(* Title: Pure/logic.ML
ID: $Id$
Author: Lawrence C Paulson, Cambridge University Computer Laboratory
Copyright Cambridge University 1992
Supporting code for defining the abstract type "thm"
*)
infix occs;
signature LOGIC =
sig
val assum_pairs: term -> (term*term)list
val auto_rename: bool ref
val close_form: term -> term
val count_prems: term * int -> int
val dest_equals: term -> term * term
val dest_flexpair: term -> term * term
val dest_implies: term -> term * term
val dest_inclass: term -> typ * class
val dest_type: term -> typ
val flatten_params: int -> term -> term
val freeze_vars: term -> term
val incr_indexes: typ list * int -> term -> term
val lift_fns: term * int -> (term -> term) * (term -> term)
val list_flexpairs: (term*term)list * term -> term
val list_implies: term list * term -> term
val list_rename_params: string list * term -> term
val mk_equals: term * term -> term
val mk_flexpair: term * term -> term
val mk_implies: term * term -> term
val mk_inclass: typ * class -> term
val mk_type: typ -> term
val occs: term * term -> bool
val rule_of: (term*term)list * term list * term -> term
val set_rename_prefix: string -> unit
val skip_flexpairs: term -> term
val strip_assums_concl: term -> term
val strip_assums_hyp: term -> term list
val strip_flexpairs: term -> (term*term)list * term
val strip_horn: term -> (term*term)list * term list * term
val strip_imp_concl: term -> term
val strip_imp_prems: term -> term list
val strip_params: term -> (string * typ) list
val strip_prems: int * term list * term -> term list * term
val thaw_vars: term -> term
val varify: term -> term
end;
functor LogicFun (structure Unify: UNIFY and Net:NET): LOGIC =
struct
structure Sign = Unify.Sign;
structure Type = Sign.Type;
(*** Abstract syntax operations on the meta-connectives ***)
(** equality **)
(*Make an equality.*)
fun mk_equals(t,u) = equals(fastype_of t) $ t $ u;
fun dest_equals (Const("==",_) $ t $ u) = (t,u)
| dest_equals t = raise TERM("dest_equals", [t]);
(** implies **)
fun mk_implies(A,B) = implies $ A $ B;
fun dest_implies (Const("==>",_) $ A $ B) = (A,B)
| dest_implies A = raise TERM("dest_implies", [A]);
(** nested implications **)
(* [A1,...,An], B goes to A1==>...An==>B *)
fun list_implies ([], B) = B : term
| list_implies (A::AS, B) = implies $ A $ list_implies(AS,B);
(* A1==>...An==>B goes to [A1,...,An], where B is not an implication *)
fun strip_imp_prems (Const("==>", _) $ A $ B) = A :: strip_imp_prems B
| strip_imp_prems _ = [];
(* A1==>...An==>B goes to B, where B is not an implication *)
fun strip_imp_concl (Const("==>", _) $ A $ B) = strip_imp_concl B
| strip_imp_concl A = A : term;
(*Strip and return premises: (i, [], A1==>...Ai==>B)
goes to ([Ai, A(i-1),...,A1] , B) (REVERSED)
if i<0 or else i too big then raises TERM*)
fun strip_prems (0, As, B) = (As, B)
| strip_prems (i, As, Const("==>", _) $ A $ B) =
strip_prems (i-1, A::As, B)
| strip_prems (_, As, A) = raise TERM("strip_prems", A::As);
(*Count premises -- quicker than (length ostrip_prems) *)
fun count_prems (Const("==>", _) $ A $ B, n) = count_prems (B,n+1)
| count_prems (_,n) = n;
(** flex-flex constraints **)
(*Make a constraint.*)
fun mk_flexpair(t,u) = flexpair(fastype_of t) $ t $ u;
fun dest_flexpair (Const("=?=",_) $ t $ u) = (t,u)
| dest_flexpair t = raise TERM("dest_flexpair", [t]);
(*make flexflex antecedents: ( [(a1,b1),...,(an,bn)] , C )
goes to (a1=?=b1) ==>...(an=?=bn)==>C *)
fun list_flexpairs ([], A) = A
| list_flexpairs ((t,u)::pairs, A) =
implies $ (mk_flexpair(t,u)) $ list_flexpairs(pairs,A);
(*Make the object-rule tpairs==>As==>B *)
fun rule_of (tpairs, As, B) = list_flexpairs(tpairs, list_implies(As, B));
(*Remove and return flexflex pairs:
(a1=?=b1)==>...(an=?=bn)==>C to ( [(a1,b1),...,(an,bn)] , C )
[Tail recursive in order to return a pair of results] *)
fun strip_flex_aux (pairs, Const("==>", _) $ (Const("=?=",_)$t$u) $ C) =
strip_flex_aux ((t,u)::pairs, C)
| strip_flex_aux (pairs,C) = (rev pairs, C);
fun strip_flexpairs A = strip_flex_aux([], A);
(*Discard flexflex pairs*)
fun skip_flexpairs (Const("==>", _) $ (Const("=?=",_)$_$_) $ C) =
skip_flexpairs C
| skip_flexpairs C = C;
(*strip a proof state (Horn clause):
(a1==b1)==>...(am==bm)==>B1==>...Bn==>C
goes to ( [(a1,b1),...,(am,bm)] , [B1,...,Bn] , C) *)
fun strip_horn A =
let val (tpairs,horn) = strip_flexpairs A
in (tpairs, strip_imp_prems horn, strip_imp_concl horn) end;
(** types as terms **)
fun mk_type ty = Const ("TYPE", itselfT ty);
fun dest_type (Const ("TYPE", Type ("itself", [ty]))) = ty
| dest_type t = raise TERM ("dest_type", [t]);
(** class constraints **)
fun mk_inclass (ty, c) =
Const (Sign.const_of_class c, itselfT ty --> propT) $ mk_type ty;
fun dest_inclass (t as Const (c_class, _) $ ty) =
((dest_type ty, Sign.class_of_const c_class)
handle TERM _ => raise TERM ("dest_inclass", [t]))
| dest_inclass t = raise TERM ("dest_inclass", [t]);
(*** Low-level term operations ***)
(*Does t occur in u? Or is alpha-convertible to u?
The term t must contain no loose bound variables*)
fun t occs u = (t aconv u) orelse
(case u of
Abs(_,_,body) => t occs body
| f$t' => t occs f orelse t occs t'
| _ => false);
(*Close up a formula over all free variables by quantification*)
fun close_form A =
list_all_free (map dest_Free (sort atless (term_frees A)),
A);
(*Freeze all (T)Vars by turning them into (T)Frees*)
fun freeze_vars(Var(ixn,T)) = Free(Syntax.string_of_vname ixn,
Type.freeze_vars T)
| freeze_vars(Const(a,T)) = Const(a,Type.freeze_vars T)
| freeze_vars(Free(a,T)) = Free(a,Type.freeze_vars T)
| freeze_vars(s$t) = freeze_vars s $ freeze_vars t
| freeze_vars(Abs(a,T,t)) = Abs(a,Type.freeze_vars T,freeze_vars t)
| freeze_vars(b) = b;
(*Reverse the effect of freeze_vars*)
fun thaw_vars(Const(a,T)) = Const(a,Type.thaw_vars T)
| thaw_vars(Free(a,T)) =
let val T' = Type.thaw_vars T
in case explode a of
"?"::vn => let val (ixn,_) = Syntax.scan_varname vn
in Var(ixn,T') end
| _ => Free(a,T')
end
| thaw_vars(Abs(a,T,t)) = Abs(a,Type.thaw_vars T, thaw_vars t)
| thaw_vars(s$t) = thaw_vars s $ thaw_vars t
| thaw_vars(b) = b;
(*** Specialized operations for resolution... ***)
(*For all variables in the term, increment indexnames and lift over the Us
result is ?Gidx(B.(lev+n-1),...,B.lev) where lev is abstraction level *)
fun incr_indexes (Us: typ list, inc:int) t =
let fun incr (Var ((a,i), T), lev) =
Unify.combound (Var((a, i+inc), Us---> incr_tvar inc T),
lev, length Us)
| incr (Abs (a,T,body), lev) =
Abs (a, incr_tvar inc T, incr(body,lev+1))
| incr (Const(a,T),_) = Const(a, incr_tvar inc T)
| incr (Free(a,T),_) = Free(a, incr_tvar inc T)
| incr (f$t, lev) = incr(f,lev) $ incr(t,lev)
| incr (t,lev) = t
in incr(t,0) end;
(*Make lifting functions from subgoal and increment.
lift_abs operates on tpairs (unification constraints)
lift_all operates on propositions *)
fun lift_fns (B,inc) =
let fun lift_abs (Us, Const("==>", _) $ _ $ B) u = lift_abs (Us,B) u
| lift_abs (Us, Const("all",_)$Abs(a,T,t)) u =
Abs(a, T, lift_abs (T::Us, t) u)
| lift_abs (Us, _) u = incr_indexes(rev Us, inc) u
fun lift_all (Us, Const("==>", _) $ A $ B) u =
implies $ A $ lift_all (Us,B) u
| lift_all (Us, Const("all",_)$Abs(a,T,t)) u =
all T $ Abs(a, T, lift_all (T::Us,t) u)
| lift_all (Us, _) u = incr_indexes(rev Us, inc) u;
in (lift_abs([],B), lift_all([],B)) end;
(*Strips assumptions in goal, yielding list of hypotheses. *)
fun strip_assums_hyp (Const("==>", _) $ H $ B) = H :: strip_assums_hyp B
| strip_assums_hyp (Const("all",_)$Abs(a,T,t)) = strip_assums_hyp t
| strip_assums_hyp B = [];
(*Strips assumptions in goal, yielding conclusion. *)
fun strip_assums_concl (Const("==>", _) $ H $ B) = strip_assums_concl B
| strip_assums_concl (Const("all",_)$Abs(a,T,t)) = strip_assums_concl t
| strip_assums_concl B = B;
(*Make a list of all the parameters in a subgoal, even if nested*)
fun strip_params (Const("==>", _) $ H $ B) = strip_params B
| strip_params (Const("all",_)$Abs(a,T,t)) = (a,T) :: strip_params t
| strip_params B = [];
(*Removes the parameters from a subgoal and renumber bvars in hypotheses,
where j is the total number of parameters (precomputed)
If n>0 then deletes assumption n. *)
fun remove_params j n A =
if j=0 andalso n<=0 then A (*nothing left to do...*)
else case A of
Const("==>", _) $ H $ B =>
if n=1 then (remove_params j (n-1) B)
else implies $ (incr_boundvars j H) $ (remove_params j (n-1) B)
| Const("all",_)$Abs(a,T,t) => remove_params (j-1) n t
| _ => if n>0 then raise TERM("remove_params", [A])
else A;
(** Auto-renaming of parameters in subgoals **)
val auto_rename = ref false
and rename_prefix = ref "ka";
(*rename_prefix is not exported; it is set by this function.*)
fun set_rename_prefix a =
if a<>"" andalso forall is_letter (explode a)
then (rename_prefix := a; auto_rename := true)
else error"rename prefix must be nonempty and consist of letters";
(*Makes parameters in a goal have distinctive names (not guaranteed unique!)
A name clash could cause the printer to rename bound vars;
then res_inst_tac would not work properly.*)
fun rename_vars (a, []) = []
| rename_vars (a, (_,T)::vars) =
(a,T) :: rename_vars (bump_string a, vars);
(*Move all parameters to the front of the subgoal, renaming them apart;
if n>0 then deletes assumption n. *)
fun flatten_params n A =
let val params = strip_params A;
val vars = if !auto_rename
then rename_vars (!rename_prefix, params)
else variantlist(map #1 params,[]) ~~ map #2 params
in list_all (vars, remove_params (length vars) n A)
end;
(*Makes parameters in a goal have the names supplied by the list cs.*)
fun list_rename_params (cs, Const("==>", _) $ A $ B) =
implies $ A $ list_rename_params (cs, B)
| list_rename_params (c::cs, Const("all",_)$Abs(_,T,t)) =
all T $ Abs(c, T, list_rename_params (cs, t))
| list_rename_params (cs, B) = B;
(*Strips assumptions in goal yielding ( [Hn,...,H1], [xm,...,x1], B )
where H1,...,Hn are the hypotheses and x1...xm are the parameters. *)
fun strip_assums_aux (Hs, params, Const("==>", _) $ H $ B) =
strip_assums_aux (H::Hs, params, B)
| strip_assums_aux (Hs, params, Const("all",_)$Abs(a,T,t)) =
strip_assums_aux (Hs, (a,T)::params, t)
| strip_assums_aux (Hs, params, B) = (Hs, params, B);
fun strip_assums A = strip_assums_aux ([],[],A);
(*Produces disagreement pairs, one for each assumption proof, in order.
A is the first premise of the lifted rule, and thus has the form
H1 ==> ... Hk ==> B and the pairs are (H1,B),...,(Hk,B) *)
fun assum_pairs A =
let val (Hs, params, B) = strip_assums A
val D = Unify.rlist_abs(params, B)
fun pairrev ([],pairs) = pairs
| pairrev (H::Hs,pairs) =
pairrev(Hs, (Unify.rlist_abs(params,H), D) :: pairs)
in pairrev (Hs,[]) (*WAS: map pair (rev Hs) *)
end;
(*Converts Frees to Vars and TFrees to TVars so that axioms can be written
without (?) everywhere*)
fun varify (Const(a,T)) = Const(a, Type.varifyT T)
| varify (Free(a,T)) = Var((a,0), Type.varifyT T)
| varify (Var(ixn,T)) = Var(ixn, Type.varifyT T)
| varify (Abs (a,T,body)) = Abs (a, Type.varifyT T, varify body)
| varify (f$t) = varify f $ varify t
| varify t = t;
end;