wenzelm@9536: (* Title: Pure/term.ML clasohm@0: ID: $Id$ wenzelm@9536: Author: Lawrence C Paulson, Cambridge University Computer Laboratory clasohm@0: Copyright Cambridge University 1992 clasohm@1364: wenzelm@4444: Simply typed lambda-calculus: types, terms, and basic operations. clasohm@0: *) clasohm@0: clasohm@1364: infix 9 $; clasohm@1364: infixr 5 -->; wenzelm@4444: infixr --->; wenzelm@4444: infix aconv; clasohm@1364: wenzelm@4444: signature BASIC_TERM = wenzelm@4444: sig wenzelm@4444: type indexname wenzelm@4444: type class wenzelm@4444: type sort wenzelm@14829: type arity wenzelm@4444: datatype typ = wenzelm@4444: Type of string * typ list | wenzelm@4444: TFree of string * sort | wenzelm@4444: TVar of indexname * sort wenzelm@4444: val --> : typ * typ -> typ wenzelm@4444: val ---> : typ list * typ -> typ wenzelm@4444: val is_TVar: typ -> bool paulson@15573: val is_funtype: typ -> bool wenzelm@4444: val domain_type: typ -> typ wenzelm@4480: val range_type: typ -> typ wenzelm@4444: val binder_types: typ -> typ list wenzelm@4444: val body_type: typ -> typ wenzelm@4444: val strip_type: typ -> typ list * typ wenzelm@4444: datatype term = wenzelm@4444: Const of string * typ | wenzelm@4444: Free of string * typ | wenzelm@4444: Var of indexname * typ | wenzelm@4444: Bound of int | wenzelm@4444: Abs of string * typ * term | gagern@15632: op $ of term * term berghofe@8408: structure Vartab : TABLE wenzelm@13000: structure Typtab : TABLE berghofe@8408: structure Termtab : TABLE wenzelm@4444: exception TYPE of string * typ list * term list wenzelm@4444: exception TERM of string * term list nipkow@7318: val is_Bound: term -> bool wenzelm@4444: val is_Const: term -> bool wenzelm@4444: val is_Free: term -> bool wenzelm@4444: val is_Var: term -> bool paulson@15573: val is_first_order: term -> bool paulson@6033: val dest_Type: typ -> string * typ list dixon@15914: val dest_TVar: typ -> indexname * sort dixon@15914: val dest_TFree: typ -> string * sort wenzelm@4444: val dest_Const: term -> string * typ wenzelm@4444: val dest_Free: term -> string * typ wenzelm@4444: val dest_Var: term -> indexname * typ wenzelm@4444: val type_of: term -> typ wenzelm@4444: val type_of1: typ list * term -> typ wenzelm@4444: val fastype_of: term -> typ wenzelm@4444: val fastype_of1: typ list * term -> typ wenzelm@10806: val list_abs: (string * typ) list * term -> term wenzelm@4444: val strip_abs_body: term -> term wenzelm@4444: val strip_abs_vars: term -> (string * typ) list wenzelm@4444: val strip_qnt_body: string -> term -> term wenzelm@4444: val strip_qnt_vars: string -> term -> (string * typ) list wenzelm@4444: val list_comb: term * term list -> term wenzelm@4444: val strip_comb: term -> term * term list wenzelm@4444: val head_of: term -> term wenzelm@4444: val size_of_term: term -> int wenzelm@4444: val map_type_tvar: (indexname * sort -> typ) -> typ -> typ wenzelm@4444: val map_type_tfree: (string * sort -> typ) -> typ -> typ wenzelm@4444: val map_term_types: (typ -> typ) -> term -> term wenzelm@4444: val it_term_types: (typ * 'a -> 'a) -> term * 'a -> 'a wenzelm@4444: val foldl_atyps: ('a * typ -> 'a) -> 'a * typ -> 'a wenzelm@8609: val foldl_term_types: (term -> 'a * typ -> 'a) -> 'a * term -> 'a wenzelm@4444: val foldl_types: ('a * typ -> 'a) -> 'a * term -> 'a wenzelm@4444: val foldl_aterms: ('a * term -> 'a) -> 'a * term -> 'a wenzelm@6548: val foldl_map_aterms: ('a * term -> 'a * term) -> 'a * term -> 'a * term wenzelm@15025: val add_term_varnames: indexname list * term -> indexname list wenzelm@15025: val term_varnames: term -> indexname list wenzelm@4444: val dummyT: typ wenzelm@4444: val itselfT: typ -> typ wenzelm@4444: val a_itselfT: typ wenzelm@4444: val propT: typ wenzelm@4444: val implies: term wenzelm@4444: val all: typ -> term wenzelm@4444: val equals: typ -> term wenzelm@4444: val strip_all_body: term -> term wenzelm@4444: val strip_all_vars: term -> (string * typ) list wenzelm@4444: val incr_bv: int * int * term -> term wenzelm@4444: val incr_boundvars: int -> term -> term wenzelm@4444: val add_loose_bnos: term * int * int list -> int list wenzelm@4444: val loose_bnos: term -> int list wenzelm@4444: val loose_bvar: term * int -> bool wenzelm@4444: val loose_bvar1: term * int -> bool wenzelm@4444: val subst_bounds: term list * term -> term wenzelm@4444: val subst_bound: term * term -> term wenzelm@4444: val subst_TVars: (indexname * typ) list -> term -> term wenzelm@4444: val betapply: term * term -> term wenzelm@4444: val eq_ix: indexname * indexname -> bool wenzelm@4444: val ins_ix: indexname * indexname list -> indexname list wenzelm@4444: val mem_ix: indexname * indexname list -> bool wenzelm@4444: val aconv: term * term -> bool wenzelm@4444: val aconvs: term list * term list -> bool wenzelm@4444: val mem_term: term * term list -> bool wenzelm@4444: val subset_term: term list * term list -> bool wenzelm@4444: val eq_set_term: term list * term list -> bool wenzelm@4444: val ins_term: term * term list -> term list wenzelm@4444: val union_term: term list * term list -> term list paulson@5585: val inter_term: term list * term list -> term list wenzelm@4444: val could_unify: term * term -> bool wenzelm@4444: val subst_free: (term * term) list -> term -> term wenzelm@4444: val subst_atomic: (term * term) list -> term -> term berghofe@15797: val typ_subst_atomic: (typ * typ) list -> typ -> typ wenzelm@4444: val subst_vars: (indexname * typ) list * (indexname * term) list -> term -> term wenzelm@4444: val typ_subst_TVars: (indexname * typ) list -> typ -> typ wenzelm@4444: val subst_Vars: (indexname * term) list -> term -> term wenzelm@4444: val incr_tvar: int -> typ -> typ wenzelm@4444: val xless: (string * int) * indexname -> bool wenzelm@4444: val atless: term * term -> bool wenzelm@4444: val insert_aterm: term * term list -> term list wenzelm@4444: val abstract_over: term * term -> term wenzelm@11922: val lambda: term -> term -> term wenzelm@4444: val absfree: string * typ * term -> term wenzelm@4444: val list_abs_free: (string * typ) list * term -> term wenzelm@4444: val list_all_free: (string * typ) list * term -> term wenzelm@4444: val list_all: (string * typ) list * term -> term wenzelm@4444: val maxidx_of_typ: typ -> int wenzelm@4444: val maxidx_of_typs: typ list -> int wenzelm@4444: val maxidx_of_term: term -> int berghofe@13665: val maxidx_of_terms: term list -> int wenzelm@4444: val variant: string list -> string -> string wenzelm@4444: val variantlist: string list * string list -> string list ballarin@15598: (* note reversed order of args wrt. variant! *) wenzelm@4444: val variant_abs: string * typ * term -> string * term wenzelm@4444: val rename_wrt_term: term -> (string * typ) list -> (string * typ) list wenzelm@4444: val add_new_id: string list * string -> string list wenzelm@4444: val add_typ_classes: typ * class list -> class list wenzelm@4444: val add_typ_ixns: indexname list * typ -> indexname list wenzelm@4444: val add_typ_tfree_names: typ * string list -> string list wenzelm@4444: val add_typ_tfrees: typ * (string * sort) list -> (string * sort) list wenzelm@4444: val typ_tfrees: typ -> (string * sort) list wenzelm@4444: val add_typ_tvars: typ * (indexname * sort) list -> (indexname * sort) list wenzelm@4444: val typ_tvars: typ -> (indexname * sort) list wenzelm@4444: val add_typ_tycons: typ * string list -> string list wenzelm@4444: val add_typ_varnames: typ * string list -> string list wenzelm@4444: val add_term_classes: term * class list -> class list wenzelm@4444: val add_term_consts: term * string list -> string list nipkow@13646: val term_consts: term -> string list obua@16108: val term_constsT: term -> (string * typ) list wenzelm@4444: val add_term_frees: term * term list -> term list wenzelm@4444: val term_frees: term -> term list wenzelm@12802: val add_term_free_names: term * string list -> string list wenzelm@4444: val add_term_names: term * string list -> string list wenzelm@4444: val add_term_tfree_names: term * string list -> string list wenzelm@4444: val add_term_tfrees: term * (string * sort) list -> (string * sort) list wenzelm@4444: val term_tfrees: term -> (string * sort) list wenzelm@4444: val add_term_tvar_ixns: term * indexname list -> indexname list wenzelm@4444: val add_term_tvarnames: term * string list -> string list wenzelm@4444: val add_term_tvars: term * (indexname * sort) list -> (indexname * sort) list wenzelm@4444: val term_tvars: term -> (indexname * sort) list wenzelm@4444: val add_term_tycons: term * string list -> string list wenzelm@4444: val add_term_vars: term * term list -> term list wenzelm@4444: val term_vars: term -> term list wenzelm@4444: val exists_Const: (string * typ -> bool) -> term -> bool nipkow@4631: val exists_subterm: (term -> bool) -> term -> bool wenzelm@4444: val compress_type: typ -> typ wenzelm@4444: val compress_term: term -> term wenzelm@15986: val show_question_marks: bool ref wenzelm@4444: end; clasohm@0: wenzelm@4444: signature TERM = wenzelm@4444: sig wenzelm@4444: include BASIC_TERM wenzelm@12981: val match_bvars: (term * term) * (string * string) list -> (string * string) list wenzelm@12981: val rename_abs: term -> term -> term -> term option wenzelm@12499: val invent_names: string list -> string -> int -> string list wenzelm@16338: val map_typ: (string -> string) -> (string -> string) -> typ -> typ wenzelm@16338: val map_term: (string -> string) -> (string -> string) -> (string -> string) -> term -> term wenzelm@12499: val add_tvarsT: (indexname * sort) list * typ -> (indexname * sort) list wenzelm@12499: val add_tvars: (indexname * sort) list * term -> (indexname * sort) list wenzelm@12499: val add_vars: (indexname * typ) list * term -> (indexname * typ) list wenzelm@12499: val add_frees: (string * typ) list * term -> (string * typ) list wenzelm@4444: val indexname_ord: indexname * indexname -> order wenzelm@4444: val typ_ord: typ * typ -> order wenzelm@4444: val typs_ord: typ list * typ list -> order wenzelm@4444: val term_ord: term * term -> order wenzelm@4444: val terms_ord: term list * term list -> order paulson@14472: val hd_ord: term * term -> order wenzelm@4444: val termless: term * term -> bool wenzelm@14786: val no_dummyT: typ -> typ wenzelm@9536: val dummy_patternN: string wenzelm@9536: val no_dummy_patterns: term -> term wenzelm@9536: val replace_dummy_patterns: int * term -> int * term wenzelm@10552: val is_replaced_dummy_pattern: indexname -> bool wenzelm@16035: val show_dummy_patterns: term -> term wenzelm@13484: val adhoc_freeze_vars: term -> term * string list wenzelm@14786: val string_of_vname: indexname -> string wenzelm@14786: val string_of_vname': indexname -> string nipkow@15612: val string_of_term: term -> string wenzelm@4444: end; wenzelm@4444: wenzelm@4444: structure Term: 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: wenzelm@4626: (* Types are classified by sorts. *) clasohm@0: type class = string; clasohm@0: type sort = class list; wenzelm@14829: type arity = string * sort list * sort; 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 wenzelm@9536: | TVar of indexname * sort; clasohm@0: paulson@6033: (*Terms. Bound variables are indicated by depth number. clasohm@0: Free variables, (scheme) variables and constants have names. wenzelm@4626: An term is "closed" if every bound variable of level "lev" wenzelm@13000: 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: wenzelm@13000: datatype term = clasohm@0: Const of string * typ wenzelm@13000: | 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: paulson@6033: (** Types **) paulson@6033: paulson@6033: fun S --> T = Type("fun",[S,T]); paulson@6033: paulson@6033: (*handy for multiple args: [T1,...,Tn]--->T gives T1-->(T2--> ... -->T)*) skalberg@15570: val op ---> = Library.foldr (op -->); paulson@6033: paulson@6033: fun dest_Type (Type x) = x paulson@6033: | dest_Type T = raise TYPE ("dest_Type", [T], []); dixon@15914: fun dest_TVar (TVar x) = x dixon@15914: | dest_TVar T = raise TYPE ("dest_TVar", [T], []); dixon@15914: fun dest_TFree (TFree x) = x dixon@15914: | dest_TFree T = raise TYPE ("dest_TFree", [T], []); paulson@6033: clasohm@0: (** Discriminators **) clasohm@0: nipkow@7318: fun is_Bound (Bound _) = true nipkow@7318: | is_Bound _ = false; nipkow@7318: 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: paulson@15573: (*Differs from proofterm/is_fun in its treatment of TVar*) paulson@15573: fun is_funtype (Type("fun",[_,_])) = true paulson@15573: | is_funtype _ = false; paulson@15573: 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@4464: fun domain_type (Type("fun", [T,_])) = T paulson@4464: and range_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 skalberg@15570: | type_of1 (Ts, Bound i) = (List.nth (Ts,i) skalberg@15570: handle Subscript => 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) wenzelm@13000: | type_of1 (Ts, f$u) = clasohm@0: let val U = type_of1(Ts,u) clasohm@0: and T = type_of1(Ts,f) clasohm@0: in case T of wenzelm@9536: Type("fun",[T1,T2]) => wenzelm@9536: if T1=U then T2 else raise TYPE wenzelm@9536: ("type_of: type mismatch in application", [T1,U], [f$u]) wenzelm@13000: | _ => raise TYPE wenzelm@9536: ("type_of: function type is expected in application", wenzelm@9536: [T,U], [f$u]) clasohm@0: end; clasohm@0: clasohm@0: fun type_of t : typ = type_of1 ([],t); clasohm@0: clasohm@0: (*Determines the type of a term, with minimal checking*) wenzelm@13000: fun fastype_of1 (Ts, f$u) = lcp@61: (case fastype_of1 (Ts,f) of wenzelm@9536: Type("fun",[_,T]) => T wenzelm@9536: | _ => raise TERM("fastype_of: expected function type", [f$u])) lcp@61: | fastype_of1 (_, Const (_,T)) = T lcp@61: | fastype_of1 (_, Free (_,T)) = T skalberg@15570: | fastype_of1 (Ts, Bound i) = (List.nth(Ts,i) skalberg@15570: handle Subscript => raise TERM("fastype_of: Bound", [Bound i])) wenzelm@13000: | fastype_of1 (_, Var (_,T)) = T lcp@61: | fastype_of1 (Ts, Abs (_,T,u)) = T --> fastype_of1 (T::Ts, u); lcp@61: lcp@61: fun fastype_of t : typ = fastype_of1 ([],t); clasohm@0: clasohm@0: skalberg@15570: val list_abs = Library.foldr (fn ((x, T), t) => Abs (x, T, t)); wenzelm@10806: clasohm@0: (* maps (x1,...,xn)t to t *) wenzelm@13000: fun strip_abs_body (Abs(_,_,t)) = strip_abs_body t clasohm@0: | strip_abs_body u = u; clasohm@0: clasohm@0: (* maps (x1,...,xn)t to [x1, ..., xn] *) wenzelm@13000: fun strip_abs_vars (Abs(a,T,t)) = (a,T) :: strip_abs_vars t clasohm@0: | strip_abs_vars u = [] : (string*typ) list; clasohm@0: clasohm@0: clasohm@0: fun strip_qnt_body qnt = clasohm@0: let fun strip(tm as Const(c,_)$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) *) skalberg@15570: val list_comb : term * term list -> term = Library.foldl (op $); clasohm@0: clasohm@0: clasohm@0: (* maps f(t1,...,tn) to (f, [t1,...,tn]) ; naturally tail-recursive*) wenzelm@13000: fun strip_comb u : term * term list = clasohm@0: let fun stripc (f$t, ts) = stripc (f, t::ts) wenzelm@13000: | 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$u, a) = iter(f, iter(u, a)) clasohm@0: | iter(Bound _, a) = a clasohm@0: in iter end clasohm@0: clasohm@0: clasohm@0: (** Connectives of higher order logic **) clasohm@0: wenzelm@375: fun itselfT ty = Type ("itself", [ty]); wenzelm@14854: val a_itselfT = itselfT (TFree ("'a", [])); wenzelm@375: clasohm@0: val propT : typ = Type("prop",[]); clasohm@0: clasohm@0: val implies = Const("==>", propT-->propT-->propT); clasohm@0: clasohm@0: fun all T = Const("all", (T-->propT)-->propT); clasohm@0: clasohm@0: fun equals T = Const("==", T-->T-->propT); clasohm@0: clasohm@0: (* maps !!x1...xn. t to t *) wenzelm@13000: fun strip_all_body (Const("all",_)$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",_)$Abs(a,T,t)) = wenzelm@13000: (a,T) :: strip_all_vars t clasohm@0: | strip_all_vars t = [] : (string*typ) list; clasohm@0: clasohm@0: (*increments a term's non-local bound variables clasohm@0: required when moving a term within abstractions clasohm@0: inc is increment for bound variables clasohm@0: lev is level at which a bound variable is considered 'loose'*) wenzelm@13000: fun incr_bv (inc, lev, u as Bound i) = if i>=lev then Bound(i+inc) else u clasohm@0: | incr_bv (inc, lev, Abs(a,T,body)) = wenzelm@9536: Abs(a, T, incr_bv(inc,lev+1,body)) wenzelm@13000: | incr_bv (inc, lev, f$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: wenzelm@12981: (*Scan a pair of terms; while they are similar, wenzelm@12981: accumulate corresponding bound vars in "al"*) wenzelm@12981: fun match_bvs(Abs(x,_,s),Abs(y,_,t), al) = wenzelm@12981: match_bvs(s, t, if x="" orelse y="" then al wenzelm@12981: else (x,y)::al) wenzelm@12981: | match_bvs(f$s, g$t, al) = match_bvs(f,g,match_bvs(s,t,al)) wenzelm@12981: | match_bvs(_,_,al) = al; wenzelm@12981: wenzelm@12981: (* strip abstractions created by parameters *) wenzelm@12981: fun match_bvars((s,t),al) = match_bvs(strip_abs_body s, strip_abs_body t, al); wenzelm@12981: wenzelm@12981: fun rename_abs pat obj t = wenzelm@12981: let wenzelm@12981: val ren = match_bvs (pat, obj, []); wenzelm@12981: fun ren_abs (Abs (x, T, b)) = skalberg@15570: Abs (getOpt (assoc_string (ren, x), x), T, ren_abs b) wenzelm@12981: | ren_abs (f $ t) = ren_abs f $ ren_abs t wenzelm@12981: | ren_abs t = t skalberg@15531: in if null ren then NONE else SOME (ren_abs t) end; clasohm@0: clasohm@0: (*Accumulate all 'loose' bound vars referring to level 'lev' or beyond. clasohm@0: (Bound 0) is loose at level 0 *) wenzelm@13000: fun add_loose_bnos (Bound i, lev, js) = wenzelm@9536: 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). wenzelm@4626: Note that for ((%x y. c) a b), the bound vars in c are x=1 and y=0 wenzelm@9536: 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: *) wenzelm@13000: fun subst_bounds (args: term list, t) : term = clasohm@0: let val n = length args; clasohm@0: fun subst (t as Bound i, lev) = wenzelm@9536: (if i Bound(i-n) (*loose: change it*)) wenzelm@9536: | subst (Abs(a,T,body), lev) = Abs(a, T, subst(body,lev+1)) wenzelm@9536: | subst (f$t, lev) = subst(f,lev) $ subst(t,lev) wenzelm@9536: | subst (t,lev) = t clasohm@0: in case args of [] => t | _ => subst (t,0) end; clasohm@0: paulson@2192: (*Special case: one argument*) wenzelm@13000: fun subst_bound (arg, t) : term = paulson@2192: let fun subst (t as Bound i, lev) = wenzelm@9536: 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 = wenzelm@13000: let fun substf u = wenzelm@9536: case gen_assoc (op aconv) (pairs, u) of skalberg@15531: SOME u' => u' skalberg@15531: | NONE => (case u of Abs(a,T,t) => Abs(a, T, substf t) wenzelm@9536: | t$u' => substf t $ substf u' wenzelm@9536: | _ => 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)) wenzelm@9536: | f$rand => abst(lev,f) $ abst(lev,rand) wenzelm@9536: | _ => u) clasohm@0: in abst(0,body) end; clasohm@0: berghofe@13665: fun lambda (v as Free (x, T)) t = Abs (x, T, abstract_over (v, t)) berghofe@13665: | lambda (v as Var ((x, _), T)) t = Abs (x, T, abstract_over (v, t)) berghofe@13665: | lambda v t = raise TERM ("lambda", [v, t]); 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 wenzelm@13000: | 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 wenzelm@13000: | 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 wenzelm@13000: | list_all ((a,T)::vars, t) = clasohm@0: (all T) $ (Abs(a, T, list_all(vars,t))); clasohm@0: wenzelm@13000: (*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) wenzelm@9536: | subst (f$t') = subst f $ subst t' skalberg@15570: | subst t = getOpt (assoc(instl,t),t) clasohm@0: in subst t end; clasohm@0: berghofe@15797: (*Replace the ATOMIC type Ti by Ui; instl = [(T1,U1), ..., (Tn,Un)].*) berghofe@15797: fun typ_subst_atomic [] T = T berghofe@15797: | typ_subst_atomic instl (Type (s, Ts)) = berghofe@15797: Type (s, map (typ_subst_atomic instl) Ts) berghofe@15797: | typ_subst_atomic instl T = getOpt (assoc (instl, T), T); berghofe@15797: 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) wenzelm@9536: | subst(T as TFree _) = T skalberg@15570: | subst(T as TVar(ixn,_)) = getOpt (assoc(iTs,ixn),T) 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 skalberg@15570: let fun subst(v as Var(ixn,_)) = getOpt (assoc(itms,ixn),v) 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 skalberg@15531: NONE => Var(ixn,typ_subst_TVars iTs T) skalberg@15531: | 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: paulson@15573: (** Identifying first-order terms **) paulson@15573: paulson@15573: (*Argument Ts is a reverse list of binder types, needed if term t contains Bound vars*) paulson@15573: fun has_not_funtype Ts t = not (is_funtype (fastype_of1 (Ts,t))); paulson@15573: kleing@15962: (*First order means in all terms of the form f(t1,...,tn) no argument has a kleing@15962: function type. The meta-quantifier "all" is excluded--its argument always kleing@15962: has a function type--through a recursive call into its body.*) paulson@15573: fun first_order1 Ts (Abs (_,T,body)) = first_order1 (T::Ts) body paulson@15954: | first_order1 Ts (Const("all",_)$Abs(a,T,body)) = paulson@15954: not (is_funtype T) andalso first_order1 (T::Ts) body paulson@15573: | first_order1 Ts t = paulson@15573: case strip_comb t of paulson@15573: (Var _, ts) => forall (first_order1 Ts andf has_not_funtype Ts) ts paulson@15573: | (Free _, ts) => forall (first_order1 Ts andf has_not_funtype Ts) ts paulson@15573: | (Const _, ts) => forall (first_order1 Ts andf has_not_funtype Ts) ts paulson@15573: | (Bound _, ts) => forall (first_order1 Ts andf has_not_funtype Ts) ts paulson@15573: | (Abs _, ts) => false (*not in beta-normal form*) paulson@15573: | _ => error "first_order: unexpected case"; paulson@15573: paulson@15573: val is_first_order = first_order1 []; paulson@15573: clasohm@0: (*Computing the maximum index of a typ*) paulson@2146: fun maxidx_of_typ(Type(_,Ts)) = maxidx_of_typs Ts clasohm@0: | maxidx_of_typ(TFree _) = ~1 paulson@2146: | maxidx_of_typ(TVar((_,i),_)) = i paulson@2146: and maxidx_of_typs [] = ~1 paulson@2146: | maxidx_of_typs (T::Ts) = Int.max(maxidx_of_typ T, maxidx_of_typs Ts); clasohm@0: clasohm@0: clasohm@0: (*Computing the maximum index of a term*) clasohm@0: fun maxidx_of_term (Const(_,T)) = maxidx_of_typ T clasohm@0: | maxidx_of_term (Bound _) = ~1 clasohm@0: | maxidx_of_term (Free(_,T)) = maxidx_of_typ T paulson@2146: | maxidx_of_term (Var ((_,i), T)) = Int.max(i, maxidx_of_typ T) paulson@2146: | maxidx_of_term (Abs (_,T,u)) = Int.max(maxidx_of_term u, maxidx_of_typ T) paulson@2146: | maxidx_of_term (f$t) = Int.max(maxidx_of_term f, maxidx_of_term t); clasohm@0: skalberg@15570: fun maxidx_of_terms ts = Library.foldl Int.max (~1, map maxidx_of_term ts); berghofe@13665: 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: wenzelm@4626: (*Dummy type for parsing and printing. Will be replaced during type inference. *) clasohm@0: val dummyT = Type("dummy",[]); clasohm@0: wenzelm@14786: fun no_dummyT typ = wenzelm@14786: let wenzelm@14786: fun check (T as Type ("dummy", _)) = wenzelm@14786: raise TYPE ("Illegal occurrence of '_' dummy type", [T], []) skalberg@15570: | check (Type (_, Ts)) = List.app check Ts wenzelm@14786: | check _ = (); wenzelm@14786: in check typ; typ end; wenzelm@14786: clasohm@0: clasohm@0: (*** Printing ***) clasohm@0: wenzelm@14676: (*Makes a variant of a name distinct from the names in bs. wenzelm@14676: First attaches the suffix and then increments this; wenzelm@12306: preserves a suffix of underscores "_". *) wenzelm@12306: fun variant bs name = wenzelm@12306: let wenzelm@12306: val (c, u) = pairself implode (Library.take_suffix (equal "_") (Symbol.explode name)); wenzelm@12902: fun vary2 c = if ((c ^ u) mem_string bs) then vary2 (Symbol.bump_string c) else c; wenzelm@14676: fun vary1 c = if ((c ^ u) mem_string bs) then vary2 (Symbol.bump_init c) else c; wenzelm@12306: in vary1 (if c = "" then "u" else c) ^ u end; clasohm@0: clasohm@0: (*Create variants of the list of names, with priority to the first ones*) clasohm@0: fun variantlist ([], used) = [] wenzelm@13000: | variantlist(b::bs, used) = clasohm@0: let val b' = variant used b clasohm@0: in b' :: variantlist (bs, b'::used) end; clasohm@0: wenzelm@14695: (*Invent fresh names*) wenzelm@14695: fun invent_names _ _ 0 = [] wenzelm@14695: | invent_names used a n = wenzelm@14695: let val b = Symbol.bump_string a in wenzelm@14695: if a mem_string used then invent_names used b n wenzelm@14695: else a :: invent_names used b (n - 1) wenzelm@14695: end; wenzelm@11353: wenzelm@4017: (** Consts etc. **) wenzelm@4017: skalberg@15574: fun add_typ_classes (Type (_, Ts), cs) = foldr add_typ_classes cs Ts 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@16294: fun add_typ_tycons (Type (c, Ts), cs) = foldr add_typ_tycons (c ins_string cs) Ts 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@9319: fun add_term_consts (Const (c, _), cs) = c ins_string 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: obua@16108: fun add_term_constsT (Const c, cs) = c::cs obua@16108: | add_term_constsT (t $ u, cs) = add_term_constsT (t, add_term_constsT (u, cs)) obua@16108: | add_term_constsT (Abs (_, _, t), cs) = add_term_constsT (t, cs) obua@16108: | add_term_constsT (_, cs) = cs; obua@16108: nipkow@13646: fun term_consts t = add_term_consts(t,[]); nipkow@13646: obua@16108: fun term_constsT t = add_term_constsT(t,[]); obua@16108: oheimb@4185: fun exists_Const P t = let wenzelm@9536: fun ex (Const c ) = P c wenzelm@9536: | ex (t $ u ) = ex t orelse ex u wenzelm@9536: | ex (Abs (_, _, t)) = ex t wenzelm@9536: | ex _ = false oheimb@4185: in ex t end; wenzelm@4017: nipkow@4631: fun exists_subterm P = nipkow@4631: let fun ex t = P t orelse nipkow@4631: (case t of nipkow@4631: u $ v => ex u orelse ex v nipkow@4631: | Abs(_, _, u) => ex u nipkow@4631: | _ => false) nipkow@4631: in ex end; nipkow@4631: 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: 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: wenzelm@12802: (*Accumulates the names of Frees in the term, suppressing duplicates.*) wenzelm@12802: fun add_term_free_names (Free(a,_), bs) = a ins_string bs wenzelm@12802: | add_term_free_names (f$u, bs) = add_term_free_names (f, add_term_free_names(u, bs)) wenzelm@12802: | add_term_free_names (Abs(_,_,t), bs) = add_term_free_names(t,bs) wenzelm@12802: | add_term_free_names (_, bs) = bs; wenzelm@12802: clasohm@0: (*Accumulates the names in the term, suppressing duplicates. clasohm@0: Includes Frees and Consts. For choosing unambiguous bound var names.*) wenzelm@10666: fun add_term_names (Const(a,_), bs) = NameSpace.base a ins_string bs paulson@2176: | add_term_names (Free(a,_), bs) = a ins_string bs clasohm@0: | add_term_names (f$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. *) skalberg@15574: fun add_typ_tvars(Type(_,Ts),vs) = foldr add_typ_tvars vs Ts clasohm@0: | add_typ_tvars(TFree(_),vs) = vs wenzelm@16294: | add_typ_tvars(TVar(v),vs) = insert (op =) v vs; clasohm@0: clasohm@0: (*Accumulates the TFrees in a type, suppressing duplicates. *) skalberg@15574: fun add_typ_tfree_names(Type(_,Ts),fs) = foldr add_typ_tfree_names fs Ts paulson@2176: | add_typ_tfree_names(TFree(f,_),fs) = f ins_string fs clasohm@0: | add_typ_tfree_names(TVar(_),fs) = fs; clasohm@0: skalberg@15574: fun add_typ_tfrees(Type(_,Ts),fs) = foldr add_typ_tfrees fs Ts wenzelm@16294: | add_typ_tfrees(TFree(f),fs) = insert (op =) f fs clasohm@0: | add_typ_tfrees(TVar(_),fs) = fs; clasohm@0: skalberg@15574: fun add_typ_varnames(Type(_,Ts),nms) = foldr add_typ_varnames nms Ts 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: skalberg@15570: fun add_typ_ixns(ixns,Type(_,Ts)) = Library.foldl add_typ_ixns (ixns,Ts) wenzelm@13000: | add_typ_ixns(ixns,TVar(ixn,_)) = if mem_ix (ixn, ixns) then ixns wenzelm@9536: 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)) = wenzelm@9536: (variant (map #1 vars @ names) a, T) :: vars skalberg@15570: in Library.foldl rename_aT ([],vars) end; clasohm@0: clasohm@0: fun rename_wrt_term t = rename_aTs (add_term_names(t,[])); clasohm@1364: paulson@1417: wenzelm@4286: (* left-ro-right traversal *) wenzelm@4286: wenzelm@4286: (*foldl atoms of type*) skalberg@15570: fun foldl_atyps f (x, Type (_, Ts)) = Library.foldl (foldl_atyps f) (x, Ts) wenzelm@4286: | foldl_atyps f x_atom = f x_atom; wenzelm@4286: wenzelm@4286: (*foldl atoms of term*) wenzelm@4286: fun foldl_aterms f (x, t $ u) = foldl_aterms f (foldl_aterms f (x, t), u) wenzelm@4286: | foldl_aterms f (x, Abs (_, _, t)) = foldl_aterms f (x, t) wenzelm@4286: | foldl_aterms f x_atom = f x_atom; wenzelm@4286: wenzelm@6548: fun foldl_map_aterms f (x, t $ u) = wenzelm@6548: let val (x', t') = foldl_map_aterms f (x, t); val (x'', u') = foldl_map_aterms f (x', u); wenzelm@6548: in (x'', t' $ u') end wenzelm@6548: | foldl_map_aterms f (x, Abs (a, T, t)) = wenzelm@6548: let val (x', t') = foldl_map_aterms f (x, t) in (x', Abs (a, T, t')) end wenzelm@6548: | foldl_map_aterms f x_atom = f x_atom; wenzelm@6548: wenzelm@4286: (*foldl types of term*) wenzelm@8609: fun foldl_term_types f (x, t as Const (_, T)) = f t (x, T) wenzelm@8609: | foldl_term_types f (x, t as Free (_, T)) = f t (x, T) wenzelm@8609: | foldl_term_types f (x, t as Var (_, T)) = f t (x, T) wenzelm@8609: | foldl_term_types f (x, Bound _) = x wenzelm@8609: | foldl_term_types f (x, t as Abs (_, T, b)) = foldl_term_types f (f t (x, T), b) wenzelm@8609: | foldl_term_types f (x, t $ u) = foldl_term_types f (foldl_term_types f (x, t), u); wenzelm@8609: wenzelm@8609: fun foldl_types f = foldl_term_types (fn _ => f); wenzelm@4286: wenzelm@12499: (*collect variables*) wenzelm@16294: val add_tvarsT = foldl_atyps (fn (vs, TVar v) => insert (op =) v vs | (vs, _) => vs); wenzelm@12499: val add_tvars = foldl_types add_tvarsT; wenzelm@16294: val add_vars = foldl_aterms (fn (vs, Var v) => insert (op =) v vs | (vs, _) => vs); wenzelm@16294: val add_frees = foldl_aterms (fn (vs, Free v) => insert (op =) v vs | (vs, _) => vs); wenzelm@12499: wenzelm@15025: (*collect variable names*) wenzelm@15025: val add_term_varnames = foldl_aterms (fn (xs, Var (x, _)) => ins_ix (x, xs) | (xs, _) => xs); wenzelm@15025: fun term_varnames t = add_term_varnames ([], t); wenzelm@4286: paulson@1417: wenzelm@4444: (** type and term orders **) wenzelm@4444: wenzelm@4444: fun indexname_ord ((x, i), (y, j)) = paulson@14472: (case Int.compare (i, j) of EQUAL => String.compare (x, y) | ord => ord); wenzelm@4444: paulson@14472: val sort_ord = list_ord String.compare; wenzelm@13000: wenzelm@4444: wenzelm@4444: (* typ_ord *) wenzelm@4444: paulson@14472: fun typ_ord (Type x, Type y) = prod_ord String.compare typs_ord (x, y) wenzelm@4444: | typ_ord (Type _, _) = GREATER wenzelm@4444: | typ_ord (TFree _, Type _) = LESS paulson@14472: | typ_ord (TFree x, TFree y) = prod_ord String.compare sort_ord (x, y) wenzelm@4444: | typ_ord (TFree _, TVar _) = GREATER wenzelm@4444: | typ_ord (TVar _, Type _) = LESS wenzelm@4444: | typ_ord (TVar _, TFree _) = LESS wenzelm@13000: | typ_ord (TVar x, TVar y) = prod_ord indexname_ord sort_ord (x, y) wenzelm@4444: and typs_ord Ts_Us = list_ord typ_ord Ts_Us; wenzelm@4444: wenzelm@4444: wenzelm@4444: (* term_ord *) wenzelm@4444: wenzelm@4444: (*a linear well-founded AC-compatible ordering for terms: wenzelm@4444: s < t <=> 1. size(s) < size(t) or wenzelm@4444: 2. size(s) = size(t) and s=f(...) and t=g(...) and f typ_ord (T, U) | ord => ord) wenzelm@4444: | term_ord (t, u) = paulson@14472: (case Int.compare (size_of_term t, size_of_term u) of wenzelm@4444: EQUAL => wenzelm@4444: let val (f, ts) = strip_comb t and (g, us) = strip_comb u in wenzelm@4444: (case hd_ord (f, g) of EQUAL => terms_ord (ts, us) | ord => ord) wenzelm@4444: end wenzelm@4444: | ord => ord) wenzelm@4444: and hd_ord (f, g) = paulson@14472: prod_ord (prod_ord indexname_ord typ_ord) Int.compare (dest_hd f, dest_hd g) wenzelm@4444: and terms_ord (ts, us) = list_ord term_ord (ts, us); wenzelm@4444: wenzelm@4444: fun termless tu = (term_ord tu = LESS); wenzelm@4444: berghofe@8408: structure Vartab = TableFun(type key = indexname val ord = indexname_ord); wenzelm@13000: structure Typtab = TableFun(type key = typ val ord = typ_ord); berghofe@8408: structure Termtab = TableFun(type key = term val ord = term_ord); berghofe@8408: wenzelm@4444: wenzelm@13000: (*** Compression of terms and types by sharing common subtrees. wenzelm@13000: Saves 50-75% on storage requirements. As it is a bit slow, wenzelm@13000: it should be called only for axioms, stored theorems, etc. wenzelm@13000: Recorded term and type fragments are never disposed. ***) paulson@1417: wenzelm@16338: paulson@1417: (** Sharing of types **) paulson@1417: wenzelm@13000: val memo_types = ref (Typtab.empty: typ Typtab.table); paulson@1417: paulson@1417: fun compress_type T = wenzelm@13000: (case Typtab.lookup (! memo_types, T) of skalberg@15531: SOME T' => T' skalberg@15531: | NONE => wenzelm@13000: let val T' = (case T of Type (a, Ts) => Type (a, map compress_type Ts) | _ => T) wenzelm@13000: in memo_types := Typtab.update ((T', T'), ! memo_types); T' end); wenzelm@13000: paulson@1417: paulson@1417: (** Sharing of atomic terms **) paulson@1417: wenzelm@13000: val memo_terms = ref (Termtab.empty : term Termtab.table); paulson@1417: paulson@1417: fun share_term (t $ u) = share_term t $ share_term u wenzelm@13000: | share_term (Abs (a, T, u)) = Abs (a, T, share_term u) paulson@1417: | share_term t = wenzelm@13000: (case Termtab.lookup (! memo_terms, t) of skalberg@15531: SOME t' => t' skalberg@15531: | NONE => (memo_terms := Termtab.update ((t, t), ! memo_terms); t)); paulson@1417: paulson@1417: val compress_term = share_term o map_term_types compress_type; paulson@1417: wenzelm@4444: wenzelm@9536: (* dummy patterns *) wenzelm@9536: wenzelm@9536: val dummy_patternN = "dummy_pattern"; wenzelm@9536: wenzelm@9536: fun is_dummy_pattern (Const ("dummy_pattern", _)) = true wenzelm@9536: | is_dummy_pattern _ = false; wenzelm@9536: wenzelm@9536: fun no_dummy_patterns tm = wenzelm@9536: if not (foldl_aterms (fn (b, t) => b orelse is_dummy_pattern t) (false, tm)) then tm wenzelm@9536: else raise TERM ("Illegal occurrence of '_' dummy pattern", [tm]); wenzelm@9536: wenzelm@11903: fun replace_dummy Ts (i, Const ("dummy_pattern", T)) = wenzelm@11903: (i + 1, list_comb (Var (("_dummy_", i), Ts ---> T), map Bound (0 upto length Ts - 1))) wenzelm@11903: | replace_dummy Ts (i, Abs (x, T, t)) = wenzelm@11903: let val (i', t') = replace_dummy (T :: Ts) (i, t) wenzelm@11903: in (i', Abs (x, T, t')) end wenzelm@11903: | replace_dummy Ts (i, t $ u) = wenzelm@11903: let val (i', t') = replace_dummy Ts (i, t); val (i'', u') = replace_dummy Ts (i', u) wenzelm@11903: in (i'', t' $ u') end wenzelm@11903: | replace_dummy _ (i, a) = (i, a); wenzelm@11903: wenzelm@11903: val replace_dummy_patterns = replace_dummy []; wenzelm@9536: wenzelm@10552: fun is_replaced_dummy_pattern ("_dummy_", _) = true wenzelm@10552: | is_replaced_dummy_pattern _ = false; wenzelm@9536: wenzelm@16035: fun show_dummy_patterns (Var (("_dummy_", _), T)) = Const ("dummy_pattern", T) wenzelm@16035: | show_dummy_patterns (t $ u) = show_dummy_patterns t $ show_dummy_patterns u wenzelm@16035: | show_dummy_patterns (Abs (x, T, t)) = Abs (x, T, show_dummy_patterns t) wenzelm@16035: | show_dummy_patterns a = a; wenzelm@16035: wenzelm@13484: wenzelm@13484: (* adhoc freezing *) wenzelm@13484: wenzelm@13484: fun adhoc_freeze_vars tm = wenzelm@13484: let wenzelm@13484: fun mk_inst (var as Var ((a, i), T)) = wenzelm@13484: let val x = a ^ Library.gensym "_" ^ string_of_int i wenzelm@13484: in ((var, Free(x, T)), x) end; wenzelm@13484: val (insts, xs) = split_list (map mk_inst (term_vars tm)); wenzelm@13484: in (subst_atomic insts tm, xs) end; wenzelm@13484: wenzelm@13484: wenzelm@14786: (* string_of_vname *) wenzelm@14786: wenzelm@15986: val show_question_marks = ref true; berghofe@15472: wenzelm@14786: fun string_of_vname (x, i) = wenzelm@14786: let wenzelm@15986: val question_mark = if ! show_question_marks then "?" else ""; wenzelm@15986: val idx = string_of_int i; wenzelm@15986: val dot = wenzelm@15986: (case rev (Symbol.explode x) of wenzelm@15986: _ :: "\\<^isub>" :: _ => false wenzelm@15986: | _ :: "\\<^isup>" :: _ => false wenzelm@15986: | c :: _ => Symbol.is_digit c wenzelm@15986: | _ => true); wenzelm@14786: in wenzelm@15986: if dot then question_mark ^ x ^ "." ^ idx wenzelm@15986: else if i <> 0 then question_mark ^ x ^ idx wenzelm@15986: else question_mark ^ x wenzelm@14786: end; wenzelm@14786: wenzelm@14786: fun string_of_vname' (x, ~1) = x wenzelm@14786: | string_of_vname' xi = string_of_vname xi; wenzelm@14786: nipkow@15612: fun string_of_term (Const(s,_)) = s nipkow@15612: | string_of_term (Free(s,_)) = s nipkow@15612: | string_of_term (Var(ix,_)) = string_of_vname ix nipkow@15612: | string_of_term (Bound i) = string_of_int i nipkow@15612: | string_of_term (Abs(x,_,t)) = "%" ^ x ^ ". " ^ string_of_term t nipkow@15612: | string_of_term (s $ t) = nipkow@15612: "(" ^ string_of_term s ^ " " ^ string_of_term t ^ ")" nipkow@15612: clasohm@1364: end; clasohm@1364: wenzelm@4444: structure BasicTerm: BASIC_TERM = Term; wenzelm@4444: open BasicTerm;