author | paulson |
Wed, 23 Jul 1997 11:54:32 +0200 | |
changeset 3565 | c64410e701fb |
parent 3558 | 258eee1a056e |
child 3577 | 9715b6e3ec5f |
permissions | -rw-r--r-- |
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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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|
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The core of Isabelle's Meta Logic: certified types and terms, meta |
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theorems, meta rules (including resolution and simplification). |
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*) |
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||
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signature THM = |
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sig |
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(*certified types*) |
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type ctyp |
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val rep_ctyp : ctyp -> {sign: Sign.sg, T: typ} |
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val typ_of : ctyp -> typ |
|
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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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|
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(*certified terms*) |
|
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type cterm |
|
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exception CTERM of string |
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val rep_cterm : cterm -> {sign: Sign.sg, t: term, T: typ, |
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maxidx: int} |
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val term_of : cterm -> term |
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val cterm_of : Sign.sg -> term -> cterm |
|
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val ctyp_of_term : cterm -> ctyp |
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val read_cterm : Sign.sg -> string * typ -> cterm |
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val read_cterms : Sign.sg -> string list * typ list -> cterm list |
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val cterm_fun : (term -> term) -> (cterm -> cterm) |
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val dest_comb : cterm -> cterm * cterm |
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val dest_abs : cterm -> cterm * cterm |
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val adjust_maxidx : cterm -> cterm |
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val capply : cterm -> cterm -> cterm |
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val cabs : cterm -> cterm -> cterm |
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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 list -> bool -> string * typ -> cterm * (indexname * typ) list |
|
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||
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(*theories*) |
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||
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(*proof terms [must DUPLICATE declaration as a specification]*) |
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datatype deriv_kind = MinDeriv | ThmDeriv | FullDeriv; |
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val keep_derivs : deriv_kind ref |
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datatype rule = |
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MinProof |
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| Oracle of theory * Sign.sg * exn |
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| Axiom of theory * string |
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| Theorem of string |
|
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| Assume of cterm |
|
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| Implies_intr of cterm |
|
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| Implies_intr_shyps |
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| Implies_intr_hyps |
|
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| Implies_elim |
|
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| Forall_intr of cterm |
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| Forall_elim of cterm |
|
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| Reflexive of cterm |
|
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| Symmetric |
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| Transitive |
|
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| Beta_conversion of cterm |
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| Extensional |
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| Abstract_rule of string * cterm |
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| Combination |
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| Equal_intr |
|
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| Equal_elim |
|
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| Trivial of cterm |
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| Lift_rule of cterm * int |
|
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| Assumption of int * Envir.env option |
|
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| Rotate_rule of int * int |
|
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| Instantiate of (indexname * ctyp) list * (cterm * cterm) list |
|
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| Bicompose of bool * bool * int * int * Envir.env |
|
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| Flexflex_rule of Envir.env |
|
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| Class_triv of theory * class |
|
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| VarifyT |
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| FreezeT |
|
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| RewriteC of cterm |
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| CongC of cterm |
|
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| Rewrite_cterm of cterm |
|
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| Rename_params_rule of string list * int; |
|
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|
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type deriv (* = rule mtree *) |
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|
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(*meta theorems*) |
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type thm |
|
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exception THM of string * int * thm list |
|
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val rep_thm : thm -> {sign: Sign.sg, der: deriv, maxidx: int, |
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shyps: sort list, hyps: term list, |
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prop: term} |
|
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val crep_thm : thm -> {sign: Sign.sg, der: deriv, maxidx: int, |
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shyps: sort list, hyps: cterm list, |
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prop: cterm} |
|
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val stamps_of_thm : thm -> string ref list |
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val tpairs_of : thm -> (term * term) list |
|
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val prems_of : thm -> term list |
|
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val nprems_of : thm -> int |
|
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val concl_of : thm -> term |
|
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val cprop_of : thm -> cterm |
|
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val extra_shyps : thm -> sort list |
|
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val force_strip_shyps : bool ref (* FIXME tmp (since 1995/08/01) *) |
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val strip_shyps : thm -> thm |
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val implies_intr_shyps: thm -> thm |
|
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val get_axiom : theory -> string -> thm |
|
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val name_thm : string * thm -> thm |
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val axioms_of : theory -> (string * thm) list |
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|
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(*meta rules*) |
|
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val assume : cterm -> thm |
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val compress : thm -> thm |
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val implies_intr : cterm -> thm -> thm |
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val implies_elim : thm -> thm -> thm |
|
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val forall_intr : cterm -> thm -> thm |
|
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val forall_elim : cterm -> thm -> thm |
|
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val flexpair_def : thm |
|
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val reflexive : cterm -> thm |
|
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val symmetric : thm -> thm |
|
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val transitive : thm -> thm -> thm |
|
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val beta_conversion : cterm -> thm |
|
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val extensional : thm -> thm |
|
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val abstract_rule : string -> cterm -> thm -> thm |
|
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val combination : thm -> 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 implies_intr_hyps : thm -> thm |
|
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val flexflex_rule : thm -> thm Sequence.seq |
|
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val instantiate : |
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(indexname * ctyp) list * (cterm * cterm) list -> 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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val freezeT : thm -> thm |
|
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val dest_state : thm * int -> |
|
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(term * term) list * term list * term * term |
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val lift_rule : (thm * int) -> thm -> thm |
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val assumption : int -> thm -> thm Sequence.seq |
|
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val eq_assumption : int -> thm -> thm |
|
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val rotate_rule : int -> int -> thm -> thm |
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val rename_params_rule: string list * int -> thm -> thm |
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val bicompose : bool -> bool * thm * int -> |
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int -> thm -> thm Sequence.seq |
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val biresolution : bool -> (bool * thm) list -> |
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int -> thm -> thm Sequence.seq |
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||
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(*meta simplification*) |
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exception SIMPLIFIER of string * thm |
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type meta_simpset |
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val dest_mss : meta_simpset -> |
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{simps: thm list, congs: thm list, procs: (string * cterm list) list} |
|
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val empty_mss : meta_simpset |
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val merge_mss : meta_simpset * meta_simpset -> meta_simpset |
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val add_simps : meta_simpset * thm list -> meta_simpset |
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val del_simps : meta_simpset * thm list -> meta_simpset |
|
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val mss_of : thm list -> meta_simpset |
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val add_congs : meta_simpset * thm list -> meta_simpset |
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val del_congs : meta_simpset * thm list -> meta_simpset |
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val add_simprocs : meta_simpset * |
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(string * cterm list * (Sign.sg -> term -> thm option) * stamp) list -> meta_simpset |
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val del_simprocs : meta_simpset * |
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(string * cterm list * (Sign.sg -> term -> thm option) * stamp) list -> meta_simpset |
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val add_prems : meta_simpset * thm list -> meta_simpset |
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val prems_of_mss : meta_simpset -> thm list |
|
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val set_mk_rews : meta_simpset * (thm -> thm list) -> meta_simpset |
|
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val mk_rews_of_mss : meta_simpset -> thm -> thm list |
|
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val set_termless : meta_simpset * (term * term -> bool) -> meta_simpset |
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val trace_simp : bool ref |
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val rewrite_cterm : bool * bool -> meta_simpset -> |
|
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(meta_simpset -> thm -> thm option) -> cterm -> thm |
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|
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val invoke_oracle : theory * Sign.sg * exn -> thm |
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end; |
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|
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structure Thm: THM = |
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struct |
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(*** Certified terms and types ***) |
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(** certified types **) |
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||
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(*certified typs under a signature*) |
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||
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datatype ctyp = Ctyp of {sign: Sign.sg, T: typ}; |
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||
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fun rep_ctyp (Ctyp args) = args; |
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fun typ_of (Ctyp {T, ...}) = T; |
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||
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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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||
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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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|
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fun ctyp_of_term (Cterm {sign, T, ...}) = Ctyp {sign=sign, T=T}; |
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||
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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; |
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|
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fun cterm_fun f (Cterm {sign, t, ...}) = cterm_of sign (f t); |
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||
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|
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exception CTERM of string; |
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|
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(*Destruct application in cterms*) |
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fun dest_comb (Cterm{sign, T, maxidx, t = A $ B}) = |
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let val typeA = fastype_of A; |
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val typeB = |
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case typeA of Type("fun",[S,T]) => S |
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| _ => error "Function type expected in dest_comb"; |
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in |
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(Cterm {sign=sign, maxidx=maxidx, t=A, T=typeA}, |
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Cterm {sign=sign, maxidx=maxidx, t=B, T=typeB}) |
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end |
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| dest_comb _ = raise CTERM "dest_comb"; |
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|
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(*Destruct abstraction in cterms*) |
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fun dest_abs (Cterm {sign, T as Type("fun",[_,S]), maxidx, t=Abs(x,ty,M)}) = |
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let val (y,N) = variant_abs (x,ty,M) |
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in (Cterm {sign = sign, T = ty, maxidx = 0, t = Free(y,ty)}, |
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Cterm {sign = sign, T = S, maxidx = maxidx, t = N}) |
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end |
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| dest_abs _ = raise CTERM "dest_abs"; |
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|
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(*Makes maxidx precise: it is often too big*) |
235 |
fun adjust_maxidx (ct as Cterm {sign, T, t, maxidx, ...}) = |
|
236 |
if maxidx = ~1 then ct |
|
237 |
else Cterm {sign = sign, T = T, maxidx = maxidx_of_term t, t = t}; |
|
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|
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|
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|
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(*Form cterm out of a function and an argument*) |
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240 |
fun capply (Cterm {t=f, sign=sign1, T=Type("fun",[dty,rty]), maxidx=maxidx1}) |
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(Cterm {t=x, sign=sign2, T, maxidx=maxidx2}) = |
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242 |
if T = dty then Cterm{t=f$x, sign=Sign.merge(sign1,sign2), T=rty, |
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maxidx=Int.max(maxidx1, maxidx2)} |
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else raise CTERM "capply: types don't agree" |
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| capply _ _ = raise CTERM "capply: first arg is not a function" |
250 | 246 |
|
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fun cabs (Cterm {t=Free(a,ty), sign=sign1, T=T1, maxidx=maxidx1}) |
248 |
(Cterm {t=t2, sign=sign2, T=T2, maxidx=maxidx2}) = |
|
249 |
Cterm {t=absfree(a,ty,t2), sign=Sign.merge(sign1,sign2), |
|
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T = ty --> T2, maxidx=Int.max(maxidx1, maxidx2)} |
1517 | 251 |
| cabs _ _ = raise CTERM "cabs: first arg is not a free variable"; |
229
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
225
diff
changeset
|
252 |
|
2509 | 253 |
|
254 |
||
574 | 255 |
(** read cterms **) (*exception ERROR*) |
250 | 256 |
|
257 |
(*read term, infer types, certify term*) |
|
949
83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
922
diff
changeset
|
258 |
fun read_def_cterm (sign, types, sorts) used freeze (a, T) = |
250 | 259 |
let |
574 | 260 |
val T' = Sign.certify_typ sign T |
261 |
handle TYPE (msg, _, _) => error msg; |
|
623 | 262 |
val ts = Syntax.read (#syn (Sign.rep_sg sign)) T' a; |
949
83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
922
diff
changeset
|
263 |
val (_, t', tye) = |
959 | 264 |
Sign.infer_types sign types sorts used freeze (ts, T'); |
574 | 265 |
val ct = cterm_of sign t' |
2979 | 266 |
handle TYPE (msg, _, _) => error msg |
2386 | 267 |
| TERM (msg, _) => error msg; |
250 | 268 |
in (ct, tye) end; |
229
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
225
diff
changeset
|
269 |
|
949
83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
922
diff
changeset
|
270 |
fun read_cterm sign = #1 o read_def_cterm (sign, K None, K None) [] true; |
229
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
225
diff
changeset
|
271 |
|
1394
a1d2735f5ade
New function read_cterms is a combination of read_def_cterm and
paulson
parents:
1258
diff
changeset
|
272 |
(*read a list of terms, matching them against a list of expected types. |
a1d2735f5ade
New function read_cterms is a combination of read_def_cterm and
paulson
parents:
1258
diff
changeset
|
273 |
NO disambiguation of alternative parses via type-checking -- it is just |
a1d2735f5ade
New function read_cterms is a combination of read_def_cterm and
paulson
parents:
1258
diff
changeset
|
274 |
not practical.*) |
a1d2735f5ade
New function read_cterms is a combination of read_def_cterm and
paulson
parents:
1258
diff
changeset
|
275 |
fun read_cterms sign (bs, Ts) = |
a1d2735f5ade
New function read_cterms is a combination of read_def_cterm and
paulson
parents:
1258
diff
changeset
|
276 |
let |
2979 | 277 |
val {tsig, syn, ...} = Sign.rep_sg sign; |
278 |
fun read (b, T) = |
|
279 |
(case Syntax.read syn T b of |
|
280 |
[t] => t |
|
281 |
| _ => error ("Error or ambiguity in parsing of " ^ b)); |
|
282 |
||
283 |
val prt = setmp Syntax.show_brackets true (Sign.pretty_term sign); |
|
284 |
val prT = Sign.pretty_typ sign; |
|
285 |
val (us, _) = |
|
286 |
Type.infer_types prt prT tsig (Sign.const_type sign) |
|
287 |
(K None) (K None) [] true (map (Sign.certify_typ sign) Ts) |
|
288 |
(ListPair.map read (bs, Ts)); |
|
289 |
in map (cterm_of sign) us end |
|
290 |
handle TYPE (msg, _, _) => error msg |
|
1394
a1d2735f5ade
New function read_cterms is a combination of read_def_cterm and
paulson
parents:
1258
diff
changeset
|
291 |
| TERM (msg, _) => error msg; |
a1d2735f5ade
New function read_cterms is a combination of read_def_cterm and
paulson
parents:
1258
diff
changeset
|
292 |
|
250 | 293 |
|
294 |
||
1529 | 295 |
(*** Derivations ***) |
296 |
||
297 |
(*Names of rules in derivations. Includes logically trivial rules, if |
|
298 |
executed in ML.*) |
|
299 |
datatype rule = |
|
2386 | 300 |
MinProof (*for building minimal proof terms*) |
301 |
| Oracle of theory * Sign.sg * exn (*oracles*) |
|
1529 | 302 |
(*Axioms/theorems*) |
2386 | 303 |
| Axiom of theory * string |
304 |
| Theorem of string |
|
1529 | 305 |
(*primitive inferences and compound versions of them*) |
2386 | 306 |
| Assume of cterm |
307 |
| Implies_intr of cterm |
|
1529 | 308 |
| Implies_intr_shyps |
309 |
| Implies_intr_hyps |
|
310 |
| Implies_elim |
|
2386 | 311 |
| Forall_intr of cterm |
312 |
| Forall_elim of cterm |
|
313 |
| Reflexive of cterm |
|
1529 | 314 |
| Symmetric |
315 |
| Transitive |
|
2386 | 316 |
| Beta_conversion of cterm |
1529 | 317 |
| Extensional |
2386 | 318 |
| Abstract_rule of string * cterm |
1529 | 319 |
| Combination |
320 |
| Equal_intr |
|
321 |
| Equal_elim |
|
322 |
(*derived rules for tactical proof*) |
|
2386 | 323 |
| Trivial of cterm |
324 |
(*For lift_rule, the proof state is not a premise. |
|
325 |
Use cterm instead of thm to avoid mutual recursion.*) |
|
326 |
| Lift_rule of cterm * int |
|
327 |
| Assumption of int * Envir.env option (*includes eq_assumption*) |
|
2671 | 328 |
| Rotate_rule of int * int |
2386 | 329 |
| Instantiate of (indexname * ctyp) list * (cterm * cterm) list |
330 |
| Bicompose of bool * bool * int * int * Envir.env |
|
331 |
| Flexflex_rule of Envir.env (*identifies unifier chosen*) |
|
1529 | 332 |
(*other derived rules*) |
2509 | 333 |
| Class_triv of theory * class |
1529 | 334 |
| VarifyT |
335 |
| FreezeT |
|
336 |
(*for the simplifier*) |
|
2386 | 337 |
| RewriteC of cterm |
338 |
| CongC of cterm |
|
339 |
| Rewrite_cterm of cterm |
|
1529 | 340 |
(*Logical identities, recorded since they are part of the proof process*) |
2386 | 341 |
| Rename_params_rule of string list * int; |
1529 | 342 |
|
343 |
||
1597
54ece585bf62
name_thm no longer takes a theory argument, as the
paulson
parents:
1580
diff
changeset
|
344 |
type deriv = rule mtree; |
1529 | 345 |
|
1597
54ece585bf62
name_thm no longer takes a theory argument, as the
paulson
parents:
1580
diff
changeset
|
346 |
datatype deriv_kind = MinDeriv | ThmDeriv | FullDeriv; |
1529 | 347 |
|
1597
54ece585bf62
name_thm no longer takes a theory argument, as the
paulson
parents:
1580
diff
changeset
|
348 |
val keep_derivs = ref MinDeriv; |
1529 | 349 |
|
350 |
||
1597
54ece585bf62
name_thm no longer takes a theory argument, as the
paulson
parents:
1580
diff
changeset
|
351 |
(*Build a minimal derivation. Keep oracles; suppress atomic inferences; |
54ece585bf62
name_thm no longer takes a theory argument, as the
paulson
parents:
1580
diff
changeset
|
352 |
retain Theorems or their underlying links; keep anything else*) |
54ece585bf62
name_thm no longer takes a theory argument, as the
paulson
parents:
1580
diff
changeset
|
353 |
fun squash_derivs [] = [] |
54ece585bf62
name_thm no longer takes a theory argument, as the
paulson
parents:
1580
diff
changeset
|
354 |
| squash_derivs (der::ders) = |
54ece585bf62
name_thm no longer takes a theory argument, as the
paulson
parents:
1580
diff
changeset
|
355 |
(case der of |
2386 | 356 |
Join (Oracle _, _) => der :: squash_derivs ders |
357 |
| Join (Theorem _, [der']) => if !keep_derivs=ThmDeriv |
|
358 |
then der :: squash_derivs ders |
|
359 |
else squash_derivs (der'::ders) |
|
360 |
| Join (Axiom _, _) => if !keep_derivs=ThmDeriv |
|
361 |
then der :: squash_derivs ders |
|
362 |
else squash_derivs ders |
|
363 |
| Join (_, []) => squash_derivs ders |
|
364 |
| _ => der :: squash_derivs ders); |
|
1597
54ece585bf62
name_thm no longer takes a theory argument, as the
paulson
parents:
1580
diff
changeset
|
365 |
|
1529 | 366 |
|
367 |
(*Ensure sharing of the most likely derivation, the empty one!*) |
|
1597
54ece585bf62
name_thm no longer takes a theory argument, as the
paulson
parents:
1580
diff
changeset
|
368 |
val min_infer = Join (MinProof, []); |
1529 | 369 |
|
370 |
(*Make a minimal inference*) |
|
371 |
fun make_min_infer [] = min_infer |
|
372 |
| make_min_infer [der] = der |
|
1597
54ece585bf62
name_thm no longer takes a theory argument, as the
paulson
parents:
1580
diff
changeset
|
373 |
| make_min_infer ders = Join (MinProof, ders); |
1529 | 374 |
|
1597
54ece585bf62
name_thm no longer takes a theory argument, as the
paulson
parents:
1580
diff
changeset
|
375 |
fun infer_derivs (rl, []) = Join (rl, []) |
1529 | 376 |
| infer_derivs (rl, ders) = |
1597
54ece585bf62
name_thm no longer takes a theory argument, as the
paulson
parents:
1580
diff
changeset
|
377 |
if !keep_derivs=FullDeriv then Join (rl, ders) |
1529 | 378 |
else make_min_infer (squash_derivs ders); |
379 |
||
380 |
||
2509 | 381 |
|
387
69f4356d915d
new datatype theory, supports 'draft theories' and incremental extension:
wenzelm
parents:
309
diff
changeset
|
382 |
(*** Meta theorems ***) |
229
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
225
diff
changeset
|
383 |
|
0 | 384 |
datatype thm = Thm of |
2386 | 385 |
{sign: Sign.sg, (*signature for hyps and prop*) |
386 |
der: deriv, (*derivation*) |
|
387 |
maxidx: int, (*maximum index of any Var or TVar*) |
|
388 |
shyps: sort list, (*sort hypotheses*) |
|
389 |
hyps: term list, (*hypotheses*) |
|
390 |
prop: term}; (*conclusion*) |
|
0 | 391 |
|
250 | 392 |
fun rep_thm (Thm args) = args; |
0 | 393 |
|
1529 | 394 |
(*Version of rep_thm returning cterms instead of terms*) |
395 |
fun crep_thm (Thm {sign, der, maxidx, shyps, hyps, prop}) = |
|
396 |
let fun ctermf max t = Cterm{sign=sign, t=t, T=propT, maxidx=max}; |
|
397 |
in {sign=sign, der=der, maxidx=maxidx, shyps=shyps, |
|
398 |
hyps = map (ctermf ~1) hyps, |
|
399 |
prop = ctermf maxidx prop} |
|
1517 | 400 |
end; |
401 |
||
387
69f4356d915d
new datatype theory, supports 'draft theories' and incremental extension:
wenzelm
parents:
309
diff
changeset
|
402 |
(*errors involving theorems*) |
0 | 403 |
exception THM of string * int * thm list; |
404 |
||
387
69f4356d915d
new datatype theory, supports 'draft theories' and incremental extension:
wenzelm
parents:
309
diff
changeset
|
405 |
|
1597
54ece585bf62
name_thm no longer takes a theory argument, as the
paulson
parents:
1580
diff
changeset
|
406 |
val stamps_of_thm = #stamps o Sign.rep_sg o #sign o rep_thm; |
0 | 407 |
|
387
69f4356d915d
new datatype theory, supports 'draft theories' and incremental extension:
wenzelm
parents:
309
diff
changeset
|
408 |
(*merge signatures of two theorems; raise exception if incompatible*) |
69f4356d915d
new datatype theory, supports 'draft theories' and incremental extension:
wenzelm
parents:
309
diff
changeset
|
409 |
fun merge_thm_sgs (th1, th2) = |
1597
54ece585bf62
name_thm no longer takes a theory argument, as the
paulson
parents:
1580
diff
changeset
|
410 |
Sign.merge (pairself (#sign o rep_thm) (th1, th2)) |
574 | 411 |
handle TERM (msg, _) => raise THM (msg, 0, [th1, th2]); |
387
69f4356d915d
new datatype theory, supports 'draft theories' and incremental extension:
wenzelm
parents:
309
diff
changeset
|
412 |
|
69f4356d915d
new datatype theory, supports 'draft theories' and incremental extension:
wenzelm
parents:
309
diff
changeset
|
413 |
|
69f4356d915d
new datatype theory, supports 'draft theories' and incremental extension:
wenzelm
parents:
309
diff
changeset
|
414 |
(*maps object-rule to tpairs*) |
69f4356d915d
new datatype theory, supports 'draft theories' and incremental extension:
wenzelm
parents:
309
diff
changeset
|
415 |
fun tpairs_of (Thm {prop, ...}) = #1 (Logic.strip_flexpairs prop); |
69f4356d915d
new datatype theory, supports 'draft theories' and incremental extension:
wenzelm
parents:
309
diff
changeset
|
416 |
|
69f4356d915d
new datatype theory, supports 'draft theories' and incremental extension:
wenzelm
parents:
309
diff
changeset
|
417 |
(*maps object-rule to premises*) |
69f4356d915d
new datatype theory, supports 'draft theories' and incremental extension:
wenzelm
parents:
309
diff
changeset
|
418 |
fun prems_of (Thm {prop, ...}) = |
69f4356d915d
new datatype theory, supports 'draft theories' and incremental extension:
wenzelm
parents:
309
diff
changeset
|
419 |
Logic.strip_imp_prems (Logic.skip_flexpairs prop); |
0 | 420 |
|
421 |
(*counts premises in a rule*) |
|
387
69f4356d915d
new datatype theory, supports 'draft theories' and incremental extension:
wenzelm
parents:
309
diff
changeset
|
422 |
fun nprems_of (Thm {prop, ...}) = |
69f4356d915d
new datatype theory, supports 'draft theories' and incremental extension:
wenzelm
parents:
309
diff
changeset
|
423 |
Logic.count_prems (Logic.skip_flexpairs prop, 0); |
0 | 424 |
|
387
69f4356d915d
new datatype theory, supports 'draft theories' and incremental extension:
wenzelm
parents:
309
diff
changeset
|
425 |
(*maps object-rule to conclusion*) |
69f4356d915d
new datatype theory, supports 'draft theories' and incremental extension:
wenzelm
parents:
309
diff
changeset
|
426 |
fun concl_of (Thm {prop, ...}) = Logic.strip_imp_concl prop; |
0 | 427 |
|
387
69f4356d915d
new datatype theory, supports 'draft theories' and incremental extension:
wenzelm
parents:
309
diff
changeset
|
428 |
(*the statement of any thm is a cterm*) |
1160 | 429 |
fun cprop_of (Thm {sign, maxidx, prop, ...}) = |
387
69f4356d915d
new datatype theory, supports 'draft theories' and incremental extension:
wenzelm
parents:
309
diff
changeset
|
430 |
Cterm {sign = sign, maxidx = maxidx, T = propT, t = prop}; |
229
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
225
diff
changeset
|
431 |
|
387
69f4356d915d
new datatype theory, supports 'draft theories' and incremental extension:
wenzelm
parents:
309
diff
changeset
|
432 |
|
0 | 433 |
|
1238 | 434 |
(** sort contexts of theorems **) |
435 |
||
436 |
(* basic utils *) |
|
437 |
||
2163 | 438 |
(*accumulate sorts suppressing duplicates; these are coded low levelly |
1238 | 439 |
to improve efficiency a bit*) |
440 |
||
441 |
fun add_typ_sorts (Type (_, Ts), Ss) = add_typs_sorts (Ts, Ss) |
|
2177
8b365a3a6ed1
Changed some mem, ins and union calls to be monomorphic
paulson
parents:
2163
diff
changeset
|
442 |
| add_typ_sorts (TFree (_, S), Ss) = ins_sort(S,Ss) |
8b365a3a6ed1
Changed some mem, ins and union calls to be monomorphic
paulson
parents:
2163
diff
changeset
|
443 |
| add_typ_sorts (TVar (_, S), Ss) = ins_sort(S,Ss) |
1238 | 444 |
and add_typs_sorts ([], Ss) = Ss |
445 |
| add_typs_sorts (T :: Ts, Ss) = add_typs_sorts (Ts, add_typ_sorts (T, Ss)); |
|
446 |
||
447 |
fun add_term_sorts (Const (_, T), Ss) = add_typ_sorts (T, Ss) |
|
448 |
| add_term_sorts (Free (_, T), Ss) = add_typ_sorts (T, Ss) |
|
449 |
| add_term_sorts (Var (_, T), Ss) = add_typ_sorts (T, Ss) |
|
450 |
| add_term_sorts (Bound _, Ss) = Ss |
|
2177
8b365a3a6ed1
Changed some mem, ins and union calls to be monomorphic
paulson
parents:
2163
diff
changeset
|
451 |
| add_term_sorts (Abs (_,T,t), Ss) = add_term_sorts (t, add_typ_sorts (T,Ss)) |
1238 | 452 |
| add_term_sorts (t $ u, Ss) = add_term_sorts (t, add_term_sorts (u, Ss)); |
453 |
||
454 |
fun add_terms_sorts ([], Ss) = Ss |
|
2177
8b365a3a6ed1
Changed some mem, ins and union calls to be monomorphic
paulson
parents:
2163
diff
changeset
|
455 |
| add_terms_sorts (t::ts, Ss) = add_terms_sorts (ts, add_term_sorts (t,Ss)); |
1238 | 456 |
|
1258 | 457 |
fun env_codT (Envir.Envir {iTs, ...}) = map snd iTs; |
458 |
||
459 |
fun add_env_sorts (env, Ss) = |
|
460 |
add_terms_sorts (map snd (Envir.alist_of env), |
|
461 |
add_typs_sorts (env_codT env, Ss)); |
|
462 |
||
1238 | 463 |
fun add_thm_sorts (Thm {hyps, prop, ...}, Ss) = |
464 |
add_terms_sorts (hyps, add_term_sorts (prop, Ss)); |
|
465 |
||
466 |
fun add_thms_shyps ([], Ss) = Ss |
|
467 |
| add_thms_shyps (Thm {shyps, ...} :: ths, Ss) = |
|
2177
8b365a3a6ed1
Changed some mem, ins and union calls to be monomorphic
paulson
parents:
2163
diff
changeset
|
468 |
add_thms_shyps (ths, union_sort(shyps,Ss)); |
1238 | 469 |
|
470 |
||
471 |
(*get 'dangling' sort constraints of a thm*) |
|
472 |
fun extra_shyps (th as Thm {shyps, ...}) = |
|
473 |
shyps \\ add_thm_sorts (th, []); |
|
474 |
||
475 |
||
476 |
(* fix_shyps *) |
|
477 |
||
478 |
(*preserve sort contexts of rule premises and substituted types*) |
|
479 |
fun fix_shyps thms Ts thm = |
|
480 |
let |
|
1529 | 481 |
val Thm {sign, der, maxidx, hyps, prop, ...} = thm; |
1238 | 482 |
val shyps = |
483 |
add_thm_sorts (thm, add_typs_sorts (Ts, add_thms_shyps (thms, []))); |
|
484 |
in |
|
1529 | 485 |
Thm {sign = sign, |
2386 | 486 |
der = der, (*No new derivation, as other rules call this*) |
487 |
maxidx = maxidx, |
|
488 |
shyps = shyps, hyps = hyps, prop = prop} |
|
1238 | 489 |
end; |
490 |
||
491 |
||
492 |
(* strip_shyps *) (* FIXME improve? (e.g. only minimal extra sorts) *) |
|
493 |
||
3061 | 494 |
val force_strip_shyps = ref true; (* FIXME tmp (since 1995/08/01) *) |
1238 | 495 |
|
496 |
(*remove extra sorts that are known to be syntactically non-empty*) |
|
497 |
fun strip_shyps thm = |
|
498 |
let |
|
1529 | 499 |
val Thm {sign, der, maxidx, shyps, hyps, prop} = thm; |
1238 | 500 |
val sorts = add_thm_sorts (thm, []); |
501 |
val maybe_empty = not o Sign.nonempty_sort sign sorts; |
|
2177
8b365a3a6ed1
Changed some mem, ins and union calls to be monomorphic
paulson
parents:
2163
diff
changeset
|
502 |
val shyps' = filter (fn S => mem_sort(S,sorts) orelse maybe_empty S) shyps; |
1238 | 503 |
in |
1529 | 504 |
Thm {sign = sign, der = der, maxidx = maxidx, |
2386 | 505 |
shyps = |
506 |
(if eq_set_sort (shyps',sorts) orelse |
|
507 |
not (!force_strip_shyps) then shyps' |
|
3061 | 508 |
else (* FIXME tmp (since 1995/08/01) *) |
2386 | 509 |
(warning ("Removed sort hypotheses: " ^ |
2962 | 510 |
commas (map Sorts.str_of_sort (shyps' \\ sorts))); |
2386 | 511 |
warning "Let's hope these sorts are non-empty!"; |
1238 | 512 |
sorts)), |
1529 | 513 |
hyps = hyps, |
514 |
prop = prop} |
|
1238 | 515 |
end; |
516 |
||
517 |
||
518 |
(* implies_intr_shyps *) |
|
519 |
||
520 |
(*discharge all extra sort hypotheses*) |
|
521 |
fun implies_intr_shyps thm = |
|
522 |
(case extra_shyps thm of |
|
523 |
[] => thm |
|
524 |
| xshyps => |
|
525 |
let |
|
1529 | 526 |
val Thm {sign, der, maxidx, shyps, hyps, prop} = thm; |
2182
29e56f003599
Removal of polymorphic equality via mem, subset, eq_set, etc
paulson
parents:
2177
diff
changeset
|
527 |
val shyps' = ins_sort (logicS, shyps \\ xshyps); |
1238 | 528 |
val used_names = foldr add_term_tfree_names (prop :: hyps, []); |
529 |
val names = |
|
530 |
tl (variantlist (replicate (length xshyps + 1) "'", used_names)); |
|
531 |
val tfrees = map (TFree o rpair logicS) names; |
|
532 |
||
533 |
fun mk_insort (T, S) = map (Logic.mk_inclass o pair T) S; |
|
2671 | 534 |
val sort_hyps = List.concat (map2 mk_insort (tfrees, xshyps)); |
1238 | 535 |
in |
1529 | 536 |
Thm {sign = sign, |
2386 | 537 |
der = infer_derivs (Implies_intr_shyps, [der]), |
538 |
maxidx = maxidx, |
|
539 |
shyps = shyps', |
|
540 |
hyps = hyps, |
|
541 |
prop = Logic.list_implies (sort_hyps, prop)} |
|
1238 | 542 |
end); |
543 |
||
544 |
||
1529 | 545 |
(** Axioms **) |
387
69f4356d915d
new datatype theory, supports 'draft theories' and incremental extension:
wenzelm
parents:
309
diff
changeset
|
546 |
|
69f4356d915d
new datatype theory, supports 'draft theories' and incremental extension:
wenzelm
parents:
309
diff
changeset
|
547 |
(*look up the named axiom in the theory*) |
69f4356d915d
new datatype theory, supports 'draft theories' and incremental extension:
wenzelm
parents:
309
diff
changeset
|
548 |
fun get_axiom theory name = |
69f4356d915d
new datatype theory, supports 'draft theories' and incremental extension:
wenzelm
parents:
309
diff
changeset
|
549 |
let |
69f4356d915d
new datatype theory, supports 'draft theories' and incremental extension:
wenzelm
parents:
309
diff
changeset
|
550 |
fun get_ax [] = raise Match |
1529 | 551 |
| get_ax (thy :: thys) = |
2386 | 552 |
let val {sign, new_axioms, parents, ...} = rep_theory thy |
1529 | 553 |
in case Symtab.lookup (new_axioms, name) of |
2386 | 554 |
Some t => fix_shyps [] [] |
555 |
(Thm {sign = sign, |
|
556 |
der = infer_derivs (Axiom(theory,name), []), |
|
557 |
maxidx = maxidx_of_term t, |
|
558 |
shyps = [], |
|
559 |
hyps = [], |
|
560 |
prop = t}) |
|
561 |
| None => get_ax parents handle Match => get_ax thys |
|
1529 | 562 |
end; |
387
69f4356d915d
new datatype theory, supports 'draft theories' and incremental extension:
wenzelm
parents:
309
diff
changeset
|
563 |
in |
69f4356d915d
new datatype theory, supports 'draft theories' and incremental extension:
wenzelm
parents:
309
diff
changeset
|
564 |
get_ax [theory] handle Match |
69f4356d915d
new datatype theory, supports 'draft theories' and incremental extension:
wenzelm
parents:
309
diff
changeset
|
565 |
=> raise THEORY ("get_axiom: no axiom " ^ quote name, [theory]) |
69f4356d915d
new datatype theory, supports 'draft theories' and incremental extension:
wenzelm
parents:
309
diff
changeset
|
566 |
end; |
69f4356d915d
new datatype theory, supports 'draft theories' and incremental extension:
wenzelm
parents:
309
diff
changeset
|
567 |
|
1529 | 568 |
|
776
df8f91c0e57c
improved axioms_of: returns thms as the manual says;
wenzelm
parents:
721
diff
changeset
|
569 |
(*return additional axioms of this theory node*) |
df8f91c0e57c
improved axioms_of: returns thms as the manual says;
wenzelm
parents:
721
diff
changeset
|
570 |
fun axioms_of thy = |
df8f91c0e57c
improved axioms_of: returns thms as the manual says;
wenzelm
parents:
721
diff
changeset
|
571 |
map (fn (s, _) => (s, get_axiom thy s)) |
df8f91c0e57c
improved axioms_of: returns thms as the manual says;
wenzelm
parents:
721
diff
changeset
|
572 |
(Symtab.dest (#new_axioms (rep_theory thy))); |
df8f91c0e57c
improved axioms_of: returns thms as the manual says;
wenzelm
parents:
721
diff
changeset
|
573 |
|
1597
54ece585bf62
name_thm no longer takes a theory argument, as the
paulson
parents:
1580
diff
changeset
|
574 |
(*Attach a label to a theorem to make proof objects more readable*) |
54ece585bf62
name_thm no longer takes a theory argument, as the
paulson
parents:
1580
diff
changeset
|
575 |
fun name_thm (name, th as Thm {sign, der, maxidx, shyps, hyps, prop}) = |
54ece585bf62
name_thm no longer takes a theory argument, as the
paulson
parents:
1580
diff
changeset
|
576 |
Thm {sign = sign, |
2386 | 577 |
der = Join (Theorem name, [der]), |
578 |
maxidx = maxidx, |
|
579 |
shyps = shyps, |
|
580 |
hyps = hyps, |
|
581 |
prop = prop}; |
|
0 | 582 |
|
583 |
||
1529 | 584 |
(*Compression of theorems -- a separate rule, not integrated with the others, |
585 |
as it could be slow.*) |
|
586 |
fun compress (Thm {sign, der, maxidx, shyps, hyps, prop}) = |
|
587 |
Thm {sign = sign, |
|
2386 | 588 |
der = der, (*No derivation recorded!*) |
589 |
maxidx = maxidx, |
|
590 |
shyps = shyps, |
|
591 |
hyps = map Term.compress_term hyps, |
|
592 |
prop = Term.compress_term prop}; |
|
564 | 593 |
|
387
69f4356d915d
new datatype theory, supports 'draft theories' and incremental extension:
wenzelm
parents:
309
diff
changeset
|
594 |
|
2509 | 595 |
|
1529 | 596 |
(*** Meta rules ***) |
0 | 597 |
|
2147 | 598 |
(*Check that term does not contain same var with different typing/sorting. |
599 |
If this check must be made, recalculate maxidx in hope of preventing its |
|
600 |
recurrence.*) |
|
601 |
fun nodup_Vars (thm as Thm{sign, der, maxidx, shyps, hyps, prop}) s = |
|
602 |
(Sign.nodup_Vars prop; |
|
603 |
Thm {sign = sign, |
|
2386 | 604 |
der = der, |
605 |
maxidx = maxidx_of_term prop, |
|
606 |
shyps = shyps, |
|
607 |
hyps = hyps, |
|
608 |
prop = prop}) |
|
2147 | 609 |
handle TYPE(msg,Ts,ts) => raise TYPE(s^": "^msg,Ts,ts); |
1495
b8b54847c77f
Added check for duplicate vars with distinct types/sorts (nodup_Vars)
nipkow
parents:
1493
diff
changeset
|
610 |
|
1220 | 611 |
(** 'primitive' rules **) |
612 |
||
613 |
(*discharge all assumptions t from ts*) |
|
0 | 614 |
val disch = gen_rem (op aconv); |
615 |
||
1220 | 616 |
(*The assumption rule A|-A in a theory*) |
250 | 617 |
fun assume ct : thm = |
229
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
225
diff
changeset
|
618 |
let val {sign, t=prop, T, maxidx} = rep_cterm ct |
250 | 619 |
in if T<>propT then |
620 |
raise THM("assume: assumptions must have type prop", 0, []) |
|
0 | 621 |
else if maxidx <> ~1 then |
250 | 622 |
raise THM("assume: assumptions may not contain scheme variables", |
623 |
maxidx, []) |
|
1529 | 624 |
else Thm{sign = sign, |
2386 | 625 |
der = infer_derivs (Assume ct, []), |
626 |
maxidx = ~1, |
|
627 |
shyps = add_term_sorts(prop,[]), |
|
628 |
hyps = [prop], |
|
629 |
prop = prop} |
|
0 | 630 |
end; |
631 |
||
1220 | 632 |
(*Implication introduction |
3529 | 633 |
[A] |
634 |
: |
|
635 |
B |
|
1220 | 636 |
------- |
637 |
A ==> B |
|
638 |
*) |
|
1529 | 639 |
fun implies_intr cA (thB as Thm{sign,der,maxidx,hyps,prop,...}) : thm = |
229
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
225
diff
changeset
|
640 |
let val {sign=signA, t=A, T, maxidx=maxidxA} = rep_cterm cA |
0 | 641 |
in if T<>propT then |
250 | 642 |
raise THM("implies_intr: assumptions must have type prop", 0, [thB]) |
1238 | 643 |
else fix_shyps [thB] [] |
1529 | 644 |
(Thm{sign = Sign.merge (sign,signA), |
2386 | 645 |
der = infer_derivs (Implies_intr cA, [der]), |
646 |
maxidx = Int.max(maxidxA, maxidx), |
|
647 |
shyps = [], |
|
648 |
hyps = disch(hyps,A), |
|
649 |
prop = implies$A$prop}) |
|
0 | 650 |
handle TERM _ => |
651 |
raise THM("implies_intr: incompatible signatures", 0, [thB]) |
|
652 |
end; |
|
653 |
||
1529 | 654 |
|
1220 | 655 |
(*Implication elimination |
656 |
A ==> B A |
|
657 |
------------ |
|
658 |
B |
|
659 |
*) |
|
0 | 660 |
fun implies_elim thAB thA : thm = |
1529 | 661 |
let val Thm{maxidx=maxA, der=derA, hyps=hypsA, prop=propA,...} = thA |
662 |
and Thm{sign, der, maxidx, hyps, prop,...} = thAB; |
|
250 | 663 |
fun err(a) = raise THM("implies_elim: "^a, 0, [thAB,thA]) |
0 | 664 |
in case prop of |
250 | 665 |
imp$A$B => |
666 |
if imp=implies andalso A aconv propA |
|
1220 | 667 |
then fix_shyps [thAB, thA] [] |
668 |
(Thm{sign= merge_thm_sgs(thAB,thA), |
|
2386 | 669 |
der = infer_derivs (Implies_elim, [der,derA]), |
670 |
maxidx = Int.max(maxA,maxidx), |
|
671 |
shyps = [], |
|
672 |
hyps = union_term(hypsA,hyps), (*dups suppressed*) |
|
673 |
prop = B}) |
|
250 | 674 |
else err("major premise") |
675 |
| _ => err("major premise") |
|
0 | 676 |
end; |
250 | 677 |
|
1220 | 678 |
(*Forall introduction. The Free or Var x must not be free in the hypotheses. |
679 |
A |
|
680 |
----- |
|
681 |
!!x.A |
|
682 |
*) |
|
1529 | 683 |
fun forall_intr cx (th as Thm{sign,der,maxidx,hyps,prop,...}) = |
229
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
225
diff
changeset
|
684 |
let val x = term_of cx; |
1238 | 685 |
fun result(a,T) = fix_shyps [th] [] |
1529 | 686 |
(Thm{sign = sign, |
2386 | 687 |
der = infer_derivs (Forall_intr cx, [der]), |
688 |
maxidx = maxidx, |
|
689 |
shyps = [], |
|
690 |
hyps = hyps, |
|
691 |
prop = all(T) $ Abs(a, T, abstract_over (x,prop))}) |
|
0 | 692 |
in case x of |
250 | 693 |
Free(a,T) => |
694 |
if exists (apl(x, Logic.occs)) hyps |
|
695 |
then raise THM("forall_intr: variable free in assumptions", 0, [th]) |
|
696 |
else result(a,T) |
|
0 | 697 |
| Var((a,_),T) => result(a,T) |
698 |
| _ => raise THM("forall_intr: not a variable", 0, [th]) |
|
699 |
end; |
|
700 |
||
1220 | 701 |
(*Forall elimination |
702 |
!!x.A |
|
703 |
------ |
|
704 |
A[t/x] |
|
705 |
*) |
|
1529 | 706 |
fun forall_elim ct (th as Thm{sign,der,maxidx,hyps,prop,...}) : thm = |
229
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
225
diff
changeset
|
707 |
let val {sign=signt, t, T, maxidx=maxt} = rep_cterm ct |
0 | 708 |
in case prop of |
2386 | 709 |
Const("all",Type("fun",[Type("fun",[qary,_]),_])) $ A => |
710 |
if T<>qary then |
|
711 |
raise THM("forall_elim: type mismatch", 0, [th]) |
|
712 |
else let val thm = fix_shyps [th] [] |
|
713 |
(Thm{sign= Sign.merge(sign,signt), |
|
714 |
der = infer_derivs (Forall_elim ct, [der]), |
|
715 |
maxidx = Int.max(maxidx, maxt), |
|
716 |
shyps = [], |
|
717 |
hyps = hyps, |
|
718 |
prop = betapply(A,t)}) |
|
719 |
in if maxt >= 0 andalso maxidx >= 0 |
|
720 |
then nodup_Vars thm "forall_elim" |
|
721 |
else thm (*no new Vars: no expensive check!*) |
|
722 |
end |
|
2147 | 723 |
| _ => raise THM("forall_elim: not quantified", 0, [th]) |
0 | 724 |
end |
725 |
handle TERM _ => |
|
250 | 726 |
raise THM("forall_elim: incompatible signatures", 0, [th]); |
0 | 727 |
|
728 |
||
1220 | 729 |
(* Equality *) |
0 | 730 |
|
1220 | 731 |
(* Definition of the relation =?= *) |
1238 | 732 |
val flexpair_def = fix_shyps [] [] |
1529 | 733 |
(Thm{sign= Sign.proto_pure, |
1597
54ece585bf62
name_thm no longer takes a theory argument, as the
paulson
parents:
1580
diff
changeset
|
734 |
der = Join(Axiom(pure_thy, "flexpair_def"), []), |
1529 | 735 |
shyps = [], |
736 |
hyps = [], |
|
737 |
maxidx = 0, |
|
738 |
prop = term_of (read_cterm Sign.proto_pure |
|
2386 | 739 |
("(?t =?= ?u) == (?t == ?u::?'a::{})", propT))}); |
0 | 740 |
|
741 |
(*The reflexivity rule: maps t to the theorem t==t *) |
|
250 | 742 |
fun reflexive ct = |
229
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
225
diff
changeset
|
743 |
let val {sign, t, T, maxidx} = rep_cterm ct |
1238 | 744 |
in fix_shyps [] [] |
1529 | 745 |
(Thm{sign= sign, |
2386 | 746 |
der = infer_derivs (Reflexive ct, []), |
747 |
shyps = [], |
|
748 |
hyps = [], |
|
749 |
maxidx = maxidx, |
|
750 |
prop = Logic.mk_equals(t,t)}) |
|
0 | 751 |
end; |
752 |
||
753 |
(*The symmetry rule |
|
1220 | 754 |
t==u |
755 |
---- |
|
756 |
u==t |
|
757 |
*) |
|
1529 | 758 |
fun symmetric (th as Thm{sign,der,maxidx,shyps,hyps,prop}) = |
0 | 759 |
case prop of |
760 |
(eq as Const("==",_)) $ t $ u => |
|
1238 | 761 |
(*no fix_shyps*) |
2386 | 762 |
Thm{sign = sign, |
763 |
der = infer_derivs (Symmetric, [der]), |
|
764 |
maxidx = maxidx, |
|
765 |
shyps = shyps, |
|
766 |
hyps = hyps, |
|
767 |
prop = eq$u$t} |
|
0 | 768 |
| _ => raise THM("symmetric", 0, [th]); |
769 |
||
770 |
(*The transitive rule |
|
1220 | 771 |
t1==u u==t2 |
772 |
-------------- |
|
773 |
t1==t2 |
|
774 |
*) |
|
0 | 775 |
fun transitive th1 th2 = |
1529 | 776 |
let val Thm{der=der1, maxidx=max1, hyps=hyps1, prop=prop1,...} = th1 |
777 |
and Thm{der=der2, maxidx=max2, hyps=hyps2, prop=prop2,...} = th2; |
|
0 | 778 |
fun err(msg) = raise THM("transitive: "^msg, 0, [th1,th2]) |
779 |
in case (prop1,prop2) of |
|
780 |
((eq as Const("==",_)) $ t1 $ u, Const("==",_) $ u' $ t2) => |
|
1634 | 781 |
if not (u aconv u') then err"middle term" |
782 |
else let val thm = |
|
1220 | 783 |
fix_shyps [th1, th2] [] |
1529 | 784 |
(Thm{sign= merge_thm_sgs(th1,th2), |
2386 | 785 |
der = infer_derivs (Transitive, [der1, der2]), |
2147 | 786 |
maxidx = Int.max(max1,max2), |
2386 | 787 |
shyps = [], |
788 |
hyps = union_term(hyps1,hyps2), |
|
789 |
prop = eq$t1$t2}) |
|
2139
2c59b204b540
Only calls nodup_Vars if really necessary. We get a speedup of nearly 6%
paulson
parents:
2047
diff
changeset
|
790 |
in if max1 >= 0 andalso max2 >= 0 |
2147 | 791 |
then nodup_Vars thm "transitive" |
792 |
else thm (*no new Vars: no expensive check!*) |
|
2139
2c59b204b540
Only calls nodup_Vars if really necessary. We get a speedup of nearly 6%
paulson
parents:
2047
diff
changeset
|
793 |
end |
0 | 794 |
| _ => err"premises" |
795 |
end; |
|
796 |
||
1160 | 797 |
(*Beta-conversion: maps (%x.t)(u) to the theorem (%x.t)(u) == t[u/x] *) |
250 | 798 |
fun beta_conversion ct = |
229
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
225
diff
changeset
|
799 |
let val {sign, t, T, maxidx} = rep_cterm ct |
0 | 800 |
in case t of |
1238 | 801 |
Abs(_,_,bodt) $ u => fix_shyps [] [] |
1529 | 802 |
(Thm{sign = sign, |
2386 | 803 |
der = infer_derivs (Beta_conversion ct, []), |
804 |
maxidx = maxidx, |
|
805 |
shyps = [], |
|
806 |
hyps = [], |
|
807 |
prop = Logic.mk_equals(t, subst_bound (u,bodt))}) |
|
250 | 808 |
| _ => raise THM("beta_conversion: not a redex", 0, []) |
0 | 809 |
end; |
810 |
||
811 |
(*The extensionality rule (proviso: x not free in f, g, or hypotheses) |
|
1220 | 812 |
f(x) == g(x) |
813 |
------------ |
|
814 |
f == g |
|
815 |
*) |
|
1529 | 816 |
fun extensional (th as Thm{sign, der, maxidx,shyps,hyps,prop}) = |
0 | 817 |
case prop of |
818 |
(Const("==",_)) $ (f$x) $ (g$y) => |
|
250 | 819 |
let fun err(msg) = raise THM("extensional: "^msg, 0, [th]) |
0 | 820 |
in (if x<>y then err"different variables" else |
821 |
case y of |
|
250 | 822 |
Free _ => |
823 |
if exists (apl(y, Logic.occs)) (f::g::hyps) |
|
824 |
then err"variable free in hyps or functions" else () |
|
825 |
| Var _ => |
|
826 |
if Logic.occs(y,f) orelse Logic.occs(y,g) |
|
827 |
then err"variable free in functions" else () |
|
828 |
| _ => err"not a variable"); |
|
1238 | 829 |
(*no fix_shyps*) |
1529 | 830 |
Thm{sign = sign, |
2386 | 831 |
der = infer_derivs (Extensional, [der]), |
832 |
maxidx = maxidx, |
|
833 |
shyps = shyps, |
|
834 |
hyps = hyps, |
|
1529 | 835 |
prop = Logic.mk_equals(f,g)} |
0 | 836 |
end |
837 |
| _ => raise THM("extensional: premise", 0, [th]); |
|
838 |
||
839 |
(*The abstraction rule. The Free or Var x must not be free in the hypotheses. |
|
840 |
The bound variable will be named "a" (since x will be something like x320) |
|
1220 | 841 |
t == u |
842 |
------------ |
|
843 |
%x.t == %x.u |
|
844 |
*) |
|
1529 | 845 |
fun abstract_rule a cx (th as Thm{sign,der,maxidx,hyps,prop,...}) = |
229
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
225
diff
changeset
|
846 |
let val x = term_of cx; |
250 | 847 |
val (t,u) = Logic.dest_equals prop |
848 |
handle TERM _ => |
|
849 |
raise THM("abstract_rule: premise not an equality", 0, [th]) |
|
1238 | 850 |
fun result T = fix_shyps [th] [] |
2386 | 851 |
(Thm{sign = sign, |
852 |
der = infer_derivs (Abstract_rule (a,cx), [der]), |
|
853 |
maxidx = maxidx, |
|
854 |
shyps = [], |
|
855 |
hyps = hyps, |
|
856 |
prop = Logic.mk_equals(Abs(a, T, abstract_over (x,t)), |
|
857 |
Abs(a, T, abstract_over (x,u)))}) |
|
0 | 858 |
in case x of |
250 | 859 |
Free(_,T) => |
860 |
if exists (apl(x, Logic.occs)) hyps |
|
861 |
then raise THM("abstract_rule: variable free in assumptions", 0, [th]) |
|
862 |
else result T |
|
0 | 863 |
| Var(_,T) => result T |
864 |
| _ => raise THM("abstract_rule: not a variable", 0, [th]) |
|
865 |
end; |
|
866 |
||
867 |
(*The combination rule |
|
3529 | 868 |
f == g t == u |
869 |
-------------- |
|
870 |
f(t) == g(u) |
|
1220 | 871 |
*) |
0 | 872 |
fun combination th1 th2 = |
1529 | 873 |
let val Thm{der=der1, maxidx=max1, shyps=shyps1, hyps=hyps1, |
2386 | 874 |
prop=prop1,...} = th1 |
1529 | 875 |
and Thm{der=der2, maxidx=max2, shyps=shyps2, hyps=hyps2, |
2386 | 876 |
prop=prop2,...} = th2 |
1836
861e29c7cada
Added type-checking to rule "combination". This corrects a fault
paulson
parents:
1802
diff
changeset
|
877 |
fun chktypes (f,t) = |
2386 | 878 |
(case fastype_of f of |
879 |
Type("fun",[T1,T2]) => |
|
880 |
if T1 <> fastype_of t then |
|
881 |
raise THM("combination: types", 0, [th1,th2]) |
|
882 |
else () |
|
883 |
| _ => raise THM("combination: not function type", 0, |
|
884 |
[th1,th2])) |
|
1495
b8b54847c77f
Added check for duplicate vars with distinct types/sorts (nodup_Vars)
nipkow
parents:
1493
diff
changeset
|
885 |
in case (prop1,prop2) of |
0 | 886 |
(Const("==",_) $ f $ g, Const("==",_) $ t $ u) => |
1836
861e29c7cada
Added type-checking to rule "combination". This corrects a fault
paulson
parents:
1802
diff
changeset
|
887 |
let val _ = chktypes (f,t) |
2386 | 888 |
val thm = (*no fix_shyps*) |
889 |
Thm{sign = merge_thm_sgs(th1,th2), |
|
890 |
der = infer_derivs (Combination, [der1, der2]), |
|
891 |
maxidx = Int.max(max1,max2), |
|
892 |
shyps = union_sort(shyps1,shyps2), |
|
893 |
hyps = union_term(hyps1,hyps2), |
|
894 |
prop = Logic.mk_equals(f$t, g$u)} |
|
2139
2c59b204b540
Only calls nodup_Vars if really necessary. We get a speedup of nearly 6%
paulson
parents:
2047
diff
changeset
|
895 |
in if max1 >= 0 andalso max2 >= 0 |
2c59b204b540
Only calls nodup_Vars if really necessary. We get a speedup of nearly 6%
paulson
parents:
2047
diff
changeset
|
896 |
then nodup_Vars thm "combination" |
2386 | 897 |
else thm (*no new Vars: no expensive check!*) |
2139
2c59b204b540
Only calls nodup_Vars if really necessary. We get a speedup of nearly 6%
paulson
parents:
2047
diff
changeset
|
898 |
end |
0 | 899 |
| _ => raise THM("combination: premises", 0, [th1,th2]) |
900 |
end; |
|
901 |
||
902 |
||
903 |
(* Equality introduction |
|
3529 | 904 |
A ==> B B ==> A |
905 |
---------------- |
|
906 |
A == B |
|
1220 | 907 |
*) |
0 | 908 |
fun equal_intr th1 th2 = |
1529 | 909 |
let val Thm{der=der1,maxidx=max1, shyps=shyps1, hyps=hyps1, |
2386 | 910 |
prop=prop1,...} = th1 |
1529 | 911 |
and Thm{der=der2, maxidx=max2, shyps=shyps2, hyps=hyps2, |
2386 | 912 |
prop=prop2,...} = th2; |
1529 | 913 |
fun err(msg) = raise THM("equal_intr: "^msg, 0, [th1,th2]) |
914 |
in case (prop1,prop2) of |
|
915 |
(Const("==>",_) $ A $ B, Const("==>",_) $ B' $ A') => |
|
2386 | 916 |
if A aconv A' andalso B aconv B' |
917 |
then |
|
918 |
(*no fix_shyps*) |
|
919 |
Thm{sign = merge_thm_sgs(th1,th2), |
|
920 |
der = infer_derivs (Equal_intr, [der1, der2]), |
|
921 |
maxidx = Int.max(max1,max2), |
|
922 |
shyps = union_sort(shyps1,shyps2), |
|
923 |
hyps = union_term(hyps1,hyps2), |
|
924 |
prop = Logic.mk_equals(A,B)} |
|
925 |
else err"not equal" |
|
1529 | 926 |
| _ => err"premises" |
927 |
end; |
|
928 |
||
929 |
||
930 |
(*The equal propositions rule |
|
3529 | 931 |
A == B A |
1529 | 932 |
--------- |
933 |
B |
|
934 |
*) |
|
935 |
fun equal_elim th1 th2 = |
|
936 |
let val Thm{der=der1, maxidx=max1, hyps=hyps1, prop=prop1,...} = th1 |
|
937 |
and Thm{der=der2, maxidx=max2, hyps=hyps2, prop=prop2,...} = th2; |
|
938 |
fun err(msg) = raise THM("equal_elim: "^msg, 0, [th1,th2]) |
|
939 |
in case prop1 of |
|
940 |
Const("==",_) $ A $ B => |
|
941 |
if not (prop2 aconv A) then err"not equal" else |
|
942 |
fix_shyps [th1, th2] [] |
|
943 |
(Thm{sign= merge_thm_sgs(th1,th2), |
|
2386 | 944 |
der = infer_derivs (Equal_elim, [der1, der2]), |
945 |
maxidx = Int.max(max1,max2), |
|
946 |
shyps = [], |
|
947 |
hyps = union_term(hyps1,hyps2), |
|
948 |
prop = B}) |
|
1529 | 949 |
| _ => err"major premise" |
950 |
end; |
|
0 | 951 |
|
1220 | 952 |
|
953 |
||
0 | 954 |
(**** Derived rules ****) |
955 |
||
1503 | 956 |
(*Discharge all hypotheses. Need not verify cterms or call fix_shyps. |
0 | 957 |
Repeated hypotheses are discharged only once; fold cannot do this*) |
1529 | 958 |
fun implies_intr_hyps (Thm{sign, der, maxidx, shyps, hyps=A::As, prop}) = |
1238 | 959 |
implies_intr_hyps (*no fix_shyps*) |
1529 | 960 |
(Thm{sign = sign, |
2386 | 961 |
der = infer_derivs (Implies_intr_hyps, [der]), |
962 |
maxidx = maxidx, |
|
963 |
shyps = shyps, |
|
1529 | 964 |
hyps = disch(As,A), |
2386 | 965 |
prop = implies$A$prop}) |
0 | 966 |
| implies_intr_hyps th = th; |
967 |
||
968 |
(*Smash" unifies the list of term pairs leaving no flex-flex pairs. |
|
250 | 969 |
Instantiates the theorem and deletes trivial tpairs. |
0 | 970 |
Resulting sequence may contain multiple elements if the tpairs are |
971 |
not all flex-flex. *) |
|
1529 | 972 |
fun flexflex_rule (th as Thm{sign, der, maxidx, hyps, prop,...}) = |
250 | 973 |
let fun newthm env = |
1529 | 974 |
if Envir.is_empty env then th |
975 |
else |
|
250 | 976 |
let val (tpairs,horn) = |
977 |
Logic.strip_flexpairs (Envir.norm_term env prop) |
|
978 |
(*Remove trivial tpairs, of the form t=t*) |
|
979 |
val distpairs = filter (not o op aconv) tpairs |
|
980 |
val newprop = Logic.list_flexpairs(distpairs, horn) |
|
1220 | 981 |
in fix_shyps [th] (env_codT env) |
1529 | 982 |
(Thm{sign = sign, |
2386 | 983 |
der = infer_derivs (Flexflex_rule env, [der]), |
984 |
maxidx = maxidx_of_term newprop, |
|
985 |
shyps = [], |
|
986 |
hyps = hyps, |
|
987 |
prop = newprop}) |
|
250 | 988 |
end; |
0 | 989 |
val (tpairs,_) = Logic.strip_flexpairs prop |
990 |
in Sequence.maps newthm |
|
250 | 991 |
(Unify.smash_unifiers(sign, Envir.empty maxidx, tpairs)) |
0 | 992 |
end; |
993 |
||
994 |
(*Instantiation of Vars |
|
1220 | 995 |
A |
996 |
------------------- |
|
997 |
A[t1/v1,....,tn/vn] |
|
998 |
*) |
|
0 | 999 |
|
1000 |
(*Check that all the terms are Vars and are distinct*) |
|
1001 |
fun instl_ok ts = forall is_Var ts andalso null(findrep ts); |
|
1002 |
||
1003 |
(*For instantiate: process pair of cterms, merge theories*) |
|
1004 |
fun add_ctpair ((ct,cu), (sign,tpairs)) = |
|
229
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
225
diff
changeset
|
1005 |
let val {sign=signt, t=t, T= T, ...} = rep_cterm ct |
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
225
diff
changeset
|
1006 |
and {sign=signu, t=u, T= U, ...} = rep_cterm cu |
0 | 1007 |
in if T=U then (Sign.merge(sign, Sign.merge(signt, signu)), (t,u)::tpairs) |
1008 |
else raise TYPE("add_ctpair", [T,U], [t,u]) |
|
1009 |
end; |
|
1010 |
||
1011 |
fun add_ctyp ((v,ctyp), (sign',vTs)) = |
|
229
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
225
diff
changeset
|
1012 |
let val {T,sign} = rep_ctyp ctyp |
0 | 1013 |
in (Sign.merge(sign,sign'), (v,T)::vTs) end; |
1014 |
||
1015 |
(*Left-to-right replacements: ctpairs = [...,(vi,ti),...]. |
|
1016 |
Instantiates distinct Vars by terms of same type. |
|
1017 |
Normalizes the new theorem! *) |
|
1529 | 1018 |
fun instantiate ([], []) th = th |
1019 |
| instantiate (vcTs,ctpairs) (th as Thm{sign,der,maxidx,hyps,prop,...}) = |
|
0 | 1020 |
let val (newsign,tpairs) = foldr add_ctpair (ctpairs, (sign,[])); |
1021 |
val (newsign,vTs) = foldr add_ctyp (vcTs, (newsign,[])); |
|
250 | 1022 |
val newprop = |
1023 |
Envir.norm_term (Envir.empty 0) |
|
1024 |
(subst_atomic tpairs |
|
1025 |
(Type.inst_term_tvars(#tsig(Sign.rep_sg newsign),vTs) prop)) |
|
1220 | 1026 |
val newth = |
1027 |
fix_shyps [th] (map snd vTs) |
|
1529 | 1028 |
(Thm{sign = newsign, |
2386 | 1029 |
der = infer_derivs (Instantiate(vcTs,ctpairs), [der]), |
1030 |
maxidx = maxidx_of_term newprop, |
|
1031 |
shyps = [], |
|
1032 |
hyps = hyps, |
|
1033 |
prop = newprop}) |
|
250 | 1034 |
in if not(instl_ok(map #1 tpairs)) |
193 | 1035 |
then raise THM("instantiate: variables not distinct", 0, [th]) |
1036 |
else if not(null(findrep(map #1 vTs))) |
|
1037 |
then raise THM("instantiate: type variables not distinct", 0, [th]) |
|
2147 | 1038 |
else nodup_Vars newth "instantiate" |
0 | 1039 |
end |
250 | 1040 |
handle TERM _ => |
0 | 1041 |
raise THM("instantiate: incompatible signatures",0,[th]) |
2671 | 1042 |
| TYPE (msg,_,_) => raise THM("instantiate: type conflict: " ^ msg, |
1043 |
0, [th]); |
|
0 | 1044 |
|
1045 |
(*The trivial implication A==>A, justified by assume and forall rules. |
|
1046 |
A can contain Vars, not so for assume! *) |
|
250 | 1047 |
fun trivial ct : thm = |
229
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
225
diff
changeset
|
1048 |
let val {sign, t=A, T, maxidx} = rep_cterm ct |
250 | 1049 |
in if T<>propT then |
1050 |
raise THM("trivial: the term must have type prop", 0, []) |
|
1238 | 1051 |
else fix_shyps [] [] |
1529 | 1052 |
(Thm{sign = sign, |
2386 | 1053 |
der = infer_derivs (Trivial ct, []), |
1054 |
maxidx = maxidx, |
|
1055 |
shyps = [], |
|
1056 |
hyps = [], |
|
1057 |
prop = implies$A$A}) |
|
0 | 1058 |
end; |
1059 |
||
1503 | 1060 |
(*Axiom-scheme reflecting signature contents: "OFCLASS(?'a::c, c_class)" *) |
399
86cc2b98f9e0
added class_triv: theory -> class -> thm (for axclasses);
wenzelm
parents:
387
diff
changeset
|
1061 |
fun class_triv thy c = |
1529 | 1062 |
let val sign = sign_of thy; |
1063 |
val Cterm {t, maxidx, ...} = |
|
2386 | 1064 |
cterm_of sign (Logic.mk_inclass (TVar (("'a", 0), [c]), c)) |
1065 |
handle TERM (msg, _) => raise THM ("class_triv: " ^ msg, 0, []); |
|
399
86cc2b98f9e0
added class_triv: theory -> class -> thm (for axclasses);
wenzelm
parents:
387
diff
changeset
|
1066 |
in |
1238 | 1067 |
fix_shyps [] [] |
1529 | 1068 |
(Thm {sign = sign, |
2386 | 1069 |
der = infer_derivs (Class_triv(thy,c), []), |
1070 |
maxidx = maxidx, |
|
1071 |
shyps = [], |
|
1072 |
hyps = [], |
|
1073 |
prop = t}) |
|
399
86cc2b98f9e0
added class_triv: theory -> class -> thm (for axclasses);
wenzelm
parents:
387
diff
changeset
|
1074 |
end; |
86cc2b98f9e0
added class_triv: theory -> class -> thm (for axclasses);
wenzelm
parents:
387
diff
changeset
|
1075 |
|
86cc2b98f9e0
added class_triv: theory -> class -> thm (for axclasses);
wenzelm
parents:
387
diff
changeset
|
1076 |
|
0 | 1077 |
(* Replace all TFrees not in the hyps by new TVars *) |
1529 | 1078 |
fun varifyT(Thm{sign,der,maxidx,shyps,hyps,prop}) = |
0 | 1079 |
let val tfrees = foldr add_term_tfree_names (hyps,[]) |
1634 | 1080 |
in let val thm = (*no fix_shyps*) |
1529 | 1081 |
Thm{sign = sign, |
2386 | 1082 |
der = infer_derivs (VarifyT, [der]), |
1083 |
maxidx = Int.max(0,maxidx), |
|
1084 |
shyps = shyps, |
|
1085 |
hyps = hyps, |
|
1529 | 1086 |
prop = Type.varify(prop,tfrees)} |
2147 | 1087 |
in nodup_Vars thm "varifyT" end |
1634 | 1088 |
(* this nodup_Vars check can be removed if thms are guaranteed not to contain |
1089 |
duplicate TVars with differnt sorts *) |
|
0 | 1090 |
end; |
1091 |
||
1092 |
(* Replace all TVars by new TFrees *) |
|
1529 | 1093 |
fun freezeT(Thm{sign,der,maxidx,shyps,hyps,prop}) = |
3410 | 1094 |
let val (prop',_) = Type.freeze_thaw prop |
1238 | 1095 |
in (*no fix_shyps*) |
1529 | 1096 |
Thm{sign = sign, |
2386 | 1097 |
der = infer_derivs (FreezeT, [der]), |
1098 |
maxidx = maxidx_of_term prop', |
|
1099 |
shyps = shyps, |
|
1100 |
hyps = hyps, |
|
1529 | 1101 |
prop = prop'} |
1220 | 1102 |
end; |
0 | 1103 |
|
1104 |
||
1105 |
(*** Inference rules for tactics ***) |
|
1106 |
||
1107 |
(*Destruct proof state into constraints, other goals, goal(i), rest *) |
|
1108 |
fun dest_state (state as Thm{prop,...}, i) = |
|
1109 |
let val (tpairs,horn) = Logic.strip_flexpairs prop |
|
1110 |
in case Logic.strip_prems(i, [], horn) of |
|
1111 |
(B::rBs, C) => (tpairs, rev rBs, B, C) |
|
1112 |
| _ => raise THM("dest_state", i, [state]) |
|
1113 |
end |
|
1114 |
handle TERM _ => raise THM("dest_state", i, [state]); |
|
1115 |
||
309 | 1116 |
(*Increment variables and parameters of orule as required for |
0 | 1117 |
resolution with goal i of state. *) |
1118 |
fun lift_rule (state, i) orule = |
|
1529 | 1119 |
let val Thm{shyps=sshyps, prop=sprop, maxidx=smax, sign=ssign,...} = state |
0 | 1120 |
val (Bi::_, _) = Logic.strip_prems(i, [], Logic.skip_flexpairs sprop) |
1529 | 1121 |
handle TERM _ => raise THM("lift_rule", i, [orule,state]) |
1122 |
val ct_Bi = Cterm {sign=ssign, maxidx=smax, T=propT, t=Bi} |
|
1123 |
val (lift_abs,lift_all) = Logic.lift_fns(Bi,smax+1) |
|
1124 |
val (Thm{sign, der, maxidx,shyps,hyps,prop}) = orule |
|
0 | 1125 |
val (tpairs,As,B) = Logic.strip_horn prop |
1238 | 1126 |
in (*no fix_shyps*) |
1529 | 1127 |
Thm{sign = merge_thm_sgs(state,orule), |
2386 | 1128 |
der = infer_derivs (Lift_rule(ct_Bi, i), [der]), |
1129 |
maxidx = maxidx+smax+1, |
|
2177
8b365a3a6ed1
Changed some mem, ins and union calls to be monomorphic
paulson
parents:
2163
diff
changeset
|
1130 |
shyps=union_sort(sshyps,shyps), |
2386 | 1131 |
hyps=hyps, |
1529 | 1132 |
prop = Logic.rule_of (map (pairself lift_abs) tpairs, |
2386 | 1133 |
map lift_all As, |
1134 |
lift_all B)} |
|
0 | 1135 |
end; |
1136 |
||
1137 |
(*Solve subgoal Bi of proof state B1...Bn/C by assumption. *) |
|
1138 |
fun assumption i state = |
|
1529 | 1139 |
let val Thm{sign,der,maxidx,hyps,prop,...} = state; |
0 | 1140 |
val (tpairs, Bs, Bi, C) = dest_state(state,i) |
250 | 1141 |
fun newth (env as Envir.Envir{maxidx, ...}, tpairs) = |
1220 | 1142 |
fix_shyps [state] (env_codT env) |
1529 | 1143 |
(Thm{sign = sign, |
2386 | 1144 |
der = infer_derivs (Assumption (i, Some env), [der]), |
1145 |
maxidx = maxidx, |
|
1146 |
shyps = [], |
|
1147 |
hyps = hyps, |
|
1148 |
prop = |
|
1149 |
if Envir.is_empty env then (*avoid wasted normalizations*) |
|
1150 |
Logic.rule_of (tpairs, Bs, C) |
|
1151 |
else (*normalize the new rule fully*) |
|
1152 |
Envir.norm_term env (Logic.rule_of (tpairs, Bs, C))}); |
|
0 | 1153 |
fun addprfs [] = Sequence.null |
1154 |
| addprfs ((t,u)::apairs) = Sequence.seqof (fn()=> Sequence.pull |
|
1155 |
(Sequence.mapp newth |
|
250 | 1156 |
(Unify.unifiers(sign,Envir.empty maxidx, (t,u)::tpairs)) |
1157 |
(addprfs apairs))) |
|
0 | 1158 |
in addprfs (Logic.assum_pairs Bi) end; |
1159 |
||
250 | 1160 |
(*Solve subgoal Bi of proof state B1...Bn/C by assumption. |
0 | 1161 |
Checks if Bi's conclusion is alpha-convertible to one of its assumptions*) |
1162 |
fun eq_assumption i state = |
|
1529 | 1163 |
let val Thm{sign,der,maxidx,hyps,prop,...} = state; |
0 | 1164 |
val (tpairs, Bs, Bi, C) = dest_state(state,i) |
1165 |
in if exists (op aconv) (Logic.assum_pairs Bi) |
|
1220 | 1166 |
then fix_shyps [state] [] |
1529 | 1167 |
(Thm{sign = sign, |
2386 | 1168 |
der = infer_derivs (Assumption (i,None), [der]), |
1169 |
maxidx = maxidx, |
|
1170 |
shyps = [], |
|
1171 |
hyps = hyps, |
|
1172 |
prop = Logic.rule_of(tpairs, Bs, C)}) |
|
0 | 1173 |
else raise THM("eq_assumption", 0, [state]) |
1174 |
end; |
|
1175 |
||
1176 |
||
2671 | 1177 |
(*For rotate_tac: fast rotation of assumptions of subgoal i*) |
1178 |
fun rotate_rule k i state = |
|
1179 |
let val Thm{sign,der,maxidx,hyps,prop,shyps} = state; |
|
1180 |
val (tpairs, Bs, Bi, C) = dest_state(state,i) |
|
1181 |
val params = Logic.strip_params Bi |
|
1182 |
and asms = Logic.strip_assums_hyp Bi |
|
1183 |
and concl = Logic.strip_assums_concl Bi |
|
1184 |
val n = length asms |
|
1185 |
fun rot m = if 0=m orelse m=n then Bi |
|
1186 |
else if 0<m andalso m<n |
|
1187 |
then list_all |
|
1188 |
(params, |
|
1189 |
Logic.list_implies(List.drop(asms, m) @ |
|
1190 |
List.take(asms, m), |
|
1191 |
concl)) |
|
1192 |
else raise THM("rotate_rule", m, [state]) |
|
1193 |
in Thm{sign = sign, |
|
1194 |
der = infer_derivs (Rotate_rule (k,i), [der]), |
|
1195 |
maxidx = maxidx, |
|
1196 |
shyps = shyps, |
|
1197 |
hyps = hyps, |
|
1198 |
prop = Logic.rule_of(tpairs, Bs@[rot (if k<0 then n+k else k)], C)} |
|
1199 |
end; |
|
1200 |
||
1201 |
||
0 | 1202 |
(** User renaming of parameters in a subgoal **) |
1203 |
||
1204 |
(*Calls error rather than raising an exception because it is intended |
|
1205 |
for top-level use -- exception handling would not make sense here. |
|
1206 |
The names in cs, if distinct, are used for the innermost parameters; |
|
1207 |
preceding parameters may be renamed to make all params distinct.*) |
|
1208 |
fun rename_params_rule (cs, i) state = |
|
3037
99ed078e6ae7
rename_params_rule used to check if the new name clashed with a free name in
nipkow
parents:
3012
diff
changeset
|
1209 |
let val Thm{sign,der,maxidx,hyps,...} = state |
0 | 1210 |
val (tpairs, Bs, Bi, C) = dest_state(state,i) |
1211 |
val iparams = map #1 (Logic.strip_params Bi) |
|
1212 |
val short = length iparams - length cs |
|
250 | 1213 |
val newnames = |
1214 |
if short<0 then error"More names than abstractions!" |
|
1215 |
else variantlist(take (short,iparams), cs) @ cs |
|
3037
99ed078e6ae7
rename_params_rule used to check if the new name clashed with a free name in
nipkow
parents:
3012
diff
changeset
|
1216 |
val freenames = map (#1 o dest_Free) (term_frees Bi) |
0 | 1217 |
val newBi = Logic.list_rename_params (newnames, Bi) |
250 | 1218 |
in |
0 | 1219 |
case findrep cs of |
3565
c64410e701fb
Now rename_params_rule merely issues warnings--and does nothing--if the
paulson
parents:
3558
diff
changeset
|
1220 |
c::_ => (warning ("Can't rename. Bound variables not distinct: " ^ c); |
c64410e701fb
Now rename_params_rule merely issues warnings--and does nothing--if the
paulson
parents:
3558
diff
changeset
|
1221 |
state) |
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1569
diff
changeset
|
1222 |
| [] => (case cs inter_string freenames of |
3565
c64410e701fb
Now rename_params_rule merely issues warnings--and does nothing--if the
paulson
parents:
3558
diff
changeset
|
1223 |
a::_ => (warning ("Can't rename. Bound/Free variable clash: " ^ a); |
c64410e701fb
Now rename_params_rule merely issues warnings--and does nothing--if the
paulson
parents:
3558
diff
changeset
|
1224 |
state) |
1220 | 1225 |
| [] => fix_shyps [state] [] |
2386 | 1226 |
(Thm{sign = sign, |
1227 |
der = infer_derivs (Rename_params_rule(cs,i), [der]), |
|
1228 |
maxidx = maxidx, |
|
1229 |
shyps = [], |
|
1230 |
hyps = hyps, |
|
1231 |
prop = Logic.rule_of(tpairs, Bs@[newBi], C)})) |
|
0 | 1232 |
end; |
1233 |
||
1234 |
(*** Preservation of bound variable names ***) |
|
1235 |
||
250 | 1236 |
(*Scan a pair of terms; while they are similar, |
0 | 1237 |
accumulate corresponding bound vars in "al"*) |
1238 | 1238 |
fun match_bvs(Abs(x,_,s),Abs(y,_,t), al) = |
1195
686e3eb613b9
match_bvs no longer puts a name in the alist if it is null ("")
lcp
parents:
1160
diff
changeset
|
1239 |
match_bvs(s, t, if x="" orelse y="" then al |
1238 | 1240 |
else (x,y)::al) |
0 | 1241 |
| match_bvs(f$s, g$t, al) = match_bvs(f,g,match_bvs(s,t,al)) |
1242 |
| match_bvs(_,_,al) = al; |
|
1243 |
||
1244 |
(* strip abstractions created by parameters *) |
|
1245 |
fun match_bvars((s,t),al) = match_bvs(strip_abs_body s, strip_abs_body t, al); |
|
1246 |
||
1247 |
||
250 | 1248 |
(* strip_apply f A(,B) strips off all assumptions/parameters from A |
0 | 1249 |
introduced by lifting over B, and applies f to remaining part of A*) |
1250 |
fun strip_apply f = |
|
1251 |
let fun strip(Const("==>",_)$ A1 $ B1, |
|
250 | 1252 |
Const("==>",_)$ _ $ B2) = implies $ A1 $ strip(B1,B2) |
1253 |
| strip((c as Const("all",_)) $ Abs(a,T,t1), |
|
1254 |
Const("all",_) $ Abs(_,_,t2)) = c$Abs(a,T,strip(t1,t2)) |
|
1255 |
| strip(A,_) = f A |
|
0 | 1256 |
in strip end; |
1257 |
||
1258 |
(*Use the alist to rename all bound variables and some unknowns in a term |
|
1259 |
dpairs = current disagreement pairs; tpairs = permanent ones (flexflex); |
|
1260 |
Preserves unknowns in tpairs and on lhs of dpairs. *) |
|
1261 |
fun rename_bvs([],_,_,_) = I |
|
1262 |
| rename_bvs(al,dpairs,tpairs,B) = |
|
250 | 1263 |
let val vars = foldr add_term_vars |
1264 |
(map fst dpairs @ map fst tpairs @ map snd tpairs, []) |
|
1265 |
(*unknowns appearing elsewhere be preserved!*) |
|
1266 |
val vids = map (#1 o #1 o dest_Var) vars; |
|
1267 |
fun rename(t as Var((x,i),T)) = |
|
1268 |
(case assoc(al,x) of |
|
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1569
diff
changeset
|
1269 |
Some(y) => if x mem_string vids orelse y mem_string vids then t |
250 | 1270 |
else Var((y,i),T) |
1271 |
| None=> t) |
|
0 | 1272 |
| rename(Abs(x,T,t)) = |
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1569
diff
changeset
|
1273 |
Abs(case assoc_string(al,x) of Some(y) => y | None => x, |
250 | 1274 |
T, rename t) |
0 | 1275 |
| rename(f$t) = rename f $ rename t |
1276 |
| rename(t) = t; |
|
250 | 1277 |
fun strip_ren Ai = strip_apply rename (Ai,B) |
0 | 1278 |
in strip_ren end; |
1279 |
||
1280 |
(*Function to rename bounds/unknowns in the argument, lifted over B*) |
|
1281 |
fun rename_bvars(dpairs, tpairs, B) = |
|
250 | 1282 |
rename_bvs(foldr match_bvars (dpairs,[]), dpairs, tpairs, B); |
0 | 1283 |
|
1284 |
||
1285 |
(*** RESOLUTION ***) |
|
1286 |
||
721
479832ff2d29
Pure/thm/norm_term_skip: new, for skipping normalization of the context
lcp
parents:
678
diff
changeset
|
1287 |
(** Lifting optimizations **) |
479832ff2d29
Pure/thm/norm_term_skip: new, for skipping normalization of the context
lcp
parents:
678
diff
changeset
|
1288 |
|
0 | 1289 |
(*strip off pairs of assumptions/parameters in parallel -- they are |
1290 |
identical because of lifting*) |
|
250 | 1291 |
fun strip_assums2 (Const("==>", _) $ _ $ B1, |
1292 |
Const("==>", _) $ _ $ B2) = strip_assums2 (B1,B2) |
|
0 | 1293 |
| strip_assums2 (Const("all",_)$Abs(a,T,t1), |
250 | 1294 |
Const("all",_)$Abs(_,_,t2)) = |
0 | 1295 |
let val (B1,B2) = strip_assums2 (t1,t2) |
1296 |
in (Abs(a,T,B1), Abs(a,T,B2)) end |
|
1297 |
| strip_assums2 BB = BB; |
|
1298 |
||
1299 |
||
721
479832ff2d29
Pure/thm/norm_term_skip: new, for skipping normalization of the context
lcp
parents:
678
diff
changeset
|
1300 |
(*Faster normalization: skip assumptions that were lifted over*) |
479832ff2d29
Pure/thm/norm_term_skip: new, for skipping normalization of the context
lcp
parents:
678
diff
changeset
|
1301 |
fun norm_term_skip env 0 t = Envir.norm_term env t |
479832ff2d29
Pure/thm/norm_term_skip: new, for skipping normalization of the context
lcp
parents:
678
diff
changeset
|
1302 |
| norm_term_skip env n (Const("all",_)$Abs(a,T,t)) = |
479832ff2d29
Pure/thm/norm_term_skip: new, for skipping normalization of the context
lcp
parents:
678
diff
changeset
|
1303 |
let val Envir.Envir{iTs, ...} = env |
1238 | 1304 |
val T' = typ_subst_TVars iTs T |
1305 |
(*Must instantiate types of parameters because they are flattened; |
|
721
479832ff2d29
Pure/thm/norm_term_skip: new, for skipping normalization of the context
lcp
parents:
678
diff
changeset
|
1306 |
this could be a NEW parameter*) |
479832ff2d29
Pure/thm/norm_term_skip: new, for skipping normalization of the context
lcp
parents:
678
diff
changeset
|
1307 |
in all T' $ Abs(a, T', norm_term_skip env n t) end |
479832ff2d29
Pure/thm/norm_term_skip: new, for skipping normalization of the context
lcp
parents:
678
diff
changeset
|
1308 |
| norm_term_skip env n (Const("==>", _) $ A $ B) = |
1238 | 1309 |
implies $ A $ norm_term_skip env (n-1) B |
721
479832ff2d29
Pure/thm/norm_term_skip: new, for skipping normalization of the context
lcp
parents:
678
diff
changeset
|
1310 |
| norm_term_skip env n t = error"norm_term_skip: too few assumptions??"; |
479832ff2d29
Pure/thm/norm_term_skip: new, for skipping normalization of the context
lcp
parents:
678
diff
changeset
|
1311 |
|
479832ff2d29
Pure/thm/norm_term_skip: new, for skipping normalization of the context
lcp
parents:
678
diff
changeset
|
1312 |
|
0 | 1313 |
(*Composition of object rule r=(A1...Am/B) with proof state s=(B1...Bn/C) |
250 | 1314 |
Unifies B with Bi, replacing subgoal i (1 <= i <= n) |
0 | 1315 |
If match then forbid instantiations in proof state |
1316 |
If lifted then shorten the dpair using strip_assums2. |
|
1317 |
If eres_flg then simultaneously proves A1 by assumption. |
|
250 | 1318 |
nsubgoal is the number of new subgoals (written m above). |
0 | 1319 |
Curried so that resolution calls dest_state only once. |
1320 |
*) |
|
1529 | 1321 |
local open Sequence; exception COMPOSE |
0 | 1322 |
in |
250 | 1323 |
fun bicompose_aux match (state, (stpairs, Bs, Bi, C), lifted) |
0 | 1324 |
(eres_flg, orule, nsubgoal) = |
1529 | 1325 |
let val Thm{der=sder, maxidx=smax, shyps=sshyps, hyps=shyps, ...} = state |
1326 |
and Thm{der=rder, maxidx=rmax, shyps=rshyps, hyps=rhyps, |
|
2386 | 1327 |
prop=rprop,...} = orule |
1529 | 1328 |
(*How many hyps to skip over during normalization*) |
1238 | 1329 |
and nlift = Logic.count_prems(strip_all_body Bi, |
1330 |
if eres_flg then ~1 else 0) |
|
387
69f4356d915d
new datatype theory, supports 'draft theories' and incremental extension:
wenzelm
parents:
309
diff
changeset
|
1331 |
val sign = merge_thm_sgs(state,orule); |
0 | 1332 |
(** Add new theorem with prop = '[| Bs; As |] ==> C' to thq **) |
250 | 1333 |
fun addth As ((env as Envir.Envir {maxidx, ...}, tpairs), thq) = |
1334 |
let val normt = Envir.norm_term env; |
|
1335 |
(*perform minimal copying here by examining env*) |
|
1336 |
val normp = |
|
1337 |
if Envir.is_empty env then (tpairs, Bs @ As, C) |
|
1338 |
else |
|
1339 |
let val ntps = map (pairself normt) tpairs |
|
2147 | 1340 |
in if Envir.above (smax, env) then |
1238 | 1341 |
(*no assignments in state; normalize the rule only*) |
1342 |
if lifted |
|
1343 |
then (ntps, Bs @ map (norm_term_skip env nlift) As, C) |
|
1344 |
else (ntps, Bs @ map normt As, C) |
|
1529 | 1345 |
else if match then raise COMPOSE |
250 | 1346 |
else (*normalize the new rule fully*) |
1347 |
(ntps, map normt (Bs @ As), normt C) |
|
1348 |
end |
|
1258 | 1349 |
val th = (*tuned fix_shyps*) |
1529 | 1350 |
Thm{sign = sign, |
2386 | 1351 |
der = infer_derivs (Bicompose(match, eres_flg, |
1352 |
1 + length Bs, nsubgoal, env), |
|
1353 |
[rder,sder]), |
|
1354 |
maxidx = maxidx, |
|
1355 |
shyps = add_env_sorts (env, union_sort(rshyps,sshyps)), |
|
1356 |
hyps = union_term(rhyps,shyps), |
|
1357 |
prop = Logic.rule_of normp} |
|
1529 | 1358 |
in cons(th, thq) end handle COMPOSE => thq |
0 | 1359 |
val (rtpairs,rhorn) = Logic.strip_flexpairs(rprop); |
1360 |
val (rAs,B) = Logic.strip_prems(nsubgoal, [], rhorn) |
|
1361 |
handle TERM _ => raise THM("bicompose: rule", 0, [orule,state]); |
|
1362 |
(*Modify assumptions, deleting n-th if n>0 for e-resolution*) |
|
1363 |
fun newAs(As0, n, dpairs, tpairs) = |
|
1364 |
let val As1 = if !Logic.auto_rename orelse not lifted then As0 |
|
250 | 1365 |
else map (rename_bvars(dpairs,tpairs,B)) As0 |
0 | 1366 |
in (map (Logic.flatten_params n) As1) |
250 | 1367 |
handle TERM _ => |
1368 |
raise THM("bicompose: 1st premise", 0, [orule]) |
|
0 | 1369 |
end; |
2147 | 1370 |
val env = Envir.empty(Int.max(rmax,smax)); |
0 | 1371 |
val BBi = if lifted then strip_assums2(B,Bi) else (B,Bi); |
1372 |
val dpairs = BBi :: (rtpairs@stpairs); |
|
1373 |
(*elim-resolution: try each assumption in turn. Initially n=1*) |
|
1374 |
fun tryasms (_, _, []) = null |
|
1375 |
| tryasms (As, n, (t,u)::apairs) = |
|
250 | 1376 |
(case pull(Unify.unifiers(sign, env, (t,u)::dpairs)) of |
1377 |
None => tryasms (As, n+1, apairs) |
|
1378 |
| cell as Some((_,tpairs),_) => |
|
1379 |
its_right (addth (newAs(As, n, [BBi,(u,t)], tpairs))) |
|
1380 |
(seqof (fn()=> cell), |
|
1381 |
seqof (fn()=> pull (tryasms (As, n+1, apairs))))); |
|
0 | 1382 |
fun eres [] = raise THM("bicompose: no premises", 0, [orule,state]) |
1383 |
| eres (A1::As) = tryasms (As, 1, Logic.assum_pairs A1); |
|
1384 |
(*ordinary resolution*) |
|
1385 |
fun res(None) = null |
|
250 | 1386 |
| res(cell as Some((_,tpairs),_)) = |
1387 |
its_right (addth(newAs(rev rAs, 0, [BBi], tpairs))) |
|
1388 |
(seqof (fn()=> cell), null) |
|
0 | 1389 |
in if eres_flg then eres(rev rAs) |
1390 |
else res(pull(Unify.unifiers(sign, env, dpairs))) |
|
1391 |
end; |
|
1392 |
end; (*open Sequence*) |
|
1393 |
||
1394 |
||
1395 |
fun bicompose match arg i state = |
|
1396 |
bicompose_aux match (state, dest_state(state,i), false) arg; |
|
1397 |
||
1398 |
(*Quick test whether rule is resolvable with the subgoal with hyps Hs |
|
1399 |
and conclusion B. If eres_flg then checks 1st premise of rule also*) |
|
1400 |
fun could_bires (Hs, B, eres_flg, rule) = |
|
1401 |
let fun could_reshyp (A1::_) = exists (apl(A1,could_unify)) Hs |
|
250 | 1402 |
| could_reshyp [] = false; (*no premise -- illegal*) |
1403 |
in could_unify(concl_of rule, B) andalso |
|
1404 |
(not eres_flg orelse could_reshyp (prems_of rule)) |
|
0 | 1405 |
end; |
1406 |
||
1407 |
(*Bi-resolution of a state with a list of (flag,rule) pairs. |
|
1408 |
Puts the rule above: rule/state. Renames vars in the rules. *) |
|
250 | 1409 |
fun biresolution match brules i state = |
0 | 1410 |
let val lift = lift_rule(state, i); |
250 | 1411 |
val (stpairs, Bs, Bi, C) = dest_state(state,i) |
1412 |
val B = Logic.strip_assums_concl Bi; |
|
1413 |
val Hs = Logic.strip_assums_hyp Bi; |
|
1414 |
val comp = bicompose_aux match (state, (stpairs, Bs, Bi, C), true); |
|
1415 |
fun res [] = Sequence.null |
|
1416 |
| res ((eres_flg, rule)::brules) = |
|
1417 |
if could_bires (Hs, B, eres_flg, rule) |
|
1160 | 1418 |
then Sequence.seqof (*delay processing remainder till needed*) |
250 | 1419 |
(fn()=> Some(comp (eres_flg, lift rule, nprems_of rule), |
1420 |
res brules)) |
|
1421 |
else res brules |
|
0 | 1422 |
in Sequence.flats (res brules) end; |
1423 |
||
1424 |
||
1425 |
||
2509 | 1426 |
(*** Meta Simplification ***) |
0 | 1427 |
|
2509 | 1428 |
(** diagnostics **) |
0 | 1429 |
|
1430 |
exception SIMPLIFIER of string * thm; |
|
1431 |
||
2509 | 1432 |
fun prtm a sign t = (writeln a; writeln (Sign.string_of_term sign t)); |
3529 | 1433 |
fun prtm_warning a sign t = (warning a; warning (Sign.string_of_term sign t)); |
1580
e3fd931e6095
Added some functions which allow redirection of Isabelle's output
berghofe
parents:
1576
diff
changeset
|
1434 |
|
209 | 1435 |
val trace_simp = ref false; |
1436 |
||
3558 | 1437 |
fun trace a = if ! trace_simp then writeln a else (); |
2509 | 1438 |
fun trace_warning a = if ! trace_simp then warning a else (); |
1439 |
fun trace_term a sign t = if ! trace_simp then prtm a sign t else (); |
|
1440 |
fun trace_term_warning a sign t = if ! trace_simp then prtm_warning a sign t else (); |
|
1441 |
fun trace_thm a (Thm {sign, prop, ...}) = trace_term a sign prop; |
|
1442 |
fun trace_thm_warning a (Thm {sign, prop, ...}) = trace_term_warning a sign prop; |
|
209 | 1443 |
|
1444 |
||
1580
e3fd931e6095
Added some functions which allow redirection of Isabelle's output
berghofe
parents:
1576
diff
changeset
|
1445 |
|
2509 | 1446 |
(** meta simp sets **) |
1447 |
||
1448 |
(* basic components *) |
|
1580
e3fd931e6095
Added some functions which allow redirection of Isabelle's output
berghofe
parents:
1576
diff
changeset
|
1449 |
|
2509 | 1450 |
type rrule = {thm: thm, lhs: term, perm: bool}; |
1451 |
type cong = {thm: thm, lhs: term}; |
|
3550 | 1452 |
type simproc = {name: string, proc: Sign.sg -> term -> thm option, lhs: cterm, id: stamp}; |
288
b00ce6a1fe27
Implemented "ordered rewriting": rules which merely permute variables, such
nipkow
parents:
274
diff
changeset
|
1453 |
|
3550 | 1454 |
fun eq_rrule ({thm = Thm {prop = p1, ...}, ...}: rrule, |
2509 | 1455 |
{thm = Thm {prop = p2, ...}, ...}: rrule) = p1 aconv p2; |
1456 |
||
3550 | 1457 |
fun eq_cong ({thm = Thm {prop = p1, ...}, ...}: cong, |
1458 |
{thm = Thm {prop = p2, ...}, ...}: cong) = p1 aconv p2; |
|
1459 |
||
1460 |
fun eq_prem (Thm {prop = p1, ...}, Thm {prop = p2, ...}) = p1 aconv p2; |
|
1461 |
||
1462 |
fun eq_simproc ({id = s1, ...}:simproc, {id = s2, ...}:simproc) = (s1 = s2); |
|
1463 |
||
1464 |
fun mk_simproc (name, proc, lhs, id) = |
|
1465 |
{name = name, proc = proc, lhs = lhs, id = id}; |
|
2509 | 1466 |
|
1467 |
||
1468 |
(* datatype mss *) |
|
288
b00ce6a1fe27
Implemented "ordered rewriting": rules which merely permute variables, such
nipkow
parents:
274
diff
changeset
|
1469 |
|
2509 | 1470 |
(* |
1471 |
A "mss" contains data needed during conversion: |
|
1472 |
rules: discrimination net of rewrite rules; |
|
1473 |
congs: association list of congruence rules; |
|
1474 |
procs: discrimination net of simplification procedures |
|
1475 |
(functions that prove rewrite rules on the fly); |
|
1476 |
bounds: names of bound variables already used |
|
1477 |
(for generating new names when rewriting under lambda abstractions); |
|
1478 |
prems: current premises; |
|
1479 |
mk_rews: turns simplification thms into rewrite rules; |
|
1480 |
termless: relation for ordered rewriting; |
|
1028 | 1481 |
*) |
0 | 1482 |
|
2509 | 1483 |
datatype meta_simpset = |
1484 |
Mss of { |
|
1485 |
rules: rrule Net.net, |
|
1486 |
congs: (string * cong) list, |
|
1487 |
procs: simproc Net.net, |
|
1488 |
bounds: string list, |
|
1489 |
prems: thm list, |
|
1490 |
mk_rews: thm -> thm list, |
|
1491 |
termless: term * term -> bool}; |
|
1492 |
||
1493 |
fun mk_mss (rules, congs, procs, bounds, prems, mk_rews, termless) = |
|
1494 |
Mss {rules = rules, congs = congs, procs = procs, bounds = bounds, |
|
1495 |
prems = prems, mk_rews = mk_rews, termless = termless}; |
|
1496 |
||
1497 |
val empty_mss = |
|
1498 |
mk_mss (Net.empty, [], Net.empty, [], [], K [], Logic.termless); |
|
1499 |
||
1500 |
||
1501 |
||
1502 |
(** simpset operations **) |
|
1503 |
||
3550 | 1504 |
(* dest_mss *) |
1505 |
||
1506 |
fun dest_mss (Mss {rules, congs, procs, ...}) = |
|
1507 |
{simps = map (fn (_, {thm, ...}) => thm) (Net.dest rules), |
|
1508 |
congs = map (fn (_, {thm, ...}) => thm) congs, |
|
1509 |
procs = |
|
1510 |
map (fn (_, {name, lhs, id, ...}) => ((name, lhs), id)) (Net.dest procs) |
|
1511 |
|> partition_eq eq_snd |
|
1512 |
|> map (fn ps => (#1 (#1 (hd ps)), map (#2 o #1) ps))}; |
|
1513 |
||
1514 |
||
1515 |
(* merge_mss *) (*NOTE: ignores mk_rews and termless of 2nd mss*) |
|
1516 |
||
1517 |
fun merge_mss |
|
1518 |
(Mss {rules = rules1, congs = congs1, procs = procs1, bounds = bounds1, |
|
1519 |
prems = prems1, mk_rews, termless}, |
|
1520 |
Mss {rules = rules2, congs = congs2, procs = procs2, bounds = bounds2, |
|
1521 |
prems = prems2, ...}) = |
|
1522 |
mk_mss |
|
1523 |
(Net.merge (rules1, rules2, eq_rrule), |
|
1524 |
generic_merge (eq_cong o pairself snd) I I congs1 congs2, |
|
1525 |
Net.merge (procs1, procs2, eq_simproc), |
|
1526 |
merge_lists bounds1 bounds2, |
|
1527 |
generic_merge eq_prem I I prems1 prems2, |
|
1528 |
mk_rews, termless); |
|
1529 |
||
1530 |
||
2509 | 1531 |
(* mk_rrule *) |
1532 |
||
1533 |
fun vperm (Var _, Var _) = true |
|
1534 |
| vperm (Abs (_, _, s), Abs (_, _, t)) = vperm (s, t) |
|
1535 |
| vperm (t1 $ t2, u1 $ u2) = vperm (t1, u1) andalso vperm (t2, u2) |
|
1536 |
| vperm (t, u) = (t = u); |
|
1537 |
||
1538 |
fun var_perm (t, u) = |
|
1539 |
vperm (t, u) andalso eq_set_term (term_vars t, term_vars u); |
|
1540 |
||
1541 |
(*simple test for looping rewrite*) |
|
1542 |
fun loops sign prems (lhs, rhs) = |
|
2792 | 1543 |
is_Var (head_of lhs) |
2509 | 1544 |
orelse |
1545 |
(exists (apl (lhs, Logic.occs)) (rhs :: prems)) |
|
1546 |
orelse |
|
1547 |
(null prems andalso |
|
1548 |
Pattern.matches (#tsig (Sign.rep_sg sign)) (lhs, rhs)); |
|
1549 |
(*the condition "null prems" in the last case is necessary because |
|
1550 |
conditional rewrites with extra variables in the conditions may terminate |
|
1551 |
although the rhs is an instance of the lhs. Example: |
|
1552 |
?m < ?n ==> f(?n) == f(?m)*) |
|
1553 |
||
1554 |
fun mk_rrule (thm as Thm {sign, prop, ...}) = |
|
1238 | 1555 |
let |
2509 | 1556 |
val prems = Logic.strip_imp_prems prop; |
1557 |
val concl = Logic.strip_imp_concl prop; |
|
1558 |
val (lhs, _) = Logic.dest_equals concl handle TERM _ => |
|
1559 |
raise SIMPLIFIER ("Rewrite rule not a meta-equality", thm); |
|
1560 |
val econcl = Pattern.eta_contract concl; |
|
1561 |
val (elhs, erhs) = Logic.dest_equals econcl; |
|
1562 |
val perm = var_perm (elhs, erhs) andalso not (elhs aconv erhs) |
|
1563 |
andalso not (is_Var elhs); |
|
1564 |
in |
|
1565 |
if not ((term_vars erhs) subset |
|
2671 | 1566 |
(union_term (term_vars elhs, List.concat(map term_vars prems)))) then |
2509 | 1567 |
(prtm_warning "extra Var(s) on rhs" sign prop; None) |
1568 |
else if not perm andalso loops sign prems (elhs, erhs) then |
|
1569 |
(prtm_warning "ignoring looping rewrite rule" sign prop; None) |
|
1570 |
else Some {thm = thm, lhs = lhs, perm = perm} |
|
0 | 1571 |
end; |
1572 |
||
2509 | 1573 |
|
1574 |
(* add_simps *) |
|
87 | 1575 |
|
2509 | 1576 |
fun add_simp |
1577 |
(mss as Mss {rules, congs, procs, bounds, prems, mk_rews, termless}, |
|
1578 |
thm as Thm {sign, prop, ...}) = |
|
1579 |
(case mk_rrule thm of |
|
87 | 1580 |
None => mss |
2509 | 1581 |
| Some (rrule as {lhs, ...}) => |
209 | 1582 |
(trace_thm "Adding rewrite rule:" thm; |
2509 | 1583 |
mk_mss (Net.insert_term ((lhs, rrule), rules, eq_rrule) handle Net.INSERT => |
1584 |
(prtm_warning "ignoring duplicate rewrite rule" sign prop; rules), |
|
1585 |
congs, procs, bounds, prems, mk_rews, termless))); |
|
0 | 1586 |
|
1587 |
val add_simps = foldl add_simp; |
|
2509 | 1588 |
|
1589 |
fun mss_of thms = add_simps (empty_mss, thms); |
|
1590 |
||
1591 |
||
1592 |
(* del_simps *) |
|
1593 |
||
1594 |
fun del_simp |
|
1595 |
(mss as Mss {rules, congs, procs, bounds, prems, mk_rews, termless}, |
|
1596 |
thm as Thm {sign, prop, ...}) = |
|
1597 |
(case mk_rrule thm of |
|
1598 |
None => mss |
|
1599 |
| Some (rrule as {lhs, ...}) => |
|
1600 |
mk_mss (Net.delete_term ((lhs, rrule), rules, eq_rrule) handle Net.DELETE => |
|
1601 |
(prtm_warning "rewrite rule not in simpset" sign prop; rules), |
|
1602 |
congs, procs, bounds, prems, mk_rews, termless)); |
|
1603 |
||
87 | 1604 |
val del_simps = foldl del_simp; |
0 | 1605 |
|
2509 | 1606 |
|
2626 | 1607 |
(* add_congs *) |
0 | 1608 |
|
2509 | 1609 |
fun add_cong (Mss {rules, congs, procs, bounds, prems, mk_rews, termless}, thm) = |
1610 |
let |
|
1611 |
val (lhs, _) = Logic.dest_equals (concl_of thm) handle TERM _ => |
|
1612 |
raise SIMPLIFIER ("Congruence not a meta-equality", thm); |
|
1613 |
(* val lhs = Pattern.eta_contract lhs; *) |
|
1614 |
val (a, _) = dest_Const (head_of lhs) handle TERM _ => |
|
1615 |
raise SIMPLIFIER ("Congruence must start with a constant", thm); |
|
1616 |
in |
|
1617 |
mk_mss (rules, (a, {lhs = lhs, thm = thm}) :: congs, procs, bounds, |
|
1618 |
prems, mk_rews, termless) |
|
0 | 1619 |
end; |
1620 |
||
1621 |
val (op add_congs) = foldl add_cong; |
|
1622 |
||
2509 | 1623 |
|
2626 | 1624 |
(* del_congs *) |
1625 |
||
1626 |
fun del_cong (Mss {rules, congs, procs, bounds, prems, mk_rews, termless}, thm) = |
|
1627 |
let |
|
1628 |
val (lhs, _) = Logic.dest_equals (concl_of thm) handle TERM _ => |
|
1629 |
raise SIMPLIFIER ("Congruence not a meta-equality", thm); |
|
1630 |
(* val lhs = Pattern.eta_contract lhs; *) |
|
1631 |
val (a, _) = dest_Const (head_of lhs) handle TERM _ => |
|
1632 |
raise SIMPLIFIER ("Congruence must start with a constant", thm); |
|
1633 |
in |
|
1634 |
mk_mss (rules, filter (fn (x,_)=> x<>a) congs, procs, bounds, |
|
1635 |
prems, mk_rews, termless) |
|
1636 |
end; |
|
1637 |
||
1638 |
val (op del_congs) = foldl del_cong; |
|
1639 |
||
1640 |
||
2509 | 1641 |
(* add_simprocs *) |
1642 |
||
3550 | 1643 |
fun add_proc (mss as Mss {rules, congs, procs, bounds, prems, mk_rews, termless}, |
1644 |
(name, lhs as Cterm {sign, t, ...}, proc, id)) = |
|
1645 |
(trace_term ("Adding simplification procedure " ^ name ^ " for:") sign t; |
|
2509 | 1646 |
mk_mss (rules, congs, |
3550 | 1647 |
Net.insert_term ((t, mk_simproc (name, proc, lhs, id)), procs, eq_simproc) |
1648 |
handle Net.INSERT => (trace_warning "ignored duplicate"; procs), |
|
2509 | 1649 |
bounds, prems, mk_rews, termless)); |
0 | 1650 |
|
3550 | 1651 |
fun add_simproc (mss, (name, lhss, proc, id)) = |
1652 |
foldl add_proc (mss, map (fn lhs => (name, lhs, proc, id)) lhss); |
|
1653 |
||
2509 | 1654 |
val add_simprocs = foldl add_simproc; |
1655 |
||
1656 |
||
1657 |
(* del_simprocs *) |
|
0 | 1658 |
|
3550 | 1659 |
fun del_proc (mss as Mss {rules, congs, procs, bounds, prems, mk_rews, termless}, |
1660 |
(name, lhs as Cterm {t, ...}, proc, id)) = |
|
2509 | 1661 |
mk_mss (rules, congs, |
3550 | 1662 |
Net.delete_term ((t, mk_simproc (name, proc, lhs, id)), procs, eq_simproc) |
1663 |
handle Net.DELETE => (trace_warning "simplification procedure not in simpset"; procs), |
|
1664 |
bounds, prems, mk_rews, termless); |
|
1665 |
||
1666 |
fun del_simproc (mss, (name, lhss, proc, id)) = |
|
1667 |
foldl del_proc (mss, map (fn lhs => (name, lhs, proc, id)) lhss); |
|
2509 | 1668 |
|
1669 |
val del_simprocs = foldl del_simproc; |
|
0 | 1670 |
|
1671 |
||
2509 | 1672 |
(* prems *) |
1673 |
||
1674 |
fun add_prems (Mss {rules, congs, procs, bounds, prems, mk_rews, termless}, thms) = |
|
1675 |
mk_mss (rules, congs, procs, bounds, thms @ prems, mk_rews, termless); |
|
1676 |
||
1677 |
fun prems_of_mss (Mss {prems, ...}) = prems; |
|
1678 |
||
1679 |
||
1680 |
(* mk_rews *) |
|
1681 |
||
1682 |
fun set_mk_rews |
|
1683 |
(Mss {rules, congs, procs, bounds, prems, mk_rews = _, termless}, mk_rews) = |
|
1684 |
mk_mss (rules, congs, procs, bounds, prems, mk_rews, termless); |
|
1685 |
||
1686 |
fun mk_rews_of_mss (Mss {mk_rews, ...}) = mk_rews; |
|
1687 |
||
1688 |
||
1689 |
(* termless *) |
|
1690 |
||
1691 |
fun set_termless |
|
1692 |
(Mss {rules, congs, procs, bounds, prems, mk_rews, termless = _}, termless) = |
|
1693 |
mk_mss (rules, congs, procs, bounds, prems, mk_rews, termless); |
|
1694 |
||
1695 |
||
1696 |
||
1697 |
(** rewriting **) |
|
1698 |
||
1699 |
(* |
|
1700 |
Uses conversions, omitting proofs for efficiency. See: |
|
1701 |
L C Paulson, A higher-order implementation of rewriting, |
|
1702 |
Science of Computer Programming 3 (1983), pages 119-149. |
|
1703 |
*) |
|
0 | 1704 |
|
1705 |
type prover = meta_simpset -> thm -> thm option; |
|
1706 |
type termrec = (Sign.sg * term list) * term; |
|
1707 |
type conv = meta_simpset -> termrec -> termrec; |
|
1708 |
||
1529 | 1709 |
fun check_conv (thm as Thm{shyps,hyps,prop,sign,der,maxidx,...}, prop0, ders) = |
432 | 1710 |
let fun err() = (trace_thm "Proved wrong thm (Check subgoaler?)" thm; |
1711 |
trace_term "Should have proved" sign prop0; |
|
1712 |
None) |
|
0 | 1713 |
val (lhs0,_) = Logic.dest_equals(Logic.strip_imp_concl prop0) |
1714 |
in case prop of |
|
1715 |
Const("==",_) $ lhs $ rhs => |
|
1716 |
if (lhs = lhs0) orelse |
|
427
4ce2ce940faf
ordered rewriting applies to conditional rules as well now
nipkow
parents:
421
diff
changeset
|
1717 |
(lhs aconv Envir.norm_term (Envir.empty 0) lhs0) |
1529 | 1718 |
then (trace_thm "SUCCEEDED" thm; |
2386 | 1719 |
Some(shyps, hyps, maxidx, rhs, der::ders)) |
0 | 1720 |
else err() |
1721 |
| _ => err() |
|
1722 |
end; |
|
1723 |
||
659
95ed2ccb4438
Prepared the code for preservation of bound var names during rewriting. Still
nipkow
parents:
623
diff
changeset
|
1724 |
fun ren_inst(insts,prop,pat,obj) = |
95ed2ccb4438
Prepared the code for preservation of bound var names during rewriting. Still
nipkow
parents:
623
diff
changeset
|
1725 |
let val ren = match_bvs(pat,obj,[]) |
95ed2ccb4438
Prepared the code for preservation of bound var names during rewriting. Still
nipkow
parents:
623
diff
changeset
|
1726 |
fun renAbs(Abs(x,T,b)) = |
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1569
diff
changeset
|
1727 |
Abs(case assoc_string(ren,x) of None => x | Some(y) => y, T, renAbs(b)) |
659
95ed2ccb4438
Prepared the code for preservation of bound var names during rewriting. Still
nipkow
parents:
623
diff
changeset
|
1728 |
| renAbs(f$t) = renAbs(f) $ renAbs(t) |
95ed2ccb4438
Prepared the code for preservation of bound var names during rewriting. Still
nipkow
parents:
623
diff
changeset
|
1729 |
| renAbs(t) = t |
95ed2ccb4438
Prepared the code for preservation of bound var names during rewriting. Still
nipkow
parents:
623
diff
changeset
|
1730 |
in subst_vars insts (if null(ren) then prop else renAbs(prop)) end; |
678
6151b7f3b606
Modified pattern.ML to perform proper matching of Higher-Order Patterns.
nipkow
parents:
659
diff
changeset
|
1731 |
|
1258 | 1732 |
fun add_insts_sorts ((iTs, is), Ss) = |
1733 |
add_typs_sorts (map snd iTs, add_terms_sorts (map snd is, Ss)); |
|
1734 |
||
659
95ed2ccb4438
Prepared the code for preservation of bound var names during rewriting. Still
nipkow
parents:
623
diff
changeset
|
1735 |
|
2509 | 1736 |
(* mk_procrule *) |
1737 |
||
1738 |
fun mk_procrule (thm as Thm {sign, prop, ...}) = |
|
1739 |
let |
|
1740 |
val prems = Logic.strip_imp_prems prop; |
|
1741 |
val concl = Logic.strip_imp_concl prop; |
|
1742 |
val (lhs, _) = Logic.dest_equals concl handle TERM _ => |
|
1743 |
raise SIMPLIFIER ("Rewrite rule not a meta-equality", thm); |
|
1744 |
val econcl = Pattern.eta_contract concl; |
|
1745 |
val (elhs, erhs) = Logic.dest_equals econcl; |
|
1746 |
in |
|
1747 |
if not ((term_vars erhs) subset |
|
2671 | 1748 |
(union_term (term_vars elhs, List.concat(map term_vars prems)))) |
1749 |
then (prtm_warning "extra Var(s) on rhs" sign prop; []) |
|
2509 | 1750 |
else [{thm = thm, lhs = lhs, perm = false}] |
1751 |
end; |
|
1752 |
||
1753 |
||
1754 |
(* conversion to apply the meta simpset to a term *) |
|
1755 |
||
1756 |
(* |
|
1757 |
we try in order: |
|
1758 |
(1) beta reduction |
|
1759 |
(2) unconditional rewrite rules |
|
1760 |
(3) conditional rewrite rules |
|
3550 | 1761 |
(4) simplification procedures |
2509 | 1762 |
*) |
1763 |
||
1764 |
fun rewritec (prover,signt) (mss as Mss{rules, procs, mk_rews, termless, ...}) |
|
2147 | 1765 |
(shypst,hypst,maxt,t,ders) = |
3550 | 1766 |
let |
1767 |
val tsigt = #tsig(Sign.rep_sg signt); |
|
1768 |
fun rew {thm as Thm{sign,der,maxidx,shyps,hyps,prop,...}, lhs, perm} = |
|
250 | 1769 |
let val unit = if Sign.subsig(sign,signt) then () |
1580
e3fd931e6095
Added some functions which allow redirection of Isabelle's output
berghofe
parents:
1576
diff
changeset
|
1770 |
else (trace_thm_warning "rewrite rule from different theory" |
446
3ee5c9314efe
rewritec now uses trace_thm for it's "rewrite rule from different theory"
clasohm
parents:
432
diff
changeset
|
1771 |
thm; |
208
342f88d2e8ab
optimized simplifier - signature of rewritten term stays constant
nipkow
parents:
200
diff
changeset
|
1772 |
raise Pattern.MATCH) |
2147 | 1773 |
val rprop = if maxt = ~1 then prop |
1774 |
else Logic.incr_indexes([],maxt+1) prop; |
|
1775 |
val rlhs = if maxt = ~1 then lhs |
|
1065
8425cb5acb77
Fixed old bug in the simplifier. Term to be simplified now carries around its
nipkow
parents:
1028
diff
changeset
|
1776 |
else fst(Logic.dest_equals(Logic.strip_imp_concl rprop)) |
3550 | 1777 |
val insts = Pattern.match tsigt (rlhs,t); |
1065
8425cb5acb77
Fixed old bug in the simplifier. Term to be simplified now carries around its
nipkow
parents:
1028
diff
changeset
|
1778 |
val prop' = ren_inst(insts,rprop,rlhs,t); |
2177
8b365a3a6ed1
Changed some mem, ins and union calls to be monomorphic
paulson
parents:
2163
diff
changeset
|
1779 |
val hyps' = union_term(hyps,hypst); |
8b365a3a6ed1
Changed some mem, ins and union calls to be monomorphic
paulson
parents:
2163
diff
changeset
|
1780 |
val shyps' = add_insts_sorts (insts, union_sort(shyps,shypst)); |
1065
8425cb5acb77
Fixed old bug in the simplifier. Term to be simplified now carries around its
nipkow
parents:
1028
diff
changeset
|
1781 |
val maxidx' = maxidx_of_term prop' |
2386 | 1782 |
val ct' = Cterm{sign = signt, (*used for deriv only*) |
1783 |
t = prop', |
|
1784 |
T = propT, |
|
1785 |
maxidx = maxidx'} |
|
3550 | 1786 |
val der' = infer_derivs (RewriteC ct', [der]); |
1529 | 1787 |
val thm' = Thm{sign = signt, |
2386 | 1788 |
der = der', |
1789 |
shyps = shyps', |
|
1790 |
hyps = hyps', |
|
1529 | 1791 |
prop = prop', |
2386 | 1792 |
maxidx = maxidx'} |
427
4ce2ce940faf
ordered rewriting applies to conditional rules as well now
nipkow
parents:
421
diff
changeset
|
1793 |
val (lhs',rhs') = Logic.dest_equals(Logic.strip_imp_concl prop') |
4ce2ce940faf
ordered rewriting applies to conditional rules as well now
nipkow
parents:
421
diff
changeset
|
1794 |
in if perm andalso not(termless(rhs',lhs')) then None else |
4ce2ce940faf
ordered rewriting applies to conditional rules as well now
nipkow
parents:
421
diff
changeset
|
1795 |
if Logic.count_prems(prop',0) = 0 |
1529 | 1796 |
then (trace_thm "Rewriting:" thm'; |
2386 | 1797 |
Some(shyps', hyps', maxidx', rhs', der'::ders)) |
0 | 1798 |
else (trace_thm "Trying to rewrite:" thm'; |
1799 |
case prover mss thm' of |
|
1800 |
None => (trace_thm "FAILED" thm'; None) |
|
1529 | 1801 |
| Some(thm2) => check_conv(thm2,prop',ders)) |
0 | 1802 |
end |
1803 |
||
225
76f60e6400e8
optimized net for matching of abstractions to speed up simplifier
nipkow
parents:
222
diff
changeset
|
1804 |
fun rews [] = None |
2509 | 1805 |
| rews (rrule :: rrules) = |
225
76f60e6400e8
optimized net for matching of abstractions to speed up simplifier
nipkow
parents:
222
diff
changeset
|
1806 |
let val opt = rew rrule handle Pattern.MATCH => None |
76f60e6400e8
optimized net for matching of abstractions to speed up simplifier
nipkow
parents:
222
diff
changeset
|
1807 |
in case opt of None => rews rrules | some => some end; |
3550 | 1808 |
|
1659 | 1809 |
fun sort_rrules rrs = let |
2386 | 1810 |
fun is_simple {thm as Thm{prop,...}, lhs, perm} = case prop of |
1811 |
Const("==",_) $ _ $ _ => true |
|
1812 |
| _ => false |
|
1813 |
fun sort [] (re1,re2) = re1 @ re2 |
|
1814 |
| sort (rr::rrs) (re1,re2) = if is_simple rr |
|
1815 |
then sort rrs (rr::re1,re2) |
|
1816 |
else sort rrs (re1,rr::re2) |
|
1659 | 1817 |
in sort rrs ([],[]) |
1818 |
end |
|
2509 | 1819 |
|
3550 | 1820 |
fun proc_rews _ ([]:simproc list) = None |
1821 |
| proc_rews eta_t ({name, proc, lhs = Cterm {t = plhs, ...}, ...} :: ps) = |
|
1822 |
if Pattern.matches tsigt (plhs, t) then |
|
3558 | 1823 |
(trace_term ("Trying procedure " ^ name ^ " on:") signt eta_t; |
1824 |
case proc signt eta_t of |
|
1825 |
None => (trace "FAILED"; proc_rews eta_t ps) |
|
3550 | 1826 |
| Some raw_thm => |
3558 | 1827 |
(trace_thm ("Procedure " ^ name ^ " proved rewrite rule:") raw_thm; |
3550 | 1828 |
(case rews (mk_procrule raw_thm) of |
3558 | 1829 |
None => (trace "IGNORED"; proc_rews eta_t ps) |
3550 | 1830 |
| some => some))) |
1831 |
else proc_rews eta_t ps; |
|
2509 | 1832 |
in |
2792 | 1833 |
(case t of |
3550 | 1834 |
Abs (_, _, body) $ u => |
2509 | 1835 |
Some (shypst, hypst, maxt, subst_bound (u, body), ders) |
1836 |
| _ => |
|
2792 | 1837 |
(case rews (sort_rrules (Net.match_term rules t)) of |
3012 | 1838 |
None => proc_rews (Pattern.eta_contract t) (Net.match_term procs t) |
2509 | 1839 |
| some => some)) |
0 | 1840 |
end; |
1841 |
||
2509 | 1842 |
|
1843 |
(* conversion to apply a congruence rule to a term *) |
|
1844 |
||
2147 | 1845 |
fun congc (prover,signt) {thm=cong,lhs=lhs} (shypst,hypst,maxt,t,ders) = |
1529 | 1846 |
let val Thm{sign,der,shyps,hyps,maxidx,prop,...} = cong |
208
342f88d2e8ab
optimized simplifier - signature of rewritten term stays constant
nipkow
parents:
200
diff
changeset
|
1847 |
val unit = if Sign.subsig(sign,signt) then () |
342f88d2e8ab
optimized simplifier - signature of rewritten term stays constant
nipkow
parents:
200
diff
changeset
|
1848 |
else error("Congruence rule from different theory") |
342f88d2e8ab
optimized simplifier - signature of rewritten term stays constant
nipkow
parents:
200
diff
changeset
|
1849 |
val tsig = #tsig(Sign.rep_sg signt) |
2147 | 1850 |
val rprop = if maxt = ~1 then prop |
1851 |
else Logic.incr_indexes([],maxt+1) prop; |
|
1852 |
val rlhs = if maxt = ~1 then lhs |
|
1065
8425cb5acb77
Fixed old bug in the simplifier. Term to be simplified now carries around its
nipkow
parents:
1028
diff
changeset
|
1853 |
else fst(Logic.dest_equals(Logic.strip_imp_concl rprop)) |
1569
a89f246dee0e
Non-matching congruence rule in rewriter is simply ignored.
nipkow
parents:
1566
diff
changeset
|
1854 |
val insts = Pattern.match tsig (rlhs,t) |
a89f246dee0e
Non-matching congruence rule in rewriter is simply ignored.
nipkow
parents:
1566
diff
changeset
|
1855 |
(* Pattern.match can raise Pattern.MATCH; |
a89f246dee0e
Non-matching congruence rule in rewriter is simply ignored.
nipkow
parents:
1566
diff
changeset
|
1856 |
is handled when congc is called *) |
1065
8425cb5acb77
Fixed old bug in the simplifier. Term to be simplified now carries around its
nipkow
parents:
1028
diff
changeset
|
1857 |
val prop' = ren_inst(insts,rprop,rlhs,t); |
2177
8b365a3a6ed1
Changed some mem, ins and union calls to be monomorphic
paulson
parents:
2163
diff
changeset
|
1858 |
val shyps' = add_insts_sorts (insts, union_sort(shyps,shypst)) |
1529 | 1859 |
val maxidx' = maxidx_of_term prop' |
2386 | 1860 |
val ct' = Cterm{sign = signt, (*used for deriv only*) |
1861 |
t = prop', |
|
1862 |
T = propT, |
|
1863 |
maxidx = maxidx'} |
|
1529 | 1864 |
val thm' = Thm{sign = signt, |
3550 | 1865 |
der = infer_derivs (CongC ct', [der]), |
2386 | 1866 |
shyps = shyps', |
1867 |
hyps = union_term(hyps,hypst), |
|
1529 | 1868 |
prop = prop', |
2386 | 1869 |
maxidx = maxidx'}; |
0 | 1870 |
val unit = trace_thm "Applying congruence rule" thm'; |
112
009ae5c85ae9
Changed the simplifier: if the subgoaler proves an unexpected thm, chances
nipkow
parents:
87
diff
changeset
|
1871 |
fun err() = error("Failed congruence proof!") |
0 | 1872 |
|
1873 |
in case prover thm' of |
|
112
009ae5c85ae9
Changed the simplifier: if the subgoaler proves an unexpected thm, chances
nipkow
parents:
87
diff
changeset
|
1874 |
None => err() |
1529 | 1875 |
| Some(thm2) => (case check_conv(thm2,prop',ders) of |
405
c97514f63633
Internale optimization of the simplifier: in case a subterm stays unchanged,
nipkow
parents:
399
diff
changeset
|
1876 |
None => err() | some => some) |
0 | 1877 |
end; |
1878 |
||
1879 |
||
405
c97514f63633
Internale optimization of the simplifier: in case a subterm stays unchanged,
nipkow
parents:
399
diff
changeset
|
1880 |
|
214
ed6a3e2b1a33
added new parameter to the simplification tactics which indicates if
nipkow
parents:
209
diff
changeset
|
1881 |
fun bottomc ((simprem,useprem),prover,sign) = |
1529 | 1882 |
let fun botc fail mss trec = |
2386 | 1883 |
(case subc mss trec of |
1884 |
some as Some(trec1) => |
|
1885 |
(case rewritec (prover,sign) mss trec1 of |
|
1886 |
Some(trec2) => botc false mss trec2 |
|
1887 |
| None => some) |
|
1888 |
| None => |
|
1889 |
(case rewritec (prover,sign) mss trec of |
|
1890 |
Some(trec2) => botc false mss trec2 |
|
1891 |
| None => if fail then None else Some(trec))) |
|
0 | 1892 |
|
1529 | 1893 |
and try_botc mss trec = (case botc true mss trec of |
2386 | 1894 |
Some(trec1) => trec1 |
1895 |
| None => trec) |
|
405
c97514f63633
Internale optimization of the simplifier: in case a subterm stays unchanged,
nipkow
parents:
399
diff
changeset
|
1896 |
|
2509 | 1897 |
and subc (mss as Mss{rules,congs,procs,bounds,prems,mk_rews,termless}) |
2386 | 1898 |
(trec as (shyps,hyps,maxidx,t0,ders)) = |
1529 | 1899 |
(case t0 of |
2386 | 1900 |
Abs(a,T,t) => |
1901 |
let val b = variant bounds a |
|
1902 |
val v = Free("." ^ b,T) |
|
2509 | 1903 |
val mss' = mk_mss (rules, congs, procs, b :: bounds, prems, mk_rews, termless) |
2386 | 1904 |
in case botc true mss' |
1905 |
(shyps,hyps,maxidx,subst_bound (v,t),ders) of |
|
1906 |
Some(shyps',hyps',maxidx',t',ders') => |
|
1907 |
Some(shyps', hyps', maxidx', |
|
1908 |
Abs(a, T, abstract_over(v,t')), |
|
1909 |
ders') |
|
1910 |
| None => None |
|
1911 |
end |
|
1912 |
| t$u => (case t of |
|
1913 |
Const("==>",_)$s => Some(impc(shyps,hyps,maxidx,s,u,mss,ders)) |
|
1914 |
| Abs(_,_,body) => |
|
1915 |
let val trec = (shyps,hyps,maxidx,subst_bound (u,body),ders) |
|
1916 |
in case subc mss trec of |
|
1917 |
None => Some(trec) |
|
1918 |
| trec => trec |
|
1919 |
end |
|
1920 |
| _ => |
|
1921 |
let fun appc() = |
|
1922 |
(case botc true mss (shyps,hyps,maxidx,t,ders) of |
|
1923 |
Some(shyps1,hyps1,maxidx1,t1,ders1) => |
|
1924 |
(case botc true mss (shyps1,hyps1,maxidx,u,ders1) of |
|
1925 |
Some(shyps2,hyps2,maxidx2,u1,ders2) => |
|
1926 |
Some(shyps2, hyps2, Int.max(maxidx1,maxidx2), |
|
1927 |
t1$u1, ders2) |
|
1928 |
| None => |
|
1929 |
Some(shyps1, hyps1, Int.max(maxidx1,maxidx), t1$u, |
|
1930 |
ders1)) |
|
1931 |
| None => |
|
1932 |
(case botc true mss (shyps,hyps,maxidx,u,ders) of |
|
1933 |
Some(shyps1,hyps1,maxidx1,u1,ders1) => |
|
1934 |
Some(shyps1, hyps1, Int.max(maxidx,maxidx1), |
|
1935 |
t$u1, ders1) |
|
1936 |
| None => None)) |
|
1937 |
val (h,ts) = strip_comb t |
|
1938 |
in case h of |
|
1939 |
Const(a,_) => |
|
1940 |
(case assoc_string(congs,a) of |
|
1941 |
None => appc() |
|
1942 |
| Some(cong) => (congc (prover mss,sign) cong trec |
|
1569
a89f246dee0e
Non-matching congruence rule in rewriter is simply ignored.
nipkow
parents:
1566
diff
changeset
|
1943 |
handle Pattern.MATCH => appc() ) ) |
2386 | 1944 |
| _ => appc() |
1945 |
end) |
|
1946 |
| _ => None) |
|
0 | 1947 |
|
1529 | 1948 |
and impc(shyps, hyps, maxidx, s, u, mss as Mss{mk_rews,...}, ders) = |
1949 |
let val (shyps1,hyps1,_,s1,ders1) = |
|
2386 | 1950 |
if simprem then try_botc mss (shyps,hyps,maxidx,s,ders) |
1951 |
else (shyps,hyps,0,s,ders); |
|
1952 |
val maxidx1 = maxidx_of_term s1 |
|
1953 |
val mss1 = |
|
2535
907a3379f165
Added warning msg when the simplifier cannot use a premise as a rewrite rule
nipkow
parents:
2509
diff
changeset
|
1954 |
if not useprem then mss else |
2620
54f21bf9522a
Made troublesome simplifier warning dependent on trace_simp.
nipkow
parents:
2535
diff
changeset
|
1955 |
if maxidx1 <> ~1 then (trace_term_warning |
2535
907a3379f165
Added warning msg when the simplifier cannot use a premise as a rewrite rule
nipkow
parents:
2509
diff
changeset
|
1956 |
"Cannot add premise as rewrite rule because it contains (type) unknowns:" |
907a3379f165
Added warning msg when the simplifier cannot use a premise as a rewrite rule
nipkow
parents:
2509
diff
changeset
|
1957 |
sign s1; mss) |
2386 | 1958 |
else let val thm = assume (Cterm{sign=sign, t=s1, |
1959 |
T=propT, maxidx=maxidx1}) |
|
1960 |
in add_simps(add_prems(mss,[thm]), mk_rews thm) end |
|
1961 |
val (shyps2,hyps2,maxidx2,u1,ders2) = |
|
1962 |
try_botc mss1 (shyps1,hyps1,maxidx,u,ders1) |
|
1963 |
val hyps3 = if gen_mem (op aconv) (s1, hyps1) |
|
1964 |
then hyps2 else hyps2\s1 |
|
2147 | 1965 |
in (shyps2, hyps3, Int.max(maxidx1,maxidx2), |
2386 | 1966 |
Logic.mk_implies(s1,u1), ders2) |
1529 | 1967 |
end |
0 | 1968 |
|
1529 | 1969 |
in try_botc end; |
0 | 1970 |
|
1971 |
||
1972 |
(*** Meta-rewriting: rewrites t to u and returns the theorem t==u ***) |
|
2509 | 1973 |
|
1974 |
(* |
|
1975 |
Parameters: |
|
1976 |
mode = (simplify A, use A in simplifying B) when simplifying A ==> B |
|
1977 |
mss: contains equality theorems of the form [|p1,...|] ==> t==u |
|
1978 |
prover: how to solve premises in conditional rewrites and congruences |
|
0 | 1979 |
*) |
2509 | 1980 |
|
1981 |
(* FIXME: check that #bounds(mss) does not "occur" in ct alread *) |
|
1982 |
||
214
ed6a3e2b1a33
added new parameter to the simplification tactics which indicates if
nipkow
parents:
209
diff
changeset
|
1983 |
fun rewrite_cterm mode mss prover ct = |
229
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
225
diff
changeset
|
1984 |
let val {sign, t, T, maxidx} = rep_cterm ct; |
2147 | 1985 |
val (shyps,hyps,maxu,u,ders) = |
1529 | 1986 |
bottomc (mode,prover,sign) mss |
2386 | 1987 |
(add_term_sorts(t,[]), [], maxidx, t, []); |
0 | 1988 |
val prop = Logic.mk_equals(t,u) |
1258 | 1989 |
in |
1529 | 1990 |
Thm{sign = sign, |
2386 | 1991 |
der = infer_derivs (Rewrite_cterm ct, ders), |
1992 |
maxidx = Int.max (maxidx,maxu), |
|
1993 |
shyps = shyps, |
|
1994 |
hyps = hyps, |
|
1529 | 1995 |
prop = prop} |
0 | 1996 |
end |
1997 |
||
1539 | 1998 |
|
2509 | 1999 |
|
2000 |
(*** Oracles ***) |
|
2001 |
||
1539 | 2002 |
fun invoke_oracle (thy, sign, exn) = |
2003 |
case #oraopt(rep_theory thy) of |
|
2386 | 2004 |
None => raise THM ("No oracle in supplied theory", 0, []) |
1539 | 2005 |
| Some oracle => |
2386 | 2006 |
let val sign' = Sign.merge(sign_of thy, sign) |
2007 |
val (prop, T, maxidx) = |
|
2008 |
Sign.certify_term sign' (oracle (sign', exn)) |
|
1539 | 2009 |
in if T<>propT then |
2010 |
raise THM("Oracle's result must have type prop", 0, []) |
|
2386 | 2011 |
else fix_shyps [] [] |
2012 |
(Thm {sign = sign', |
|
2013 |
der = Join (Oracle(thy,sign,exn), []), |
|
2014 |
maxidx = maxidx, |
|
2015 |
shyps = [], |
|
2016 |
hyps = [], |
|
2017 |
prop = prop}) |
|
1539 | 2018 |
end; |
2019 |
||
0 | 2020 |
end; |
1503 | 2021 |
|
2022 |
open Thm; |