (thm as Thm{hyps,sign,prop,maxidx,...}) =
clasohm@0
  1070
  let val prems = Logic.strip_imp_prems prop
clasohm@0
  1071
      val concl = Pattern.eta_contract (Logic.strip_imp_concl prop)
clasohm@0
  1072
      val (lhs,rhs) = Logic.dest_equals concl handle TERM _ =>
clasohm@0
  1073
                      raise SIMPLIFIER("Rewrite rule not a meta-equality",thm)
nipkow@288
  1074
      val perm = var_perm(lhs,rhs) andalso not(lhs=rhs)
nipkow@288
  1075
  in if not perm andalso loops sign prems (lhs,rhs)
clasohm@0
  1076
     then (prtm "Warning: ignoring looping rewrite rule" sign prop; None)
nipkow@288
  1077
     else Some{thm=thm,lhs=lhs,perm=perm}
clasohm@0
  1078
  end;
clasohm@0
  1079
nipkow@87
  1080
local
nipkow@87
  1081
 fun eq({thm=Thm{prop=p1,...},...}:rrule,
nipkow@87
  1082
        {thm=Thm{prop=p2,...},...}:rrule) = p1 aconv p2
nipkow@87
  1083
in
nipkow@87
  1084
nipkow@405
  1085
fun add_simp(mss as Mss{net,congs,bounds,prems,mk_rews},
clasohm@0
  1086
             thm as Thm{sign,prop,...}) =
nipkow@87
  1087
  case mk_rrule thm of
nipkow@87
  1088
    None => mss
nipkow@87
  1089
  | Some(rrule as {lhs,...}) =>
nipkow@209
  1090
      (trace_thm "Adding rewrite rule:" thm;
nipkow@209
  1091
       Mss{net= (Net.insert_term((lhs,rrule),net,eq)
nipkow@209
  1092
                 handle Net.INSERT =>
nipkow@87
  1093
                  (prtm "Warning: ignoring duplicate rewrite rule" sign prop;
nipkow@87
  1094
                   net)),
nipkow@405
  1095
           congs=congs, bounds=bounds, prems=prems,mk_rews=mk_rews});
nipkow@87
  1096
nipkow@405
  1097
fun del_simp(mss as Mss{net,congs,bounds,prems,mk_rews},
nipkow@87
  1098
             thm as Thm{sign,prop,...}) =
nipkow@87
  1099
  case mk_rrule thm of
nipkow@87
  1100
    None => mss
nipkow@87
  1101
  | Some(rrule as {lhs,...}) =>
nipkow@87
  1102
      Mss{net= (Net.delete_term((lhs,rrule),net,eq)
nipkow@87
  1103
                handle Net.INSERT =>
nipkow@87
  1104
                 (prtm "Warning: rewrite rule not in simpset" sign prop;
nipkow@87
  1105
                  net)),
nipkow@405
  1106
             congs=congs, bounds=bounds, prems=prems,mk_rews=mk_rews}
nipkow@87
  1107
nipkow@87
  1108
end;
clasohm@0
  1109
clasohm@0
  1110
val add_simps = foldl add_simp;
nipkow@87
  1111
val del_simps = foldl del_simp;
clasohm@0
  1112
clasohm@0
  1113
fun mss_of thms = add_simps(empty_mss,thms);
clasohm@0
  1114
nipkow@405
  1115
fun add_cong(Mss{net,congs,bounds,prems,mk_rews},thm) =
clasohm@0
  1116
  let val (lhs,_) = Logic.dest_equals(concl_of thm) handle TERM _ =>
clasohm@0
  1117
                    raise SIMPLIFIER("Congruence not a meta-equality",thm)
clasohm@0
  1118
      val lhs = Pattern.eta_contract lhs
clasohm@0
  1119
      val (a,_) = dest_Const (head_of lhs) handle TERM _ =>
clasohm@0
  1120
                  raise SIMPLIFIER("Congruence must start with a constant",thm)
nipkow@405
  1121
  in Mss{net=net, congs=(a,{lhs=lhs,thm=thm})::congs, bounds=bounds,
clasohm@0
  1122
         prems=prems, mk_rews=mk_rews}
clasohm@0
  1123
  end;
clasohm@0
  1124
clasohm@0
  1125
val (op add_congs) = foldl add_cong;
clasohm@0
  1126
nipkow@405
  1127
fun add_prems(Mss{net,congs,bounds,prems,mk_rews},thms) =
nipkow@405
  1128
  Mss{net=net, congs=congs, bounds=bounds, prems=thms@prems, mk_rews=mk_rews};
clasohm@0
  1129
clasohm@0
  1130
fun prems_of_mss(Mss{prems,...}) = prems;
clasohm@0
  1131
nipkow@405
  1132
fun set_mk_rews(Mss{net,congs,bounds,prems,...},mk_rews) =
nipkow@405
  1133
  Mss{net=net, congs=congs, bounds=bounds, prems=prems, mk_rews=mk_rews};
clasohm@0
  1134
fun mk_rews_of_mss(Mss{mk_rews,...}) = mk_rews;
clasohm@0
  1135
clasohm@0
  1136
wenzelm@250
  1137
(*** Meta-level rewriting
clasohm@0
  1138
     uses conversions, omitting proofs for efficiency.  See
wenzelm@250
  1139
        L C Paulson, A higher-order implementation of rewriting,
wenzelm@250
  1140
        Science of Computer Programming 3 (1983), pages 119-149. ***)
clasohm@0
  1141
clasohm@0
  1142
type prover = meta_simpset -> thm -> thm option;
clasohm@0
  1143
type termrec = (Sign.sg * term list) * term;
clasohm@0
  1144
type conv = meta_simpset -> termrec -> termrec;
clasohm@0
  1145
nipkow@305
  1146
datatype order = LESS | EQUAL | GREATER;
nipkow@288
  1147
nipkow@305
  1148
fun stringord(a,b:string) = if a<b then LESS  else
nipkow@305
  1149
                            if a=b then EQUAL else GREATER;
nipkow@305
  1150
nipkow@305
  1151
fun intord(i,j:int) = if i<j then LESS  else
nipkow@305
  1152
                      if i=j then EQUAL else GREATER;
nipkow@288
  1153
nipkow@305
  1154
(* FIXME: "***ABSTRACTION***" is a hack and makes the ordering non-linear *)
nipkow@305
  1155
fun string_of_hd(Const(a,_)) = a
nipkow@305
  1156
  | string_of_hd(Free(a,_))  = a
nipkow@305
  1157
  | string_of_hd(Var(v,_))   = Syntax.string_of_vname v
nipkow@305
  1158
  | string_of_hd(Bound i)    = string_of_int i
nipkow@305
  1159
  | string_of_hd(Abs _)      = "***ABSTRACTION***";
nipkow@288
  1160
nipkow@305
  1161
(* a strict (not reflexive) linear well-founded AC-compatible ordering
nipkow@305
  1162
 * for terms:
nipkow@305
  1163
 * s < t <=> 1. size(s) < size(t) or
nipkow@305
  1164
             2. size(s) = size(t) and s=f(...) and t = g(...) and f<g or
nipkow@305
  1165
             3. size(s) = size(t) and s=f(s1..sn) and t=f(t1..tn) and
nipkow@305
  1166
                (s1..sn) < (t1..tn) (lexicographically)
nipkow@305
  1167
 *)
nipkow@288
  1168
nipkow@288
  1169
(* FIXME: should really take types into account as well.
nipkow@305
  1170
 * Otherwise not linear *)
nipkow@305
  1171
fun termord(t,u) =
nipkow@305
  1172
      (case intord(size_of_term t,size_of_term u) of
nipkow@305
  1173
         EQUAL => let val (f,ts) = strip_comb t and (g,us) = strip_comb u
nipkow@305
  1174
                  in case stringord(string_of_hd f, string_of_hd g) of
nipkow@305
  1175
                       EQUAL => lextermord(ts,us)
nipkow@305
  1176
                     | ord   => ord
nipkow@305
  1177
                  end
nipkow@305
  1178
       | ord => ord)
nipkow@305
  1179
and lextermord(t::ts,u::us) =
nipkow@305
  1180
      (case termord(t,u) of
nipkow@305
  1181
         EQUAL => lextermord(ts,us)
nipkow@305
  1182
       | ord   => ord)
nipkow@305
  1183
  | lextermord([],[]) = EQUAL
nipkow@305
  1184
  | lextermord _ = error("lextermord");
nipkow@288
  1185
nipkow@305
  1186
fun termless tu = (termord tu = LESS);
nipkow@288
  1187
nipkow@208
  1188
fun check_conv(thm as Thm{hyps,prop,...}, prop0) =
nipkow@112
  1189
  let fun err() = (trace_thm "Proved wrong thm (Check subgoaler?)" thm; None)
clasohm@0
  1190
      val (lhs0,_) = Logic.dest_equals(Logic.strip_imp_concl prop0)
clasohm@0
  1191
  in case prop of
clasohm@0
  1192
       Const("==",_) $ lhs $ rhs =>
clasohm@0
  1193
         if (lhs = lhs0) orelse
clasohm@0
  1194
            (lhs aconv (Envir.norm_term (Envir.empty 0) lhs0))
nipkow@208
  1195
         then (trace_thm "SUCCEEDED" thm; Some(hyps,rhs))
clasohm@0
  1196
         else err()
clasohm@0
  1197
     | _ => err()
clasohm@0
  1198
  end;
clasohm@0
  1199
clasohm@0
  1200
(*Conversion to apply the meta simpset to a term*)
nipkow@208
  1201
fun rewritec (prover,signt) (mss as Mss{net,...}) (hypst,t) =
nipkow@225
  1202
  let val t = Pattern.eta_contract t;
nipkow@288
  1203
      fun rew {thm as Thm{sign,hyps,maxidx,prop,...}, lhs, perm} =
wenzelm@250
  1204
        let val unit = if Sign.subsig(sign,signt) then ()
nipkow@208
  1205
                  else (writeln"Warning: rewrite rule from different theory";
nipkow@208
  1206
                        raise Pattern.MATCH)
nipkow@208
  1207
            val insts = Pattern.match (#tsig(Sign.rep_sg signt)) (lhs,t)
clasohm@0
  1208
            val prop' = subst_vars insts prop;
clasohm@0
  1209
            val hyps' = hyps union hypst;
nipkow@208
  1210
            val thm' = Thm{sign=signt, hyps=hyps', prop=prop', maxidx=maxidx}
clasohm@0
  1211
        in if nprems_of thm' = 0
clasohm@0
  1212
           then let val (_,rhs) = Logic.dest_equals prop'
nipkow@288
  1213
                in if perm andalso not(termless(rhs,t)) then None
nipkow@288
  1214
                   else (trace_thm "Rewriting:" thm'; Some(hyps',rhs)) end
clasohm@0
  1215
           else (trace_thm "Trying to rewrite:" thm';
clasohm@0
  1216
                 case prover mss thm' of
clasohm@0
  1217
                   None       => (trace_thm "FAILED" thm'; None)
nipkow@112
  1218
                 | Some(thm2) => check_conv(thm2,prop'))
clasohm@0
  1219
        end
clasohm@0
  1220
nipkow@225
  1221
      fun rews [] = None
nipkow@225
  1222
        | rews (rrule::rrules) =
nipkow@225
  1223
            let val opt = rew rrule handle Pattern.MATCH => None
nipkow@225
  1224
            in case opt of None => rews rrules | some => some end;
clasohm@0
  1225
clasohm@0
  1226
  in case t of
nipkow@208
  1227
       Abs(_,_,body) $ u => Some(hypst,subst_bounds([u], body))
nipkow@225
  1228
     | _                 => rews(Net.match_term net t)
clasohm@0
  1229
  end;
clasohm@0
  1230
clasohm@0
  1231
(*Conversion to apply a congruence rule to a term*)
nipkow@208
  1232
fun congc (prover,signt) {thm=cong,lhs=lhs} (hypst,t) =
clasohm@0
  1233
  let val Thm{sign,hyps,maxidx,prop,...} = cong
nipkow@208
  1234
      val unit = if Sign.subsig(sign,signt) then ()
nipkow@208
  1235
                 else error("Congruence rule from different theory")
nipkow@208
  1236
      val tsig = #tsig(Sign.rep_sg signt)
clasohm@0
  1237
      val insts = Pattern.match tsig (lhs,t) handle Pattern.MATCH =>
clasohm@0
  1238
                  error("Congruence rule did not match")
clasohm@0
  1239
      val prop' = subst_vars insts prop;
nipkow@208
  1240
      val thm' = Thm{sign=signt, hyps=hyps union hypst,
clasohm@0
  1241
                     prop=prop', maxidx=maxidx}
clasohm@0
  1242
      val unit = trace_thm "Applying congruence rule" thm';
nipkow@112
  1243
      fun err() = error("Failed congruence proof!")
clasohm@0
  1244
clasohm@0
  1245
  in case prover thm' of
nipkow@112
  1246
       None => err()
nipkow@112
  1247
     | Some(thm2) => (case check_conv(thm2,prop') of
nipkow@405
  1248
                        None => err() | some => some)
clasohm@0
  1249
  end;
clasohm@0
  1250
clasohm@0
  1251
nipkow@405
  1252
nipkow@214
  1253
fun bottomc ((simprem,useprem),prover,sign) =
nipkow@405
  1254
  let fun botc fail mss trec =
nipkow@405
  1255
            (case subc mss trec of
nipkow@405
  1256
               some as Some(trec1) =>
nipkow@405
  1257
                 (case rewritec (prover,sign) mss trec1 of
nipkow@405
  1258
                    Some(trec2) => botc false mss trec2
nipkow@405
  1259
                  | None => some)
nipkow@405
  1260
             | None =>
nipkow@405
  1261
                 (case rewritec (prover,sign) mss trec of
nipkow@405
  1262
                    Some(trec2) => botc false mss trec2
nipkow@405
  1263
                  | None => if fail then None else Some(trec)))
clasohm@0
  1264
nipkow@405
  1265
      and try_botc mss trec = (case botc true mss trec of
nipkow@405
  1266
                                 Some(trec1) => trec1
nipkow@405
  1267
                               | None => trec)
nipkow@405
  1268
nipkow@405
  1269
      and subc (mss as Mss{net,congs,bounds,prems,mk_rews})
nipkow@208
  1270
               (trec as (hyps,t)) =
clasohm@0
  1271
        (case t of
clasohm@0
  1272
            Abs(a,T,t) =>
nipkow@405
  1273
              let val b = variant bounds a
nipkow@405
  1274
                  val v = Free("." ^ b,T)
nipkow@405
  1275
                  val mss' = Mss{net=net, congs=congs, bounds=b::bounds,
clasohm@0
  1276
                                 prems=prems,mk_rews=mk_rews}
nipkow@405
  1277
              in case botc true mss' (hyps,subst_bounds([v],t)) of
nipkow@405
  1278
                   Some(hyps',t') =>
nipkow@405
  1279
                     Some(hyps', Abs(a, T, abstract_over(v,t')))
nipkow@405
  1280
                 | None => None
nipkow@405
  1281
              end
clasohm@0
  1282
          | t$u => (case t of
nipkow@405
  1283
              Const("==>",_)$s  => Some(impc(hyps,s,u,mss))
nipkow@405
  1284
            | Abs(_,_,body) =>
nipkow@405
  1285
                let val trec = (hyps,subst_bounds([u], body))
nipkow@405
  1286
                in case subc mss trec of
nipkow@405
  1287
                     None => Some(trec)
nipkow@405
  1288
                   | trec => trec
nipkow@405
  1289
                end
nipkow@405
  1290
            | _  =>
nipkow@405
  1291
                let fun appc() =
nipkow@405
  1292
                          (case botc true mss (hyps,t) of
nipkow@405
  1293
                             Some(hyps1,t1) =>
nipkow@405
  1294
                               (case botc true mss (hyps1,u) of
nipkow@405
  1295
                                  Some(hyps2,u1) => Some(hyps2,t1$u1)
nipkow@405
  1296
                                | None => Some(hyps1,t1$u))
nipkow@405
  1297
                           | None =>
nipkow@405
  1298
                               (case botc true mss (hyps,u) of
nipkow@405
  1299
                                  Some(hyps1,u1) => Some(hyps1,t$u1)
nipkow@405
  1300
                                | None => None))
clasohm@0
  1301
                    val (h,ts) = strip_comb t
clasohm@0
  1302
                in case h of
clasohm@0
  1303
                     Const(a,_) =>
clasohm@0
  1304
                       (case assoc(congs,a) of
clasohm@0
  1305
                          None => appc()
nipkow@208
  1306
                        | Some(cong) => congc (prover mss,sign) cong trec)
clasohm@0
  1307
                   | _ => appc()
clasohm@0
  1308
                end)
nipkow@405
  1309
          | _ => None)
clasohm@0
  1310
nipkow@208
  1311
      and impc(hyps,s,u,mss as Mss{mk_rews,...}) =
nipkow@405
  1312
        let val (hyps1,s1) = if simprem then try_botc mss (hyps,s)
nipkow@405
  1313
                             else (hyps,s)
nipkow@405
  1314
            val mss1 =
nipkow@405
  1315
              if not useprem orelse maxidx_of_term s1 <> ~1 then mss
nipkow@405
  1316
              else let val thm = Thm{sign=sign,hyps=[s1],prop=s1,maxidx= ~1}
nipkow@214
  1317
                   in add_simps(add_prems(mss,[thm]), mk_rews thm) end
nipkow@405
  1318
            val (hyps2,u1) = try_botc mss1 (hyps1,u)
nipkow@405
  1319
            val hyps3 = if s1 mem hyps1 then hyps2 else hyps2\s1
nipkow@405
  1320
        in (hyps3, Logic.mk_implies(s1,u1)) end
clasohm@0
  1321
nipkow@405
  1322
  in try_botc end;
clasohm@0
  1323
clasohm@0
  1324
clasohm@0
  1325
(*** Meta-rewriting: rewrites t to u and returns the theorem t==u ***)
clasohm@0
  1326
(* Parameters:
wenzelm@250
  1327
   mode = (simplify A, use A in simplifying B) when simplifying A ==> B
clasohm@0
  1328
   mss: contains equality theorems of the form [|p1,...|] ==> t==u
clasohm@0
  1329
   prover: how to solve premises in conditional rewrites and congruences
clasohm@0
  1330
*)
clasohm@0
  1331
nipkow@405
  1332
(*** FIXME: check that #bounds(mss) does not "occur" in ct alread ***)
nipkow@214
  1333
fun rewrite_cterm mode mss prover ct =
lcp@229
  1334
  let val {sign, t, T, maxidx} = rep_cterm ct;
nipkow@214
  1335
      val (hyps,u) = bottomc (mode,prover,sign) mss ([],t);
clasohm@0
  1336
      val prop = Logic.mk_equals(t,u)
nipkow@208
  1337
  in  Thm{sign= sign, hyps= hyps, maxidx= maxidx_of_term prop, prop= prop}
clasohm@0
  1338
  end
clasohm@0
  1339
clasohm@0
  1340
end;
wenzelm@250
  1341