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The one-sided pattern matching seems to be a peculiarity of Elixir. The post above discusses an implementation of full unification without that restriction. To

The one-sided pattern matching seems to be a peculiarity of Elixir. The post above discusses an implementation of full unification without that restriction. To clarify, unification is not generally restricted to one-sided matching only. Is unification unnecessary for pattern matching? I think that depends on what you meany by "pattern matching". In programming cirlces "pattern matching" usually means matching strings. Now, unification is Turing-complete pattern matching, meaning that it goes well beyond e.g. regular expressions that can only match the set of strings recognised by regular automata. For instance, in Prolog, you can unify a variable with an entire Prolog program and call the program at runtime, etc. So if you need "pattern matching" only to match strings then you probably don't need the full power of unification. If I understand correctly (not an expert) Hindley-Milner type checking, the type checking that uses unification, relies exactly on that ability of unification to match entire programs. Anyway that kind of type checking is indeed pattern matching by unification. So it's not different than pattern matching on strings with regular expressions. The difference is only in what kinds of strings can be matched.

troupo 2y ago
> The one-sided pattern matching seems to be a peculiarity of Elixir. And Erlang. And Haskell. And OCaml. And F#. And... As far as I understand, only Prolog has unification (out of more-or-less used/known languages). And in languages that require (rather awkward and verbose) workarounds for this functionality, it's hard to see the immediate value of unification.
- YeGoblynQueenne 2y ago
  >> And Erlang. And Haskell. And OCaml. And F#. And.. Thanks, I didn't know that. I took the article to mean that this kind of one-sided pattern matching is unique in Elixir. My misreading. From what I've seen it's true that most languages that have support for pattern matching have special constructs for it, whereas in Prolog it's baked in to the only data structure in the language, the term, which can be a single variable (a logic variable that can unify with ... anything). I don't know how useful or not unification would be in a language other than Prolog to be honest. In Prolog it's an integral component of the Resolution-based theorem prover used as an interpreter of Prolog programs: resolution proceeds by unifying Horn goals to the heads of definite clauses, to produce new goals, recursively. More over, when one runs a Prolog "query" the result of the query itself is the substitution of the variables in the query, i.e. the substitution that makes the query true [1]; a substitution derived and propagated by unification. I like how George W. Lloyd describes the use of unification in Prolog. Apologies in advance for the long-form quote: The idea that first order logic, or at least substantial subsets of it, could be used as a programming language was revolutionary, because, until 1972, logic had only ever been used as a specification or declarative language in computer science. However, what [R. Kowalski, Predicate Logic as a Programming Language, 1974] shows is that logic has a procedural interpretation, which makes it very effective as a programming language. Briefly, a program clause A <- B1, ..., Bn is regarded as a procedure definition. If <- C1, ..., Ck is a goal, then each Cj is regarded as a procedure call. A program is run by giving it an initial goal. If the current goal is <- C1, ..., Ck, a step in the computation involves unifying some Cj with the head A of a program clause A <- B1, ... Bn and thus reducing the current goal to the goal <-(C1, ..., Cj-1, B1, ..., Bn, Cj+1, ..., Ck)θ, where θ is the unifying substitution. Unification thus becomes a uniform mechanism for parameter passing, data selection and data construction. The computation terminates when the empty goal is produced. And that's first-order SLD-Resolution, with unification, in a nutshell! From George Lloyd: Foundations of Logic Programming, second Ed. 1993. There's a copy of the book here: https://archive.org/details/foundationsoflog0000lloy_o7l2 https://archive.org/details/foundationsoflog0000lloy_o7l2 But it's a limited preview :/ ________ [1] ... well, the substitution that makes the Horn goal that we call a "query" false, in reality, because Prolog proves things by refutation but we fudge it a bit.
  - jerf 2y ago
    When you're using pattern matching to also create variables, it's just really confusing to be able to create variables with both sides of the expression. It can get confusing enough as it is. Haskell has some extensions to pattern matching that AIUI are generally considered just too "powerful" to generally use, as it makes it very difficult to read, for instance. Plus to a first approximation you can always just swap the binding from the right to the left. A deeper analysis may reveal there's some case you can't do that, there's a lot to pattern matching and I'm not going to try to sit here and construct a case where you can't, but certainly the most common cases (by far) would just require a simple swap, so it's not an onerous requirement. And if you did construct a case where you can't, you could make a very solid software engineering case that you just shouldn't do that and should do it it two parts. To the extent this doesn't apply to prolog, it would be when prolog is functioning directly as a logic language rather than a programming language, and to be honest I'd still advise against a prolog programmer binding variables on both sides of an expression unless they're forced to for some reason just because if nothing else, you may have to understand your own code a week later. Note this specifically applies to binding variables; I'm not bothered by two already-bound variables being matched against each other, that's just prolog functioning as designed.
  - jpt4 2y ago
    The Curry-Howard Correspondence is more of an observation than a theorem, but insofar as it describes the general concept of relating logics and programming languages, what is the CHC for logic programming languages? If strikes me that LP directly instantiates and manipulates logical expressions, in a "self-dual" sense; or, is it that the various "proof procedures" of the logic side map to "proof search" algorithms on the computing side?
- throwawaymaths 2y ago
  >And Erlang. And Haskell. And OCaml. And F#. And... JavaScript (maps), Rust, Ruby, Python...
  - __jonas 2y ago
    What do you mean by this? Do maps in JavaScript have some kind of pattern matching?
    - munificent 2y ago
      JavaScript supports destructuring lists and objects (sort of like maps): https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Operators/Destructuring_assignment https://developer.mozilla.org/en-US/docs/Web/JavaScript/Refe... It's not full pattern matching because as far as I know they don't support refutable patterns, but it handles destructuring and binding to variables.
      - __jonas 2y ago
        ah, it didn’t occur to me to view destructuring as pattern matching but I guess it is a bit similar.
  - weatherlight 2y ago
    It's not the same. > [a, 2, 2, b] = [1, 2, 2, 3] [1, 2, 2, 3] > a 1 > b 3 > [foo, 2, bar] = [3,3,3] %MatchError{term: [3, 3, 3]} > foo %CompileError{description: "undefined function foo/0 (there is no such import)", file: "nofile", line: 1} Ruby does something similar but the variables are bound in the scope of the case block.
    - gergo_barany 2y ago
      What's not the same as what? Based on your examples it looks like you're saying that unification is not the same as pattern matching. But nobody said it was.
- weatherlight 2y ago
  its not quite the same. you have to write quiet a bit of OCaml or Haskell to do the following. [foo, [2, 3, bar], baz, 5] = [1,[2,3,4], 5] If there's a match, the bindings "foo", "bar", "baz" will be bound to the values on the right hand side. if not an exception will be thrown (You are right, though, Erlang and Elixir have the same semantics, both being on the BEAM)
ReleaseCandidat 2y ago
> I think that depends on what you meany by "pattern matching" Oh, yes, that's true. "Pattern matching" as that what normally is used in "functional programming languages". This kind of pattern matching does not need unification. The IMHO best (correct, but understandable and with all needed definitions) explanation of it is in chapters 4 "STRUCTURED TYPES AND THE SEMANTICS OF PATTERN-MATCHING" and 5 "EFFICIENT COMPILATION OF PATTERN-MATCHING" of Peyton Jones et al., "The implementation of functional programming languages". https://simon.peytonjones.org/slpj-book-1987/ https://simon.peytonjones.org/slpj-book-1987/ > In programming cirlces "pattern matching" usually means matching strings. Depends on the "circle" ;) https://en.wikipedia.org/wiki/Pattern_matching https://en.wikipedia.org/wiki/Pattern_matching
- YeGoblynQueenne 2y ago
  Thanks, I don't really know much about Functional Programming. My expertise is in logic programming which btw is a different paradigm. I've heard it said that they're similar and it seems to me the reason was the support for pattern matching in functional languages. I agree that what "pattern matching" means depends on a programmer's background. It's interesting that the wikipedia article that you link to does not mention "unification" at all and only has one reference in Prolog as one of a group of example languages with a "pattern matching construct"; which is not how I would describe the use of the unification algorithm in Prolog. To be honest, I am not sure what is meant by "pattern matching". It seems to be a loosely defined term, like "Finite State Machine" (as opposed to "Finite State Automaton"). I expect that the book you linked to has a more formal treating, perhaps, but from what I can tell from a quick look the "pattern matching" here is based on types. In Prolog, unification is used to bind values to logic variables, which do not have types. So a variable, X, in Prolog can unify, i.e. "match with" absolutely anything. A "pattern" then can be formed by constructing terms (the only data structure in Prolog) with "holes" like p(X, a, b, Y,[1,2,3|Tail], f(Z)) etc. where capital letters are variables. One use of this ability is to manipulate singly-linked lists to insert in or remove elements from their tail, where normally only the head of such a list can be accessed directly. What I mean is that in Prolog a list is denoted by the special syntax [H|T] where H is the head of a list (and can be any term, including another list) and T is the tail of the list, another list. Normally one appends to a list in Prolog using the append/3 predicate: append([], L, L). append([H|T], L, [H|R]) :- append(T, L, R). This works on ordinary lists, but it is also possible to define a "difference list" as a term, e.g. like: [a,b,c,d|T]-T Where T is a variable bound to the end of the tail of the list. Two difference lists like that one can be appended with the following predicate: append_dl(Xs-Ys, Ys-Zs, Xs-Zs). For example: ?- Xs = [a,b,c,d|T1]-T1, Ys = [e,f,g,h|T2]-T2, append_dl(Xs,Ys,Zs). Xs = [a,b,c,d,e,f,g,h|T2]-[e,f,g,h|T2], T1 = [e,f,g,h|T2], Ys = [e,f,g,h|T2]-T2, Zs = [a,b,c,d,e,f,g,h|T2]-T2. The result of appending is in Zs, but you can see the result of the intermediary unification steps in the other variables echoed in the Prolog REPL (the "listener"). Of course, because this is Prolog you can also use the same predicate to split a list: ?- Xs = [a,b,c,d|T1]-T1, Zs = [a,b,c,d,e,f,g,h|T2]-T2, append_dl(Xs,Ys,Zs). Xs = [a,b,c,d,e,f,g,h|T2]-[e,f,g,h|T2], T1 = [e,f,g,h|T2], Zs = [a,b,c,d,e,f,g,h|T2]-T2, Ys = [e,f,g,h|T2]-T2. Where Ys is what remains if we split Xs from Zs. Appending or splitting lists like this is preferred to append/3 because it appends the two lists in a single operation so it can be used to economically put a list together in a loop. The same technique is used with Prolog's Definite Clause Grammars where the "difference" in a difference list is the start and end of a string accepted by a grammar, acting as a parser. https://en.wikipedia.org/wiki/Definite_clause_grammar https://en.wikipedia.org/wiki/Definite_clause_grammar Sterling and Shapiro's "The Craft of Prolog" has a nice chapter on "Incomplete Data Structures" using difference lists and patterns with "holes" but I don't think there's a free version online, unfortunately.
gergo_barany 2y ago
> Now, unification is Turing-complete pattern matching No. First-order syntactic unification is not Turing complete. The combination of unification and resolution is Turing complete. > For instance, in Prolog, you can unify a variable with an entire Prolog program and call the program at runtime, etc. Lots of languages allow you to do this. Lisp had "eval" ten years before Prolog existed. Unification is not necessary for this. Prolog is great, unification is great. Some other things are great too.

troupo 2y ago

> The one-sided pattern matching seems to be a peculiarity of Elixir. And Erlang. And Haskell. And OCaml. And F#. And... As far as I understand, only Prolog has unification (out of more-or-less used/known languages). And in languages that require (rather awkward and verbose) workarounds for this functionality, it's hard to see the immediate value of unification.

YeGoblynQueenne 2y ago
>> And Erlang. And Haskell. And OCaml. And F#. And.. Thanks, I didn't know that. I took the article to mean that this kind of one-sided pattern matching is unique in Elixir. My misreading. From what I've seen it's true that most languages that have support for pattern matching have special constructs for it, whereas in Prolog it's baked in to the only data structure in the language, the term, which can be a single variable (a logic variable that can unify with ... anything). I don't know how useful or not unification would be in a language other than Prolog to be honest. In Prolog it's an integral component of the Resolution-based theorem prover used as an interpreter of Prolog programs: resolution proceeds by unifying Horn goals to the heads of definite clauses, to produce new goals, recursively. More over, when one runs a Prolog "query" the result of the query itself is the substitution of the variables in the query, i.e. the substitution that makes the query true [1]; a substitution derived and propagated by unification. I like how George W. Lloyd describes the use of unification in Prolog. Apologies in advance for the long-form quote: The idea that first order logic, or at least substantial subsets of it, could be used as a programming language was revolutionary, because, until 1972, logic had only ever been used as a specification or declarative language in computer science. However, what [R. Kowalski, Predicate Logic as a Programming Language, 1974] shows is that logic has a procedural interpretation, which makes it very effective as a programming language. Briefly, a program clause A <- B1, ..., Bn is regarded as a procedure definition. If <- C1, ..., Ck is a goal, then each Cj is regarded as a procedure call. A program is run by giving it an initial goal. If the current goal is <- C1, ..., Ck, a step in the computation involves unifying some Cj with the head A of a program clause A <- B1, ... Bn and thus reducing the current goal to the goal <-(C1, ..., Cj-1, B1, ..., Bn, Cj+1, ..., Ck)θ, where θ is the unifying substitution. Unification thus becomes a uniform mechanism for parameter passing, data selection and data construction. The computation terminates when the empty goal is produced. And that's first-order SLD-Resolution, with unification, in a nutshell! From George Lloyd: Foundations of Logic Programming, second Ed. 1993. There's a copy of the book here: https://archive.org/details/foundationsoflog0000lloy_o7l2 https://archive.org/details/foundationsoflog0000lloy_o7l2 But it's a limited preview :/ ________ [1] ... well, the substitution that makes the Horn goal that we call a "query" false, in reality, because Prolog proves things by refutation but we fudge it a bit.
- jerf 2y ago
  When you're using pattern matching to also create variables, it's just really confusing to be able to create variables with both sides of the expression. It can get confusing enough as it is. Haskell has some extensions to pattern matching that AIUI are generally considered just too "powerful" to generally use, as it makes it very difficult to read, for instance. Plus to a first approximation you can always just swap the binding from the right to the left. A deeper analysis may reveal there's some case you can't do that, there's a lot to pattern matching and I'm not going to try to sit here and construct a case where you can't, but certainly the most common cases (by far) would just require a simple swap, so it's not an onerous requirement. And if you did construct a case where you can't, you could make a very solid software engineering case that you just shouldn't do that and should do it it two parts. To the extent this doesn't apply to prolog, it would be when prolog is functioning directly as a logic language rather than a programming language, and to be honest I'd still advise against a prolog programmer binding variables on both sides of an expression unless they're forced to for some reason just because if nothing else, you may have to understand your own code a week later. Note this specifically applies to binding variables; I'm not bothered by two already-bound variables being matched against each other, that's just prolog functioning as designed.
- jpt4 2y ago
  The Curry-Howard Correspondence is more of an observation than a theorem, but insofar as it describes the general concept of relating logics and programming languages, what is the CHC for logic programming languages? If strikes me that LP directly instantiates and manipulates logical expressions, in a "self-dual" sense; or, is it that the various "proof procedures" of the logic side map to "proof search" algorithms on the computing side?
throwawaymaths 2y ago
>And Erlang. And Haskell. And OCaml. And F#. And... JavaScript (maps), Rust, Ruby, Python...
- __jonas 2y ago
  What do you mean by this? Do maps in JavaScript have some kind of pattern matching?
  - munificent 2y ago
    JavaScript supports destructuring lists and objects (sort of like maps): https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Operators/Destructuring_assignment https://developer.mozilla.org/en-US/docs/Web/JavaScript/Refe... It's not full pattern matching because as far as I know they don't support refutable patterns, but it handles destructuring and binding to variables.
    - __jonas 2y ago
      ah, it didn’t occur to me to view destructuring as pattern matching but I guess it is a bit similar.
- weatherlight 2y ago
  It's not the same. > [a, 2, 2, b] = [1, 2, 2, 3] [1, 2, 2, 3] > a 1 > b 3 > [foo, 2, bar] = [3,3,3] %MatchError{term: [3, 3, 3]} > foo %CompileError{description: "undefined function foo/0 (there is no such import)", file: "nofile", line: 1} Ruby does something similar but the variables are bound in the scope of the case block.
  - gergo_barany 2y ago
    What's not the same as what? Based on your examples it looks like you're saying that unification is not the same as pattern matching. But nobody said it was.
weatherlight 2y ago
its not quite the same. you have to write quiet a bit of OCaml or Haskell to do the following. [foo, [2, 3, bar], baz, 5] = [1,[2,3,4], 5] If there's a match, the bindings "foo", "bar", "baz" will be bound to the values on the right hand side. if not an exception will be thrown (You are right, though, Erlang and Elixir have the same semantics, both being on the BEAM)

ReleaseCandidat 2y ago

> I think that depends on what you meany by "pattern matching" Oh, yes, that's true. "Pattern matching" as that what normally is used in "functional programming languages". This kind of pattern matching does not need unification. The IMHO best (correct, but understandable and with all needed definitions) explanation of it is in chapters 4 "STRUCTURED TYPES AND THE SEMANTICS OF PATTERN-MATCHING" and 5 "EFFICIENT COMPILATION OF PATTERN-MATCHING" of Peyton Jones et al., "The implementation of functional programming languages". https://simon.peytonjones.org/slpj-book-1987/ https://simon.peytonjones.org/slpj-book-1987/ > In programming cirlces "pattern matching" usually means matching strings. Depends on the "circle" ;) https://en.wikipedia.org/wiki/Pattern_matching https://en.wikipedia.org/wiki/Pattern_matching

YeGoblynQueenne 2y ago
Thanks, I don't really know much about Functional Programming. My expertise is in logic programming which btw is a different paradigm. I've heard it said that they're similar and it seems to me the reason was the support for pattern matching in functional languages. I agree that what "pattern matching" means depends on a programmer's background. It's interesting that the wikipedia article that you link to does not mention "unification" at all and only has one reference in Prolog as one of a group of example languages with a "pattern matching construct"; which is not how I would describe the use of the unification algorithm in Prolog. To be honest, I am not sure what is meant by "pattern matching". It seems to be a loosely defined term, like "Finite State Machine" (as opposed to "Finite State Automaton"). I expect that the book you linked to has a more formal treating, perhaps, but from what I can tell from a quick look the "pattern matching" here is based on types. In Prolog, unification is used to bind values to logic variables, which do not have types. So a variable, X, in Prolog can unify, i.e. "match with" absolutely anything. A "pattern" then can be formed by constructing terms (the only data structure in Prolog) with "holes" like p(X, a, b, Y,[1,2,3|Tail], f(Z)) etc. where capital letters are variables. One use of this ability is to manipulate singly-linked lists to insert in or remove elements from their tail, where normally only the head of such a list can be accessed directly. What I mean is that in Prolog a list is denoted by the special syntax [H|T] where H is the head of a list (and can be any term, including another list) and T is the tail of the list, another list. Normally one appends to a list in Prolog using the append/3 predicate: append([], L, L). append([H|T], L, [H|R]) :- append(T, L, R). This works on ordinary lists, but it is also possible to define a "difference list" as a term, e.g. like: [a,b,c,d|T]-T Where T is a variable bound to the end of the tail of the list. Two difference lists like that one can be appended with the following predicate: append_dl(Xs-Ys, Ys-Zs, Xs-Zs). For example: ?- Xs = [a,b,c,d|T1]-T1, Ys = [e,f,g,h|T2]-T2, append_dl(Xs,Ys,Zs). Xs = [a,b,c,d,e,f,g,h|T2]-[e,f,g,h|T2], T1 = [e,f,g,h|T2], Ys = [e,f,g,h|T2]-T2, Zs = [a,b,c,d,e,f,g,h|T2]-T2. The result of appending is in Zs, but you can see the result of the intermediary unification steps in the other variables echoed in the Prolog REPL (the "listener"). Of course, because this is Prolog you can also use the same predicate to split a list: ?- Xs = [a,b,c,d|T1]-T1, Zs = [a,b,c,d,e,f,g,h|T2]-T2, append_dl(Xs,Ys,Zs). Xs = [a,b,c,d,e,f,g,h|T2]-[e,f,g,h|T2], T1 = [e,f,g,h|T2], Zs = [a,b,c,d,e,f,g,h|T2]-T2, Ys = [e,f,g,h|T2]-T2. Where Ys is what remains if we split Xs from Zs. Appending or splitting lists like this is preferred to append/3 because it appends the two lists in a single operation so it can be used to economically put a list together in a loop. The same technique is used with Prolog's Definite Clause Grammars where the "difference" in a difference list is the start and end of a string accepted by a grammar, acting as a parser. https://en.wikipedia.org/wiki/Definite_clause_grammar https://en.wikipedia.org/wiki/Definite_clause_grammar Sterling and Shapiro's "The Craft of Prolog" has a nice chapter on "Incomplete Data Structures" using difference lists and patterns with "holes" but I don't think there's a free version online, unfortunately.

gergo_barany 2y ago

> Now, unification is Turing-complete pattern matching No. First-order syntactic unification is not Turing complete. The combination of unification and resolution is Turing complete. > For instance, in Prolog, you can unify a variable with an entire Prolog program and call the program at runtime, etc. Lots of languages allow you to do this. Lisp had "eval" ten years before Prolog existed. Unification is not necessary for this. Prolog is great, unification is great. Some other things are great too.