clasohm@1460: (* Title: Pure/term.ML clasohm@0: ID: $Id$ clasohm@1460: Author: Lawrence C Paulson, Cambridge University Computer Laboratory clasohm@0: Copyright Cambridge University 1992 clasohm@1364: clasohm@1364: Simply typed lambda-calculus: types, terms, and basic operations clasohm@0: *) clasohm@0: clasohm@1364: infix 9 $; clasohm@1364: infixr 5 -->; clasohm@1364: infixr --->; clasohm@1364: infix aconv; clasohm@1364: clasohm@0: clasohm@1364: structure Term = clasohm@1364: struct clasohm@0: clasohm@0: (*Indexnames can be quickly renamed by adding an offset to the integer part, clasohm@0: for resolution.*) clasohm@0: type indexname = string*int; clasohm@0: clasohm@0: (* Types are classified by classes. *) clasohm@0: type class = string; clasohm@0: type sort = class list; clasohm@0: clasohm@0: (* The sorts attached to TFrees and TVars specify the sort of that variable *) clasohm@0: datatype typ = Type of string * typ list clasohm@0: | TFree of string * sort clasohm@1460: | TVar of indexname * sort; clasohm@0: clasohm@0: fun S --> T = Type("fun",[S,T]); clasohm@0: clasohm@0: (*handy for multiple args: [T1,...,Tn]--->T gives T1-->(T2--> ... -->T)*) clasohm@0: val op ---> = foldr (op -->); clasohm@0: clasohm@0: clasohm@0: (*terms. Bound variables are indicated by depth number. clasohm@0: Free variables, (scheme) variables and constants have names. clasohm@0: An term is "closed" if there every bound variable of level "lev" clasohm@0: is enclosed by at least "lev" abstractions. clasohm@0: clasohm@0: It is possible to create meaningless terms containing loose bound vars clasohm@0: or type mismatches. But such terms are not allowed in rules. *) clasohm@0: clasohm@0: clasohm@0: clasohm@0: datatype term = clasohm@0: Const of string * typ clasohm@0: | Free of string * typ clasohm@0: | Var of indexname * typ clasohm@0: | Bound of int clasohm@0: | Abs of string*typ*term wenzelm@3965: | op $ of term*term; clasohm@0: clasohm@0: clasohm@0: (*For errors involving type mismatches*) clasohm@0: exception TYPE of string * typ list * term list; clasohm@0: clasohm@0: (*For system errors involving terms*) clasohm@0: exception TERM of string * term list; clasohm@0: clasohm@0: clasohm@0: (*Note variable naming conventions! clasohm@0: a,b,c: string clasohm@0: f,g,h: functions (including terms of function type) clasohm@0: i,j,m,n: int clasohm@0: t,u: term clasohm@0: v,w: indexnames clasohm@0: x,y: any clasohm@0: A,B,C: term (denoting formulae) clasohm@0: T,U: typ clasohm@0: *) clasohm@0: clasohm@0: clasohm@0: (** Discriminators **) clasohm@0: clasohm@0: fun is_Const (Const _) = true clasohm@0: | is_Const _ = false; clasohm@0: clasohm@0: fun is_Free (Free _) = true clasohm@0: | is_Free _ = false; clasohm@0: clasohm@0: fun is_Var (Var _) = true clasohm@0: | is_Var _ = false; clasohm@0: clasohm@0: fun is_TVar (TVar _) = true clasohm@0: | is_TVar _ = false; clasohm@0: clasohm@0: (** Destructors **) clasohm@0: clasohm@0: fun dest_Const (Const x) = x clasohm@0: | dest_Const t = raise TERM("dest_Const", [t]); clasohm@0: clasohm@0: fun dest_Free (Free x) = x clasohm@0: | dest_Free t = raise TERM("dest_Free", [t]); clasohm@0: clasohm@0: fun dest_Var (Var x) = x clasohm@0: | dest_Var t = raise TERM("dest_Var", [t]); clasohm@0: clasohm@0: paulson@4064: fun domain_type (Type("fun", [T,_])) = T; paulson@4064: clasohm@0: (* maps [T1,...,Tn]--->T to the list [T1,T2,...,Tn]*) clasohm@0: fun binder_types (Type("fun",[S,T])) = S :: binder_types T clasohm@0: | binder_types _ = []; clasohm@0: clasohm@0: (* maps [T1,...,Tn]--->T to T*) clasohm@0: fun body_type (Type("fun",[S,T])) = body_type T clasohm@0: | body_type T = T; clasohm@0: clasohm@0: (* maps [T1,...,Tn]--->T to ([T1,T2,...,Tn], T) *) clasohm@0: fun strip_type T : typ list * typ = clasohm@0: (binder_types T, body_type T); clasohm@0: clasohm@0: clasohm@0: (*Compute the type of the term, checking that combinations are well-typed clasohm@0: Ts = [T0,T1,...] holds types of bound variables 0, 1, ...*) clasohm@0: fun type_of1 (Ts, Const (_,T)) = T clasohm@0: | type_of1 (Ts, Free (_,T)) = T clasohm@0: | type_of1 (Ts, Bound i) = (nth_elem (i,Ts) clasohm@1460: handle LIST _ => raise TYPE("type_of: bound variable", [], [Bound i])) clasohm@0: | type_of1 (Ts, Var (_,T)) = T clasohm@0: | type_of1 (Ts, Abs (_,T,body)) = T --> type_of1(T::Ts, body) clasohm@0: | type_of1 (Ts, f$u) = clasohm@0: let val U = type_of1(Ts,u) clasohm@0: and T = type_of1(Ts,f) clasohm@0: in case T of clasohm@1460: Type("fun",[T1,T2]) => clasohm@1460: if T1=U then T2 else raise TYPE clasohm@1460: ("type_of: type mismatch in application", [T1,U], [f$u]) clasohm@1460: | _ => raise TYPE clasohm@1460: ("type_of: function type is expected in application", clasohm@1460: [T,U], [f$u]) clasohm@0: end; clasohm@0: clasohm@0: fun type_of t : typ = type_of1 ([],t); clasohm@0: clasohm@0: (*Determines the type of a term, with minimal checking*) lcp@61: fun fastype_of1 (Ts, f$u) = lcp@61: (case fastype_of1 (Ts,f) of clasohm@1460: Type("fun",[_,T]) => T clasohm@1460: | _ => raise TERM("fastype_of: expected function type", [f$u])) lcp@61: | fastype_of1 (_, Const (_,T)) = T lcp@61: | fastype_of1 (_, Free (_,T)) = T lcp@61: | fastype_of1 (Ts, Bound i) = (nth_elem(i,Ts) clasohm@1460: handle LIST _ => raise TERM("fastype_of: Bound", [Bound i])) lcp@61: | fastype_of1 (_, Var (_,T)) = T lcp@61: | fastype_of1 (Ts, Abs (_,T,u)) = T --> fastype_of1 (T::Ts, u); lcp@61: lcp@61: fun fastype_of t : typ = fastype_of1 ([],t); clasohm@0: clasohm@0: clasohm@0: (* maps (x1,...,xn)t to t *) clasohm@0: fun strip_abs_body (Abs(_,_,t)) = strip_abs_body t clasohm@0: | strip_abs_body u = u; clasohm@0: clasohm@0: clasohm@0: (* maps (x1,...,xn)t to [x1, ..., xn] *) clasohm@0: fun strip_abs_vars (Abs(a,T,t)) = (a,T) :: strip_abs_vars t clasohm@0: | strip_abs_vars u = [] : (string*typ) list; clasohm@0: clasohm@0: clasohm@0: fun strip_qnt_body qnt = clasohm@0: let fun strip(tm as Const(c,_)$Abs(_,_,t)) = if c=qnt then strip t else tm clasohm@0: | strip t = t clasohm@0: in strip end; clasohm@0: clasohm@0: fun strip_qnt_vars qnt = clasohm@0: let fun strip(Const(c,_)$Abs(a,T,t)) = if c=qnt then (a,T)::strip t else [] clasohm@0: | strip t = [] : (string*typ) list clasohm@0: in strip end; clasohm@0: clasohm@0: clasohm@0: (* maps (f, [t1,...,tn]) to f(t1,...,tn) *) clasohm@0: val list_comb : term * term list -> term = foldl (op $); clasohm@0: clasohm@0: clasohm@0: (* maps f(t1,...,tn) to (f, [t1,...,tn]) ; naturally tail-recursive*) clasohm@0: fun strip_comb u : term * term list = clasohm@0: let fun stripc (f$t, ts) = stripc (f, t::ts) clasohm@0: | stripc x = x clasohm@0: in stripc(u,[]) end; clasohm@0: clasohm@0: clasohm@0: (* maps f(t1,...,tn) to f , which is never a combination *) clasohm@0: fun head_of (f$t) = head_of f clasohm@0: | head_of u = u; clasohm@0: clasohm@0: clasohm@0: (*Number of atoms and abstractions in a term*) clasohm@0: fun size_of_term (Abs (_,_,body)) = 1 + size_of_term body clasohm@0: | size_of_term (f$t) = size_of_term f + size_of_term t clasohm@0: | size_of_term _ = 1; clasohm@0: nipkow@949: fun map_type_tvar f (Type(a,Ts)) = Type(a, map (map_type_tvar f) Ts) nipkow@949: | map_type_tvar f (T as TFree _) = T nipkow@949: | map_type_tvar f (TVar x) = f x; nipkow@949: nipkow@949: fun map_type_tfree f (Type(a,Ts)) = Type(a, map (map_type_tfree f) Ts) nipkow@949: | map_type_tfree f (TFree x) = f x nipkow@949: | map_type_tfree f (T as TVar _) = T; nipkow@949: clasohm@0: (* apply a function to all types in a term *) clasohm@0: fun map_term_types f = clasohm@0: let fun map(Const(a,T)) = Const(a, f T) clasohm@0: | map(Free(a,T)) = Free(a, f T) clasohm@0: | map(Var(v,T)) = Var(v, f T) clasohm@0: | map(t as Bound _) = t clasohm@0: | map(Abs(a,T,t)) = Abs(a, f T, map t) clasohm@0: | map(f$t) = map f $ map t; clasohm@0: in map end; clasohm@0: clasohm@0: (* iterate a function over all types in a term *) clasohm@0: fun it_term_types f = clasohm@0: let fun iter(Const(_,T), a) = f(T,a) clasohm@0: | iter(Free(_,T), a) = f(T,a) clasohm@0: | iter(Var(_,T), a) = f(T,a) clasohm@0: | iter(Abs(_,T,t), a) = iter(t,f(T,a)) clasohm@0: | iter(f$u, a) = iter(f, iter(u, a)) clasohm@0: | iter(Bound _, a) = a clasohm@0: in iter end clasohm@0: clasohm@0: clasohm@0: (** Connectives of higher order logic **) clasohm@0: wenzelm@375: val logicC: class = "logic"; wenzelm@375: val logicS: sort = [logicC]; wenzelm@375: wenzelm@375: fun itselfT ty = Type ("itself", [ty]); wenzelm@375: val a_itselfT = itselfT (TFree ("'a", logicS)); wenzelm@375: clasohm@0: val propT : typ = Type("prop",[]); clasohm@0: clasohm@0: val implies = Const("==>", propT-->propT-->propT); clasohm@0: clasohm@0: fun all T = Const("all", (T-->propT)-->propT); clasohm@0: clasohm@0: fun equals T = Const("==", T-->T-->propT); clasohm@0: clasohm@0: fun flexpair T = Const("=?=", T-->T-->propT); clasohm@0: clasohm@0: (* maps !!x1...xn. t to t *) clasohm@0: fun strip_all_body (Const("all",_)$Abs(_,_,t)) = strip_all_body t clasohm@0: | strip_all_body t = t; clasohm@0: clasohm@0: (* maps !!x1...xn. t to [x1, ..., xn] *) clasohm@0: fun strip_all_vars (Const("all",_)$Abs(a,T,t)) = clasohm@1460: (a,T) :: strip_all_vars t clasohm@0: | strip_all_vars t = [] : (string*typ) list; clasohm@0: clasohm@0: (*increments a term's non-local bound variables clasohm@0: required when moving a term within abstractions clasohm@0: inc is increment for bound variables clasohm@0: lev is level at which a bound variable is considered 'loose'*) clasohm@0: fun incr_bv (inc, lev, u as Bound i) = if i>=lev then Bound(i+inc) else u clasohm@0: | incr_bv (inc, lev, Abs(a,T,body)) = clasohm@1460: Abs(a, T, incr_bv(inc,lev+1,body)) clasohm@0: | incr_bv (inc, lev, f$t) = clasohm@0: incr_bv(inc,lev,f) $ incr_bv(inc,lev,t) clasohm@0: | incr_bv (inc, lev, u) = u; clasohm@0: clasohm@0: fun incr_boundvars 0 t = t clasohm@0: | incr_boundvars inc t = incr_bv(inc,0,t); clasohm@0: clasohm@0: clasohm@0: (*Accumulate all 'loose' bound vars referring to level 'lev' or beyond. clasohm@0: (Bound 0) is loose at level 0 *) clasohm@0: fun add_loose_bnos (Bound i, lev, js) = paulson@2176: if i= k clasohm@0: | loose_bvar(f$t, k) = loose_bvar(f,k) orelse loose_bvar(t,k) clasohm@0: | loose_bvar(Abs(_,_,t),k) = loose_bvar(t,k+1) clasohm@0: | loose_bvar _ = false; clasohm@0: nipkow@2792: fun loose_bvar1(Bound i,k) = i = k nipkow@2792: | loose_bvar1(f$t, k) = loose_bvar1(f,k) orelse loose_bvar1(t,k) nipkow@2792: | loose_bvar1(Abs(_,_,t),k) = loose_bvar1(t,k+1) nipkow@2792: | loose_bvar1 _ = false; clasohm@0: clasohm@0: (*Substitute arguments for loose bound variables. clasohm@0: Beta-reduction of arg(n-1)...arg0 into t replacing (Bound i) with (argi). clasohm@0: Note that for ((x,y)c)(a,b), the bound vars in c are x=1 and y=0 clasohm@1460: and the appropriate call is subst_bounds([b,a], c) . clasohm@0: Loose bound variables >=n are reduced by "n" to clasohm@0: compensate for the disappearance of lambdas. clasohm@0: *) clasohm@0: fun subst_bounds (args: term list, t) : term = clasohm@0: let val n = length args; clasohm@0: fun subst (t as Bound i, lev) = paulson@2580: (if i Bound(i-n) (*loose: change it*)) clasohm@1460: | subst (Abs(a,T,body), lev) = Abs(a, T, subst(body,lev+1)) clasohm@1460: | subst (f$t, lev) = subst(f,lev) $ subst(t,lev) clasohm@1460: | subst (t,lev) = t clasohm@0: in case args of [] => t | _ => subst (t,0) end; clasohm@0: paulson@2192: (*Special case: one argument*) paulson@2192: fun subst_bound (arg, t) : term = paulson@2192: let fun subst (t as Bound i, lev) = paulson@2192: if i true clasohm@0: | (Var _, _) => true clasohm@0: | (Const(a,_), Const(b,_)) => a=b andalso matchrands(t,u) clasohm@0: | (Free(a,_), Free(b,_)) => a=b andalso matchrands(t,u) clasohm@0: | (Bound i, Bound j) => i=j andalso matchrands(t,u) clasohm@0: | (Abs _, _) => true (*because of possible eta equality*) clasohm@0: | (_, Abs _) => true clasohm@0: | _ => false clasohm@0: end; clasohm@0: clasohm@0: (*Substitute new for free occurrences of old in a term*) clasohm@0: fun subst_free [] = (fn t=>t) clasohm@0: | subst_free pairs = clasohm@0: let fun substf u = clasohm@1460: case gen_assoc (op aconv) (pairs, u) of clasohm@1460: Some u' => u' clasohm@1460: | None => (case u of Abs(a,T,t) => Abs(a, T, substf t) clasohm@1460: | t$u' => substf t $ substf u' clasohm@1460: | _ => u) clasohm@0: in substf end; clasohm@0: clasohm@0: (*a total, irreflexive ordering on index names*) clasohm@0: fun xless ((a,i), (b,j): indexname) = i Abs(a, T, abst(lev+1, t)) clasohm@1460: | f$rand => abst(lev,f) $ abst(lev,rand) clasohm@1460: | _ => u) clasohm@0: in abst(0,body) end; clasohm@0: clasohm@0: clasohm@0: (*Form an abstraction over a free variable.*) clasohm@0: fun absfree (a,T,body) = Abs(a, T, abstract_over (Free(a,T), body)); clasohm@0: clasohm@0: (*Abstraction over a list of free variables*) clasohm@0: fun list_abs_free ([ ] , t) = t clasohm@0: | list_abs_free ((a,T)::vars, t) = clasohm@0: absfree(a, T, list_abs_free(vars,t)); clasohm@0: clasohm@0: (*Quantification over a list of free variables*) clasohm@0: fun list_all_free ([], t: term) = t clasohm@0: | list_all_free ((a,T)::vars, t) = clasohm@0: (all T) $ (absfree(a, T, list_all_free(vars,t))); clasohm@0: clasohm@0: (*Quantification over a list of variables (already bound in body) *) clasohm@0: fun list_all ([], t) = t clasohm@0: | list_all ((a,T)::vars, t) = clasohm@0: (all T) $ (Abs(a, T, list_all(vars,t))); clasohm@0: clasohm@0: (*Replace the ATOMIC term ti by ui; instl = [(t1,u1), ..., (tn,un)]. clasohm@0: A simultaneous substitution: [ (a,b), (b,a) ] swaps a and b. *) clasohm@0: fun subst_atomic [] t = t : term clasohm@0: | subst_atomic (instl: (term*term) list) t = clasohm@0: let fun subst (Abs(a,T,body)) = Abs(a, T, subst body) clasohm@1460: | subst (f$t') = subst f $ subst t' clasohm@1460: | subst t = (case assoc(instl,t) of clasohm@1460: Some u => u | None => t) clasohm@0: in subst t end; clasohm@0: lcp@728: (*Substitute for type Vars in a type*) clasohm@0: fun typ_subst_TVars iTs T = if null iTs then T else clasohm@0: let fun subst(Type(a,Ts)) = Type(a, map subst Ts) clasohm@1460: | subst(T as TFree _) = T clasohm@1460: | subst(T as TVar(ixn,_)) = clasohm@0: (case assoc(iTs,ixn) of None => T | Some(U) => U) clasohm@0: in subst T end; clasohm@0: lcp@728: (*Substitute for type Vars in a term*) clasohm@0: val subst_TVars = map_term_types o typ_subst_TVars; clasohm@0: lcp@728: (*Substitute for Vars in a term; see also envir/norm_term*) clasohm@0: fun subst_Vars itms t = if null itms then t else clasohm@0: let fun subst(v as Var(ixn,_)) = clasohm@0: (case assoc(itms,ixn) of None => v | Some t => t) clasohm@0: | subst(Abs(a,T,t)) = Abs(a,T,subst t) clasohm@0: | subst(f$t) = subst f $ subst t clasohm@0: | subst(t) = t clasohm@0: in subst t end; clasohm@0: lcp@728: (*Substitute for type/term Vars in a term; see also envir/norm_term*) clasohm@0: fun subst_vars(iTs,itms) = if null iTs then subst_Vars itms else clasohm@0: let fun subst(Const(a,T)) = Const(a,typ_subst_TVars iTs T) clasohm@0: | subst(Free(a,T)) = Free(a,typ_subst_TVars iTs T) clasohm@0: | subst(v as Var(ixn,T)) = (case assoc(itms,ixn) of clasohm@0: None => Var(ixn,typ_subst_TVars iTs T) clasohm@0: | Some t => t) clasohm@0: | subst(b as Bound _) = b clasohm@0: | subst(Abs(a,T,t)) = Abs(a,typ_subst_TVars iTs T,subst t) clasohm@0: | subst(f$t) = subst f $ subst t clasohm@0: in subst end; clasohm@0: clasohm@0: clasohm@0: (*Computing the maximum index of a typ*) paulson@2146: fun maxidx_of_typ(Type(_,Ts)) = maxidx_of_typs Ts clasohm@0: | maxidx_of_typ(TFree _) = ~1 paulson@2146: | maxidx_of_typ(TVar((_,i),_)) = i paulson@2146: and maxidx_of_typs [] = ~1 paulson@2146: | maxidx_of_typs (T::Ts) = Int.max(maxidx_of_typ T, maxidx_of_typs Ts); clasohm@0: clasohm@0: clasohm@0: (*Computing the maximum index of a term*) clasohm@0: fun maxidx_of_term (Const(_,T)) = maxidx_of_typ T clasohm@0: | maxidx_of_term (Bound _) = ~1 clasohm@0: | maxidx_of_term (Free(_,T)) = maxidx_of_typ T paulson@2146: | maxidx_of_term (Var ((_,i), T)) = Int.max(i, maxidx_of_typ T) paulson@2146: | maxidx_of_term (Abs (_,T,u)) = Int.max(maxidx_of_term u, maxidx_of_typ T) paulson@2146: | maxidx_of_term (f$t) = Int.max(maxidx_of_term f, maxidx_of_term t); clasohm@0: clasohm@0: clasohm@0: (* Increment the index of all Poly's in T by k *) nipkow@949: fun incr_tvar k = map_type_tvar (fn ((a,i),S) => TVar((a,i+k),S)); clasohm@0: clasohm@0: clasohm@0: (**** Syntax-related declarations ****) clasohm@0: clasohm@0: clasohm@0: (*Dummy type for parsing. Will be replaced during type inference. *) clasohm@0: val dummyT = Type("dummy",[]); clasohm@0: clasohm@0: (*scan a numeral of the given radix, normally 10*) clasohm@0: fun scan_radixint (radix: int, cs) : int * string list = clasohm@0: let val zero = ord"0" clasohm@0: val limit = zero+radix clasohm@0: fun scan (num,[]) = (num,[]) clasohm@1460: | scan (num, c::cs) = clasohm@1460: if zero <= ord c andalso ord c < limit clasohm@1460: then scan(radix*num + ord c - zero, cs) clasohm@1460: else (num, c::cs) clasohm@0: in scan(0,cs) end; clasohm@0: clasohm@0: fun scan_int cs = scan_radixint(10,cs); clasohm@0: clasohm@0: clasohm@0: (*** Printing ***) clasohm@0: clasohm@0: clasohm@0: (*Makes a variant of the name c distinct from the names in bs. clasohm@0: First attaches the suffix "a" and then increments this. *) clasohm@0: fun variant bs c : string = paulson@2138: let fun vary2 c = if (c mem_string bs) then vary2 (bump_string c) else c paulson@2138: fun vary1 c = if (c mem_string bs) then vary2 (c ^ "a") else c clasohm@0: in vary1 (if c="" then "u" else c) end; clasohm@0: clasohm@0: (*Create variants of the list of names, with priority to the first ones*) clasohm@0: fun variantlist ([], used) = [] clasohm@0: | variantlist(b::bs, used) = clasohm@0: let val b' = variant used b clasohm@0: in b' :: variantlist (bs, b'::used) end; clasohm@0: wenzelm@4017: wenzelm@4017: wenzelm@4017: (** Consts etc. **) wenzelm@4017: wenzelm@4017: fun add_typ_classes (Type (_, Ts), cs) = foldr add_typ_classes (Ts, cs) wenzelm@4017: | add_typ_classes (TFree (_, S), cs) = S union cs wenzelm@4017: | add_typ_classes (TVar (_, S), cs) = S union cs; wenzelm@4017: wenzelm@4017: fun add_typ_tycons (Type (c, Ts), cs) = foldr add_typ_tycons (Ts, c ins cs) wenzelm@4017: | add_typ_tycons (_, cs) = cs; wenzelm@4017: wenzelm@4017: val add_term_classes = it_term_types add_typ_classes; wenzelm@4017: val add_term_tycons = it_term_types add_typ_tycons; wenzelm@4017: wenzelm@4017: fun add_term_consts (Const (c, _), cs) = c ins cs wenzelm@4017: | add_term_consts (t $ u, cs) = add_term_consts (t, add_term_consts (u, cs)) wenzelm@4017: | add_term_consts (Abs (_, _, t), cs) = add_term_consts (t, cs) wenzelm@4017: | add_term_consts (_, cs) = cs; wenzelm@4017: oheimb@4185: fun exists_Const P t = let oheimb@4185: fun ex (Const c ) = P c oheimb@4185: | ex (t $ u ) = ex t orelse ex u oheimb@4185: | ex (Abs (_, _, t)) = ex t oheimb@4185: | ex _ = false oheimb@4185: in ex t end; wenzelm@4017: wenzelm@4017: (*map classes, tycons*) wenzelm@4017: fun map_typ f g (Type (c, Ts)) = Type (g c, map (map_typ f g) Ts) wenzelm@4017: | map_typ f _ (TFree (x, S)) = TFree (x, map f S) wenzelm@4017: | map_typ f _ (TVar (xi, S)) = TVar (xi, map f S); wenzelm@4017: wenzelm@4017: (*map classes, tycons, consts*) wenzelm@4017: fun map_term f g h (Const (c, T)) = Const (h c, map_typ f g T) wenzelm@4017: | map_term f g _ (Free (x, T)) = Free (x, map_typ f g T) wenzelm@4017: | map_term f g _ (Var (xi, T)) = Var (xi, map_typ f g T) wenzelm@4017: | map_term _ _ _ (t as Bound _) = t wenzelm@4017: | map_term f g h (Abs (x, T, t)) = Abs (x, map_typ f g T, map_term f g h t) wenzelm@4017: | map_term f g h (t $ u) = map_term f g h t $ map_term f g h u; wenzelm@4017: wenzelm@4017: wenzelm@4017: clasohm@0: (** TFrees and TVars **) clasohm@0: clasohm@0: (*maps (bs,v) to v'::bs this reverses the identifiers bs*) clasohm@0: fun add_new_id (bs, c) : string list = variant bs c :: bs; clasohm@0: clasohm@0: (*Accumulates the names in the term, suppressing duplicates. clasohm@0: Includes Frees and Consts. For choosing unambiguous bound var names.*) paulson@2176: fun add_term_names (Const(a,_), bs) = a ins_string bs paulson@2176: | add_term_names (Free(a,_), bs) = a ins_string bs clasohm@0: | add_term_names (f$u, bs) = add_term_names (f, add_term_names(u, bs)) clasohm@0: | add_term_names (Abs(_,_,t), bs) = add_term_names(t,bs) clasohm@0: | add_term_names (_, bs) = bs; clasohm@0: clasohm@0: (*Accumulates the TVars in a type, suppressing duplicates. *) clasohm@0: fun add_typ_tvars(Type(_,Ts),vs) = foldr add_typ_tvars (Ts,vs) clasohm@0: | add_typ_tvars(TFree(_),vs) = vs clasohm@0: | add_typ_tvars(TVar(v),vs) = v ins vs; clasohm@0: clasohm@0: (*Accumulates the TFrees in a type, suppressing duplicates. *) clasohm@0: fun add_typ_tfree_names(Type(_,Ts),fs) = foldr add_typ_tfree_names (Ts,fs) paulson@2176: | add_typ_tfree_names(TFree(f,_),fs) = f ins_string fs clasohm@0: | add_typ_tfree_names(TVar(_),fs) = fs; clasohm@0: clasohm@0: fun add_typ_tfrees(Type(_,Ts),fs) = foldr add_typ_tfrees (Ts,fs) clasohm@0: | add_typ_tfrees(TFree(f),fs) = f ins fs clasohm@0: | add_typ_tfrees(TVar(_),fs) = fs; clasohm@0: nipkow@949: fun add_typ_varnames(Type(_,Ts),nms) = foldr add_typ_varnames (Ts,nms) paulson@2176: | add_typ_varnames(TFree(nm,_),nms) = nm ins_string nms paulson@2176: | add_typ_varnames(TVar((nm,_),_),nms) = nm ins_string nms; nipkow@949: clasohm@0: (*Accumulates the TVars in a term, suppressing duplicates. *) clasohm@0: val add_term_tvars = it_term_types add_typ_tvars; clasohm@0: clasohm@0: (*Accumulates the TFrees in a term, suppressing duplicates. *) clasohm@0: val add_term_tfrees = it_term_types add_typ_tfrees; clasohm@0: val add_term_tfree_names = it_term_types add_typ_tfree_names; clasohm@0: nipkow@949: val add_term_tvarnames = it_term_types add_typ_varnames; nipkow@949: clasohm@0: (*Non-list versions*) clasohm@0: fun typ_tfrees T = add_typ_tfrees(T,[]); clasohm@0: fun typ_tvars T = add_typ_tvars(T,[]); clasohm@0: fun term_tfrees t = add_term_tfrees(t,[]); clasohm@0: fun term_tvars t = add_term_tvars(t,[]); clasohm@0: nipkow@949: (*special code to enforce left-to-right collection of TVar-indexnames*) nipkow@949: nipkow@949: fun add_typ_ixns(ixns,Type(_,Ts)) = foldl add_typ_ixns (ixns,Ts) paulson@2176: | add_typ_ixns(ixns,TVar(ixn,_)) = if mem_ix (ixn, ixns) then ixns paulson@2176: else ixns@[ixn] nipkow@949: | add_typ_ixns(ixns,TFree(_)) = ixns; nipkow@949: nipkow@949: fun add_term_tvar_ixns(Const(_,T),ixns) = add_typ_ixns(ixns,T) nipkow@949: | add_term_tvar_ixns(Free(_,T),ixns) = add_typ_ixns(ixns,T) nipkow@949: | add_term_tvar_ixns(Var(_,T),ixns) = add_typ_ixns(ixns,T) nipkow@949: | add_term_tvar_ixns(Bound _,ixns) = ixns nipkow@949: | add_term_tvar_ixns(Abs(_,T,t),ixns) = nipkow@949: add_term_tvar_ixns(t,add_typ_ixns(ixns,T)) nipkow@949: | add_term_tvar_ixns(f$t,ixns) = nipkow@949: add_term_tvar_ixns(t,add_term_tvar_ixns(f,ixns)); nipkow@949: clasohm@0: (** Frees and Vars **) clasohm@0: clasohm@0: (*a partial ordering (not reflexive) for atomic terms*) clasohm@0: fun atless (Const (a,_), Const (b,_)) = a insert_aterm(t,vars) clasohm@0: | Abs (_,_,body) => add_term_vars(body,vars) clasohm@0: | f$t => add_term_vars (f, add_term_vars(t, vars)) clasohm@0: | _ => vars; clasohm@0: clasohm@0: fun term_vars t = add_term_vars(t,[]); clasohm@0: clasohm@0: (*Accumulates the Frees in the term, suppressing duplicates*) clasohm@0: fun add_term_frees (t, frees: term list) = case t of clasohm@0: Free _ => insert_aterm(t,frees) clasohm@0: | Abs (_,_,body) => add_term_frees(body,frees) clasohm@0: | f$t => add_term_frees (f, add_term_frees(t, frees)) clasohm@0: | _ => frees; clasohm@0: clasohm@0: fun term_frees t = add_term_frees(t,[]); clasohm@0: clasohm@0: (*Given an abstraction over P, replaces the bound variable by a Free variable clasohm@0: having a unique name. *) clasohm@0: fun variant_abs (a,T,P) = clasohm@0: let val b = variant (add_term_names(P,[])) a paulson@2192: in (b, subst_bound (Free(b,T), P)) end; clasohm@0: clasohm@0: (* renames and reverses the strings in vars away from names *) clasohm@0: fun rename_aTs names vars : (string*typ)list = clasohm@0: let fun rename_aT (vars,(a,T)) = clasohm@1460: (variant (map #1 vars @ names) a, T) :: vars clasohm@0: in foldl rename_aT ([],vars) end; clasohm@0: clasohm@0: fun rename_wrt_term t = rename_aTs (add_term_names(t,[])); clasohm@1364: paulson@1417: paulson@1417: paulson@1426: (*** Compression of terms and types by sharing common subtrees. paulson@1426: Saves 50-75% on storage requirements. As it is fairly slow, paulson@1426: it is called only for axioms, stored theorems, etc. ***) paulson@1417: paulson@1417: (** Sharing of types **) paulson@1417: paulson@1417: fun atomic_tag (Type (a,_)) = if a<>"fun" then a else raise Match paulson@1417: | atomic_tag (TFree (a,_)) = a paulson@1417: | atomic_tag (TVar ((a,_),_)) = a; paulson@1417: paulson@1417: fun type_tag (Type("fun",[S,T])) = atomic_tag S ^ type_tag T paulson@1417: | type_tag T = atomic_tag T; paulson@1417: paulson@1417: val memo_types = ref (Symtab.null : typ list Symtab.table); paulson@1417: paulson@1417: fun find_type (T, []: typ list) = None paulson@1417: | find_type (T, T'::Ts) = paulson@1417: if T=T' then Some T' paulson@1417: else find_type (T, Ts); paulson@1417: paulson@1417: fun compress_type T = paulson@1417: let val tag = type_tag T paulson@1417: val tylist = the (Symtab.lookup (!memo_types, tag)) clasohm@1460: handle _ => [] paulson@1417: in paulson@1417: case find_type (T,tylist) of clasohm@1460: Some T' => T' paulson@1417: | None => clasohm@1460: let val T' = clasohm@1460: case T of clasohm@1460: Type (a,Ts) => Type (a, map compress_type Ts) clasohm@1460: | _ => T clasohm@1460: in memo_types := Symtab.update ((tag, T'::tylist), !memo_types); clasohm@1460: T clasohm@1460: end paulson@1417: end paulson@1417: handle Match => paulson@1417: let val Type (a,Ts) = T paulson@1417: in Type (a, map compress_type Ts) end; paulson@1417: paulson@1417: (** Sharing of atomic terms **) paulson@1417: paulson@1417: val memo_terms = ref (Symtab.null : term list Symtab.table); paulson@1417: paulson@1417: fun find_term (t, []: term list) = None paulson@1417: | find_term (t, t'::ts) = paulson@1417: if t=t' then Some t' paulson@1417: else find_term (t, ts); paulson@1417: paulson@1417: fun const_tag (Const (a,_)) = a paulson@1417: | const_tag (Free (a,_)) = a paulson@1417: | const_tag (Var ((a,i),_)) = a paulson@1417: | const_tag (t as Bound _) = ".B."; paulson@1417: paulson@1417: fun share_term (t $ u) = share_term t $ share_term u paulson@1417: | share_term (Abs (a,T,u)) = Abs (a, T, share_term u) paulson@1417: | share_term t = paulson@1417: let val tag = const_tag t clasohm@1460: val ts = the (Symtab.lookup (!memo_terms, tag)) clasohm@1460: handle _ => [] paulson@1417: in clasohm@1460: case find_term (t,ts) of clasohm@1460: Some t' => t' clasohm@1460: | None => (memo_terms := Symtab.update ((tag, t::ts), !memo_terms); clasohm@1460: t) paulson@1417: end; paulson@1417: paulson@1417: val compress_term = share_term o map_term_types compress_type; paulson@1417: clasohm@1364: end; clasohm@1364: clasohm@1364: open Term;