Simple Kombinator Interpreter

Welcome to the combinatory logic interpreter.

Type an expression in the entry field and click ▶︎. A valid expression contains one or more terms and parenthesis around groups of terms. Unknown terms will be left as is.

New terms can be declared by prepending "name = " to the expression. They will appear in the box on the right and can be clicked to add them to the expression.

Enter ? to get detailed info on syntax.

The interpreter honors the following rules:

• Terms are accepted in the form of upper-case latin letters, or lower case identifiers. Uppercase letter terms are assumed to always be one letter and do not require spaces around them.
• A program consists of one or more statements, separated by semicolons (;). A statement may contain terms, parentheses (( and )), and whitespace. Parentheses may be omitted.
• Unknown terms are assumed to be free variables and will be left as is. Known terms and their reduction rules (or implementations) are listed in the right panel.
• If a statement is prepended with identifier = , it defines a new temporary term that can be used in further expressions.
• If that happens to the last statement in the group, it will be permanently added to list of available terms, overriding the existing term with the same name.
• An x->y->z-><some expression> is a lambda expression. Lambdas may be mixed with ordinary combinators. Please use Haskell instead.
• A non-negative integer is assumed to be a church number, i.e. a term with two arguments x and y returning x(...{n times}...(x(y)...).

Examples:

• SIIx evaluates to x(x) // where x is a free variable;
• T = S(K(SI))K declares the T combinator;
• M = SII; Mx evaluates to x(x), M will not be available afterwards;
• 5 x y evaluates to x(x(x(x(x(y)))));
• x->y->x is an equivalent of Kx.

Enter '?' to get this message again.