--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/Pure/logic.ML Thu Sep 16 12:20:38 1993 +0200
@@ -0,0 +1,298 @@
+(* Title: logic
+ 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 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 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 Type = Unify.Sign.Type;
+
+(*** Abstract syntax operations on the meta-connectives ***)
+
+(** equality **)
+
+(*Make an equality. DOES NOT CHECK TYPE OF u! *)
+fun mk_equals(t,u) = equals(type_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. DOES NOT CHECK TYPE OF u! *)
+fun mk_flexpair(t,u) = flexpair(type_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;
+
+
+(*** 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;